This equation shows how the revenue at Jill's Auto Wash depends on the number of
customers
d = 18c
The variable c represents the number of customers, and the variable d represents the
revenue. In all, how many customers does Jill's Auto Wash need to serve in order to have a
total of $18 in revenue?

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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Using the given linear equation, the value of A, B and C are -1, -4 and -10 respectively

A linear equation is an algebraic equation that represents a straight line when plotted on a graph. It consists of variables, constants, and coefficients, with the variables raised to the power of 1 (i.e., not squared or cubed). The general form of a linear equation with one variable is:

y = mx + b

where;

The given equation is y = -3x - 4

To find the missing values;

A = -3(-1) - 4

A = 3 - 4

A = -1

To find B;

B = -3(0) - 4

B = 0 - 4

B = -4

C = -3(2) - 4

C = -6 - 4

C = -10

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The lowest point on the graph occurs at point (3π/2,  -1)

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation

The attached graph shows sine function graph plotted with the interval [0, 2pi]

The lowest point is observed to occur at  (3π/2,  -1)

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The average rate of change of y with respect to x over the interval [1, 5] for function \(y=4x^{2}\) is 24.

To find the average rate, follow these steps:

Therefore, the average rate of change of y with respect to x over the interval [1, 5] for the function \(y=4x^{2}\)  is 24.

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Answer:

14.93°

Step-by-step explanation:

Using trigonometry :

From the diagram attached :

Angle of elevation = x

To obtain the value of x

Tan x = opposite / Adjacent

Tan x = 8 / 30

Tan x = 0.266666

x = tan^-1(0.26666)

x = 14.93°

Therefore, the angle of elevation is 14.93°

Answer:

Step-by-step explanation:

finding the first term by putting n=1

t(1)=4.\((1)^{2}\) +2 = 4.1 +2 = 4+2 = 6

finding the second term by putting n=2

t(2)=4.\((2)^{2}\) +2 = 4.4 +2 = 16+2 = 18

finding the third term by putting n=3

t(3)=4.\((3)^{2}\) +2 = 4.9 +2 = 36+2 = 38

hence first three terms are:

               6,18,38,......,4\(n^{2}\) +2

9514 1404 393

Answer:

  3r +5c = 60

  6r +4c = 80

Step-by-step explanation:

There are many aspects of "this situation" that could be described by equations. We are guessing that you want equations that will help you determine the costs of a record and a CD, assuming the costs are the same for each instance of the media.

Let r and c represent the costs of a record and a CD, respectively.

  3r +5c = 60 . . . . . . . the value of the first purchase

  6r +4c = 80 . . . . . . . the value of the second purchase

These equations comprise a linear system describing an aspect of the situation.

_____

Comment on the question

The numbers make no sense, as the cost of a CD is $(6 2/3), the cost of a record is $(8 8/9).

Option B is correct. It is a plot of the independent and dependent variables.

A scatter diagram is a type of plot or graph that uses Cartesian coordinates to display the values of two variables for a set of data. It is a simple yet powerful way to visualize the relationship between two variables.

The points on the plot represent the values of two variables, the independent variable (X-axis) and the dependent variable (Y-axis). Scatter diagrams provide a visual representation of the relationship between the two variables, which makes it easier to identify patterns such as linear or non-linear relationships.

They also can show correlations, or lack thereof, between two or more variables. Additionally, scatter diagrams can provide insight into the strength of the relationship between the two variables as well as how much of the variation in the dependent variable is explained by the independent variable. For example, a correlation coefficient of 1 indicates a perfect linear relationship, while a correlation coefficient of 0 indicates no relationship between the two variables.

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(a) The values of x that satisfy y = -√2/2 in the interval [0, 4π] are: x = π/4, 3π/4, 5π/4, 7π/4, 9π/4, 11π/4, 13π/4, 15π/4.

(b) All x-values except those listed in part (a) satisfy y > -√2/2 in the interval [0, 4π].

(c) All x-values except those listed in part (a) satisfy y < -√2/2 in the interval [0, 4π].

To find the values of x that satisfy the given conditions, we need to examine the graph of the equation y = sin(x) on the interval [0, 4π].

(a) For y = -√2/2:

Looking at the unit circle or the graph of the sine function, we can see that y = -√2/2 corresponds to two points in each period: -π/4 and -3π/4.

