Given:
Consider the pentagon MVEDR is dilated with the origin as the center of dilation using the rule [tex](x,y)\to(\dfrac{2}{3}x,\dfrac{2}{3}y)[/tex] to create pentagon M'V'E'D'R'.
To find:
The correct statement.
Solution:
If a figure dilated by factor k, then the rule of dilation is
[tex](x,y)\to (kx,ky)[/tex]
Here,
If k>1, then the image is larger than the original figure.
If k<1, then the image is smaller than the original figure.
We have,
[tex](x,y)\to(\dfrac{2}{3}x,\dfrac{2}{3}y)[/tex]
Here, M'V'E'D'R' is image and MVEDR is original figure. The scale factor is
[tex]k=\dfrac{2}{3}<1[/tex]
Pentagon M'V'E'D'R' is smaller than pentagon MVEDR because the scale factor is less than 1.
Therefore, the correct option is B.
Option (B). Pentagon M'V'E'D'R' is smaller than pentagon MVDER because the scale factor is less than 1.
Transformation of a point by dilation: If a point (x, y) is dilated by a scale factor 'k' about the origin,
image point formed will follow the rule,
(x, y) → (kx, ky)
If k > 1, image will be lager than the preimage.If k < 1, image will be smaller than the preimage.
Given in the question,
Rule for the transformation → [tex](x,y)\rightarrow (\frac{2}{3}x,\frac{2}{3}y)[/tex]
Here, [tex]k=\frac{2}{3}[/tex] which is less than 1.
Therefore, image pentagon M'V'E'D'R' will be smaller than the original pentagon MVDER.
Option (B) will be the correct option.
Learn more about the transformation of a figure here,
https://brainly.com/question/2298651?referrer=searchResults
Solves a systems of linear equations in two variables.
Solve the following systems by graphing
1) 2x + y = 5 and x-3y = - 8
2) 6x - 3y = - 9 and 2x + 2y = -6
Solve the following systems by substitution
3) y = 5x-3 and -x - 5y = - 11
4) 2x - 6 = 24 and x - 5y - 22
Solve the following systems by elimination
5) - 4x - 2y = -2 and 4x + 8y = -24
6) x - y = 11 and 2x + y = 19
Consider these functions:
f(x) = 2x3 + 3
g(x) = x – 4
What is the value of g(f(x))?
Answer:
2x^3+3-4
Step-by-step explanation:
Answer:
2x^3 - 1
Step-by-step explanation:
Plato/Edmentum
PLEASE HELP FAST POINTS AND BRAINLIST FOR ANSWER!
Answer:
y = 10x
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope m = 10
y-intercept b = 0
Step 2: Write function
Plug in variables into the general form.
y = 10x + 0
y = 10x
Answer:
y = 10x
Step-by-step explanation:
Equation of a line: y = mx + b
y = 10x + 0 is also y = 10x
(6x^3-x^4+7)+(7x^4-3+2x^2
Answer:
6x⁴ + 6x³ + 2x² + 4
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(6x³ - x⁴ + 7) + (7x⁴ - 3 + 2x²)
Step 2: Simplify
Combine like terms (x⁴): 6x⁴ + 6x³ + 2x² + 7 - 3Combine like terms (Z): 6x⁴ + 6x³ + 2x² + 4Find the difference.
89 – 52.05
A. 36.95
B. 35.95
C. 37.95
D. 37.05
What is the x-intercept of the graph that is shown below?
(-2,0)
(-1,2)
(0,4)
(4,0)
Solve the system of equations by graphing:
y= 2x +8
-x+y=0
Answer:
Slope = 4.000/2.000 = 2.000
Slope = 2.000/2.000 = 1.000
Step-by-step explanation:
the first answer is for the first problem and the second answer is for the second problem. Hoped it helped i tried my best.
The midpoint of ab is m(5-2). If the coordinates of a are (6,-5), what are the coordinates of b
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x4+81) / (x-3)
The x-intercept can be found by putting in zero for y. Find the x-intercept.
-3x + 5y 30
21 feet of yarn costs $42.70. What is the price per yard?
divide the numbers and you will get your answer.
(4x + 3y)^2 please tell me the wander ✌️
Answer:
16x^2+24xy+9y^2
Step-by-step explanation:
16x^2+24xy+9y^2
Sixty-five percent of what number is 26?
Answer:
40
Step-by-step explanation:
40 x 0.65 = 26
26 ÷ 0.65 = 40
Noah bought a computer cartridge for $28.50. Sales tax on the
cartridge was 6.5%. What was the total amount that Noah paid for the
cartridge? ( I need this answer ASAP)
Total = purchase price x ( 1 + sales tax )
Total = 28.50 x 1.065
Total = $30.35
Gabriel is 12 years old, and his younger brother Elias is 2 years old.
How old will each of them be when Gabriel is twice as old as Elias?
Gabriel will be 20, Elias will be 10
We can use an equation to map out and solve for each age.
