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2 years ago

13

On a map, two cities are 5 3/4 inches apart. the scale of the map is 1/2 inch equals 3 miles. what is the actual distance betwee

n the towns?

1 answer:

lina2011 [118]2 years ago

8 0

Answer:

18

Step-by-step explanation:

5.5 x 3=16.5

Add 1.5 and you get 18

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Ricky buys a remote car. He applies a markup of 10%. Write two expressions that represent the price of the car

Softa [21]

Answer:

we have to learn this in middle school

Step-by-step explanation:

3 0

3 years ago

Identify the constant of proportionality from the graph.<br><br>A. 1/2<br>B. 8<br>C. 2<br>D. 5

LuckyWell [14K]

I believe the answer is C

6 0

3 years ago

g A 5 foot tall man walks at 10 ft/s toward a street light that is 20 ft above the ground. What is the rate of change of the len

vredina [299]

Answer:

$-\frac{10}{3}ft/s$

Step-by-step explanation:

We are given that

Height of man=5 foot

$\frac{dy}{dt}=-10ft/s$

Height of street light=20ft

We have to find the rate of change of the length of his shadow when he is 25 ft form the street light.

ABE and CDE are similar triangle because all right triangles are similar.

$\frac{20}{5}=\frac{x+y}{x}$

$4=\frac{x+y}{x}$

$4x=x+y$

$4x-x=y$

$3x=y$

$3\frac{dx}{dt}=\frac{dy}{dt}$

$\frac{dx}{dt}=\frac{1}{3}(-10)=-\frac{10}{3}ft/s=-\frac{10}{3}ft/s$

Hence, the rate of change of the length of his shadow when he is 25 ft from the street light= $-\frac{10}{3}ft/s$

7 0

3 years ago

Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

Solve5(2x-3) = 3(x+4)

balu736 [363]

$5(2x-3)=3(x+4) \\
10x-15=3x+12 \\
10x-3x=12+15 \\
7x=27 \\
x=\frac{27}{7}=3 \frac{6}{7}$

3 0

3 years ago

Read 2 more answers