What is the value of X?

Enter your answer in the box.

Answer:

(x^2 +6)/2

or  1/2 x^2 +3

Step-by-step explanation:

f(x)= sqrt(2x-6)

y =sqrt(2x-6)

To find the inverse function, we interchange the x and y and solve for y

x = sqrt(2y-6)

Square each side

x^2 = sqrt(2y-6)^2

x^2 = 2y-6

Add 6 to each to each side

x^2 +6 = 2y-6+6

x^2 +6 = 2y

Divide each side by 2

(x^2 +6)/2 = 2y/2

(x^2 +6)/2 = y

The inverse function is

(x^2 +6)/2

or  1/2 x^2 +3

Two functions f(x) and g(x) are inverses if:

f(g(x)) = x = g(f(x))

The solution is:

[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]

Now we want to find the inverse function to:

[tex]f(x) = \sqrt{2x - 6}[/tex]

Because this is a square root function, we know that the inverse must be a quadratic function, so let's try with something like:

[tex]g(x) = a*x^2 + c[/tex]

Now we can use the first property to get:

[tex]g(f(x)) = a*f(x)^2 + c = x\\\\ = a*\sqrt{2x - 6}^2 + c = x\\\\= a*(2x - 6) + c = x\\\\2*a*x -6*a + c = x[/tex]

Then we must have:

2*a  =1

a = 1/2

And:

-6*a + c = 0

-6*(1/2) + c = 0

-3 + c = 0

c = 4

Then the inverse function is:

[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]

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Answer:

226.50

Step-by-step explanation:

11.50*15=172.5(0)+4.50*12=54.0226.50

Answer:

It’s $226.50

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

8x10= 18

Area of the rectangular cutting board is 80 square inches.

According to the problem,

∴ Area of the rectangle = (8 x 10) square inches

                                 = 80 square inches

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Answer:

The Constant of Proportionality is 4.

Step-by-step explanation:

This is because in the table provided,

The correct answer to the question is 4.

I did the quiz and got an A on it.

Hope it helps, I'm on K12 OHVA aswell.

To find the value of x in the equation 4(px+1)=64, you divide by 4, simplify, and then divide 15 by p, resulting in x = 15/p. Substituting p=-5 gives x=-3.

To solve the equation 4(px+1)=64 and find the value of x in terms of p, we follow these steps:

Divide both sides of the equation by 4 to isolate the term with x: (px+1) = 64/4

Further simplify to get px + 1 = 16

Subtract 1 from both sides to get px = 16 - 1

Finally, divide by p to solve for x: x = (16 - 1) / p = 15/p

The value of x in terms of p is 15/p.

Substitute p = -5 into the equation to find the value of x when p is -5:

x = 15 / -5

x equals -3

Answer:

The correct option is b. 15

Explanation:

We are given that a freight train travels at an average speed of 60 mph.

Also we are given that the average speed of passenger train is 72 mph.

We are also given that the freight train leaves 3 hours before passenger train. So the number of miles covered by freight train in 3 hours is:

[tex]3 \times 60 = 180[/tex] miles.

Let X be the number of hours it takes the passenger train to catch up the freight train.

Therefore, we have:

[tex]180 + 60 \times X = 72 \times X[/tex]

[tex]72X-60X = 180[/tex]

[tex]12X=180[/tex]

[tex]X=\frac{180}{12}[/tex]

[tex]X=15[/tex]

Therefore, the passenger train will take 15 hours to catch up the freight train.

Answer:

sorry im answering late but the answer is C. 18

Step-by-step explanation:

60 x 18 = 1,080

72 started 3 hours later so that means you subtract 3 from 18 which equals 15 and 72 x 15 = 1,080

ur answer is 18

Answers:

Equation is 2*(2*W+W) = 102

Width is 17

Length is 34

=============================

Explanation:

L = 2*W because the length is twice the width

2*(L+W) = P is the perimeter formula

Replace P with the given perimeter (102). Also replace L with 2*W. Then isolate W

2*(L+W) = P

2*(2*W+W) = 102

2*(3W) = 102

6W = 102

6W/6 = 102/6

W = 17

If the width is W = 17, then the length is

L = 2*W = 2*17 = 34

So the width and length of this rectangle is 17 by 34

---------

Check:

P = 2*(L+W)

P = 2*(34+17)

P = 2*51

P = 102

Answer is confirmed

To find the length and width of a rectangle with given perimeter and lengths as twice of the width, first plug the length into the perimeter formula. Solve the resulting equation for width. Substitute this width into the length formula to get the length.

