Triangle \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is the result of dilating \triangle ABC△ABCtriangle, A, B, C about point AAA by a scale factor of \dfrac23
3
2
start fraction, 2, divided by, 3, end fraction.
Determine whether each claim about the properties of \triangle ABC△ABCtriangle, A, B, C and \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is true or false.
Answers
The shape of the image of ΔABC following a dilation by a scale factor of [tex]\dfrac{2}{3}[/tex] is the same as the shape of ΔABC but the sizes of the sides of ΔA'B'C' are [tex]\dfrac{2}{3}[/tex] smaller
The correct options with regards the given statements are;
The measure of ∠B and ∠B' are equal is TrueThe coordinates of A and A' are the same is TrueReasons:
The dilation lengths of the sides of ΔABC are AB, AC, BC
The given scale factor of dilation = [tex]\dfrac{2}{3}[/tex]
Therefore;
The lengths of the sides of ΔA'B'C' are [tex]\dfrac{2}{3} \cdot \overline {A'B'}[/tex], [tex]\dfrac{2}{3} \cdot \overline {A'C'}[/tex], [tex]\dfrac{2}{3} \cdot \overline {B'C'}[/tex]
Which gives;
[tex]\dfrac{\overline{A'B'}}{\overline{AB}}} = \dfrac{\overline{A'C'}}{\overline{AC}}} = \dfrac{\overline{B'C'}}{\overline{BC}}} = \dfrac{2}{3}[/tex]
Given that the ratio of the corresponding sides of ΔABC and ΔA'B'C' are equal, ΔABC is similar to ΔA'B'C' by triangle similarity theorem
Therefore;
∠A = ∠A', ∠B = ∠B', and ∠C = ∠C' by definition of triangle similarity
Which gives;
The statement; The measure of ∠B and ∠B' are equal is True
Second part;
The center of dilation of ΔABC is point A, therefore, the distance between point A and point A' following a dilation is zero
Therefore, given that there is no difference, we have;
The coordinates of point A = The coordinates of point A'
Therefore;
The statement, the coordinates of A and A' are the same is True
Learn more here:
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Answer:
False
True
Step-by-step explanation:
A dilation multiplies the distance of every point from the center of dilation by the scale factor. So a dilation moves every point except the center of dilation.
Point A is the center of dilation, so the coordinates of A and A′, are the same.
Dilations multiply every length in the figure by the scale factor, so AB and A'B' do not have the same length.
Related Questions
Drag each expression to show whether it is equivalent to 4 × 5 or to 2 × 4 × 5.
Answers
Answer:
1st one: 4x5x2: in the 2nd box
2nd one: (4x2)+(4x3) : in the 1st box
3rd one: 2x(4x5): in the 2nd box
Last one: 4x(1+4): in the 1st box
Step-by-step explanation:
For the first one: 4x5x2, you can multiply any 2 numbers together example- you can multiply 4x5, 5x2, 4x2 then multiply the third digit I did 4x5=(20) x2= 40.. 5x2 =10 x4=40.. see they'll all end up to 40.
For the second one: (4x2)=8 (4x3)=12 add 8 and 12 it'll equal 20
For the third one: 2x(4x5) start by multiplying 4 and 5 which is 20, then multiply 20 by 2 =40
For the fourth one: 4x(1+4) 1+4=5, multiply 5 by 4 and get 20
The first box equals 40, the second box equals 20
And always remember to answer the problem in the parenthesis first, then continue with the rest of the problem. Hope this helps!! And I hope I didn't confuse any of you.. Let me know if you have any questions or if I made a mistake somewhere but besides all that have a great day! :)
4 × 5 equivalent to (4×2) + (4×3) and 4(1+4), 2 × 4 × 5 is equivalent to 4×5×2 and 2(4×5)
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 4×5×2 = 40
=(4×2) + (4×3) = 8+12 = 20
= 2(4×5) = 40
= 4(1+4) = 4(5) = 20
We have:
4 × 5 = 20 2 × 4 × 5 = 40
(4×2) + (4×3) 4×5×2
4(1+4) 2(4×5)
Thus, 4 × 5 equivalent to (4×2) + (4×3) and 4(1+4), 2 × 4 × 5 is equivalent to 4×5×2 and 2(4×5)
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what is p divided by 10?
Answers
What number is represented by point B?
image
-0.3
-1
-0.6
-3
Answers
Answer:
Its -0.3 *fixed*
Step-by-step explanation:
The start says -2 and the end is 0.
A= -1 so between 0 and -1 your in the decimals place so its -0.3
Answer:
c
Step-by-step explanation:
PLZ HELP!!!!!!!!!!!!
Answers
Answer:
Maria has 24 if her friend has 6, she has 40 if her friend has 10, and she has 80 if her friend has 20.
