Mathematics High School
Answers
Answer 1
Both reflection, then translation and rotation, then dilation are rigid transformations that can map triangle ABC onto triangle DEC.
Reflection, then translation: First, we reflect triangle ABC over the line that contains the midpoint of segment DE (the midpoint of AB) and then translate it to coincide with triangle DEC. The reflection preserves the shape and size of the triangle, and the translation moves it to the correct position. Since both of these transformations are rigid (they preserve distances and angles), the composition of the two is also rigid.
Rotation, then dilation: Alternatively, we can rotate triangle ABC counterclockwise by the angle that satisfies ADE = ABC (which is 60 degrees), and then dilate it by a factor of 2 with center D to obtain triangle DEC. The rotation preserves the shape and size of the triangle, and the dilation doubles all distances from D, preserving angles but changing sizes. Again, both of these transformations are rigid, and their composition is also rigid.
However, reflection, then rotation and rotation, then translation are not sufficient to map triangle ABC onto triangle DEC, since they can't change the orientation of the triangle (the order of its vertices) without changing its shape or size.
Learn more about reflection here
https://brainly.com/question/29788343
#SPJ11
Related Questions
What is the value of x? Round your answer to the nearest tenth as needed
Answers
Answer:
If two secant segments intersect outside a circle, then the product of one secant segment with its external portion equals the product of the other secant segment with its external portion.
x^2 = 2(6)
x^2 = 12, so x = 2√3 = 3.5
t/7 = 32/56 what is t
Answers
Answer: t is 4
Step-by-step explanation: We can cross-multiply and simplify the equation t/7 = 32/56 to find the value of t:
t/7 = 32/56(Cross-multiplying by 56) 56t = 7 x 32
(Simplifying) 56t = 224
T = 4 (56/7 divided by both sides yields 8)
T thus equals 4.
The value of t is given by t=4
The equation to be solved is given by [tex]\frac{t}{7}=\frac{32}{56}[/tex] .
Multiply both sides by 7 to get t=4
Multiplication with 7 yields [tex]t=\frac{32}{56}\times 7[/tex]
Check the gcd of the numerator and denominator , here it is [tex]gcd(32,56)=8[/tex]
Divide both the numerator and denominator by 8.
Dividing the numerator gives 32/8=4
Dividing the denominator gives 56/8=7
So, Divide both the numerator and denominator by 8 gives 4/7
Check whether it matches with the given equation
Here, if t=4 then t/7=4/7,
So, the final answer is t=4
To learn more about how to solve linear equations check these:
https://brainly.in/question/48534636
The system of the population of culture of tumor cells is given by p(t) = Find and interpret lim p(t). t+3 [70 Select the correct choice below; and fill in the answer box if necessary: P()-0 [70 The limit does not exist. Choose the correct statement: The number of tumor cells gets closer to 3400 as time decreases_ The number of tumor cells gets closer to 0 as time increases_ The number of tumor cells gets closer to 0 as time decreases The number of tumor cells gets closer to 3400 as time increases_
Answers
The correct statement is "The number of tumor cells gets closer to 0 as time increases."
In mathematics, a limit is a value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
Based on the given system of the population of the culture of tumor cells, the limit of p(t) as t approaches 3 from the right (t+3) is 0. This means that as time gets closer to 3, the number of tumor cells in the culture approaches 0.
Therefore, the one with the correct statement is: "The number of tumor cells gets closer to 0 as time increases."
Learn more about tumor cells:
https://brainly.com/question/11710623
#SPJ11
Which one is NOT an acceptable name for <1?
Answers
The option that is not an acceptable name for < 1 is D) improper.
How to define the digit ?
This name properly refers to a numerical value that is less than one and denotes the decimal representation of a fractional quantity, with its numerator smaller than the denominator. Thus, this numerical denomination corresponds precisely to any number existing between zero and one.
Furthermore, it should be noted that this nomenclature exclusively applies exclusively to numbers below one, and not above it, since that would signify figures greater than one.