Years gone by = x
12+x=2(2+x)
12+x=4+2x
x=8
12+8=20, 2+8 =10
When a person 6 feet tall casts a shadow
10 feet long, how tall is a nearby tree
which casts a shadow of 45 feet?
Answer:
75 feet
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
Proportion
6 feet man/10 feet shadow = x (tree) / 45 feet (shadow)
6/10 = x /45 Cross multiply
10x = 45*6
10x = 270
x = 270/10
x = 27
The tree is 27 feet long
During the basketball season, diane took 134 shots and made about 56% of them. a.) how many shots did diane make? b.) the team made a total of 498 shots. what precent of the teams made shots did diane make
Answer:
75 shots and 15.1%
Step-by-step explanation:
What is the reason for step 3 in the two column proof below
1. ZPQR is a right angle
1. Given
2. MZPQR = 90°
2. Definition of Right Angle
3. m_PQS + MZSQR = m_PQR
3. ?
4. MZPQS + m_SQR = 90°
4. Substitution Property of Equality
5. ZPQS and 2SQR are complementary 5. Definition of Complementary Angles
Definition of Congruent Angles
Vertical Angles Congruence Theorem
Angle Addition Postulate
Definition of Angle Bisector
Answer:
The correct option is;
Angle Addition Postulate;
Step-by-step explanation:
The given two column proof can be presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠PQR is a right angle [tex]{}[/tex] Given
2. m∠PQR = 90° [tex]{}[/tex] Definition of Right Angle
3. m∠PQS + m∠SQR = m∠PQR [tex]{}[/tex] Angle Addition Postulate
4. m∠PQS + m∠SQR = 90° [tex]{}[/tex] Substitution property of equality
5. ∠PQS and ∠SQR are complementary Definition of complementary angles
Given that the angle m∠PQR has angles m∠PQS and m∠SQR arranged adjacent to each other while sharing the same boundary segment, QS we have by the angle addition postulate;
m∠PQR is the sum of the angles m∠PQS and m∠SQR, therefore;
m∠PQR = m∠PQS + m∠SQR = 90°.
Why are the solutions to the proportions StartFraction 40 over 8 EndFraction = StartFraction x over 10 EndFraction and StartFraction x over 40 EndFraction = StartFraction 10 over 8 EndFraction the same?
Answer:Because both result in the equation 8x = 400 which simplifies to 50.
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
no need
What is the measure of
Factorize completely 25x^2-90x+81
Answer:
Factor using the perfect square rule.
( 5 x + 9 ) ^2
HOPE THIS HELPS!!!
Step-by-step explanation:
OPEN PERENTHESIS FIVE X PLUS NINE CLOSED PERENTHESIS TO THE SECOND POWER
In Landon's math class, there are 12 boys and 15 girls. Which of the following is the ratio of boys to girls in Landon's math class?
Answer: 9/4
Step-by-step explanation:
12/(12+15) = 12/27 = 9/4
Lacy pays $15 for each hour of golf lessons and $10 for equipment rental. If the lesson is more than 3 hours long, she only pays $5 for equipment rental. Is the total cost of Lacy's lesson a function of the number of hours scheduled? Use a table to help explain your answer. Show your work.
Answer:
60
Step-by-step explanation:
15x3=45
5x3=15
15+45=60
Someone please help solve this!! I’ll give brainlist
Answer:
Inital height is 20
Step-by-step explanation:
h= (-5x-5)(x-4)
h= -5x^2+15x+20
will mark brainliest to whoever can answer
Answer:
A. 7
Step-by-step explanation:
h(x)=2x + 4
2(7)=14
14+4=18
3÷4 is 34. What is 14 of 3?
a.3/4
b.13 of 4
c.43
d.1 1/4
Answer
well i know that the accual answer would be 466.6.
Step-by-step explanation:
What is the sum of 2/7 + 2/5 ?
please help 10 points and brainlest
Answer:
2/7 + 2/5=24/35
Find the value of the expressions when; a2+b +7 when a=5 and b=11.
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y > 3x + 10 y is less than negative 3 over 4 times x minus 1 Part A: Clearly describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points) Part B: Is the point (8, 10) a solution to this system? Explain how you know
Answer:
See attached graph, and answers.
Step-by-step explanation:
The inequalities are given as;
i) y>3x+10
ii) y<-3/4x -1
Graphing the inequalities gives the following result
The solution area is that which is shaded and the lines are broken lines not complete
From the graph the solution is: { -2.9,1.2}
The point {8,10} is not a solution to the system. This is because it is not in the shaded area that represent the solution to the inequalities.
1) Given that the measure of Angle 2 = 115 degrees and the measure of Angle 8 = 115 degrees, is line m parallel to line p?
Answer:
YES
Step-by-step explanation:
When a transversal cuts two parallel lines, the alternate interior angles are congruent. So, for two lines to be parallel, their alternate interior angles has to be equal.
Angle 2 and angle 8 are alternate interior angles. They both measure 115°. Since these alternate interior angles are congruent, therefore, line m is parallel to line p.