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telo118 [61]
3 years ago
15

What is the x-value at which the graphs of y = x2 – 2x + 1 and y = x2 + 2x – 7 inter- sect?

Mathematics
1 answer:
Kitty [74]3 years ago
5 0

Answer:

x = 2

Step-by-step explanation:

Both equations are equal to y, so they're also equal to each other.  We then set them equal to each other:

x^2 - 2x + 1  =  x^2 + 2x - 7

We now do algebra to isolate x.  Subtract 1 from both sides.

x^2 - 2x  =  x^2 + 2x - 8

Subtract 2x from both sides.

x^2 - 4x  =  x^2 - 8

Subtract x^2 from both sides.

-4x = -8

Divide both sides by -4.

x = 2

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<h3>Given</h3>
  • 5 movies and 2 video games rent for $26
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<h3>Find</h3>
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<h3>Solution</h3>

Let m and v represent the rental cost of a movie and a video game, respectively. The given information can be expressed in two equations:

... 5m +2v = 26

... 3m +8v = 53

Using Cramer's rule, we can find the solution to be

... m = (2·53 -8·26)/(2·3-8·5) = -102/-34 = 3

... v = (26·3-53·5)/-34 = 5.50

The rental cost for each movie is $3; for each video game is $5.50.

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6 0
3 years ago
A pie costs $12.55. If it has a diameter of 12 inches what is the cost per square inch of the pie.
uysha [10]

Answer:

The cost per square inch of the pie is $0.111 or 11 cents

Step-by-step explanation:

The shape of a pie is circular.

The area of a circle (pie) = πr²

From the question ,

Diameter = 12 inches

Radius = Diameter/2

Radius = 12 inches/2

Radius = 6 inches.

Hence, the area of the pie = π × 6²

= 113.09733553 square inches

A pie costs $12.55

The cost per square inches of the pie is calculated as:

113.09733553 square inches = $12.55

1 square inch = $x

Cross Multiply

113.09733553x = $12.55

x = $12.55/113.09733553

x = $0.1109663631

Approximately

x = $0.111

Therefore, the cost per square inch of the pie is $0.111 or 11 cents

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