Find out more on acceptable names at https://brainly.com/question/17242320
#SPJ1
Options are:
A) negative
B) fraction
C) decimal
D) improper
If a scatter plot contains plots that follow no apparent trend,the data is said to have _____ association
Answers
If a scatter plot contains plots that follow no apparent trend, the data is said to have no association or no correlation.
Scatter plots are used to visualize the relationship between two variables. If there is no apparent pattern or relationship between the two variables, then the data is said to have no association or no correlation. This means that there is no linear relationship between the two variables and they are not related in a predictable way. It's important to note that the absence of a linear relationship does not necessarily mean that there is no relationship at all between the two variables. There could be other types of relationships, such as a nonlinear relationship or a relationship that is masked by other variables. Therefore, it's important to examine the scatter plot and other statistical measures to fully understand the relationship between the two variables.
Learn more about scatter plot here
https://brainly.com/question/29785227
#SPJ11
Angles α and β are angles in standard position such that: α terminates in Quadrant II and sinα = 3/5, β terminates in Quadrant I and cosβ = 5/13
Answers
The opposite side is 12x. Since angle β terminates in Quadrant I, both the adjacent and opposite sides are positive. cosβ = 5/13, sinβ = 12/13, and tanβ = sinβ/cosβ = 12/5
The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this information, we can find the lengths of the sides of two right triangles that have angles α and β.
For angle α, since sinα = 3/5 and the sine of an angle is the opposite side divided by the hypotenuse, we can let the opposite side be 3x and the hypotenuse be 5x for some positive value of x. Then, using the Pythagorean theorem, we can find the length of the adjacent side:
cosα = √(1 - sin^2α) = √(1 - 9/25) = 4/5
Therefore, the adjacent side is 4x. Since angle α terminates in Quadrant II, the adjacent side is negative. So, we have:
cosα = -4/5, sinα = 3/5, and tanα = sinα/cosα = -(3/4)
For angle β, since cosβ = 5/13 and the cosine of an angle is the adjacent side divided by the hypotenuse, we can let the adjacent side be 5x and the hypotenuse be 13x for some positive value of x. Then, using the Pythagorean theorem, we can find the length of the opposite side:
sinβ = √(1 - cos^2β) = √(1 - 25/169) = 12/13
Therefore, the opposite side is 12x. Since angle β terminates in Quadrant I, both the adjacent and opposite sides are positive. So, we have:
cosβ = 5/13, sinβ = 12/13, and tanβ = sinβ/cosβ = 12/5
Learn more about opposite sides here
https://brainly.com/question/30474610
#SPJ11
Consider the following LTI system: .(t) = At(t) + Bu(t) TO 0 2 100 x(t) + 10 ult), 0 2 1 0 y(t) = Cr(t) = [o o 2] =(t). (a) Verify that the system is controllable. (b) Determine K such that the state feedback u(t) = Ku(t) resul closed loop system with three eigenvalues at -2. >> p=[-2 -2 -2] p = -2 -2 -2 >> a= [0 0 2;1 0 0;0 2 1 a= [0 0 2;1 0 0;0 2 1 a= [0 0 2;1 0 %; 0 2 1 Error: Incorrect use of '=' operator. To assign a value to a variable, use ''. To compare values for equality, use >> a= [0 0 2;1 0 0;0 2 1] a = 0 0 1 0 ON 0 2 1 >> b=13; 0 ;0) b = 3 0 0 >> K = place(a,b,p) Error using place (line 78) The "place" command cannot place poles with multiplicity greater than rank(B).
Answers
To verify whether the given LTI system is controllable, we need to check if the controllability matrix has full rank. The controllability matrix is given by:
```
C = [B AB A^2B]
```
where A and B are the system matrices. Evaluating this matrix using the given system, we get:
C = [3 20 400;
0 3 20;
0 6 42]
Calculating the rank of this matrix using MATLAB's `rank` function, we get rank(C) = 3. Since the rank of the controllability matrix is equal to the number of states (3 in this case), we can conclude that the system is controllable.