In the interval [0, 4π], we have four periods of the sine function, so we need to consider the following values of x:

x₁ = π/4, x₂ = 3π/4, x₃ = 5π/4, x₄ = 7π/4, x₅ = 9π/4, x₆ = 11π/4, x₇ = 13π/4, x₈ = 15π/4.

Therefore, the values of x that satisfy y = -√2/2 in the interval [0, 4π] are:

x = π/4, 3π/4, 5π/4, 7π/4, 9π/4, 11π/4, 13π/4, 15π/4.

(b) For y > -√2/2:

Since -√2/2 is the minimum value of the sine function, any value of x that produces a y-value greater than -√2/2 will satisfy the condition.

In the interval [0, 4π], all x-values except those listed in part (a) will satisfy y > -√2/2.

(c) For y < -√2:

Again, since -√2/2 is the minimum value of the sine function, any value of x that produces a y-value less than -√2/2 will satisfy the condition.

In the interval [0, 4π], all x-values except those listed in part (a) will satisfy y < -√2/2.

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Answer:

10 9/14

Step-by-step explanation:

7+3=10

1/2=7/14

1/7=2/14

The problem involves a line segment divided into two parts in a specific ratio. The ratio of the length of the lesser part to the length of the greater part is found to be (√2 - 1).

Let the length of the whole line segment be x, and let y be the length of the greater part. Then the length of the lesser part is (x - y).

According to the problem statement, the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole. Mathematically, we can write this as:

(x - y)/y = y/x

Simplifying this equation, we get:

x^2 - y^2 = y^2

x^2 = 2y^2

Taking the square root of both sides, we get:

x = y√2

Therefore, the value of the ratio of the lesser part to the greater part is:

(x - y)/y = (√2 - 1)

So, the answer will be (√2 - 1).

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Answer:

(x-7)(x+6)

factor and see what works

2x+5y=10

Move constant to the left by adding its opposite to both sides

2x+5y-10=10-10

the sum of two opposites equals 0

Answer: 2x+5y-10=0

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The value of y can be determined by solving the system of equations derived from the given information. The correct equation is y = 2.

Let's assign variables to the unknowns. Let x represent the value of x and y represent the value of y. We can form two equations based on the given information:

The sum of two times x and 3 times y is 5:

2x + 3y = 5

The difference of x and y is 5:

x - y = 5

To find the value of y, we can solve this system of equations. One way to do this is by elimination or substitution. Let's use substitution to solve the system.

From equation 2, we can express x in terms of y:

x = y + 5

Substituting this value of x into equation 1:

2(y + 5) + 3y = 5

2y + 10 + 3y = 5

5y + 10 = 5

5y = -5

y = -1

Therefore, the value of y is -1, which corresponds to option d: y = -1.

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Answer:

842.87 (rounded to 2 dp)

Step-by-step explanation:

Dunno just blag it

Work Shown:

f(x) = 4x^(-2) + (1/4)x^2 + 4

f ' (x) = 4*(-2)x^(-3) + (1/4)*2x .... power rule

f ' (x) = -8x^(-3) + (1/2)x

f ' (2) = -8(2)^(-3) + (1/2)*(2)

f ' (2) = 0

Finding the derivative, we have that f'(2) = 0, option D.

-----------------------------

\((x^n)^{\prime} = nx^{n-1}\)

-----------------------------

The function is:

\(f(x) = 4x^{-2} + \frac{x^2}{4} + 4\)

The derivatives are:

\((4x^{-2})^{\prime} = -2 \times 4x^{-2 -1} = -8x^{-3}\)

\((\frac{x^2}{4})^{\prime} = \frac{2x}{4}\)

\((4)^{\prime} = 0\)

Thus, the derivative of the function is:

\(f^{\prime}(x) = -8x^{-3} + \frac{2x}{4} = -\frac{8}{x^3} + \frac{2x}{4}\)

At x = 2:

\(f^{\prime}(2) = -\frac{8}{2^3} + \frac{2(2)}{4} = -1 + 1 = 0\)

Thus f'(2) = 0, option D.

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If so, then I can provide a brief explanation of this statement, which is known as the Side-Angle-Side (SAS) congruence theorem.

