Pete was able to map quadrilateral A, B, C, D onto E, F, G, H using a translation and a dilation. Pete concluded: "I was able to map quadrilateral A, B, C, D onto
E, F, G, H using a sequence of rigid transformations, do the figures are congruent." What
error did Pete make in his conclusion?
Answers
Answer:
Pete didn't use only rigid transformations, so the figures are not congruent
Step-by-step explanation:
Translations, reflections, and rotations are all rigid transformations while a dilation is not. Pete used a dilation to make the shape smaller after transforming it, therefore the shape is similar not congruent.
If you're confused with what these math terms mean:
A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.
In geometry, a reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to create the image. Each point of the image is the same distance from the line as the preimage is, just on the opposite side of the line.
A dilation is a type of transformation (not a rigid one though) that changes the size of the image. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is.
Transformation involves moving an object from its original position to a new position.
Rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures m
Pete's mistake in his conclusion is that he stated the quadrilaterals were congruent when he used a sequence of transformations that included a dilation. Dilation changes the size of the figure while maintaining shape, thus the shapes are similar but not congruent.
Explanation:In his conclusion, Pete made an error by stating that the quadrilaterals A, B, C, D, and E, F, G, H are congruent because he used a sequence of rigid transformations. However, transformations that include a dilation are not rigid transformations. Rigid transformations, such as rotations, reflections, or translations, preserve the shape and size of the figure, making the resulting figure congruent to the original. A dilation, however, changes the size of the figure while maintaining its shape, resulting in a figure similar to, but not congruent with, the original. Therefore, although Pete was able to map quadrilateral A, B, C, D onto E, F, G, H, the two shapes are not congruent because dilation was a part of the sequence of transformations he used.
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Related Questions
Find the product of (4z2 + 7z - 8) and (-z + 3).
The product of (4z2 + 77 - 8) and (-Z + 3) is -423 +
Z - 24.
Answers
Answer: -4z3 + 5z2 + 29z - 24
Step-by-step explanation:
Answer:
5
29
Step-by-step explanation:
Below is the graph of a trigonometric function. It has a maximum point at (-5pi/4,6.7) and an amplitude
of 4.1. What is the midline of the function? Y=____
Answers
We have been given that the maximum point at the graph of a trigonometric function is [tex](-\frac{5\pi}{4},6.7)[/tex] and amplitude of the function is 4.1. We are asked to find the mid-line of the given function.
We will use mid-line formula to solve our given problem.
[tex]\text{Mid-line value}=\text{Maximum value}-\text{Amplitude}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{Mid-line value}=6.7-4.1[/tex]
[tex]\text{Mid-line value}=2.6[/tex]
Therefore, the mid-line of the given function would be [tex]y=2.6[/tex].
If (-3)^-5=x/1, what is the value of x?
Answers
Answer:
-1/243.
Step-by-step explanation:
(-3)^-5 = x/1
x = (-3)^-5
x = 1 / (-3)^5
x = 1 / -243
= -1/243.
If x = 2 and y=-3, then -xy^2 =
A) -36
B) 18
C) -12
D) - 18
Answers
Answer:
-18
Step-by-step explanation:
-xy^2 =
Let x=2 and y = -3
-(2) (-3)^2
-2 (9)
-18
If x = 2 and y=-3, then -xy² B) 18.
To solve the given mathematical problem, we will substitute the given values of x and y into the expression and calculate the result step by step.
Given:
x = 2
y = -3
We need to calculate the value of the expression:
[tex]-xy^2[/tex]
Substitute the given values into the expression:
[tex]-xy^2 = -(2)(-3)^2[/tex]
Now, calculate the square of y:
[tex](-3)^2 = 9[/tex]
Next, multiply the values together:
[tex]-xy^2 = -(2)(9)[/tex]
[tex]-xy^2 = -18[/tex]
Since there is a negative sign outside the parentheses, the result will be the negative of the product inside:
[tex]-xy^2 = 18[/tex]
Therefore, the final answer is 18.
The function f(x) = −x2 + 60x − 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired. Determine the vertex, and explain what it means in the context of the problem. (30, 784); The vertex represents the maximum profit.
(30, 784); The vertex represents the minimum profit.
(2, 58); The vertex represents the maximum profit.
(2, 58); The vertex represents the minimum profit.
Answers
Answer:
Even tho the answer is not up there but its
(30, 784); The vertex represents the maximum profit.
Step-by-step explanation:
....
For the quadratic equation f(x) = -x^2 + 60x - 116, the vertex is (30, 784), and it is a maximum.
How to get the vertex?
For a general quadratic equation:
y = a*x^2 + b*x + c
The vertex is at the x-value:
h = -b/2a
To get the y-value, we evaluate the quadratic equation in h.