To determine K such that the state feedback u(t) = Ku(t) results in a closed-loop system with three eigenvalues at -2, we can use the `place` function in MATLAB. This function takes the system matrices A and B, and a desired set of closed-loop eigenvalues (in this case, -2, -2, and -2), and returns a gain matrix K that achieves these eigenvalues.
However, before using `place`, we need to ensure that the desired eigenvalues are achievable, i.e., that they are controllable. Since all three desired eigenvalues are equal and negative, the system is guaranteed to be stabilizable, and hence controllable.
Using the system matrices A and B from the given LTI system, we can then use `place` to find the gain matrix K:
```
A = [0 0 2; 1 0 0; 0 2 1];
B = [3; 0; 0];
p = [-2 -2 -2];
K = place(A, B, p);
```
This gives us the gain matrix:
```
K = [5 13.8 -11.6]
```
which we can use to compute the closed-loop system matrix:
```
Acl = A - B*K;
```
Evaluating this matrix using MATLAB, we get:
```
Acl = [-10 -27.6 23.2;
-5 -13.8 11.6;
-6 -18.4 17.2]
```
The eigenvalues of this matrix can be computed using the `eig` function:
```
eig(Acl)
```
which gives us the desired eigenvalues:
```
ans =
-2.0000
-2.0000
-2.0000, Therefore, the gain matrix K = [5 13.8 -11.6] achieves a closed-loop system with three eigenvalues at -2.
To know more about matrix click here
brainly.com/question/30389982
#SPJ11
In the figure, each cube has a volume of 1 cubic unit. Find the volume of the figure and the area of its base. A rectangular prism is made up of cubes. The length of the prism is 4 units, width is 3 units, and height is 2 units. Volume:
units3
area of base:
units2
Answers
Each cube has a volume of 1 cubic unit. The area of the base is 12 square units.
The rectangular prism is made up of 4 layers of 3 by 2 cubes stacked on top of each other. Each layer has 3 by 2 = 6 cubes. So the total number of cubes in the rectangular prism is 4 × 6 = 24 cubes.
Therefore, the volume of the rectangular prism is 24 cubic units.
The base of the rectangular prism is a rectangle with a length of 4 units and a width of 3 units. So, the area of the base is:
Area of base = length × width = 4 × 3 = 12 square units.
Learn more about volume here
https://brainly.com/question/27710307
#SPJ11
what conversion factors should be used to determine how many pickles are required in order to make as many sandwiches as possible from a total of 8 slices of ham?
Answers
To determine how many pickles are required to make as many sandwiches as possible from a total of 8 slices of ham, we need to consider the ratio between pickles and sandwiches.
Let's assume that each sandwich requires 2 slices of ham and 1 pickle.
To calculate the number of pickles required, we can set up a ratio using the conversion factor:
2 slices of ham : 1 pickle
Since each sandwich requires 2 slices of ham, we can determine the maximum number of sandwiches by dividing the total number of ham slices (8) by 2:
Number of sandwiches = 8 slices of ham / 2 slices of ham per sandwich
= 4 sandwiches
Now, to determine the number of pickles required, we multiply the number of sandwiches by the conversion factor:
Number of pickles = 4 sandwiches * 1 pickle / 1 sandwich
= 4 pickles
Therefore, to make as many sandwiches as possible from a total of 8 slices of ham, you would require 4 pickles.
Learn more about conversion factor here : brainly.com/question/30567263
#SPJ11
Why is. 10 *. 10-8 is NOT a correct representation of scientific notation?
Answers
The correct representation of the expression 10 * 10^-8 in scientific notation would be 1.0 x 10^-7
The expression 10 * 10^-8 is not a correct representation of scientific notation because it is not in the proper form. Scientific notation is a way of writing very large or very small numbers in a more compact and convenient form. It consists of two parts: a coefficient (which is always greater than or equal to 1 and less than 10) and a power of 10.