In this problem, we have a rectangle where the length (L) = 2 * width (W). Also, the perimeter of the rectangle (P) = 2L + 2W. The given perimeter is 102 inches.

Since L = 2W, substituting this equation into the formula for perimeter, we get P = (2*2W) + 2W = 102.

This simplifies to 6W = 102, and therefore W = 102 / 6 = 17 inches. Substituting the width back into the equation L = 2W, we find that the length (L) is 2 * 17 = 34 inches.

So, the width is 17 inches and the length is 34 inches.

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Answer:

110 Walnuts

Step-by-step explanation:

Firstly, there are 6 bags and 330 walnuts. You divide 330 by 6 and you get 55. 330/6. Now, you multiply 55 by 2 and you get your answer. So basically in each bag there are 55 walnuts and if you multiply that by 6 you get 330 again. Hope this helped!

Answer:

110 walnuts

Step-by-step explanation:

330÷6 is 55

55•2 is 110

Answer:

12

Step-by-step explanation:

Answer:

x = -9, -3

Step-by-step explanation:

x^2 + 12x + 27 = 0

We need 2 numbers whose product is  + 27 and whose sum is + 12. These are 3 and 9. So the factors are:-

(x + 3)(x + 9)  and this = 0

So (x + 3) = 0  or x + 9 = 0

x = -3 , -9

Answer:

-5 and 7

Step-by-step explanation:

we need to find numbers a and b such that a+b=-2 and ab=-35.

a=5 and b=-7 satisfy both conditions, so our equation can be re-written:

(x + 5)(x-7) = 0

According to the zero-product property, we know that

x+5=0 or x-7=0, which means

x=-5x or x=7

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Answer:

Correct choice is B

Step-by-step explanation:

The function [tex]f(x)=20x[/tex] represents the situation, where x is the number of sold video games and f(x) is the total cost of sold games.

Jason  must sell a minimum of 5 games, this means that [tex]x\ge 5.[/tex] He has 30 video games he can sell, then [tex]x\le 30.[/tex] Thus, the domain of the function is [tex]5\le x\le 30.[/tex]

The range of the function f(x) is

[tex]20\cdot 5\le f(x)\le 20\cdot 30,\\ \\100\le f(x)\le 600.[/tex]

[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\text{We have}\\\\\text{endpoint}\ (-2,\ -14)\to x_1=-2,\ y_1=-14\\\\\text{midpoint}\ (-11,\ -20)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-2+x_2}{2}=-11\qquad\text{multiply both sides by 2}\\\\-2+x_2=-22\qquad\text{add 2 to both sides}\\\\\boxed{x_2=-20}\\\\\dfrac{-14+y_2}{2}=-20\qquad\text{multiply both sides by 2}\\\\-14+y_2=-40\qquad\text{add 14 to both sides}\\\\\boxed{y_2=-26}\\\\Answer:\ \boxed{(-20,\ -26)}[/tex]

Final answer:

To find the other endpoint of a line segment when given the midpoint and one endpoint, use the formulas x2 = 2xm - x1 and y2 = 2ym - y1. For the given midpoint (-11, -20) and endpoint (-2, -14), the other endpoint is calculated to be (-20, -26).

Explanation:

To find the coordinates of the other endpoint of a segment when the midpoint and one endpoint are known, the midpoint formula can be used in reverse. For a line segment with endpoints (x1, y1) and (x2, y2) and midpoint (xm, ym), the coordinates of the midpoint are found by the formulas xm = (x1 + x2)/2 and ym = (y1 + y2)/2. If one endpoint is known, say (x1, y1) = (-2, -14) and the midpoint is (xm, ym) = (-11, -20), we can find the other endpoint (x2, y2) by rearranging the formulas: x2 = 2xm - x1 and y2 = 2ym - y1.

Calculating the values we get:

x2 = 2(-11) - (-2) = -22 + 2 = -20

y2 = 2(-20) - (-14) = -40 + 14 = -26

Therefore, the coordinates of the other endpoint are (-20, -26).

Final answer:

Ms. Keller will grade 17.5 projects in seven hours at her current rate of 2.5 projects per hour.

Explanation:

The student's question is about determining at what rate Ms. Keller is grading projects and how many projects she will grade in seven hours based on her current pace. Since Ms. Keller has graded five projects in two hours, her grading rate is 5 projects / 2 hours, which simplifies to 2.5 projects per hour. To find out how many projects Ms. Keller will grade in seven hours at this rate, we multiply 2.5 projects/hour by 7 hours, resulting in 17.5 projects.

Therefore, Ms. Keller will grade 17.5 projects in seven hours at a rate of 2.5 projects per hour.

Answer:

2.  C. { 0, 1, 2}

3.  B. 53

6.  P = 14n + 10

Step-by-step explanation:

2.  The domain is the input values (or the x values)

The domain is { 0,1,2}

3.  f(x) = 5x+3

 where x is the number of minutes.  We will let x = 10

f(10 ) = 5*10 +3

       = 50+3

      = 53

53 cars will pass

6.  When we have 1 trapezoid, the perimeter is 5+5+8+6 = 24

When we have 2 trapezoids, the perimeter is 5+8+6+5+8+6 = 38

We add 14, when we add a second trapezoid

P = 14n + 10

p(1) = 14+10   Check for 1 trapezoid

p(2) = 14*2 +10 = 28+10 = 38    check for 2 trapezoids

2. You're given a function that maps 1 to 1, 0 to 0, and 2 to -1. The domain is the set of points that are given to the function as inputs, {1, 0, 2}, which is equivalent to the set listed in option C.

3. Evaluate [tex]f(x)[/tex] at [tex]x=10[/tex]:

[tex]f(10)=5(10)+3=50+3=53[/tex]

so the answer is B.

6. Each trapezoid in the chain contributes a copy of 8 and 6 (a total of 14), so that we should expect the total perimeter to contain [tex]14n[/tex]. The remaining two sides contribute a constant 10 regardless of [tex]n[/tex]. So the perimeter is given by the formula in D, [tex]P=14n+10[/tex].

Answer:

12x

Step-by-step explanation:

number 1 is 12x bcuz two x plues ten equals 12x although i did it another way i still got it right just letting you no im working on the second one

The outside angle is equal to the sum of the two opposite inside angles.

So you have:

X + 82 = 2X+10

Subtract 1 X from each side:

82 = X+10

Subtract 10 from each side:

x = 72

Now you can calculate the exterior angle by replacing x with 72:

2x+10 = 2(72) +10 = 144+10 = 154

Answer:

Step-by-step explanation:

Set A: {32, 12, 24, 46, 18, 22, 14}

Mean =24 : Median =22:

Mean>Median hence positive skewed

Set B: {4, 12, 11, 14, 11, 5, 12, 13, 18, 14}

Mean =11.4 and median = 12

Mean <Median, hence negative skewed

Set C: {5, 4, 9, 12, 14, 26, 22, 18}

Mean=13.75 and median = 13

Mean >Median hence positive skewed

Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6}

Mean =2.8 Median = 2.5

Mean>Median Hence positive skewed

Answer:

W = [tex]\frac{V}{LH}[/tex]

Step-by-step explanation:

given the formula V = LWH

to solve for W divide both sides by LH, hence

W = [tex]\frac{V}{LH}[/tex]

Answer: ∠R = 137°

Step-by-step explanation:

The opposite angles of a quadrilateral are supplementary (equal to 180°).

