What is the value of z in the equation 11 + z = 6?

66
5
−5
1

The original problem is translated into a quadratic equation. By following the process of expanding, moving all terms to one side and solving the resulting equation yield the overall possible solutions x = 4 or x = 1.

The question is asking to solve for a number based on a given condition. In this case, let's symbolize this unknown number with x. The problem can be written as an algebraic equation which is (x-9)^2 = x-3. You solve it first by expanding the equation, then move all terms to one side of the equation, to get a quadratic equation. Then, solve the quadratic equation to get the possible values of x. If you follow these steps, you will find that the possible solutions for this equation are x = 4 or x = 1.

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The correct step in the expansion of (x+y)^4 is to determine the coefficients for each term using the binomial formula.

The correct step in the expansion of (x+y)^4 using the binomial formula is to determine the coefficients for each term.

In this case, the coefficients can be found using the formula n choose k, where n is the exponent (4) and k is the power of either x or y in each term.

For example, the term with x^3*y would have a coefficient of 4 choose 3, which is equal to 4.

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Answer: B)  [tex]V=\pi r^2 h[/tex]

Step-by-step explanation:

Given: DeAndre has two glass cylinders .

To determine which cylinder will hold the most water, we need to find the volume of both the containers.

We know that the volume of cylinder is given by :-

[tex]V=\pi r^2 h[/tex]

Therefore, the formulas will help him determine which cylinder could hold the most water will be :

[tex]V=\pi r^2 h[/tex]

Answer: V = 2712.94 cubic inches.

Step-by-step explanation: The prop is formed with two objects: cone and half of a sphere. To calculate the volume, find the volume of the cone and the half-sphere and add them together.

Volume of Cone:

V₁ = [tex]\frac{1}{3}.B.h[/tex]

B is area of the base

h is height

Since the cone has its base as a circle, the volume will be:

V₁ = [tex]\frac{1}{3}[/tex].π.[tex]r^{2}[/tex].h

V₁ = [tex]\frac{1}{3}[/tex] . 3.14 . [tex]9^{2}[/tex] . 14

V₁ = 1186.9 cubic inches

Volume of Half-Sphere:

V₂ = [tex]\frac{2}{3}[/tex].π.[tex]r^{3}[/tex]

V₂ = [tex]\frac{2}{3}[/tex] . 3.14 . [tex]9^{3}[/tex]

V₂ = 1526.04 cubic inches

Total Volume:

V = V₁ + V₂

V = 1186.9 + 1526.04

V = 2712.94 cubic inches

The volume of the prop is V = 2712.94 cubic inches

Answer:

One of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed

Step-by-step explanation:

A relation f is said to be a function if for each and every element of it's domain there exists a unique image in it's codomain.

As per the graph, ordered pairs are [tex]\left ( 1,3 \right )\,,\,\left ( 2,1 \right )\,,\,\left ( -2,2 \right )\,,\,\left (1 ,-2 \right )\,,\,\left ( 5,-4 \right )\,,\,\left ( -4,-4 \right )\,,\,\left ( -5,-3 \right )[/tex]

Here,  all the ordered pairs have unique image except [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex]

Here , element 1 of domain has two images 3 and - 2 .

We know that as per definition for each and every element of the domain there should be a unique image in the codomain.

So, one of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed in order to make it a function.

To find the number of students in a group who spent a total of $15.20, with each student spending $1.90, divide the total amount by the amount each student spent, resulting in 8 students.

The question asks how many students were in a group if they spent $15.20 altogether, with each student spending $1.90. To find the number of students, divide the total amount spent by the amount each student spent. This calculation is performed by dividing $15.20 by $1.90.

Calculation: $15.20 ÷ $1.90 = 8 students

Therefore, there were 8 students in the group.