Step-by-step explanation:
if she has four times as many as her friend, you multiply the amount by 4 and theirs you're answer
which expressions represents a 20% discount off the price of an item that originally cost D dollars
Answers
Answer:
D - (D/5)
Step-by-step explanation:
Let's imagine that D equals 100 dollars -
Well, we know that to get 20% of an amount, we need to divide the amount by five. So let's do that -
100 / 5 = 20
We now know that 20% of 100 dollars is equal to 20 dollars. We have now finished the first part. On to the second part.
We now need to take away 20% of 100 dollars off of 100 dollars - this is the price of the item after the discount.
100 - 20 = 80 dollars.
We now fit in D instead of 100 dollars -
D - (D/5)
First Street and Main Street come together diagonally at a four-way intersection, as shown below
Answers
Answer:
what answer do i give like what is the question
Step-by-step explanation:
Answer: It is 105
Step-by-step explanation:
i just know
Help me this one is for 10 points.
Answers
Answer:
its 3 square centimeters
Answer:
3
Step-by-step explanation:
Formula for finding triangle 1/2 bh (Half times the base times the height). So multiply 3 x 2 to get 6. then divide 6 by 2 to equal 3.
Hope this helps :)
Please help me! Thank you!
Answers
Answer:
false
Step-by-step explanation:
Answer:
It's actually True
Step-by-step explanation:
If you look at the graph there is a pattern between all the points on it. And if you follow the pattern it shows 18 and 30 line up. :))
I need help please !!
Answers
Answer:
59
Step-by-step explanation:
it has the most dots
A cylindrical candle has a diameter of 9 cm and height 12 cm.
It is placed in a cylindrical box.
There is a space of 0.5 cm between the candle and the box to allow for packing material.
a.) What is the height of the cylindrical box?
b.) What is the radius of the cylindrical box?
c.) What is the surface area of the box?
Answers
Answer:
a. 13 cm
b. 5cm
im not sure what c is and if a and b are correct i tried
Step-by-step explanation:
Which statements about the value of the digits in the number 6,666,666 are true?
Select each correct answer.
The digit in the hundreds place is 60 times the value of the digit in the tens place.
The digit in the ten thousands place is 10 times the value of the digit in the thousands place.
The digit in the hundred thousands place is 1/10 the value of the digit in the millions place.
The digit in the thousands place is 1/6 the value of the digit in the ten thousands place.
Answers
B. The digit in the hundred thousands place is 1/10 the value of the digit in the millions place.
C. The digit in the ten thousands place is 10 times the value of the digit in the thousands place.
Hope this helps !
Photon
How do I solve the surface area of a hexagonal prism when the hexagon base has an area of 509 in2 and a height of 14 in? I don't need the answer I need an explanation.
Answers
Answer:
use the formula SA = 6(a + h), where s = side length of the base, a = apothem length, and h = height of the prism.
Use the algebra tiles to help you solve the equation x2-3=7.
Answers
Step-by-step explanation:
ANSWER Solve for x |x+2|-3=7. |x+2|-3=7|x+ 2|-3 = 7. Move all terms not containing |x+2||x+ 2 | to the right side of the equation.
Answer: √ 10 , − √ 10
Step-by-step explanation: Mark as brainlyest plz
give the slope between the points (-4,-1) (-7,-10)
Answers
PLEASE HELP IM GIVING BRAINLIEST!!!!
parallel lines r and s are cut by two transversals, parallel lines t and u.
How many angles are alternate exterior angles with angle 5?
Answers
Angle 5,7,11,9,13,15,1,3 are alternate exterior angles with angle 5
sorry if im wrong
How many ten thousands are equal to 4 hundred thousands?
Answers
Answer:
40
Step-by-step explanation:
10×4 ten thousands=40 ten thousands=4 hundred thousands.
In the table, Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10."
Pattern A 10 15 20 25 30
Pattern B 20 30 40 50 60
Which statement is true?
Every term in Pattern B is 10 times the corresponding term in Pattern A.
Every term in Pattern B is 10 more than the corresponding term in Pattern A.
Every term in Pattern B is 1/2 the corresponding term in Pattern A.
Every term in Pattern B is 2 times the corresponding term in Pattern A.
Answers
Answer:
D) every term in pattern B is 2 times the corresponding term in Pattern A
Step-by-step explanation:
i know things
Answer: Every term in pattern B is 2 times the corresponding term in pattern A (the last one)
Step-by-step explanation:I think it is , because 5x2=10 and you are multiplying pattern A x2 to get the number at the bottom
Anyone have D-i-s-c-o-r-d my name on there is Bulletproof
1.) Solve -23.7 + d = -48.57.
Answers
Answer:
d= -24.87
Step-by-step explanation:
-23.7+d= -48.57
+23.7 +23.7
d= -24.87
Answer:
No I don't sorry but the answer is -24.87
Step-by-step explanation:
Explain how to solve the equation 3.5n = 10.5 what is the value of n explain
Answers
Answer:
n=3
Step-by-step explanation:
Hope this helps
3.5n/3.4=10.5/3.5
n=3
3x + 1 = –11
a. –36
b. –3
c. –30
d. –4
Answers
Explain how you can tell whether a group of ratios represents a proportional relationship.
