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grin007 [14]
2 years ago
5

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}

so

\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}

x=12\sqrt{2}\ in

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.

_____

<em>Comment on tools</em>

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 ________<br> 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 <br><br>This is Trigonometry​
Sladkaya [172]

Answer:

x ≈ 20.42, y ≈ 11.71

Step-by-step explanation:

Using the cosine ratio on the right triangle on the right, that is

cos20° = \frac{adjacent}{hypotenuse} = \frac{11}{y}

Multiply both sides by y

y × cos20° = 11 ( divide both sides by cos20° )

y = \frac{11}{cos20} ≈ 11.71

Using the sine ratio on the right triangle on the left, that is

sin35° = \frac{opposite}{hypotenuse} = \frac{y}{x} = \frac{11.71}{x}

Multiply both sides by x

x × sin35° = 11.71 ( divide both sides by sin35° )

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5 0
3 years ago
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Write the exponential function.
sertanlavr [38]

Answer:

f(x) = 10*(b)^x

Step-by-step explanation:

exponential function : y=a*(b)^x

where a = y intercept and b = factor ( what you multiply by )

looking at the table the y intercept is at (0,10) so a = 10

so we now have y = 10 * (b)^x

to find the factor we simply plug in one of the ordered pairs.

note that the ordered pair chosen does not effect the outcome

i chose (2,250)

we have y = 10 * (b)^x

(x,y) = (2,250)

250 = 10 * (b)^2

divide both sides by 10

25 = b^2

take the square root of both sides

5 = b

the final equation would be f(x) = 10 * (b)^x

5 0
2 years ago
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