A recipe requires 1/4 cup of oil every 2/3 cup of water. How much oil (in cups) is needed per cup of water?
(I’ll give points + brainalist for the correct answer)
A. 3/8
B. 1/6
C. 8/3
D. 6

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:

4 Zebras

Step-by-step explanation:

I can only see that she have 5 elephants, possibly more, however it's cut off. If that's true. Then:

If she has 5 elephants (which is currently what she has the most of) and 2 zebras. She needs 4 more zebras. Then she will have 6 zebras. More then any other animal.

Answer:

assuming the elephant has the most dots, as i cant see the full picture, then she needs to collect 4 more because she has 2 already.

Step-by-step explanation:

The elephant has 5 dots

the zebra has 2 dots

4+2=6

(-b±√(b²-4ac))/(2a)

Answer:

x=120±6434−−−√

x=−4.996

x=244.996

Find the Solution for

−125x2+30000x+153000=0

using the Quadratic Formula where

a = -125, b = 30000, and c = 153000

x=−b±b2−4ac−−−−−−−√2a

x=−30000±300002−4(−125)(153000)−−−−−−−−−−−−−−−−−−−−−√2(−125)

x=−30000±900000000−−76500000−−−−−−−−−−−−−−−−−−−√−250

x=−30000±976500000−−−−−−−−√−250

The discriminant b2−4ac>0

so, there are two real roots.

Simplify the Radical:

x=−30000±1500434−−−√−250

x=−30000−250±1500434−−−√−250

Simplify fractions and/or signs:

x=120±6434−−−√

which becomes

x=−4.996

x=244.996

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:

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:

x midpoint 5

y midpoint 2

(5,2)

Answer: A

Step-by-step explanation:

The equation sin²(2π)+ cos²(2π) = 1 will be 0² + 1² = 1. Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The equation is given below.

sin²(2π)+ cos²(2π) = 1

We know that the value of sin 2π is 0 and the value of cos 2π is 1.

Then the equation will be

0² + 1² = 1

Then the correct option is A.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2

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:

200

Step-by-step explanation:

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

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:

the answer is 3/8

Step-by-step explanation:

Answer:

x = 33°

Step-by-step explanation:

57 + 90 + x = 180

147 + x = 180

x = 33

Answer:

68

Step-by-step explanation:

I literally just used a calculator LOL

Answer:

c is the answer

Step-by-step explanation:

Answer:

B. 4x ≤ 320

Step-by-step explanation:

Not sure how to explain my thinking. However, 4x must be smaller than 320 because she cannot spend more than that.

Answer:

Step-by-step explanation:

b

Answer:

it's called property tax

Step-by-step explanation:

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

Answer:

running

Step-by-step explanation:

Answer:

<

Step-by-step explanation:

<

Answer:

Step-by-step explanation:

y= -1/4x

Answer:

hope this help you look it once

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:

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.

Answer:

0.42

Step-by-step explanation:

they are both multiples of 0.06

think of it like 6 x 6= 36 and 6 x 8 = 48

6 x 7 = 42 would be halfway

Answer:

0.42

Step-by-step explanation:

To find the half, add da numbers and divide by 2. So 0.36 and 0.48 added together is 0.84. That divided by 2 is 0.42.

Answer:

HAHAHAHAHAHHAHAHAHHAAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA

Step-by-step explanation: