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2 years ago

Look at the function below. f(x)=−x2−2x+8

Mathematics

1 answer:

enyata [817]2 years ago

7 0

Answer:

f(x) = -1(x+1)² + 9

Step-by-step explanation:

f(x) = -x² - 2x + 8

This is a down-opening parabola. Put the equation into vertex form. The y-coordinate of the vertex is the maximum.

factor out the leading coefficient

f(x) = -1(x²+2x) + 8

Complete the square

coefficient of x term: 2

divide in half: 1

square it: 1²

use 1² to complete the square:

f(x) = -1(x²+2x+1²) + 1² + 8

f(x) = -1(x+1)² + 9

vertex (-1,9)

maximum value of f(x) = 9

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The hypotenuse of a 45 45 90 triangle measures 24 inches. what is the length of one leg of the triangle?

frosja888 [35]

Answer:

$12\sqrt{2}\ in$

Step-by-step explanation:

we know that

A $45\°-45\°-90\°$ right triangle has two equal legs

Let

x-----> the length side of the leg of the triangle

y------> the length side of the hypotenuse

$sin(45\°)=cos(45\°)=\frac{\sqrt{2}}{2}$

$cos(45\°)=\frac{x}{y}$

$\frac{x}{y}=\frac{\sqrt{2}}{2}$

in this problem we have

$y=24\ in$

substitute the value of y and solve for x

$\frac{x}{24}=\frac{\sqrt{2}}{2}$

$x=24\frac{\sqrt{2}}{2}$

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5 0

3 years ago

Read 2 more answers

To buy a car, you borrow $25,000 with a term of three years at an APR of 6.5%. What is your monthly

Finger [1]

Answer:

$766.23

Step-by-step explanation:

The amortization formula is appropriate for this. (Better, use a financial calculator or spreadsheet.)

A = P(r/12)/(1 -(1 +r/12)^-(12t))

where P is the amount borrowed (25,000), r is the annual rate (0.065), and t is the number of years (3).

Putting the given numbers into the formula, we have ...

A = $25,000(0.065/12)/(1 -(1 +0.065/12)^(-36))

A = $25,000(.00541667)/(1 -1.00541667^-36)

A = $25,000(0.00541667)/(0.1767322)

A = $766.23

The monthly payment is $766.23.

_____

Comment on tools

A graphing or scientific calculator is useful for these. Something like a TI-84, or any of the equivalents, will have financial calculations like this built in. There are also numerous apps available for phone or tablet that will do financial calculations.

4 0

3 years ago

In general, the value measured by the horizontal axis is called the ________ variable.

bixtya [17]

Answer:

independent

Step-by-step explanation:

We put the independent variable on the x axis ( or horizontal) and the dependent variable on the y axis ( or vertical)

7 0

3 years ago

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Plzzzz help me on this questions fast This is Trigonometry