Since ∠P and ∠R are opposite angles, their sum is 180°

∠P + ∠R = 180°

y + 3y + 8 = 180

4y + 8 = 180

4y = 172

y = 43

∠R = 3y + 8

     = 3(43) + 8

     = 129 + 8

     = 137

Answer: 8.75

Step-by-step explanation: Divide 166.25 by 19

Mr Rice will purchase 8.75 ft of edging

if we derive equation for this question, then we have:

166.25 = 19Y

Y= [tex]\frac{166.25}{19 }[/tex]

Y= 8.75

To determine the lengths of edging Mr Rice will need to purchase, the total length of edging on the flower beds (166.25) will be divided by the total length of an edging being sold (19) i.e. 166.25 ÷ 19

= 166.25 ÷ 19

= [tex]\frac{166.25}{19 }[/tex]

= 8.75

Therefore, the total length of edging Mr Rice will need to purchase is 9 ft.

The above mathematical expression is a number problem, and was solved with the aid of division.

The term, division, is a basic arithmetic operation which deals with splitting or dividing two or more numerical values into different equal part.

In this case, it could be observed that the significant numbers that were divided are 166.25 and 19, resulting to 8.75. It is also a function of BODMAS (which is an order of operations).

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Answer:

The price of dinner before sales tax and tip is $60.

Step-by-step explanation:

Let the price of before sales tax and tip be x.

The amount of tip is 20% of the price of dinner. So, the amount of tip is

[tex]\frac{20}{100}x[/tex]

The amount of sales tax is 11% of the price of dinner. So, the amount of sales tax is

[tex]\frac{11}{100}x[/tex]

It is given that Zoe paid $18.60 in sales tax and tips for her dinner. Therefore the sum of tip and sales tax is $18.60.

[tex]\frac{20}{100}x+\frac{11}{100}x=18.60[/tex]

[tex]\frac{20+11}{100}x=18.60[/tex]

[tex]31x=1860[/tex]

[tex]x=60[/tex]

Therefore the price of dinner before sales tax and tip is $60.

Answer:

y = x^2 +3x-10

Step-by-step explanation:

If we know the roots of a quadratic function, we know that

y = (x -a) (x-b)  where a and b are the roots

y = (x-2 ) (x--5)

y = (x-2)(x+5)

We need to foil this out to get this in standard form of ax^2 + bx+c

FOIL  (x-2) (x+5)

First x*x:  x^2

outer : 5*x = 5x

inner:  -2x  = -2x

last :  -2*5  = -10

Add them up

x^2 +5x-2x-10

x^2 +3x-10

Final answer:

A quadratic equation in standard form with roots 2 and -5 is obtained by multiplying (x - 2)(x + 5), which simplifies to x² + 3x - 10 = 0.

Explanation:

To write a quadratic equation in standard form with integer coefficients that has roots 2 and -5, we use the fact that if α and β are roots of a quadratic equation, the equation can be written as:

ax² + bx + c = 0

Where:

The quadratic equation in standard form using the roots 2 and -5 is given by:

(x - 2)(x + 5) = 0

Expanding this we get:

x² + 5x - 2x - 10

Which simplifies to:

x² + 3x - 10 = 0

Thus, the quadratic equation with integer coefficients and roots 2 and -5 is x² + 3x - 10 = 0.

Answer:

The more 'chocolatey' chocolate milk is the one prepared by Nell's mom.

Step-by-step explanation:

This problem can be solved by establishing the ratio of chocolate syrup for one ounce of milk in each beverage.

For mom's chocolate milk:

[tex]\frac{30mL}{2ounces} = 15\frac{mL}{ounce}[/tex]

For dad's chocolate milk:

[tex]\frac{65mL}{5ounces} = 13\frac{mL}{ounce}[/tex]

We know that:

15 > 13

So we can conclude that mom's chocolate milk is more 'chocolatey'.

Answer:

[tex]f(x)=33*(1.07)^x[/tex]

Step-by-step explanation:

Let f(x) be our exponential growth function representing growth after x years.

We are asked to find the exponential function that satisfies the given conditions: Initial value = 33, increasing at a rate of 7% per year.

Since an exponential growth function is in form: [tex]y=a*(1+r)^x[/tex], where a= initial value of function and r = growth rate in decimal form.

Given:

a=33  

r=7%.

Let us convert our given rate in decimal form.

[tex]7\text{ percent}=\frac{7}{100}=0.07[/tex]

Now let us substitute our given values in exponential function form:

[tex]f(x)=33*(1+0.07)^x[/tex]

[tex]f(x)=33*(1.07)^x[/tex]

Therefore, the exponential function that satisfies our given conditions will be [tex]f(x)=33*(1.07)^x[/tex].

