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Dafna1 [17]
2 years ago
12

The product of a number and 4 increased by 16 is -2

Mathematics
1 answer:
Art [367]2 years ago
3 0
The answer is -4.5

To solve these types of problems it's best to work backwards.
-2 - 16 = -18
4 x (n) = -18
n = -18/4
n = -4.5

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What is 10+0.6 (pls show steps on how you got an awnser :) )
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10.6

Step-by-step explanation:

ok so, since 10 doesn't have any decimals you can just add the 0.6 to 10 so it makes 10.6.

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Audrey and Lauren began reading a novel on the same day. Audrey reads 15 pages a day and Lauren reads 5 pages a day. If Audrey i
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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
Tommy wants to buy a new bike. Tommy has $199, which is $35 less than he needs. Which equation or inequality represents the cost
malfutka [58]

Answer:

Option (d) is correct.

Step-by-step explanation:

The initial amount Tommy has = $ 199

The actual amount that Tommy needs to purchase bike = 199 + 35 = $ 234

This is the price of the bike.

This condition can be true from option (d).

From option (d)

119 < b + 35

Put b = 234 we get

119 < 234 + 35

119 < 269

Thus the condition satisfied. so option (d) is correct.

4 0
3 years ago
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