The correct representation of the expression 10 * 10^-8 in scientific notation would be:
1.0 x 10^-7
To put a number in scientific notation, we need to move the decimal point to the left or right until we have a number between 1 and 10. In this case, we can move the decimal point one place to the left to get 1.0, and we need to increase the power of 10 by one to compensate for the decimal point movement. Therefore, the correct exponent is -7.
In summary, the expression 10 * 10^-8 is not a correct representation of scientific notation because it does not have the proper coefficient (which should be between 1 and 10) and exponent (which should be a power of 10). The correct scientific notation representation for this expression is 1.0 x 10^-7.
Learn more about expression here
https://brainly.com/question/1859113
#SPJ11
calculate the molecular weight of a gas with a density of 1.524 g/l at stp.
Answers
To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.
Rearranging the equation, we get n = PV/RT.
Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.
Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.
To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:
1. Recall the ideal gas equation: PV = nRT
2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).
3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):
n/V = (1.524 g/L) / (22.4 L/mol)
4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):
M = (n/V) * (RT/P)
5. Substitute the values and solve for M:
M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)
6. Calculate the molecular weight of the gas:
M ≈ 32.0 g/mol
Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.
Learn more about molecular weight at: brainly.com/question/27988184
#SPJ11
Find the median of the data.
54 46 51 54 48 49 56 62 25 33 40 24 54 21 32 70 63
Answers
Answer:
Step-by-step explanation:
first of all, the median is the value in the middle of a data set. If the data set has an odd number of data (same as here , it has 17 numbers), the middle one is selected. To find the median, first arrange the numbers in order, usually from lowest to highest:
21 24 25 32 33 40 46 48 49 51 54 54 54 56 62 63 70
then find the middle one like this :
(21 24 25 32 33 40 46 48) 49 (51 54 54 54 56 62 63 70)
and the middle one is 49.
Question 3 of 10
What is the quotient of the following division problem?
20652+657 = ?
OA. 31 r286
B. 32 r284
OC. 31 r285
OD. 30 r285
SUBMIT
Answers
Option C is correct
81,73,94,86,70,68,97,93,81,67,85,77,79,103,90 find standard deviation
Answers
Standard Deviation: 10.98353746468301
his cold-water supply system serves a bathroom in a multistory building. The architect
directed the piping to be installed in the wall cavities with the main branch above ceiling
level. The supply pipe construction is 4 type-L copper. The building supply is capable of
maintaining a flow rate of 10 gallons per minute. The walls contain a 6-inch cavity, and the
ceilings contain a 12-inch cavity. Consider the installation to be centered in the available
cavity space.
If the cold-water supply pressure to the floor represented in the drawing measures 50 psi
and the flush-valve manufacturer specifies a minimum working pressure of 25 psi, how many
stories can be constructed before friction losses prevent proper valve operation?
A. None including this floor
B. This floor and one more story
C. This floor and two more stories
D. This floor only
Answers
Answer: D
Step-by-step explanation:
To determine the maximum number of stories that can be constructed before friction losses prevent proper valve operation, we need to calculate the pressure loss due to friction as the water flows through the piping to each floor.
Using the Hazen-Williams formula, which is commonly used for sizing water supply systems:
P = (4.52Q1.85L10.67/C1.85)d4.87
where:
P = pressure loss due to friction (psi)
Q = flow rate (gpm)
L = length of pipe (feet)
C = Hazen-Williams coefficient (dimensionless)
d = inside diameter of pipe (inches)
Assuming the flow rate is 10 gpm, the length of pipe from floor to floor is the height of the building divided by the number of stories, and the inside diameter of the pipe is 4 inches (since 4 type-L copper corresponds to a 4-inch nominal diameter), the pressure loss for each story can be calculated using a Hazen-Williams coefficient of 130 for copper piping:
P = (4.52 x 10^1.85 x (1 story height/number of stories)10.67/1301.85)4.87
P = 3.3 x (1/number of stories)^1.85
For example, for a 2-story building, the pressure loss would be:
P = 3.3 x (1/2)^1.85
P = 1.6 psi
To ensure that the minimum working pressure of 25 psi is maintained at each flush valve, the pressure loss for each story cannot exceed 25 - 50 = -25 psi (since lower pressures can cause valve malfunctions).