Answer:

1. [tex]a_{n}=\frac{1}{3} a_{n-1}[/tex] where [tex]a_{1} =27[/tex]

2. [tex]2^{x+1}[/tex]

3. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Step-by-step explanation:

1. The recursive formula is defined as an implicit way of writing the rule of a function or pattern. It is implicit because it uses previous terms to find the next term in the pattern. We multiply, add, subtract or divide a previous term by a constant value or expression to find the next. In this case, 27 becomes 9 through division by 3 or multiplication by 1/3. The pattern continues 9(1/3)=3 and so forth.

2. The function f(x) is an exponential and has a general form of [tex]y=ab^x[/tex]. We know f(x) is [tex]2^x[/tex]. The points of g(x) all changed from f(x) by shifting over to the left. This transformation occurred by [tex]2^{x+1}[/tex].

3. Domain is defined as the set of all x-values. Range is defined as the set of all y-values. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Answer:

(4,3,2)

Step-by-step explanation:

We can solve this via matrices, so the equations given can be written in matrix form as:

[tex]\left[\begin{array}{cccc}3&2&1&20\\1&-4&-1&-10\\2&1&2&15\end{array}\right][/tex]

Now I will shift rows to make my pivot point (top left) a 1 and so:

[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\2&1&2&15\\3&2&1&20\end{array}\right][/tex]

Next I will come up with algorithms that can cancel out numbers where R1 means row 1, R2 means row 2 and R3 means row three therefore,

-2R1+R2=R2 , -3R1+R3=R3

[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\0&9&4&35\\0&14&4&50\end{array}\right][/tex]

[tex]\frac{R_2}{9}=R_2[/tex]

[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\0&1&\frac{4}{9}&\frac{35}{9}\\0&14&4&50\end{array}\right][/tex]

4R2+R1=R1 , -14R2+R3=R3

[tex]\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&-\frac{20}{9}&-\frac{40}{9}\end{array}\right][/tex]

[tex]-\frac{9}{20}R_3=R_3[/tex]

[tex]\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&1&2\end{array}\right][/tex]

[tex]-\frac{4}{9}R_3+R_2=R2[/tex] , [tex]-\frac{7}{9}R_3+R_1=R_1[/tex]

[tex]\left[\begin{array}{cccc}1&0&0&4\\0&1&0&3\\0&0&1&2\end{array}\right][/tex]

Therefore the solution to the system of equations are (x,y,z) = (4,3,2)

Note: If answer choices are given, plug them in and see if you get what is "equal to".  Meaning plug in 4 for x, 3 for y and 2 for z in the first equation and you should get 20, second equation -10 and third 15.

Answer:

C on edge

Step-by-step explanation:

: )

Answer: 42°

Step-by-step explanation: In this problem, we're given that the measures of two complementary angles are in the ratio 7 to 8 and we're asked to find the measure of the smaller angle.

Since our two angles are in the ratio 7 to 8, let's represent the angles as 7x and 8x. We will call 7x an angle and 8x its complement. Now, remember that if two angles are complementary, then the sum of their measures is 90 degrees. So we can set up the equation 7x + 8x = 90.

Simplifying on the left side, we have 15x = 90.

Dividing both sides by 15, we find that x = 6.

So the measure of our first angle, 7x, is 7(6) or 42°.

The measure of its complement, 8x, is 8(6) or 48°.

Finally, notice that if we add our two angles together, we have 42 + 48 which equals 90 so our answer checks. This means that the smaller angle is 42°. Image is provided below.

Answer: B

Step-by-step explanation:

The correct option is c.

The units of area are always square units because they are the product of two lengths dimensions. This could be square meters, square centimeters, or any other square unit.

The units of area are always square units. This is because area is defined as the product of two lengths dimensions. This applies whether you're calculating the area of a rectangle (length x width), a circle (pi x radius²), or any other shape. In the standard system of international units (SI), the base unit for length is meters, so area would be in square meters (m²). However, this can be adapted to any unit of length, such as centimeters, so area could also be measured in square centimeters (cm²).

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