Answer: [tex] fg(x)=4x^3+12x^2-5x-15[/tex]

Step-by-step explanation:

Given: [tex]f(x)=4x^2-5\text{ and } g(x)=x+3[/tex]

We know that for any function f(x) and g(x), the multiplication function (fg) (x) is given by :-

[tex]fg(x)=f(x)g(x)[/tex]

Now, for the given functions, we have

[tex]fg(x)=(4x^2-5)(x+3)\\\\\Rightarrow\ fg(x)=4x^2(x+3)-5(x+3)\\\\\Rightarrow\ fg(x)=4x^3+12x^2-5x-15[/tex]

The cost formula for maintenance cost is : y = 3.33x + 10000

The cost formula for maintenance cost can be written in the form :

Using the pair of points ;

Slope = (14000 - 20000) / (7200 - 9000)

Slope = -6000 / 1800

Slope, b = 3.33

We have ;

y = 3.33x + c

Using the point (9000, 20000)

20000 = 3.33(9000) + c

20000 = 30000 + c

c = 10000

Now we have;

y = 3.33x + 10000

The cost formula for maintenance cost is : y = 3.33x + 10000

The average rate of change of the function over the interval is 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 6 + 3x

The interval is given as

From x = 1 to x = 8

The function is a linear function

This means that it has a constant average rate of change

So, we have

f(1) = 6 + 3(1) = 9

f(8) = 6 + 3(8) = 30

Next, we have

Rate = (30 - 9)/(8 - 1)

Evaluate

Rate = 3

Hence, the rate is 3

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Question

Find the average value gave of the function g on the given interval. g(x) = 6 + 3x , [1, 8]

Answer:

The answer is (2,1)

Step-by-step explanation:

Given a vector in the plane, we can describe the rotation as a function :

X is the vector

T is the function that represents the rotation

[tex]T(X)=AX[/tex]

Where A is the rotation matrix

The rotation matrix about the origin in counterclockwise sense for an angle ''a'' is :

[tex]A=\left[\begin{array}{cc}cos(a)&-sin(a)\\sin(a)&cos(a)\end{array}\right][/tex]

If we replace ''a'' by 90 ⇒

[tex]\left[\begin{array}{cc}cos(90)&-sin(90)\\sin(90)&cos(90)\\\end{array}\right][/tex]

[tex]A=\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right][/tex]

If we want to rotate the vector D = (1,-2) :

[tex]T(D)=AD=\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right]\left[\begin{array}{c}1&-2\end{array}\right]=\left[\begin{array}{c}2&1\end{array}\right][/tex]

The rotation of the vector (1,-2) about the origin for an angle of 90 and in counterclockwise sense is (2,1)

Answer:

(1 pt) ~2,6,7~

Step-by-step explanation:

Answer:

The answer is C: rw ◦ RM,180°

Step-by-step explanation:

I had this question on edge

Answer:

the correct answer is 18 i hope this helps you

The length of each edge of a cube with a total surface area of 486 square units is 9 units, obtained by dividing the total surface area by 6 to get the area of one face and then taking the square root.

To find the length of each edge of a cube when you have the total surface area, you need to understand that a cube has 6 faces that are all squares of the same size. Since the total surface area of the cube is given as 486 square units, we can find the area of one face by dividing the total surface area by 6. Once we have the area of one face, we can find the length of one edge by taking the square root of that area because the area of a square is equal to the length of one side squared (Area = side x side).

Let's calculate:

Therefore, the length of each edge of the cube is 9 units.

Answer:

Let x represent the number of blueberry muffins [tex]x\geq 0[/tex]

Let y represent the number of bran muffins [tex]y\geq 0[/tex]

Tray of blueberry muffins: 1/3 cup of oil & 2 eggs

Tray of bran muffins: 1/2 cup of oil & 1 egg

Alan has 4 cups of oil and 12 eggs on hand.

He sells a tray of blueberry muffins for $12 each.

He sells a tray of bran muffins for $9 each.

[tex]\frac{x}{3}+\frac{y}{2}\leq 12[/tex]

The constraints for the problem are 4 cups of oil and 12 eggs.

Alan should not exceed 4 cups of oil and 12 eggs as it will create shortage. He should get the correct proportion of both the muffins to maximize his profit.

In equation form it is : [tex]\frac{x}{3}+\frac{y}{2}\leq 4[/tex]