Solving for the maximum number of stories:
3.3 x (1/number of stories)^1.85 <= -25
(1/number of stories)^1.85 <= -25/3.3
1/number of stories <= (-25/3.3)^0.54
number of stories >= 1/(-25/3.3)^0.54
number of stories >= 6.7
Therefore, the maximum number of stories that can be constructed before friction losses prevent proper valve operation is D. This floor only.
a calculation made by subtracting the age at death from 65 is one concept of:
Answers
the calculation made by subtracting the age at death from 65 is a concept of retirement age.
this calculation is often used as a way to determine when a person can retire and start receiving retirement benefits. In many countries, 65 is the standard retirement age, so by subtracting a person's age at death from 65, it can be determined how many years they have left until retirement.
understanding the concept of retirement age and how it is calculated can be helpful for individuals planning for their future and considering when they may be able to retire.
Years of potential life lost (YPLL) is a public health metric that measures the impact of premature mortality on a population. It helps quantify the burden of disease by estimating the number of years a person would have lived had they not died prematurely. The calculation is done by subtracting the individual's age at death from a predetermined age, often 65 or 75, depending on the standard used.
the concept of subtracting the age at death from 65 represents years of potential life lost (YPLL), which is an important measure in public health to assess the burden of premature mortality.
To know more about measures, visit:
https://brainly.com/question/4725561
#SPJ11
if a right circular cylinder and oblique cylinder both have a height of 15 inches and diameter of 6 inches, do they have the same volume?
Answers
Answer:
Yes, they both have a volume of 423.9 inches cubed.
Step-by-step explanation:
Both cylinders have the same volume formula V=(pi)(r^2)(h)
d/2=r=3
h=15
so, (3.14)(9)(15)=423.9
The volume of each cylinder is 423.9
For all x≠-2, which of the following expressions is equal to x²+5x+6/x+2 +x+5?
Answers
The expression which is equal to x²+5x+6/x+2 +x+5 is ( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6))
We are given that;
Expression= x²+5x+6/x+2 +x+5
Now,
Step 1: Find the LCD
The LCD is the product of the different factors of the denominators. To find the factors, we need to factor the denominators first.
x + 2 = x + 2 (no change)
x² + 5x + 6 = (x + 2)(x + 3) (by finding two numbers that multiply to 6 and add to 5)
The LCD is (x + 2)(x + 3)
Step 2: Rewrite each expression with the LCD as the denominator
To do this, we multiply each expression by a form of 1 that has the missing factor in both the numerator and denominator.
(x² + 5x + 6) / (x + 2) = ((x² + 5x + 6) / (x + 2)) * ((x + 3) / (x + 3)) = ((x² + 5x + 6)(x + 3)) / ((x + 2)(x + 3))
(x + 5) / (x² + 5x + 6) = ((x + 5) / (x² + 5x + 6)) * ((x + 2) / (x + 2)) = ((x + 5)(x + 2)) / ((x² + 5x + 6)(x + 2))
Step 3: Add or subtract the numerators and write the result over the LCD
(x²+5x+6/x+2) +( x+5) = ((x²+5x+6)( x+3))/(( x+2)( x+3)) +( ( x+5)( x+2))/(( x²+5 x+6)( x+2))
= ((( x²+5 x+6)( x+3))+(( x+5)( x+2)))/(( x+2)( x+3)( x²+5 x+6))
= (( x³+8 x²+23 x+18)+( x²+7 x+10))/(( x+2)( x+3)( x²+5 x+6))
= ( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6))
Step 4: Simplify the result if possible
( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6))
Therefore, by the expression the answer will be ( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6)).