According to this theorem, two triangles are congruent if they have two pairs of corresponding sides that are congruent, and the included angles between these sides are also congruent.

To prove this theorem, we can use the fact that congruent triangles have corresponding angles and sides that are equal in measure.

Thus, if two triangles have two pairs of congruent sides and a congruent included angle, then we can use the angle-side-angle (ASA) postulate to show that they are congruent.

Specifically, we can say that the two triangles have a common angle between the two pairs of congruent sides, and the third corresponding angle is also congruent by virtue of the congruent included angle.

For example, suppose we have two triangles, ABC and DEF, as shown below:

A                    D

/ \                  / \

B-------C E-------F

Suppose we know that AB ≅ DE, BC ≅ EF, and ∠ABC ≅ ∠DEF. To show that triangle ABC ≅ triangle DEF, we can use the ASA postulate as follows:

By definition, AB ≅ DE and BC ≅ EF.

By the congruent included angle, ∠ABC ≅ ∠DEF.

Therefore, Since the triangles share the common side BC/EF, we have the common angle at B/C congruent to the corresponding angle at E/F.

By ASA postulate, we can conclude that triangle ABC ≅ triangle DEF.

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To complete the square for the equation \(x^2 + 8x + 32 = (x - h)^2 + 16\),

we need to choose h = -2.

To complete the square for the given equation

\(x^2 + 8x + 32 = (x - h)^2 + 16\),

we need to express the left-hand side of the equation in the form

\((x - p)^2 + q\), where p and q are constants.

We can start by expanding the right-hand side of the equation:

\((x - h)^2 + 16 = x^2 - 2hx + h^2 + 16\)

Now we can compare the coefficients of \(x^2\), x, and the constant term on both sides of the equation:

\(x^2 + 8x + 32 = (x - p)^2 + q\)

=> \(p^2 = 0\) (since the coefficient of \(x^2\) is 1 on both sides)

=> -2hp = 8 (since the coefficient of x is 8 on the left-hand side)

=> h = -2 (solving for h)

=> q = \(h^2 + 16\) = 20 (since the constant term on the right-hand side is 16)

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The complete question may be:

What value of h is needed to complete the square for the equation \(x^2+8 x+32=(x-h)^2+16\) ?

Answer:

median: 9

mean:11

mode: 7 or 9

range 13

Step-by-step explanation:

hope it helped!

Answer:

the answer is 5x divide by 12

Answer: Answer

4.0/5

37

jdoe0001

Genius

13.9K answers

122.5M people helped

check the picture below.

notice, the cross-section is just a 6x36 rectangle, and its area is, well just 6*36.

Step-by-step explanation: hope this helped

I think it would be ef because they are across from each other.

Answer:

lineAF, CE, EF

Step-by-step explanation:

Every line except AB, because a line don't curve.

Hope u understood.

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Thank You

Answer:

28°

Step-by-step explanation:

Supplementary angles sum to 180°

( dozen sixes) + 80

= 12 × 6 + 80

= 72 + 80

= 152°

supplement = 180° - 152° = 28°

Answer:

452/2 = 226

Step-by-step explanation:

45 divided by 2 is 22 and the remainder would be 12, which could be divided by 2 again to get 6. Add this to the total and you get 226.

Hope this helps! :D

The function that takes an input, adds 2, and then multiplies by 3 is a linear function with two operations: addition and multiplication. It can be represented by the equation y = 3(x + 2), where x is the input and y is the output.

To describe the function that adds 2 to the input and then multiplies by 3, we can break it down into two steps. First, we add 2 to the input, which can be represented by (x + 2). This expression ensures that the input is increased by 2.

The next step is to multiply the result by 3. Multiplying the expression (x + 2) by 3 gives us 3(x + 2). This step ensures that the increased input is further multiplied by 3.

Combining the two steps, we have the equation y = 3(x + 2), where y represents the output of the function. This equation indicates that the input (x) is first incremented by 2 and then multiplied by 3 to produce the final output (y).

Therefore, the function that takes an input, adds 2, and then multiplies by 3 can be described by the equation y = 3(x + 2).

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Answer:

The volume of Cone B is twice the volume of Cone A.

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h  where r is the radius and h is the height.

