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3 years ago

Solve for the unknown check your solution by substituting it in the original equation. -X+11=-2X-7

Mathematics

1 answer:

Debora [2.8K]3 years ago

8 0

Answer:

Step-by-step explanation:

-X+11=-2X-7

11=3X-7

18=3X

18/3= 6

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A church window consisting of a rectangle topped by a semicircle is to have perimeter p . find the radius of the semicircle if t

Y_Kistochka [10]

Answer:

$r=\dfrac{p}{4+\pi}$

Step-by-step explanation:

Let r be the radius of the semicircle, then 2r is the width of the rectangle. Let y be the length of the rectangle. The perimeter of the window consists of two lengths, one width and length of semicircle, then

$p=2y+2r+\pi r.$

Express y:

$y=\dfrac{p-2r-\pi r}{2}.$

The area of the window is

$A=y\cdot 2r+\dfrac{1}{2}\pi r^2.$

Substitute y into the area expression:

$A=\dfrac{p-2r-\pi r}{2}\cdot 2r+\dfrac{1}{2}\pi r^2=pr-2r^2-\pi r^2+\dfrac{1}{2}\pi r^2=pr-2r^2-\dfrac{1}{2}\pi r^2.$

Find the derivative A':

$A'=p-4r-\pi r.$

Equate A' to 0:

$p-4r-\pi r=0\Rightarrow r=\dfrac{p}{4+\pi}.$

When $r$ then $A'>0$ and the function A is increasing, when $r>\dfrac{p}{4+\pi},$ then $A'$ and the function A is decreasing. This means that at point $r=\dfrac{p}{4+\pi}$ the function A takes it maximal value (the area is maximal).

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3 years ago

Two mechanics Worked on a car The first mechanic charge $55 per hour The second mechanic charge $80 per hour the mechanics work

Tems11 [23]

a = hours worked by the first mechanic

b = hours worked by the second mechanic.

since the first mechanic charges $55 per hour, then for "a" hours that'd be a total of 55*a or 55a, likewise, for the second mechanic that'd be a total charge of 80*b or 80b.

we know all hours combined are 15, so then a + b = 15.

we also know that all charges combined are $950, so 55a + 80b = 950.

$\bf \begin{cases} a+b=15\\ \boxed{b}=15-a\\ \cline{1-1} 55a+80b=950 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{55a+80\left( \boxed{15-a} \right)=950} \\\\\\ 55a+1200-80a=950\implies -25a+1200=950\implies -25a=-250 \\\\\\ a=\cfrac{-250}{-25}\implies \blacktriangleright a = 10\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=15-a\implies }b=15-10\implies \blacktriangleright b=5 \blacktriangleleft$

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3 years ago

Darius's sister Rachel bought m mystery books for $6.50 each. Shown three ways to write an algebraic expression that represents

Rashid [163]

1.) 6.50(m)= x
2.) x= 6.00m + 50
3.)6.50m-0= x

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3 years ago

Please answer correctly

marysya [2.9K]

Answer:

Option (1)

Step-by-step explanation:

We need a recursive formula.

Eliminate option 3.

The common ratio is 2.

Eliminate options 2 and 4.

So, the answer is option 1.

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2 years ago

Which of the following is a reduction in the price of the vehicle, generally offered by the manufacturer?

netineya [11]

Answer:

Need more information

Step-by-step explanation:

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4 years ago

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Solve for the unknown check your solution by substituting it in the original equation. -X+11=-2X-7​

Solve for the unknown check your solution by substituting it in the original equation. -X+11=-2X-7