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2 years ago

What is the solution of this equation -12x-7=53

Mathematics

2 answers:

umka21 [38]2 years ago

8 0

Answer:

<em>x </em>= -5

Step-by-step explanation:

You have to work backwards.

53 + 7 = 60

60 ÷ 12 = 5

Add the negative »»» -5

Taya2010 [7]2 years ago

5 0

X= -5

Explanation: Move the constant to the right-hand side and change its sign, Add the numbers, Divide both sides of the equation by -12.

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3 years ago

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

How many solutions does the system formed by x - y = 3 and ay + 3a = 0 have for a non zero number a? Explain and show how you ge

dlinn [17]

Solve both equations for y:
$x-y=3 \ \ \ |-x \\
-y=-x+3 \ \ \ |\times (-1) \\
y=x-3 \\ \\
ay+3a=0 \ \ \ |-3a \\
ay=-3a \ \ \ |\div a, a \not= 0 \\
y=-3$

Set the expressions equal to each other:
$y=y \\ x-3=-3 \ \ \ |+3 \\
x=0 \\ \\
(x,y)=(0,-3)$

So, for every nonzero number a the system of equations has one solution.

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3 years ago

42 = -7 (z - 3)<br><br> z = ?

liubo4ka [24]

Answer:

The answer to your question is z = -3

Step-by-step explanation:

Expand 42 = -7(z - 3)

42 = -7z + 21

Simplify 7z = -42 + 21

7z = -21

Clear z z = $\frac{-21}{7}$