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2 years ago

The function f is defined by f(x) = x^2 + 3x -10 , if f(x + 5) = x^2 + kx + 30, k=

Mathematics

1 answer:

boyakko [2]2 years ago

6 0

Answer:

k = 13

Step-by-step explanation:

substitute x = x + 5 into f(x) , that is

f(x + 5) = (x + 5)² + 3(x + 5) - 10 ← expand squared factor using FOIL

= x² + 10x + 25 + 3x + 15 - 10

= x² + 13x + 30

compare this with f(x + 5) = x² + kx + 30

for the 2 expressions to be equal , then k = 13

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Answer:

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Step-by-step explanation:

Part A) Find $sin(\alpha)\ and\ cos(\beta)$

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

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simplify

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we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

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Applying the Pythagorean Theorem

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simplify

$tan(\alpha)=\frac{4}{\sqrt{33}}$

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$\alpha+\beta=90^o$ ---> by complementary angles

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Answer:

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Step-by-step explanation:

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Matching up this vocabulary with what you see, you realize ...

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