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We have the following:

Therefore:

3x+6=4x+7 //// = //// 3x-1=4x

3(x+6)=4x+7 //// = //// 3x+18=4x+7

4x+3x=7-6 //// = //// 7x=1

Replace the variable in an equation with to write it in function notation. In function notation, the equation would be stated as follows: f (x) = x + 30000, where is the mileage displayed on the odometer.

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The quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.

According to the question,

We have the following expressions:

[tex]3x^{3} -15x-13[/tex] is divided by (x+2)

First, we  will look at some of the rules of the synthetic division:

We have to make the quotient in such a way that it is same as the term with the highest power in the dividend.

We change signs after solving using one complete term of the quotient.

We have to solve this using the synthetic division method:

x+2 )[tex]3x^{3} -15x-13[/tex]( [tex]3x^{2} -6x-3[/tex]

       [tex]3x^{3} +6x^{2}[/tex]

      _-___-_____

              [tex]-6x^{2} -15x-13[/tex]

              [tex]-6x^{2} -12x[/tex]

             +         +

                _________

                          -3x-13

                          -3x-6

                          +   +

                        _______

                              -7

Hence, the quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.

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The equation for F is,

Determine the value of F.

Thus value of F is 210.

Below is the figure of the triangle

We have three unkown variables which are x, y, and z

Firstly, let us find the unknown side z

To find z, we will be applying SOH CAH TOA

The longest side is z

The opposite sides is 39

Find x

X can be find by applying the SOH CAH TOA

Let z = opposite

let x = adjacent

Find y

let y = adjacent

x = Hypotenus

Applying SOH, CAH TOA

The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17).

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given lines,

y = −10x − 3

−y = 11x + 5 → y = -11x - 5

The value of the function at the point of intersection is always the same.

So,

−10x − 3 = -11x - 5

-10x + 11x = -5 + 3

x = -2

So,y = -10(-2) - 3 = 17

Hence "The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17)".

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The most appropriate choice for maxima and minima of a function will be given by

Rectangle of length 72 feet and breadth 36 feet has largest area

What is maxima and minima?

Maxima of function f(x) is the maximum value of the function and minima of function f(x) is the minimum value of the function.

Here,

Let the length be x feet and breadth be y feet

The farmer has 144 feet of fencing

Three of the sides will require fencing and the fourth wall already exists.

So,

x + y + y =1 44

x + 2y = 144

Area of rectangle(A) = xy [tex]ft^2[/tex]

                               = (144 - 2y)y

                               = [tex]144y - 2y^2[/tex]

[tex]\frac{dA}{dy} = \frac{d}{dy}(144y - 2y^2)[/tex]

     = [tex]144 - 2\times 2y^{2-1}\\144 - 4y[/tex]

For largest area,

[tex]\frac{dA}{dy} = 0[/tex]

[tex]144 - 4y = 0 \\4y = 144\\y = \frac{144}{4}\\y = 36[/tex]

[tex]\frac{d^2A}{dy^2} = \frac{d}{dy}(144 - 4y)\\=0-4\\=-4 < 0[/tex]

Hence area is maximum

For largest area, y = 36 feet

[tex]x = 144 - 2\times 36\\x = 144-72\\[/tex]

[tex]x = 72[/tex] feet

So length of rectangle is 72 feet, breadth of rectangle is 36 feet

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205 air conditioners must be produced and sold to have a yearly profit of $45,000.

As per the relation representing p and x, x is the number of air conditioners so p must be the profit. Keep the value of profit to find the value of x.

45000 = x² + 15x - 100

Shifting 100 to Left Hand Side of the equation

45000 + 100 = x² + 15x

Performing addition on Left Hand Side of the equation

45100 = x² + 15x

Rearranging the equation

x² + 15x - 45100 = 0

Factorising the equation to find the value of x

x² + 220x - 205x - 45100 = 0

x(x + 220) -205 (x + 220) = 0

(x - 205) (x + 220) = 0

x = 205, - 220

The number of air conditioners produced and sold can not be negative. So, the value of x and hence the number of air conditioners is 205.

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Answer:

Step-by-step explanation:

0.033

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 32 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies {\Large \begin{array}{llll} y-\stackrel{y_1}{1}=\stackrel{m}{- 32}(x-\stackrel{x_1}{2}) \end{array}}[/tex]

Answer: 2%

Step-by-step explanation:

Exponential growth functions are of the form [tex]P(1+r)^t[/tex], where r is the rate of change. From the equation, we see that r=0.02, and converting this to a percentage, we get 2%.

Answer:

-1.12 or -28?/25 or -1 3/25

Step-by-step explanation:

Answer:  If we take the aerobics class, then we will be in good shape for the ski trip

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

Explanation:

The conditional statement in bold is of the form "If P, then Q" where

P and Q are placeholders for logical statements, in much a similar fashion that x = 2 has x as a placeholder for the number 2.

Given the function below,

Let us now plot the graph in order to obtain the end behaviours.

From the graph above, we can conclude that

Hence, the correct answer is Option D.

A pancakes require 3.5 cups of milk and 1 cup of flour, or a ratio of 3.5:1 or a fraction of

(3.5) / (1)

If you have 4.6 cups of milk you need x cups of flour

Set up a ratio of

Answer:

  33w² +660w

Step-by-step explanation:

You want the expression for the volume of a cuboid with dimensions in inches of 33, (w+20), and (w).

