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2 years ago

jim drove 168 miles in 4 hours. if he keep the same pace, how long will if take him to drive 504 miles

1 answer:

6 0

You would first put 168 over 4 and simplify to get 42 over 1. Then you would divide 504 by 42 to get 12. You would have to drive 12 hours to get 504 miles.

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A - 7 x 2 for a = 15

marysya [2.9K]

Answer:

a- 7 x 2 is a = 14

.........

4 0

3 years ago

Ruth is making a necklace for a friend . she has 3 different types of clasps, 2 different chains , and 5 different cnarms. if sh

natita [175]

The answer I think is D)30 because they want to know how many she can make so just multiple 5*2*3

8 0

3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

3 0

3 years ago

Y=4x+7 what are the intercepts of the line

VikaD [51]

To find the intercepts you sub the opposite value for 0
To find y:
<span>Y=4(0)+7
0*4=0+7=7
y=7

To find x:
0=4x+7
Subtract 7 from both sides
-7=4x
divide both sides by 4

x=-7/4

Final answer:
x-intercept: (-7/4,0)
y-intercept: (0,7) </span>

4 0

3 years ago

Tell whether the valuation is a solution of the inequality r + 4 > 8 ; r = 2

aleksandr82 [10.1K]

Answer:

Not a solution.

Step-by-step explanation:

Step 1: Write inequality

r + 4 > 8

Step 2: Solve for <em>r</em>

Subtract 4 on both sides: r > 4

Step 3: Determine

r = 2

2 > 4 = FALSE

3 0

3 years ago