Answers
Answer:
To see if multiple ratios are proportional, you could write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportional ratios.
(Hope this helps!! Btw, I am the first to answer.)
A group of ratios represents a proportional relationship. When the connection is proportional if the ratio remains constant. Explanation is given.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Ratio:
The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
An ordered pair of integers a and b,
represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
The ratios between the two variables should be considered in order to determine whether a relationship is proportional.
The connection is proportional if the ratio remains constant.
Therefore, the relationship is proportional if the ratio remains constant.
To learn more about the proportional relationship;
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Carrie and Diana ate lunch at a restaurant.
They ordered 1 pizza that cost $13.02.
Diana ordered chicken wings for $12.99 and a drink for $3.25.
Carrie ordered a salad for $6.25 and a drink for $3.25.
They left a $10.00 tip.
Diana paid for her food, plus half the cost of the pizza and half the tip. What was the total amount Diana paid?
A.$33.78
B.$27.75
C.$27.04
D.$20.77
Answers
Answer:
B) 27.75
Step-by-step explanation:
12.99+3.25=16.24
Half the tip is 5
5+16.24=21.24
Half the pizza is 6.51
21.24+6.51=27.75
The total amount paid by Diana will be equal to $27.75. Hence, option B is correct.
What is arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data given in the question,
Price of pizza = $13.02
Half price of pizza paid by Diana = 13.02/2 = $6.51
Price of chicken wings ordered by Diana = $12.99 and,
Price of drink that is also ordered by Diana = $3.25
Then, tip price is $10 which is paid half by Diana = $5
Then, the total expenditure by Diana will be,
= 6.51 + 12.99 + 3.25 + 5
= $27.75
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A right circular cone has a radius of 8 in. and a slant height of 12 in. These dimensions are multiplied by 6. By what factor is the surface area multiplied?
Answers
Answer:
Factor: 36
Step-by-step explanation:
Ratio of sides
1 : 6
Ratio of areas
1² : 6²
1 : 36
Giving brainliest !!!!!!!
Answers
Answer:
its A :D.
Step-by-step explanation:
I need help :) please and thank u if u get it right i will give u brainlist :)
Answers
Hi, can someone please help me?
Answers
Answer:
Eddie
Step-by-step explanation:
Lynn finished her mile in 9 minutes. We can tell this as in the chart after 9 minutes, she had ran 1 mile. Eddie runs at a constant speed of 7.5 miles per hour, and we have to convert this to minutes per mile. To do this, we can divide the number of minutes in an hour (60), by 7.5. We can do this as every hour has 60 minutes, and we know Eddie can run 7.5 miles in those 60 minutes. When we divide 60 by 7.5, we are finding how long it takes in minutes to run one mile, for Eddie. When we do this we get 8, so Eddie is faster.
can you help me with these two questions? thanks lol
Answers
Answer:
Step-by-step explanation:
1. 10 pi
2 C
1.10 pi
2.C
I think
Mon poured 100 kg of water into 10 kg of salt. He made ___ kg of ___% salt solution.
Answers
Answer:
10kg of 10%
Step-by-step explanation:
It was possible to move up in social class in ancient Egyptian society.
Please select the best answer from the choices provided
T
F
Egyptians were known for their advancements in all of the following except
a.
mathematics
c.
military strength
b.
herbalism
d.
astronomy
.
The people of ancient Egypt and Nubia were completely isolated from others because of the surrounding desert.
t
f
The Nile River is composed of two smaller rivers, the Blue Nile and the Black Nile.
Please select the best answer from the choices provided
T
F
The Nile River affected ancient Egyptian life by creating
a.
hot winds that blew across the land.
b.
Lower and Upper Egypt.
c.
rich farmland in the river valley.
d.
a large desert.
Pyramids were built to serve as ______ .
a.
palaces for the pharaoh
c.
compasses for traders
b.
astronomical observatories,
d.
a tomb for the pharaoh
Herodotus said “The Nile, when it floods, spreads over not only the Delta but parts of what are called Libya and Arabia for two days’ journey in either direction, more or less. . . .This that I have mentioned was the subject of my persistent asking why, and also why it is that it is the only river that has no breezes blowing from it.”
—Herodotus, The History, 2.19
How far could one walk before finding the end of the Nile’s flood?
a.
two miles
c.
two leagues
b.
two weeks’ journey
d.
two days’ journey
plz plz plz hury
Answers
Answer:
t , c , f , t , a , b , c
Step-by-step explanation:
What must you assume when you use a rate to make a prediction?
A. That the rate does change
B.That the rate does not change
Answers
Answer:
That the rate doesn't change.
Step-by-step explanation:
If you assume that the rate changes then you will not be able to find the answer.
Please can you mark me brainliest?