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MA_775_DIABLO [31]
3 years ago
11

A company sells widgets. The amount of profit , ymade by the company, is related to the selling price of each widget, x, by the

given equation. Using this equation, find the maximum amount of profit the company can make, to the nearest Dollar.
y=-x^2+64x-292
Mathematics
1 answer:
Bezzdna [24]3 years ago
7 0

Answer:

$732

Step-by-step explanation:

Given

y \to profit

x \to widgets

y = -x^2 + 64x - 292

Required

The maximum profit

First, we calculate the maximum amount of widgets that can be sold using:

x = -\frac{b}{2a}

Where:

a = -1; b = 64; x = -292

So, we have:

x = -\frac{64}{2 * -1}

x = -\frac{64}{-2}

x = -(-32)

x = 32

The maximum profit is:

y = -x^2 + 64x - 292

y = -(32)^2 + 64 * 32 - 292

Using a calculator, we have:

y = 732

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Help!
Olin [163]

Answer:

2/16

1/8

Step-by-step explanation:

8/1=8

2/16=0.125 which is equal to 1/8

2/14=1/7

1/8=1/8 is 2/16 simplified so they are the same

14/2=7

6 0
3 years ago
Solve<br><img src="https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B1%7D%7Bp%7D%20%2B%20%5Cdfrac%7B1%7D%7Bq%7D%20%2B%20%5Cdfrac%7B1%7D
Nostrana [21]

Answer:

\displaystyle   \begin{cases} \displaystyle  {x} _{1} =  - p \\   \displaystyle x _{2}   =  -  q \end{cases}

Step-by-step explanation:

we would like to solve the following equation for x:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}  +  \frac{1}{x}  =  \frac{1}{p  + q + x}

to do so isolate \frac{1}{x} to right hand side and change its sign which yields:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{1}{p  + q + x}  -  \frac{1}{x}

simplify Substraction:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{x - (q + p +  x)}{x(p  + q + x)}

get rid of only x:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{  - (q + p )}{x(p  + q + x)}

simplify addition of the left hand side:

\displaystyle  \frac{q + p}{pq}     =  \frac{  - (q + p )}{x(p  + q + x)}

divide both sides by q+p Which yields:

\displaystyle  \frac{1}{pq}     =  \frac{  -1}{x(p  + q + x)}

cross multiplication:

\displaystyle    x(p  + q + x)  =   - pq

distribute:

\displaystyle    xp  + xq +  {x}^{2} =   - pq

isolate -pq to the left hand side and change its sign:

\displaystyle    xp  + xq +  {x}^{2} + pq =  0

rearrange it to standard form:

\displaystyle   {x}^{2} +    xp  + xq  + pq =  0

now notice we end up with a <u>quadratic</u><u> equation</u> therefore to solve so we can consider <u>factoring</u><u> </u><u>method</u><u> </u><u> </u>to use so

factor out x:

\displaystyle  x( {x}^{} +   p ) + xq  + pq =  0

factor out q:

\displaystyle  x( {x}^{} +   p ) +q (x + p)=  0

group:

\displaystyle  ( {x}^{} +   p ) (x + q)=  0

by <em>Zero</em><em> product</em><em> </em><em>property</em> we obtain:

\displaystyle   \begin{cases} \displaystyle  {x}^{} +   p  = 0 \\   \displaystyle x + q=  0 \end{cases}

cancel out p from the first equation and q from the second equation which yields:

\displaystyle   \begin{cases} \displaystyle  {x}^{}   =  - p \\   \displaystyle x  =  -  q \end{cases}

and we are done!

3 0
3 years ago
Cora gave her a ​$4.40 tip. The tip was ​20% of the cost of the haircut. Write an equation to find​ b, the cost of the haircut .
Damm [24]

Answer:

3.52

Step-by-step explanation:

do 4.40*.20. youll get .88, then subtract .88 from 4.40. pls give brainliest

7 0
2 years ago
When think of a number double it<br> and add five and get 13 What the number I<br> Thought
aev [14]

Let the no be x

ATQ

\\ \sf\longmapsto 2x+5=13

\\ \sf\longmapsto 2x=13-5

\\ \sf\longmapsto 2x=8

\\ \sf\longmapsto x=\dfrac{8}{2}

\\ \sf\longmapsto x=4

3 0
3 years ago
Try It for Example 3: Is 3.14144144414444... a rational number? Explain your reasoning. *
chubhunter [2.5K]

it's irrational

A rational number can be put over a fraction, while this number continues forever

5 0
3 years ago
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