Gertrude bought a used car for $14,890. She was surprised that the dealer then added $1,280.54 as a sales tax. What was the sales tax rate for this purchase? Report your answer to one decimal place.

Answer:

(a) The average rate of change is 0

(b) The values of x are: [tex]x =4\ or\ x = -4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 16 - x^2; [-4,4][/tex]

Solving (a): The average rate of change (m)

This is calculated using:

[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex][a,b] = [-4,4][/tex]

So:

[tex]m = \frac{f(4) - f(-4)}{4 - -4}[/tex]

[tex]m = \frac{f(4) - f(-4)}{8}[/tex]

Solve f(4) and f(-4)

[tex]f(4) = 16 - (4^2) = 16 - 16 = 0[/tex]

[tex]f(-4) = 16 - (-4^2) = 16 - 16 = 0[/tex]

So:

[tex]m = \frac{f(4) - f(-4)}{8}[/tex]

[tex]m = \frac{0 - 0}{8}[/tex]

[tex]m = \frac{0}{8}[/tex]

[tex]m = 0[/tex]

Solving (b): All values of x where [tex]f(x) = m[/tex]

In (a), we have:

[tex]m = 0[/tex]

So:

[tex]f(x) = 0[/tex]

So, we have:

[tex]f(x) = 16 - x^2[/tex]

[tex]16 - x^2=0[/tex]

Express 16 as [tex]4^2[/tex]

[tex]4^2 - x^2=0[/tex]

Apply difference of two squares

[tex](4 - x)(4 + x) = 0[/tex]

Split

[tex]4 - x =0; 4 + x = 0[/tex]

Solve for x

[tex]x =4\ or\ x = -4[/tex]

We will find that the average of the function over the given interval is 0, and the two values of x such that the function is equal to the average are x = -4 and x = 4.

To find the average of a function f(x) over an interval [a, b] we need to compute:

[tex]\frac{f(b) - f(a)}{b -a}[/tex]

In this case we have:

f(x) = 16 - x^2

And the interval is:

[-4, 4]

We will get:

[tex]\frac{(16 - (4)^2) - (16 - (-4))^2}{4 - (-4)} = \frac{0}{8} = 0[/tex]

So the function has an average of 0 over that interval.

B) Here we just need to solve:

f(x) = 16 - x^2 = 0

We will get:

16 - x^2 = 0

16 = x^2

±√16 = x

±4 = x

So the solutions are x = 4 and x = -4.

If you want to learn more about averages of functions, you can read:

https://brainly.com/question/16033358

Answer:

Yx3 > X

Step-by-step explanation:

Hope this helps! Owa Owa!

Answer: i dont know

Step-by-step explanation:

Answer:

x midpoint 5

y midpoint 2

(5,2)

Answer:

200

Step-by-step explanation:

Answer:

the answer is 3/8

Step-by-step explanation:

Answer:

Your equation is:

(x−5)2+(y+8)2=92

Expanding from general form you can write this as:

x2−10x+y2+14y+−8=0

Step-by-step explanation:

i think its correct ig don't know sry but i tried hope it helps you ✨

Answer:

[tex](x+5)^2+(y-8)^2=81[/tex]

Step-by-step explanation:

General equation of a circle is [tex](x-a)^2+(y-b)^2=r^2[/tex].

Center coordinates = (-5, 8)

a = -5           b = 8          r = 9

[tex]\\(x+5)^2+(y-8)^2=9^2[/tex]

[tex](x+5)^2+(y-8)^2=81[/tex]

Please do mark as brainliest. Hope this helps! :)

Answer:

did you find out the answer

Step-by-step explanation:

The Probability that a dart will hit a spot in the shaded circle is 25%.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Here,

Area of Circle = πr²

radius of bigger circle = 6 cm

Area of bigger Circle = π X 6²

                                   = 36π sq. cm

radius of smaller circle = 3 cm

Area of small circle = π X 3²

                                =  9π sq. cm

Probability = Small circle / bigger circle

                  = 9π / 36π

                  = 1/4

                  = 0.25 or 25%

Thus, the Probability that a dart will hit a spot in the shaded circle is 25%.

