Jaiden earned $84 last week. Peter earned only $12. Jaiden's earnings are how many times greater than Peter's.

let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

\(f^(-1)(2) = 6\), which is consistent with our earlier result.

A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.

Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?

Solution:

To find f^(-1)(2), we need to find the value of x such that  \(f(x) = 2\) . We can set up an equation:

\(f(x) = \sqrt(2x - 8) = 2\)

Squaring both sides, we get:

\(2x - 8 = 4\)

\(2x = 12\)

\(x = 6\)

Therefore, \(f^(-1)(2) = 6.\)

We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:

\(f(f^(-1)(x)) = x\)

We can substitute x = 2 and solve for f^(-1)(2):

\(f(f^(-1)(2)) = 2\)

\(f^(-1)(2) = (f(6))^(-1)\)

f(6) = √(2(6) - 8) = √4 = 2

Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.

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Answer:

The  confidence interval is  \(0.304 < p < 0.324\)

Step-by-step explanation:

From the question we are told

      The sample proportion \(\r p = 0.314\)

      The margin of error  is \(E = 0.01\)

The confidence interval for  p is mathematically represented as

       \(\r p - E < p < \r p + E\)

=>    \(0.314 - 0.01 < p < 0.314 + 0.01\)

=>   \(0.304 < p < 0.324\)

Answer:

x=6.93

Step-by-step explanation:

use the Pythagorean theorem

8^2=(0.5 x 8)^2+x^2

64=16+x^2

x^2=48

x=6.93

Answer:x= Square root 48

Step-by-step explanation:

Answer:

f(h(-1)) = -1

Step-by-step explanation:

f(x) = (x-4)/3

h(x) = 3x + 4

f(h(-1)) = ?

So first off we need to solve for h(-1):

h(x) = 3x + 4

h(-1) = 3(-1) + 4

h(-1) = 1

Next, we plug this value into the f(x) equation:

f(x) = (x-4)/3

f(1) = (1-4)/3

f(1) = -1

f(h(-1)) may look confusing but it is just f(x) with x being the resulting value for h(-1)

Thus we can say that f(h(-1)) is equal to -1

Answer: Chad Makes $1.50 more

Step-by-step explanation:

You have to divide 30 from 4 to see Horatio’s hourly rate which is 7.5 and then you will see that 9 - 7.5 is 1.5. I hope this helped

Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Answer:

7 units because (6x-22)=(2×+6)

(A) The expression to represent the elevation level of city D, in feet will be :  \(D = \frac{1}{4} * [C]\)    
(B) The elevation of city D will be -6 feet. The negative here shows that city D is below sea level.

In the question, it is given that city A is 96 feet below sea level, city C is 24 feet below sea level, and the elevation of city D is 1 over 4th of the elevation of C. Since, City A & C are both below sea level their elevation will be negative. So, by these we get elevations:

For City A,  A = -96

      City C,  C = -24

      City D,  \(D = \frac{1}{4} *[C]\)      ----> Equation (1)

By Equation (1) we get the representation of elevation for City D.

Now, Calculating the elevation of city D, we will put the value of city C in equation (1).

        =>   \(D = \frac{1}{4} *[-24]\)

        =>   \(D = -6\\\)

The negative sign here shows that the elevation is below sea level for city D.

Hence, the expression representing the elevation of city D will be \(D = \frac{1}{4} * [C]\) and, the elevation of city D will be -6.

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The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Which expression represents the correct form for the quotient and remainder?

(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)

This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.

The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.

The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.

To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.

The result is 4x².

Then, subtract 4x² from 8x²³ to get the remainder of 4x³.

Next, divide 4x² into 21².

The result is 33x.

Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.

Finally, divide 4x²-33x into 67x.

The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.

This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.

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Use the remainder theorem: we can decompose the given polynomial in terms of quotient and remainder polynomials \(q(x)\) and \(r(x)\), respectively, such that

\(x^4 - 5x^3 + x^2 - 10x - 5 = (x + 3) q(x) + r(x)\)

Then letting x = -3 makes the quotient term vanish, and we're left with a remainder of

\(r(-3) = (-3)^4 - 5\times(-3)^4 + (-3)^2 - 10\times(-3) - 5 = \boxed{250}\)

Let's denote the three numbers A, B, and C.

Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.

Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.

Let's list the possible combinations:

These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).

Answer: the answer is b

Step-by-step explanation:

Domain and ranges of inverse functions are swapped.

Domain of the original is the range of the inverse and vice versa.

From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5

To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".

Looking at the number line, we can see the following values:

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

From this list, the values that "m" could take are:

-2, -3.5, 0, -5

These values are present on the number line, indicating that they are possible values for "m".

Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.

It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.

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Answer:

What might be one result of state constitutions that limited the power of the governor?

The answer is B. Why B? Well if you look at the Bill Of Rights you see the constitution banned the governor from taking any far actions on the stall.

Step-by-step explanation:

Hope this helped!

The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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Answer:

260 Meters Below the Surface

Step-by-step explanation:

"Dove 450 meters" = - 450

"Climbed 270 meters" = +270

"Dove 80 meters more" = - 80

-450+270-80

-180-80

-180+(-80)

-260 or 260 Meters Below the Surface

Answer:

9 bags

Step-by-step explanation:

2 1/4 ÷ 1/4

9/4 ÷ 1/4

9/4 x 4/1 = 9

After adding 5 to both sides what did Michele get? Let's see

\(3x-5 + 5 = -10 + 5\\3x= -5\)

If she wants to find the value of \(x\) then she needs to have only the variable \(x\) on the left hand side. What she must do so that \(3x\) becomes just \(x\)?  What do you have to do to the number 3 so it becomes a 1? That's right, she must divide by 3!

So, after dividing both sides by 3:

\(\frac{3x}{3} = \frac{-10}{3} \\\\\boxed{x=\frac{-10}{3}}\)

Thus, the correct answer is letter B

Answer: a=101 b=79 c=83 d=97

Answer:

9

Step-by-step explanation:

Use the law of sines to find angle A then u can find b easily

Answer:

24% or 0.24

Step-by-step explanation:

100% or 1 minus 76% or 0.76. That makes 24% or 0.24.

To answer the question you should prob just put in 0.24.

Solution:

We can use the following formula:

Here A is the initial amount at the account;

W is the monthly withdrawn value;

r is the nominal monthly percentage.

n is the number of withdrawing periods (months, in this case).

Now, in this case, we have the following data:

and the number of payment periods (= the number of months) is

Applying these data to the formula given at the beginning of this explanation, we obtain:

this is equivalent to:

solving for W, we get:

Thus, the correct solution is:

You will be able to withdraw about $2311.78 every month for 20 years.

Answer:

13 miles

Step-by-step explanation:

For this equation you would use the Pythagorean Theorem. \(a^{2}+b^{2} =c^{2}\) .

12 x 12 = 144

5 x 5 = 25

144 + 25 = 169

\(\sqrt{169}\) = 13

Answer:

$11.50 per hour

p = 11.5 * x

Step-by-step explanation:

Betsy is paid $92 per 8 hours, or $11.50 per hour, so h (the per hour pay) is 11.50

If p is the pay, h is per hour pay, and x is hours, the formula would be

p = h * x + 0

p = 11.5 * x

Answer:

1288 c m 3

Step-by-step explanation:

To work out volume, you just do the simple calculation of height x width x length. So what we need to do here is 6 x 7.5 x 22.9 =  

1212.5 c m 3  .

The decimal is a 5 so that is rounded up to give the nearest meter hence the answer to the question is  

1288 c m 3  .