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-BARSIC- [3]
3 years ago
10

Find the approximate perimeter of ABC plotted below.

Mathematics
1 answer:
maksim [4K]3 years ago
8 0

Answer:

B. 21.2

Step-by-step explanation:

Perimeter of ∆ABC = AB + BC + AC

A(-4, 1)

B(-2, 3)

C(3, -4)

✔️Distance between A(-4, 1) and B(-2, 3):

AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

AB = \sqrt{(-2 - (-4))^2 + (3 - 1)^2} = \sqrt{(2)^2 + (2)^2)}

AB = \sqrt{4 + 4}

AB = \sqrt{16}

AB = 4 units

✔️Distance between B(-2, 3) and C(3, -4):

BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

BC = \sqrt{(3 - (-2))^2 + (-4 - 3)^2} = \sqrt{(5)^2 + (-7)^2)}

BC = \sqrt{25 + 49}

BC = \sqrt{74}

BC = 8.6 units (nearest tenth)

✔️Distance between A(-4, 1) and C(3, -4):

AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

AC = \sqrt{(3 - (-4))^2 + (-4 - 1)^2} = \sqrt{(7)^2 + (-5)^2)}

AC = \sqrt{47 + 25}

AC = \sqrt{74}

AC = 8.6 units (nearest tenth)

Perimeter of ∆ABC = 4 + 8.6 + 8.6 = 21.2 units

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Answer:

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Step-by-step explanation:

y=-x+2\\y=3x-4

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y=3x-4

Add 4

y+4=3x

Divide by 3.

x=\frac{y+4}{3}

Now, plug the value of y in the formula, or you can plug the value of x in the other equation. I'll take this one.

x=\frac{y+4}{3}

x=\frac{(-x+2)+4}{3}

x=\frac{-x+2+4}{3}

x=\frac{-x+6}{3}

Multiply by 3 to get rid of the denominator.

3x=-x+6

add x

3x+x=6

Combine like terms;

4x=6

Divide by 4.

x=\frac{6}{4}

Simplify.

x=\frac{3}{2}

Now that you found the value of x, replace it in any of the equations to find y.

y=-x+2\\y=-(\frac{3}{2})+2\\ y=-\frac{3}{2}+2

y=\frac{-3+2*2}{2} \\y=\frac{-3+4}{2} \\y=\frac{1}{2}

Proof:

y=3x-4\\\frac{1}{2}=3(\frac{3}{2})-4\\\frac{1}{2}=(\frac{9}{2})-4

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\frac{1}{2}=\frac{9-8}{2}

\frac{1}{2}=\frac{1}{2}

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The equation for the cost in dollars of producing automobile tires is c = 0.000015x2 - 0.03x + 35, where x is the number of tire
statuscvo [17]
The cost function is
c = 0.000015x² - 0.03x + 35
where x = number of tires.

To find the value of x that minimizes cost, the derivative of c with respect to x should be zero. Therefore
0.000015*2x - 0.03 = 0
0.00003x = 0.03
x = 1000

Note:
The second derivative of c with respect to x is positive (= 0.00003), so the value for x will yield the minimum value.

The minimum cost is
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Answer:
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3 0
3 years ago
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