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3 years ago

What is the minimum value for g(x)=x^2-10x+16? Enter your answer in the box.

Mathematics

1 answer:

Anna71 [15]3 years ago

6 0

Answer:

- 9

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/subtract (half the coefficient of the x- term)² to x² - 10x

g(x) = x² - 10x + (- 5)² - (- 5)² + 16

= x² - 10x + 25 - 25 + 16

= (x - 5)² - 9 ← in vertex form

vertex = (5, - 9), hence

minimum value = - 9

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2 years ago

Please solve the following sum or difference identity.

xxTIMURxx [149]

Answer:

$sin(A - B) = \frac{4}{5}$

Step-by-step explanation:

Given:

$sin(A) = \frac{24}{25}$

$sin(B) = -\frac{4}{5}$

Need:

$sin(A - B)$

First, let's look at the identities:

sum: $sin(A + B) = sinAcosB + cosAsinB$

difference: $sin(A - B) = sinAcosB - cosAsinB$

The question asks to find sin(A - B); therefore, we need to use the difference identity.

Based on the given information (value and quadrant), we can draw reference triangles to find the simplified values of A and B.

sin(A) = $\frac{24}{25}$

cos(A) = $\frac{7}{25}$

sin(B) = $-\frac{4}{5}$

cos(B) = $\frac{3}{5}$

Plug these values into the difference identity formula.

$sin(A - B) = sinAcosB - cosAsinB$

$sin(A - B) = (\frac{24}{25})(\frac{3}{5}) - (-\frac{4}{5})(\frac{7}{25})$

Multiply.

$sin(A - B) = (\frac{72}{125}) + (\frac{28}{125})$

Add.

$sin(A - B) = \frac{4}{5}$

This is your answer.

Hope this helps!

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