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3 years ago

The average rate of change of a function f(x) = x2 between x = 3 and x = 9 is

Mathematics

1 answer:

masya89 [10]3 years ago

6 0

Answer:

12.

Step-by-step explanation:

Average rate of change = (value of the function when x = 9 - value when x=3)

(9 - 3)

= f(9) - f(3) / (9-3)

= (9^2 - 3^2) / (9-3)

= 72 / 6

= 12.

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An architect wants to draw a rectangle with a diagonal of 13 centimeters. The length of the rectangle is to be 3 centimeters mor

butalik [34]

Answer:

The rectangle is 3.2 cm by 12.6 cm

Step-by-step explanation:

See attached image for a diagram.

Choose w to represent the width because the length is described by referring to the width: it's 3 more than (add 3) triple (multiplied by 3) the width.

Length = 3w + 3

The diagonal forms two right triangles, each with leg = w, other leg = 3w + 3, hypotenuse = 13.

The Pythagorean Theorem says $(\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2$ so

$w^2+(3w+3)^2=13^2\\\\w^2+9w^2+18w+9=169\\\\10w^2+18w-160=0\\\\5w^2+9w-80=0\\$

Now solve using the Quadratic Formula with $a=5,\,b=9,\,c=-80$ .

$w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-9\pm\sqrt{81+1600}}{10}\\\\w=\frac{-9\pm\sqrt{1681}}{10}\\\\w=\frac{-9\pm41}{10}\\\\w=-5\text{ or }w=3.2$

The negative root makes no sense as a distance, so the width of the rectangle is 3.2 cm. The length is 3(3.2) + 3 = 12.6 cm.

5 0

3 years ago

Find (f*f)(x) for the function f(x)=8x+9 and simplify

Alexus [3.1K]

Answer:

f(fx) = 64x + 81

Step-by-step explanation:

f(x) = 8x + 9

f(fx) = 8(8x+9) + 9

= 64x + 72 + 9

= 64x + 81

(Correct me if i am wrong)

5 0

3 years ago

Read 2 more answers

The state fair charges $14 for

Scrat [10]

Answer:

$s=6r+14$

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

$s=mr+b$

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

The slope is equal to

$m=\$6\ per\ ride$

The y-intercept is equal to

$b=\$14$

substitute the given values

$s=6r+14$

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4 years ago

I need help with this question

Varvara68 [4.7K]

The distance between Hadley and Greenville is 16 miles.

29-13=16

6 0

4 years ago

A video game system that normally sells for $249 is on sale 15% off. Which expression can be used to find the amount of the disc

maks197457 [2]

Answer:

D, B and E

Step-by-step explanation:

To find the discount we write it as

Discount=15% of $249

We can write the above as

1)15/100×249(E)

2)0.15×249 (B)

3)3/20×100 (D)

4 0

3 years ago

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