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3 years ago

Y=x+2 Y=x-1 How many solutions does the system of equations have

Mathematics

1 answer:

Mkey [24]3 years ago

6 0

Answer:

the system has no solutions

Step-by-step explanation:

substract both equations and the result will be:

y - y = x - x + 2 + 1

0 = 3 is incompatible, so, no solution

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For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.

gayaneshka [121]

Hello!

To find the maximum value of the function f(x) = -3(x - 10)(x - 4), the easiest way is to find the vertex using the formula: x = -b/2a.

Firstly, we need to simplify f(x).

f(x) = -3(x - 10)(x - 4)

f(x) = -3(x² - 14x + 40)

f(x) = -3x² + 42x + -120

Since the equation f(x) is now simplified to standard form, we can find the vertex.

a = -3, b = 42, and c = -120

x = -(42)/2(-3) = -42/-6 = 7

Then, we substitute 7 into the the function f(x) = -3(x - 10)(x - 4), or

f(x) = -3x² + 42x + -120, to find the y-value of the vertex.

f(x) = -3(7 - 10)(7 - 4)

f(x) = -3(-3)(4)

f(x) = 27

The vertex of f(x) is (7, 27).

Therefore, the maximum x-value for the function f(x) is 7.

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3 years ago

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