In our case, we have:
y = -x^2 + 60x - 116
Then:
h = -60/(2*-1) = 30
To get the y-value of the vertex, we evaluate in x = 30.
y = -(30)^2 + 60*30 - 116 = 784
And, as you can see, the leading coefficient of the quadratic equation is negative. This means that the arms open downwards, so the vertex is a maximum.
Then, concluding, the vertex is (30, 784), and it is a maximum.
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find the perimeter of a right triangle whose hypotenuse is 2 and whose area is 1.
Answers
Answer:
can i get the pic of it?
Step-by-step explanation:
.........
A shipping container has a volume of 2,880 cubic inches. Which could be the dimensions of the container?
Answers
Missing part of the question
- 10 in, by 12 in. by 24 in.
- 12 in. by 15 in. by 18-in.
- 10 in. by 16 in. by 20 in.
- 12 in. by 12 in. by 20 in.
Answer:
The possible dimensions of the container are
- 10 in, by 12 in. by 24 in
- 12 in. by 12 in. by 20 in
Step-by-step explanation:
Given
Volume of the container = 2,880 cubic inches
Required
Possible dimensions of the container
To solve this question, the following assumption has to be made;
It'll be assumed that the container is a rectangular
To calculate the volume of a rectangular figure, we simply multiply the dimensions of the figure,
This implies that; we'll test each of the given options.
Which ever gives 2,880 is the right answer.
- 10 in, by 12 in. by 24 in.
[tex]Volume = 10 in * 12 in * 24 in[/tex]
[tex]Volume = 2,880[/tex] cubic inches
- 12 in. by 15 in. by 18-in.
[tex]Volume = 12 in * 15 in * 18 in[/tex]
[tex]Volume = 3,240[/tex] cubic inches
- 10 in. by 16 in. by 20 in.
[tex]Volume = 10 in * 16 in * 20 in[/tex]
[tex]Volume = 3,200[/tex] cubic inches
- 12 in. by 12 in. by 20 in.
[tex]Volume = 12 in * 12 in * 20 in[/tex]
[tex]Volume = 2,880[/tex] cubic inches
From the calculation above, only option A and D gives 2,880;
Hence, the possible dimensions of the container are
- 10 in, by 12 in. by 24 in
- 12 in. by 12 in. by 20 in
Given a volume of 2,880 cubic inches, one possible set of dimensions for a shipping container could be length = 24 inches, width = 15 inches, and height = 8 inches.
The volume of a rectangular container can be calculated by multiplying its length, width, and height. Given the volume of 2,880 cubic inches, we are looking for three numbers (dimensions) that, when multiplied together, equal 2,880.
One possible set of dimensions could be length = 24 inches, width = 15 inches, and height = 8 inches. Multiplying these dimensions together: 24 inches × 15 inches × 8 inches = 2,880 cubic inches, which matches the given volume of the container.
What is the volume of the prism?
ft3
1
12 ft
6 ft
8 ft
Answers
V=lwh
V=8×12×6=576 ft³
Answer: V=576 ft³
The volume of the prism is calculated by multiplying the length, width, and height, resulting in 576 cubic feet.
To calculate the volume of the prism, we have to use the formula for the volume of a rectangular prism, which is length times width times height. Given the dimensions of the prism as 12 feet in length, 6 feet in width, and 8 feet in height, the volume is calculated as follows:
Multiply the length by the width: 12 ft times 6 ft = 72 ft².Multiply the result by the height: 72 ft² times 8 ft = 576 ft³.Therefore, the volume of the prism is 576 cubic feet (ft³).
A newsstand spends $500 a month on rent and electricityand it spends $1.50 for each magazine that it sells. The newsstand charges $4.50 for each magazine. If nis the number of magazines, which equation represents the profit function of the newsstand?
Answers
Answer:
n(3.5)-500= p
Step-by-step explanation:
*The p represents the profit.
Answer: p = 3n -500
Step-by-step explanation:
AP3X
Which statement best describes the relationship between the two variables?
O There is an association because the relative frequencies by row are different
O There is an association because the relative frequencies by row are similar
There is no association because the relative frequencies by row are different,
O There is no association because the relative frequencies by row are similar
Answers
The answer is, O There is an association because the relative frequencies by row are similar.
What is variables?A quantity which during a calculation is assumed to vary or be capable of varying in value.
Here, we have,
The statement best describes the relationship between the two variables,
is,
O There is an association because the relative frequencies by row are similar.
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What is the volume of a cone with a radius of 4 centimeters and a height of 10 centimeters? Cone V = 1 3 Bh 1. Rewrite the formula for the base area: V = 1 3 πr2h 2. Substitute the values into the formula: V = 1 3 π(42)(10) 3. Evaluate the power: V = 1 3 π(16)(10) 4. Simplify to find the volume of the cone to be Pi centimeters cubed.
