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svetlana [45]
3 years ago
7

solve x^2-8x=20 by completing the square. Which is the solution set of the equation? a {2, 10} b {-2, 10} c {2, -10} d {-2, -10}

Mathematics
1 answer:
torisob [31]3 years ago
7 0

Answer:

B is the correct answer.

Step-by-step explanation:

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First let's make both the miles and the hours ran improper fractions:

26+\frac{1}{5}=\frac{131}{5}\\ 5+\frac{4}{5}=\frac{29}{5}

So, to find our miles per hour, we have to divide the miles by the hours to get: \frac{\frac{131}{5}\text{miles}}{\frac{29}{5}\text{hours}}=\frac{131\text{miles}}{29\text{hours}} \\ \text{ Now we have to divide the top and the bottom by 29 to get our miles per hour so: }\\ \frac{\frac{131}{29}}{\text{hour}} \approx \frac{4.52 \text{miles}}{\text{hour}}

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13

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Line segment 19 units long running from (x,0) ti (0, y) show the area of the triangle enclosed by the segment is largest when x=
Debora [2.8K]
The area of the triangle is

A = (xy)/2

Also,

sqrt(x^2 + y^2) = 19

We solve this for y.

x^2 + y^2 = 361

y^2 = 361 - x^2

y = sqrt(361 - x^2)

Now we substitute this expression for y in the area equation.

A = (1/2)(x)(sqrt(361 - x^2))

A = (1/2)(x)(361 - x^2)^(1/2)

We take the derivative of A with respect to x.

dA/dx = (1/2)[(x) * d/dx(361 - x^2)^(1/2) + (361 - x^2)^(1/2)]

dA/dx = (1/2)[(x) * (1/2)(361 - x^2)^(-1/2)(-2x) + (361 - x^2)^(1/2)]

dA/dx = (1/2)[(361 - x^2)^(-1/2)(-x^2) + (361 - x^2)^(1/2)]

dA/dx = (1/2)[(-x^2)/(361 - x^2)^(1/2) + (361 - x^2)/(361 - x^2)^(1/2)]

dA/dx = (1/2)[(-x^2 - x^2 + 361)/(361 - x^2)^(1/2)]

dA/dx = (-2x^2 + 361)/[2(361 - x^2)^(1/2)]

Now we set the derivative equal to zero.

(-2x^2 + 361)/[2(361 - x^2)^(1/2)] = 0

-2x^2 + 361 = 0

-2x^2 = -361

2x^2 = 361

x^2 = 361/2

x = 19/sqrt(2)

x^2 + y^2 = 361

(19/sqrt(2))^2 + y^2 = 361

361/2 + y^2 = 361

y^2 = 361/2

y = 19/sqrt(2)

We have maximum area at x = 19/sqrt(2) and y = 19/sqrt(2), or when x = y.
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3 years ago
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