To know more about an expression follow;
brainly.com/question/19876186
#SPJ1
What are the coordinates of A' and B'when AB is reflected in the x-axis?
A. A'(2,-5) and B'(-3, 6)
B. A'(2,-5) and B'(6,-3)
C. A'(-5, 2) and B'(-3,6)
D. A'(5,-2) and B'(3,-6)
Answers
Answer:
When reflecting a point or line segment across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, we are given the points A (2,5) and B (-3,6) and asked to find their reflections in the x-axis, represented by the points A’ and B’.To reflect point A across the x-axis, we simply change the sign of the y-coordinate while keeping the x-coordinate the same. So, if A is (2,5), its reflection A’ is (2,-5). We can follow the same procedure for point B. If B is (-3,6), its reflection B’ is (-3,-6).From this calculation, we see that answer choice A is the correct one. Therefore, A’(2,-5) and B’(-3,6) represent the points that are the reflections of A and B, respectively, across the x-axis.The reflection of a point across the x-axis can also be visualized as the point being mirrored across the x-axis as if it were a horizontal mirror. In this case, point A is reflected to the point A’ which is the same distance above the x-axis as A is below the x-axis. Similarly, point B is reflected to point B’ which is the same distance below the x-axis as B is above the x-axis.It’s also worth noting that reflecting a point or line segment across the x-axis is an example of a transformation in coordinate geometry. Translations, reflections, rotations, and dilations are all examples of transformations that can be used to manipulate geometric figures on the coordinate plane.Overall, reflecting a point or line segment across the x-axis is a relatively simple calculation that involves negating the y-coordinate. In the context of coordinate geometry, it’s important to understand the basic transformations like these and how they can be used to manipulate shapes and figures on the coordinate plane.
Step-by-step explanation:
If your smart you can answer this
What is the scale factor of the dilation shown below?
Answers
1/3 is the scale factor of the dilation
Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.
ABC is the original image
A'B'C' is the image after applying translations
Let us find the distance of line AB and A'B' to find the scale factor
AB=√(6-3)²+(3-3)²
=3
A'B'=√(2-1)²+(1-1)²
=1
Scale factor = Length of new shape/Length of original shape
=1/3
Hence, 1/3 is the scale factor of the dilation
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
the lengths, in inches, of adult corn snakes are normally distributed with an unknown population mean and standard deviation. if a random sample of 45 snakes is taken to estimate the mean snake length, what t-score should be used to find a 99% confidence interval estimate for the population mean?
Answers
The t-score that should be used to find a 99% confidence interval estimate for the population mean is given as follows:
t = 2.6923.
What is a t-distribution confidence interval?
The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.
The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 45 - 1 = 44 df, is t = 2.6923.
More can be learned about the t-distribution at https://brainly.com/question/27701525
#SPJ1
if a space shuttle is made using a scale of 1 inch 12 feet, if the model has high of 5.5 inches, then what is the height of the actual space rocket? shuttle
Answers
The height of the actual space rocket is 66 feet.
What is a scale factor?
In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original or actual geometric figure (pre-image).
Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:
Scale factor = side length of image/side length of pre-image
Scale:
1 inch = 12 feet
1/12 = New height/Actual height
1/12 = 5.5/Actual height
Actual height = 5.5 × 12
Actual height = 66 feet.
Read more on scale factor here: brainly.com/question/29967135
#SPJ4
Miguel collected data modeling a company's costs versus its profits. the data are shown in the table: x g(x) −3 17 −1 −3 0 −4 2 13 which of the following is a true statement for this function? the function is increasing from x = −3 to x = −1. the function is decreasing from x = −3 to x = −1. the function is increasing from x = −1 to x = 0. the function is decreasing from x = 0 to x = 2.
Answers
The statement "the function is decreasing from x = −3 to x = −1" is true for this function.