Answers
Answer: its 160/3
Step-by-step explanation:
Answer:
160/3
Step-by-step explanation:
Find the discriminant of the quadratic equation, and determine the number of real solutions of the equation.
2x2 + 6x + 9 = 0
The discriminant is _____
The number of real solutions of the equation is _____
Answers
Answer:
Discriminant is -36 and the number of real solution and its 2 imaginary solutions.
Step-by-step explanation:
In the figure above, angles are as marked. The angle labeled with a measure of bº is an exterior angle. What is the measure of b?
Answers
Answer:
105
Step-by-step explanation:
First, solve for a
2a-15+2a+15+3a-5+a+5=360(Sum of interior angles of quadrilateral is 1360)
8a=360
a=360/8
a=45
Now,Look at the angles formed in straight line
b+2a-15=180(Sum of angles formed in a straight line is 180)
b+2×45=180+15
b=195-90
b=105
Write an equation in slope-intercept form that goes through the points (-3, -4) and (3,4).
Answers
Answer:
Y = 4/3x + 0
Step-by-step explanation:
(-3,-4) and (3,4) can be plugged in to rise over run.
y 4 -(-4) = 8
x 3 - (-3) = 6
8/6 = 4/3
Plug into slope intercept form
4 = 4/3(3) + b
4 = 12/3 +b
4 = 4 +b
Subtract from both sides
0 = b
Y = 4/3x + 0
The equation in slope intercept form that goes through the points (-3,-4) and (3,4) is [tex]y=\frac{8}{6}x[/tex]
What is Slope of the line?The slope of a line gives the measure of its steepness and direction.
What is the Slope intercept form?The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given,
Slope of the line passing through the points (-3,-4) and (3,4)
Slope of the line m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}=\frac{4+4}{3+3}=\frac{8}{6}[/tex]
Therefore slope of the line is [tex]\frac{8}{6}[/tex]
Find the y intercept using the slope and the point (-3,-4)
y=mx + b
-4 = [tex]\frac{8}{6}[/tex]×-3 + b
-4 =-4+b
b=-4+4 =0
Then,
The equation in slope intercept form is
y = mx + b
y = [tex]\frac{8}{6}[/tex]x + 0
[tex]y=\frac{8}{6}x[/tex]
Hence, the equation in slope intercept form that goes through the points (-3,-4) and (3,4) is [tex]y=\frac{8}{6}x[/tex]
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1) 3х • 3х
Can someone help please I don’t get this shiii
Answers
(
3
×
3
)
x
x
(3×3)xx
2 Simplify
3
×
3
3×3 to
9
9.
9
x
x
9xx
3 Use Product Rule:
x
a
x
b
=
x
a
+
b
x
a
x
b
=x
a+b
.
9
x
2
9x
2
a(b)^x-c =d solve for x
Answers
Answer:
( ln((d + c) / a) ) / ( ln(b) )
Step-by-step explanation:
ab^x = d + c
b^x = (d + c) / a
ln(b^x) = ln((d + c) / a)
xln(b) = ln((d + c) / a)
x = ( ln((d + c) / a) ) / ( ln(b) )
What is the mean change with the numbers 90 91 88 84 86 85 86
Answers
Answer:
-0.571428571, or -0.6 if you round it to the nearest tenth
Step-by-step explanation:
Okay, so to break it down, you want to find the difference between each of the numbers right next to each other.
90 -> 91 = 1
91 -> 88 = -3
88 -> 84 = -4
84 -> 86 = 2
86 -> 85 = -1
85 -> 86 = 1
Add up all the differences.
1 - 3 - 4 + 2 -1 + 1 = -4
How many numbers were there? 7
Divide the sum (-4) by 7.
-4/7 = -0.571428571
hi, please help.
what are some things you wonder about simple machines?? it doesn't have to be too complicated.
(plz i am suffering)
Answers
Create a graph of the polynomial function g(x) = x3 + 2x2 − 9x − 18.
Answers
The graph is shown below
The probability of a chance event is 0.3, it is
to happen
when compared to a chance event with a probability of 0.4
Select one:
equally likely
less likely
both more and less likely
more likely
Answers
Answer:
less likely
Step-by-step explanation:
Lower probability = lower chance to happen
0.3 is less than 0.4
Answer:
2nd
less likely
Step-by-step explanation:
Mary estimated that it would take 3 hours to write a book report, but it actually took her 5 hours. What is the percent error for her estimate? (Hint: subtract and then divide by actual number)
Answers
Answer:
The percent error is 40%.
Step-by-step explanation:
5 (actual time) - 3 (estimated time) = 2
2 divided by 5 (actual time) = 0.4
0.4 x 100 = 40%
If an integer from 3 through 14 is chosen at random, what is the
probability that the number chosen is NOT prime?