The volume of a cuboid is the product of its dimensions:

  V = HLW

  V = (33)(w +20)(w) = 33(w² +20w)

  V = 33w² +660w . . . . expression for volume

__

Additional comment

Comparing coefficients, you see ...

Answer:

the value of x is 32 degree

Step-by-step explanation:

100 + 68 +x = 180

168 +x=180

x= 180- 168

x= 32 degree

Answer:

62

Step-by-step explanation:

x + 87 and 2x are linear pair angles.

Sum of linear pair angles is 180,

x + 87 + 2x = 180

x + 2x + 87 = 180

3x + 87 = 180

3x = 180 - 87

3x = 93

x = 93 / 3

x = 31

2x

= 2 * 31

= 62

The value for the A³ matrix will be [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]

In the given question, it is stated that A is a given matrix. We have to find out the values of A³. This can be done by product of A*A*A. The product should follow the properties of the Matrix. First, we will find out the value of A². So calculating, we get:

=> [tex]A^{2} = \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]

=> [tex]A^{2} = \left[\begin{array}{ccc}-25+0 &1 -1\\0+0&0 + 1\end{array}\right][/tex]

=> [tex]A^{2} = \left[\begin{array}{ccc}-25 &0\\0&1\end{array}\right][/tex]

Now we will calculate the value of A³. We can calculate the value of A³ by using the values of A² because we know that A³ = A².A. So, after calculating we get:

=> [tex]A^{3} = \left[\begin{array}{ccc}-25&0\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]

=> [tex]A^{3} = \left[\begin{array}{ccc}75+0&0 + 0\\0+0&0+1\end{array}\right][/tex]

=> [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]

Hence we get value for [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]

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Answer:

y=2/3x+4

Step-by-step explanation:

To do this, this equation must be taken to the form

So,

Then a positive slope of 2/5 tells you that for every 2 units on the y-axis there are 5 units on the x-axis. And 3 tells you that the line intercepts the y-axis at 3.

The circumference of the circle is

The given situation represents a random sample because, in statistics, a simple random sampling refers to the subset of individuals chosen from a larger set called population, where the sample is chosen randomly.

In this case, the dialed number are a random event, so it can be called a simple random sample.

Answer:

The solution to the inequality is;

Explanation:

Given the inequality;

Firstly, let's multiply both sides of the equation by 9;

Then we can multiply both sides by -1.

Note that when we multiply both sides by a negative number(-1) the sign will change;

So;

The solution to the inequality is;

Okay, here we have this:

Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:

Finally we obtain that the solution to the system is:

The linear regression equation is y = 15430.5034 + 301.2586x .

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x + y=7 and x - y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage. There are three steps in the substitution technique: For each variable, solve a single equation. Solve the other equation by substituting (plugging in) this expression. Find the corresponding variable by substituting the value back into the original equation.

∑x = 56

∑ y = 109453.5

∑ x² = 760

∑ x × y = 1093064.7

Substitute the upper values

6a + 56b = 109453.5

56a + 760b = 1093064.7

Solve the above 2 equations

a = 15430.5034

b = 301.2586

Now substitute the values in y = a + bx

y = 15430.5034 + 301.2586x

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We are looking for the point at which the compensation from Plan A is less than the compensation from Plan B.

Plan A = 850 +0.1x

Plan B= 1050+(x-7000)(0.14)

Plan A < Plan B

850 +0.1x <1050+(x-7000)(0.14)

then we sill simplify

850+0.1x < 1050+0.14x-980

850+0.1x<70+0.14x

then we isolate the x

0.1x-0.14x<70-850

-0.04x<-780

x>-780/-0.04

x>19500

In this case the monthly sales x need to be greater than 19500 (x>19500), in order that Plan B were better than plan A.

EXPLANATION

Since the line segment is 7 units long, we can apply the following relationship:

(x_1+ 7 , y_1) = (x_2 , y_2)

The coordinate of the endpoint is as follows:

We can get to this point by applying the distance formula as follows:

Applying the square power to both sides:

Subtracting numbers:

Now, if the x_2 coordinate is -3, the value of y_2 will be as follows:

Subtracting -4 to both sides:

Applying the square root to both sides:

Adding +4 to both sides:

In conclusion, the equation to get the coordinate from a given point is,

Answer: The answer is -1

Answer:  [tex]3\sqrt{2}+3\sqrt{5}[/tex]

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

Work Shown:

[tex]\sqrt{3}\left(\sqrt{6}+\sqrt{15}\right)\\\\\sqrt{3}*\sqrt{6}+\sqrt{3}*\sqrt{15}\\\\\sqrt{3*6}+\sqrt{3*15}\\\\\sqrt{18}+\sqrt{3*3*5}\\\\\sqrt{9*2}+\sqrt{9*5}\\\\\sqrt{9}*\sqrt{2}+\sqrt{9}*\sqrt{5}\\\\3\sqrt{2}+3\sqrt{5}\\\\[/tex]

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

Explanation:

I distributed and used the idea that sqrt(A*B) = sqrt(A)*sqrt(B) to combine square roots, but also to break them up when factor out the largest perfect square factor.

Optionally for the last step, you could factor out 3, but your teacher may want you to leave it like shown.