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3 years ago

Is there a dilation that maps shape I onto shape II? If so, what is the scale factor and is it an enlargement or a reduction?

Mathematics

1 answer:

Gre4nikov [31]3 years ago

6 0

Answer:

Enlargement.

Scale Factor: 3

Step-by-step explanation:

Use points to find the enlargement. Typically, you will use all the points.

A(1 , 1) ⇒ A'(3 , 3)

B(2 , 1) ⇒ B'(6 , 3)

C(1 , 2) ⇒ C'(3 , 6)

D(2 , 2) ⇒ D'(6 , 6)

To find the scale factor, simply divide the Point' with the original Point. Use any number.

A'(3 , 3)/(A(1 , 1)) = 3

B'(6 , 3)/(B(2 , 1)) = 3

C'(3 , 6)/(C(1 , 2)) = 3

D'(6 , 6)/(D(2 , 2)) = 3

Your scale factor is 3.

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Find the max/min value of f(x) = 2x2 + 3x - 5

Lelechka [254]

Answer:

The minimum value is $(-\frac{3}{4},-\frac{49}{8})$ or $(-0.75,-6.125)$

Step-by-step explanation:

we have

$f(x)=2x^{2}+3x-5$

This is the equation a vertical parabola open upward

The vertex represent a minimum

The general equation in vertex form is

$f(x)=a(x-h)^2+k$

where

(h,k) is the vertex

Convert the given function in vertex form

$f(x)=2x^{2}+3x-5$

Factor 2

$f(x)=2(x^{2}+\frac{3}{2}x)-5$

Complete the square

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}$

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}$

Rewrite as perfect squares

$f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}$

The vertex is the point $(-\frac{3}{4},-\frac{49}{8})$

8 0

3 years ago

The coordinates of the vertices of ΔMDT are M (4, −3),D (−6, −1), and T (7, −8). Identify the perimeter of ΔMDT. Round each side

Ganezh [65]

$M=(4,-3)\qquad D=(-6,-1)\qquad T=(7,-8)\\\\\\
|MD|=\sqrt{\big(-6-4\big)^2+\big(-1-(-3)\big)^2}=\sqrt{\big(-10\big)^2+\big(-1+3\big)^2}=\\\\=\sqrt{100+2^2}=\sqrt{104}\approx\boxed{10.2}\\\\\\\\
|DT|=\sqrt{\big(7-(-6)\big)^2+\big(-8-(-1)\big)^2}=\sqrt{\big(7+6\big)^2+\big(-8+1\big)^2}=\\\\=\sqrt{13^2+(-7)^2}=\sqrt{169+49}=\sqrt{218}\approx\boxed{14.8}\\\\$

$|TM|=\sqrt{\big(4-7\big)^2+\big(-3-(-8)\big)^2}=\sqrt{\big(-3\big)^2+\big(-3+8\big)^2}=\\\\=\sqrt{9+5^2}=\sqrt{9+25}=\sqrt{34}\approx\boxed{5.8}$

So the perimeter:

$P_{\Delta MDT}=|MD|+|DT|+|TM|\approx10.2+14.8+5.8=\boxed{30.8}$

Answer C.

4 0

4 years ago

Solve for x. Show your Work.

andreyandreev [35.5K]

Answer:

50+3x+4 = 90

54+3x = 90

3x = 90-54

3x = 36

x = 12

3x+4 = 3(12)+4

= 36+4

= 40

5 0

3 years ago

601.584 to the nearest tenth

son4ous [18]

The answer is 601.6
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7 0

3 years ago

Five soccer players each contributed an equal share toward a $50 gift for their coach. Write and solve an algebraic equation to

shtirl [24]

5x = 50
Where x represents the (equal) amount of money each player contributed
As you can see, you can easily solve the equation above to get:
x = 10
Each player contributed $10 toward a $50 gift.

5 0

4 years ago