Learn more about Probability from:

https://brainly.com/question/11234923

#SPJ2

Answer:

ok? pulls out really rare pokemon card ;)

Step-by-step explanation:

Answer:

x = 33°

Step-by-step explanation:

57 + 90 + x = 180

147 + x = 180

x = 33

Answer:

D

Step-by-step explanation:

Tust me Plz

Answer:

D

Step-by-step explanation:

5+6 then multiply by 3

(5+6) x 3 or 3 x (5+6)

Answer:

C

Step-by-step explanation:

Basically, ignore Cleveland bc it is just there to throw you off. Next, I recommend making a number line and plot these numbers.

-15 F -13 F -12 F -10 F -9 F

______________l______l_______l_________l________l__________l_________

Now go through the different options based on if they are warmer (or a bigger number): A (the first one) is not true because -15 is less than -13. B is not true bc is says on the left when it's on the right. D is incorrect because 12 is to the right, not the left :)

The answer is C by order of elimination and by logicccc :)

Hope this helped!!! (psstttt! there's a brainiest button that will really help me :)

Answer:

Step-by-step explanation:

y= -1/4x

Answer:

After 30 years

Step-by-step explanation:

population×2=20 years

population×2×1.5=20×1.5 years

population×3=30 years

Answer:

7(-4 - x) = -28 - 7x

-7(4 - x) = -28 + 7x

7(4 + x) = 28 + 7x

-7(-4 + x) = 28 - 7x

Step-by-step explanation:

To apply the distributive property, use the term outside the bracket to multiply each of the term you have inside the bracket.

Thus:

✔️7(-4 - x) = 7(-4) +7(-x)

= -28 - 7x

✔️-7(4 - x) = -7(4) -7(-x)

= -28 + 7x

✔️7(4 + x) = 7(4) + 7(+x)

28 + 7x

✔️-7(-4 + x) = -7(-4) -7(+x)

= 28 - 7x

Answer:

93 becouse you add 75 plus 2x10 is 20 so 75 plus is 105 so 14.75 plus .20 is 15.05

Step-by-step explanation:

Answer:

it's called property tax

Step-by-step explanation:

when you have to pay taxes on property you have its property tax

Answer:

x =35

y=72.5 and the 2nd y also equals 72.5

Step-by-step explanation:

x=35- it is a vertical angle

both ys + 35 makes a straight line (180)

2y+35=180

2y=145 (subtract 35 from both sides)

y=72.5 (divide by 2)

Answer:

A,D,F are less then 1/2

Step-by-step explanation:

Answer:

1/8

1/16

1/6

Step-by-step explanation:

1. 1/2 = 0.5              2. 1/2 = 0.5

  1/6 = 0.167               1/8 = 0.125

9514 1404 393

Answer:

  3 ft

Step-by-step explanation:

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given information, we can solve for h.

  15 ft² = 1/2(4 ft +6 ft)h

  15 ft² = (5 ft)h

  h = (15 ft²)/(5 ft) = 3 ft

The height of the trapezoid is 3 feet.

9514 1404 393

Answer:

  d  an = 6n^2 -4

Step-by-step explanation:

You only need to look at the values of the expressions for n=1 to determine the correct formula.

For n=1, the formula values are ...

The rule for the sequence is ...

  [tex]a_n=6n^2-4[/tex]

Answer:

hope this help you look it once

[tex]\mathcal\pink{The \: answer \: is }[/tex]

only one window has height that is a whole number of centimeters

[tex]\mathcal{HOPE \: IT \: HELPS}[/tex]

[tex]\huge\pink{mark \: as \: brainliest}[/tex]

Answer:

80 square units

Step-by-step explanation:

beep

Answer:

68

Step-by-step explanation:

I literally just used a calculator LOL