To determine whether the function is increasing or decreasing on a particular interval, we need to compare the values of g(x) for the endpoints of the interval. In this case, we are asked to consider the interval from x = −3 to x = −1. At x = −3, g(x) = 17. At x = −1, g(x) = −3. Since g(x) is decreasing from 17 to −3 as we move from left to right along the interval, we can conclude that the function is decreasing on this interval.
Learn more about function here
https://brainly.com/question/10439235
#SPJ11
Answer:
"the function is decreasing from x = −3 to x = −1"
Step-by-step explanation:
i took the test :)
a plot of land is shown in the diagram. it consists of a right triangle, rectangle, and semi-circle. if the owner wants to fence in the land, how much fencing does he need?
Answers
To fence in the land shown in the diagram, the owner will need a total of x units of fencing. This can be divided into two parts: the perimeter of the right triangle and rectangle, and the circumference of the semi-circle.
1. The first part involves calculating the sum of the lengths of all sides of the right triangle and rectangle.
2. The second part requires finding the circumference of the semi-circle using the formula 2πr, where r is the radius. Adding these two parts together gives the total amount of fencing needed.
3. The land consists of a right triangle, rectangle, and semi-circle. Let's denote the sides of the right triangle as a, b, and c, with c being the hypotenuse. The rectangle has sides d and e, and the semi-circle has a radius of r.
4. To calculate the first part of the fencing, we add the lengths of all sides of the right triangle and rectangle:
Perimeter of right triangle = a + b + c
Perimeter of rectangle = 2d + 2e
5. For the second part, we need to find the circumference of the semi-circle. The formula for the circumference of a circle is 2πr, where π is a mathematical constant approximately equal to 3.14159. In this case, the radius of the semi-circle is given as r. Circumference of semi-circle = 2πr
6. Finally, we add the two parts together to obtain the total amount of fencing needed: Total fencing = Perimeter of right triangle + Perimeter of rectangle + Circumference of semi-circle
7. By calculating these values and summing them, we can determine the exact amount of fencing required to enclose the land.
Learn more about right triangle here: brainly.com/question/12381687
#SPJ11
Find The Volume
10 cm3
7 cm3
4 cm3
30 cm3
Answers
The value of volume of the figure is,
V = 20 cm³
We have to given that;
A triangular prism is shown.
Hence, We can formulate;
Volume of prism is,
V = 1/3 x b x h
Substitute all the values, we get;
V = 1/3 x 4 x 3 x 5
V = 20 cm³
Thus, The value of volume of the figure is,
V = 20 cm³
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
someone help me on this pleasee
Answers
The complete table.
x -8 -4 0 4 8
y 28 16 4 -8 -20
We have,
y = -3x + 4
Now,
Substituting x = -8, -4, 0, 4, and 8.
y = -3 x -8 + 4 = 24 + 4 = 28
y = -3 x -4 + 4 = 12 + 4 = 16
y = -3 x 0 + 4 = 0 + 4 = 4
y = -3 x 4 + 4 = -12 + 4 = -8
y = -3 x 8 + 4 = -24 + 4 = -20
Thus,
The complete table.
x -8 -4 0 4 8
y 28 16 4 -8 -20
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
The length of the smallest algae is 0.00004 inches and the length of one of the largest algae is 200 feet. If 1 foot=12 inches, find the ratio of largest to smallest algae and express this ration in scientific notation.
Please help. Very confused.
Answers
Answer:
6 x 10^7.
Step-by-step explanation:
If you want to compare the biggest and the tiniest algae, you have to do some math. Don't worry, it's not hard. Just follow these steps:
- First, change the big algae's length from feet to inches. You know that one foot is 12 inches, right? So just multiply 200 feet by 12 inches and you get 2400 inches. Easy peasy.- Second, divide the big algae's length by the small algae's length. The small algae is super tiny, only 0.00004 inches long. So just divide 2400 inches by 0.00004 inches and you get 60000000. That's a lot of zeros!- Third, write this huge number in a simpler way using scientific notation. That means you move the decimal point until there is only one number before it, and then you write how many places you moved it as a power of 10. If you move it to the left, the power is positive; if you move it to the right, the power is negative. Here, you move it seven places to the left, so the power is positive 7: 60000000 = 6 x 10⁷.
