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2 years ago

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

Mathematics

1 answer:

Agata [3.3K]2 years ago

7 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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3 years ago

Which ordered pair would form a proportional relationship with the point graphed below?

nevsk [136]

Answer:

(90,60)

Step-by-step explanation:

if you look closely through the linear graph, the line crosses through (90,60) and not the other given pairs.

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3 years ago

Read 2 more answers

Gravel is being dumped from a conveyor belt at a rate of 20 ft3 /min and its coarseness is such that it forms a pile in the shap

pantera1 [17]

Answer:

The height of the pile is increasing at the rate of $\mathbf{ \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

Step-by-step explanation:

Given that :

Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min

i.e $\dfrac{dV}{dt}= 20 \ ft^3/min$

we know that radius r is always twice the diameter d

i.e d = 2r

Given that :

the shape of a cone whose base diameter and height are always equal.

then d = h = 2r

h = 2r

r = h/2

The volume of a cone can be given by the formula:

$V = \dfrac{\pi r^2 h}{3}$

$V = \dfrac{\pi (h/2)^2 h}{3}$

$V = \dfrac{1}{12} \pi h^3$

$V = \dfrac{ \pi h^3}{12}$

Taking the differentiation of volume V with respect to time t; we have:

$\dfrac{dV}{dt }= (\dfrac{d}{dh}(\dfrac{\pi h^3}{12})) \times \dfrac{dh}{dt}$

$\dfrac{dV}{dt }= (\dfrac{\pi h^2}{4} ) \times \dfrac{dh}{dt}$

we know that:

$\dfrac{dV}{dt}= 20 \ ft^3/min$

So;we have:

$20= (\dfrac{\pi (15)^2}{4} ) \times \dfrac{dh}{dt}$

$20= 56.25 \pi \times \dfrac{dh}{dt}$

$\mathbf{\dfrac{dh}{dt}= \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

The height of the pile is increasing at the rate of $\mathbf{ \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

8 0

3 years ago

Among the contestants in a competition are 50 women and 26 men. If 5 winners are randomly selected, qhat js the probability that

liq [111]

Answer:

Probability that all winner are men = 0.0035 (Approx.)

Step-by-step explanation:

Given:

Number of women = 50

Number of men = 26

Total number winner = 5

Find:

Probability that all winner are men

Computation:

Total competitor = 50 + 26 = 76

Probability that all winner are men = 26/76 x 25/75 x 24/74 x 23/73 x 22/72

Probability that all winner are men = 7,893,600 / 2,216,980,800

Probability that all winner are men = 0.0035 (Approx.)

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3 years ago

Solve 2x2 8x - 12 = 0 by completing the square. show step-by-step solution

malfutka [58]

Group x terms
(2x^2+8x)-12=0
undistribute 2
2(x^2+4x)-12=0
take 1/2 of 4 and square it, add negative and positive of it insde (2^2=4)
2(x^2+4x+4-4)-12=0
factor perfect square
2((x+2)^2-4)-12=0
distribute
2(x+2)^2-8-12=0
2(x+2)^2-20=0
add 20 to both sides
2(x+2)^2=20
divide both sides by 2
(x+2)^2=10
sqrt both sides, remember to take positive and negative root
x+2=+/-√10
minus 2 both sides

x=-2+√10 and -2-√10

8 0

3 years ago