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3 years ago

Write each equation in slope-intercept form. a 5x+y=23 b 2x−y=14

Mathematics

1 answer:

densk [106]3 years ago

6 0

Answer:

A) y=23-5x

b) y= -14+2x

Step-by-step explanation:

a) 5x+y=23

-5x -5x

___________

y=23-5x

2x-y=14

-2x -2x

_________

-y=14-2x

__ ___

-1 -1

y=-14+2x

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4 years ago

Justify each step in the solution of 5x+15=0

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Subtract 15 from both sides.

5x=-15

Divide by 5

x=-5

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4 years ago

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You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

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1 year ago

The tires on your bicycle have a radius of 8 inches. How many rotations does each tire make when you travel 700 feet? Round your

Inessa [10]

"One rotation" would be the circumference of the wheel, which is

C = 2*pi*r, or (here) C = 2*pi*(8 inches) = 16*pi inches.

1 ft
Convert this to feet: 16*pi inches times ---------------
12 inches

Here "inches" cancels out and you are left with (4/3)pi ft.

So, one rotation of the wheel moves you and your bike forward (4/3)pi ft.

Divide this into 700 feet:

700 ft 2100
------------- = --------- rotations = 525 rotations (answer)
(4/3) pi ft 4

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4 years ago

Which expression is equivalent to (r^-7)^6?<br>A: r^42<br>B: 1/r^42<br>C: -7r^6<br>D: 1/r

cricket20 [7]

Answer:

Step-by-step explanation:

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3 years ago