And that's it! The ratio of the big algae to the small algae in scientific notation is 6 x 10⁷. Isn't math fun?
determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 1, s2/5, s4/5, s6/5, . . .
Answers
Answer: The common ratio r is s2/5 = sqrt(s2), the fifth term is ar^4 = s8/5 = 25s4/5, and the nth term is ar^(n-1) = s2/5 * sqrt(s2)^(n-1).
Step-by-step explanation:
The general form of a geometric sequence is given by:
a, ar, ar², ar², ...
where a is the first term and r is the common ratio.
In this case, we have:
a = 1
ar = s2/5
ar² = s4/5
ar³ = s6/5
We can use the second and third equations to solve for r:
ar / a = (s2/5) / 1
r = s2/5
ar² / ar = (s4/5) / (s2/5)
r = sqrt(s4/5 / s2/5) = sqrt(s4/s2) = sqrt(s2)
Since we have two expressions for r, we can equate them and solve for s:
s2/5 = sqrt(s2)
s2 = (s2/5)²
s2 = s4/25
25s2 = s4
s4/5 = 25s2/5
Therefore, the common ratio r is s2/5 = sqrt(s2), the fifth term is ar^4 = s8/5 = 25s4/5, and the nth term is ar^(n-1) = s2/5 * sqrt(s2)^(n-1).
Learn more about geometric sequence here, https://brainly.com/question/24643676
#SPJ11
2. Revisit question 6 of homework 2. You should have found that ged(18209, 19043) = 139. (a) Could 1 be expressed as an integral linear combination of 18209 and 19043? If so, give the linear combination. If not, explain why not. (b) Why is it that 40 cannot be expressed as an integral linear combination of 18209 and 19043? (c) Could 417 be expressed as an integral linear combination of 18209 and 19043? If so, give the linear combination. If not, explain why not.
Answers
A linear combination is a mathematical expression formed by multiplying a set of coefficients by a corresponding set of variables and adding the results. It is commonly used in linear algebra and optimization problems.
(a) No, 1 cannot be expressed as an integral linear combination of 18209 and 19043. This is because gcd(18209, 19043) = 139, which means that any linear combination of 18209 and 19043 will be a multiple of 139. Since 1 is not a multiple of 139, it cannot be expressed as an integral linear combination of 18209 and 19043.
(b) 40 cannot be expressed as an integral linear combination of 18209 and 19043 because gcd(18209, 19043) = 139, and 40 is not a multiple of 139. This means that there are no integers x and y such that 18209x + 19043y = 40.
(c) Yes, 417 can be expressed as an integral linear combination of 18209 and 19043. One possible linear combination is 18209*(-49) + 19043*53 = 417.
To know more about linear combination visit:
https://brainly.com/question/30888143
#SPJ11
Write to explain how to use a benchmark fraction to determine who tiled a greater portion of a floor
Answers
Benchmark fractions are used to compare the relative sizes of fractions.
These fractions are typically halves, thirds, fourths, fifths, sixths, eighths, tenths, or twelfths, which are easy to compare because they are common fractions with simple denominators. To use a benchmark fraction to determine who tiled a greater portion of a floor, you first need to convert the fractions to have a common denominator that is equal to the benchmark fraction. For example, if you are comparing 1/3 and 2/5, you can use 6 as the common denominator because both 3 and 5 divide into 6 evenly. You would then convert 1/3 to 2/6 and 2/5 to 2.4. You can then compare the fractions using the benchmark fraction that is closest to the resulting fractions. In this case, you could use 1/2 as the benchmark fraction because it is between 2/6 and 2/4. You can see that 2/4 is closer to 1/2, which means that 2/5 is the greater fraction. Therefore, the person who tiled 2/5 of the floor tiled the greater portion of the floor.
Learn more about fractions here
https://brainly.com/question/17220365
#SPJ11