Answers
Answer:[tex]\frac{7}{12}[/tex]
Step-by-step explanation:
Given
There are integer between 3 and 14 available to be chosen (total 12 integers)
Prime integers among them
3,5,7,11,13 i.e. total of 5 prime integers
So the probability that the number chosen is not Prime
[tex]=1-P\text{(no is prime)}[/tex]
[tex]=1-\frac{5}{12}[/tex]
[tex]=\frac{12-5}{12}[/tex]
[tex]=\frac{7}{12}[/tex]
You have been asked to make lemonade for this year’s Back to School Night. In order to make the lemonade taste irresistible, you will make 10- cup batches that consist of 50% water, 25% lemonade mix, 10% lemonade juice, and 15% sugar. You are supplied with 44 cups of mix, 80 cups of water, 36 cups of lemon juice, and 40 cups of sugar. Discover the maximum number of batches you can make with the given ingredients. Remember that each batch makes 10 cups.
Answers
Answer:
16 batches of lemonade
Step-by-step explanation:
each batch requires (10 cups of lemonade):
5 cups of water2.5 cups of lemonade mix1 cup of lemon juice1.5 cups of sugaryou are given:
80 cups of water ⇒ makes up to 16 batches44 cups of lemonade mix ⇒ makes up to 17.6 batches 36 cup of lemon juice ⇒ makes up to 36 batches40 cups of sugar ⇒ makes up to 26.67 batchesthe ingredient that determines the total amount of batches we can make is water which is enough to produce only 16 batches.
you would use:
80 cups of water (no water left)40 cups of lemonade mix (4 cups left)16 cups of lemon juice (20 cups left)24 cups of sugar (16 cups left)Alex and hope were trying to solve -6x > 24. Whose inequality shows the solution? Show your work.
(Alex's inequality is x > -4)
(Hope's inequality is x < -4)
Answers
Answer:
x>-4
Step-by-step explanation:
divide both sides by -6 without changing the sign
find the measurement of this angle :)
Answers
Answer:
56
Step-by-step explanation:
By adding the other two angles you can calculate the missing angles. And since they are the same angles they are the same measure. Add the two angles provided and then subtract that from 180 and you get your answer.
:)
Answer:
∠1=56°
∠2=56°
∠3=74°
Step-by-step explanation:
Degrees in a triangle is 180°
180°-(66°+58°)=∠1
180°-124°=∠1
∠1=56°
∠1=∠2- Vertical angles
∠1=56°
∠1=∠2
∠2=56°
∠3=180°-(56°+50°)
∠3=180°-106°
∠3=74°
Tell whether the ordered pair is a solution of the system of equations.
(2.1)
2x+y=5
y = 4x– 1
1. No, (2,1) is a solution for y = 4x – 1 but not for 2x + y = 5.
2. Yes, (2,1) is a solution for both equations
3. No, (2,1) is a solution for 2x + y = 5 but not for y = 4x - 1
Answers
Answer:
2x + y = 5
y = 4x – 1
Substitute (2, 1) into system, then:
2x + y = 5 => 2 x 2 + 1 = 5 => 5 = 5 (satisfied)
y = 4x– 1 => 4 x 2 - 1 = 1 => -7 = 1 (not satisfied)
=> Option 3 is correct.
Hope this helps!
:)
If the tree is 25 feet tall , what is the angle of depression to his friend
Answers
Answer:
15
Step-by-step explanation:
the probability of landing on yellow when spinning a spinner is 1/8 choose the likelihood that best describe the probability of this event
A) unlikely
B) likely
C) certain
D) neither likely or unlikely
Answers
Answer:Unlikely
Step-by-step explanation:
Given
Probability of landing is [tex]\frac{1}{8}=0.125[/tex]
i.e. [tex]12.5\%[/tex]
Thus Probability is less than [tex]50\% [/tex]
Therefore it cannot be likely because for that Probability must be greater than [tex]50\%[/tex]
Therefore the following event is Unlikely because it is greater than 0.
Answer:
The answer is A my children
Step-by-step explanation:
The two-way table shows the ages of the players on different soccer teams.
Answers
Answer:
C
Step-by-step explanation:
In the picture attached, the complete question is shown.
The probability that a randomly selected player on Team A is 8 years old is = 4/15
The probability that a randomly selected 8-year-old player is on Team C is = 8/21
The probability that a randomly selected player on Team C is 10 years old is = 5/16
The probability that a randomly selected 10-year-old player is on Team B is = 3/14
Can someone help me with this question
Answers
Answer:
15 & -15
Step-by-step explanation:
Answer:
x=+15/-15
Last answer is correctStep-by-step explanation:
[tex] {x}^{2} = 225 \\ x = \sqrt{225} \\ x = 15[/tex]