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anastassius [24]

3 years ago

5

The distance driven in miles is proportional to the time driven in hours. Ebony drives at a constant rate and plots her progress

on a coordinate plane. The point (3, 180) is plotted. At what rate is Ebony driving in miles per hour?
A) 40 mph
B) 50 mph
C) 60 mph
D) 70 mph

1 answer:

kati45 [8]3 years ago

5 0

Ebony is driving 60 mph.

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For each sentence below, find the value of x that makes each sentence true.

vitfil [10]

<u>ANSWER</u>

1. $x=\frac{1}{2}$

2. $x=1$

<u>QUESTION 1</u>

The first sentence is $(5^{\frac{1}{5}})^5=25^x$ .

Recall that;

$(a^m)^n=a^{mn}$

We simplify the left hand side by applying this property to get;

$5^{\frac{1}{5}\times 5}=25^x$ .

$\Rightarrow 5^{1}=25^x$ .

We now rewrite the right hand side too in an index form to obtain;

$\Rightarrow 5^{1}=5^{2x}$

We now equate the exponents to get;

$\Rightarrow 1=2x$ .

$\Rightarrow \frac{1}{2}=x$

$\Rightarrow x=\frac{1}{2}$ .

<u>QUESTION 2</u>

The second sentence is $(8^{\frac{1}{3}})^2=4^x$

We simplify the left hand side first to get;

$(2^{3\times \frac{1}{3}})^2=4^x$

$2^2=4^x$

We now rewrite the left hand side too in index form to obtain;

$2^2=2^{2x}$

We equate the exponents to get;

$2=2x$

This implies that;

$1=x$

or

$x=1$

4 0

3 years ago

5. Two similar figures have volumes 27 in.? and 125 in.?. The surface area of the smaller figure is 63 in.. (1 point)

GREYUIT [131]

Answer:

$175\ in^{2}$

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> volume of the larger solid

y----> volume of the smaller solid

$z^{3}=\frac{x}{y}$

we have

$x=125\ in^{3}$

$y=27\ in^{3}$

substitute

$z^{3}=\frac{125}{27}$

$z=\frac{5}{3}$

step 2

Find the surface area of the larger solid

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the larger solid

y----> surface area of the smaller solid

$z^{2}=\frac{x}{y}$

we have

$z=\frac{5}{3}$

$y=63\ in^{2}$

substitute

$(\frac{5}{3})^{2}=\frac{x}{63}$

$x=\frac{25}{9}*63=175\ in^{2}$

3 0

3 years ago

I need help plz help me !!

elena-14-01-66 [18.8K]

Answer:

110

Step-by-step explanation:

y = 11/6x where x is in minutes

there are 60 minutes in an hour

plug in 60 as x

11/6 *60 = 11*10 = 110

6 0

3 years ago

Read 2 more answers

Tim plans to spend 40 hours on exercise training to earn a private trainer license. He has saved $2,000

grigory [225]

Answer:

round it then divide it by 5

Step-by-step explanation:

6 0

3 years ago

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Write and solve a proportion to answer the question. 36 is 0.9% of what number w? =0.9100

pickupchik [31]

Answer:

Step-by-step explanation:

The question can be written out like this:

36 = 0.009x

Multiply both sides by 1,000:

9x = 36,000

Divide both sides by 9:

x = 4,000

8 0

3 years ago