Cone A

d = diameter

r = radius

h = height

V = 1/3 pi r^2 h

Cone B

The diameter is double the diameter of A.

2d  so the radius is 2r

The height is half the height of A.

1/2 h

Substitute into the equation for volume.

V = 1/3 pi ( 2r)^2 (1/2 h)

V = 1/3 pi (4r^2) (1/2h)

V = 1/3 pi 2r^2 h

The volume of Cone B is twice the volume of Cone A.

Answer:

Cone B has a greater volume.

Step-by-step explanation:

Cone B has the greatest volume.

The volume of a cone is calculated using the following formula:

\(\boxed{\bold{\tt{Volume\: of\:cone = \frac{1}{3}\pi*r^2h}}}\)

where:

For Cone A.

\(\boxed{\bold{\tt{Volume\: of\:cone\: (A)= \frac{1}{3}\pi*r^2h}}}\)

For Cone B

In this case, the radius of Cone B is double the radius of Cone A, and the height of Cone B is half the height of Cone A. This means:

radius(r)=2r

height(h)= \(\tt{\frac{1}{2}*\frac{h}{2}}\)

\(\boxed{\bold{\tt{Volume\: of\:cone\: (B)= \frac{1}{3}\pi*(2r)^2*\frac{h}{2}}}}\)

\(\boxed{\bold{\tt{Volume \: of\:cone (B)= 2*\frac{1}{3}\pi*r^2h}}}\)

\(\boxed{\bold{\tt{Volume(B) =2*Volume\: of\:cone(A)}}}\)

Since the volume of cone B is twice the volume of Cone A.

Therefore, Cone B has a greater volume.

Answer:

Step-by-step explanation:

Let's name the radius of the circle "r". Because the circumference of the circle grows at a constant rate of 6 inches per second, we can apply the calculation C = 2 * pi * r to calculate the rate at which the radius grows.

dC/dt = 2 * pi * dr/dt = 6 inches/second

Because the square is parallel to the circle, the length of one of its sides equals the diameter of the circle. As a result, the square's perimeter equals four times the diameter of the circle or P = 4 * 2 * r.

As a result, the pace at which the square's perimeter grows is:

dP/dt equals 4 * 2 * dr/dt equals 8 * dr/dt

Substituting the dr/dt value from the first equation:

dP/dt = 8 * dC/dt = 8 * 6 inches per second = 48 inches per second

The pace at which the perimeter of the square is growing is 48 inches/second

b) The circle's area is determined by A = pi * r2.

If A = 257 square inches, we may calculate the value of r at that moment.

sqrt(A/pi) = sqrt(257/pi)

The rate of growth in the circle area is dA/dt = 2 * pi * r * dr/dt.

Substituting the dr/dt value from the first equation and the r value from above:

dA/dt = 2 pi * sqrt(257/pi) * 6 in/sec = 12 sqrt(257) in/sec

The area enclosed between the circle and the square equals the square's area minus the circle's area.

Let's call the square's side length s.

enclosed area = s2 - A = s2 - pi * r2

d(s2 - pi * r2)/dt = 2sds/dt is the rate of expansion of the enclosed area.

We may calculate the rate of increase of the enclosed area by substituting the value of ds/dt from the first equation.

ds/dt = dP/dt / 4 = 48 inches per second / 4 = 12 inches per second

d(s^2 - pi * r^2)

/dt = 2 * s * ds/dt = 2 * s * 12 inches/sec = 24 * s

The rate of expansion in the area enclosed between the circle and the square is 24*s inches/sec at the instant when the size of the circle is 257 square inches.

Please note that s is not supplied in the issue, thus it's impossible to determine the precise value of the rate of increase in the area contained.

Answer:

(6, - 3 )

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The lines intersect at (6, - 3 ) ← solution

Answer:

P(paranthesis) E(exponents) M(multiplication) D(division) A(addition) S(subtraction)

Step-by-step explanation:

It is the order in how you solve an equation. If there is something with paranthesis around it then solve it first. Then exponents then multiplication ect.

PEMDAS is the order that you solve a problem.

PEMDAS stands for:

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.

In the equation

2 + 3 * 5,

first you would do 3 * 5 because multiplication is before addition.

2 + 15

Then you would do the addition to get the answer:

17.

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