Use the factor theorem to determine if( x - 2) + (x + 4) are factors of the function below

By definition, the Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

The equation of a line that passes through the Origin has the following form:

Where "m" is the slope of the line.

In this case, you have the first line that passes through the Origin:

You can identify that its slope is:

You also know the second equation, which is written in Slope-Intercept form:

You can identify that:

By definition, the slopes of parallel lines are equal. Then, since:

These lines are parallel.

The answer is: True.

Question 13.

Part (a).

Given the solution:

All real numbers

We have the expression:

3(4x + 2) = ________

Let's complete the equation in order to obtain the indicated solution.

For a solution to be all real numbers, the equation must be true.

hence, we have:

After solving we have:

0 = 0

This means the system has infinitely many solutions, therefore, the solution is all real numbers.

ANSWER:

3(4x + 2) = 3(4x + 2)

Answer:

Step-by-step explanation:

B'' = (-7, 8)

The points of the triangle are:

A = ( - 6, 3 ) B = ( - 4, 7 ) C = ( - 2, 3 )

The first transformation:

2 units up and 3 units right

B' = (-4+3, 7+2)

B' = (-1, 9)

Second transformation:

1 unit down, 6 units left

B'' = (-1-6, 9-1)

B'' = (-7, 8)

Answer:

-1

Step-by-step explanation:

[tex]\frac{\frac{64}{-12+4}}{(6)^2+(-30)+2} \\ \\ =\frac{\frac{64}{-8}}{36-30+2} \\ \\ =\frac{-8}{8} \\ \\ =-1[/tex]

Solution:

Step 1: Find the equation of the line in the graph.

Two points the line pass through are (0, -4) and (2, -3)

Thus,

The equation of the graph is 2y = x - 8

Step 2:

Solve the two equations simultaneously to detemine the solution to the systems of equations

2y = x - 8 ------------------------equation (1)

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

Add both equations to eliminate x

2y + y = x - 8 + (-x) + 2

3y = x -8-x+2

3y = -8 + 2

3y = -6

y = -6/3

y = -2

Substitute y = -2 into equation (2)

y = -x + 2

-2 = -x + 2

-2 -2 = -x

-4 = -x

-x = -4

Divide both sides by -1

x = 4

Hence, the solution to the system of equations is (4, -2)

The correct option is option D

To solve the question, choose values for x to find its corresponding image y. Then, plot the points and connect them.

Step 01: Choosing x = -2.

Substituting x by -2 in the equation:

So, the first point is (-2, 2/9).

Step 02: Choosing x = -1.

Substituting x by -1 in the equation:

So, the second point is (-1, 2/3).

Step 03: Choosing x = 0.

Substituting x by 0 in the equation:

So, the third point is (0, 2).

Step 04: Choosing x = 1.

Substituting x by 1 in the equation:

So, the fourth point is (1, 6).

Step 05: Write the points in a table.

x y (x, y)

-2 2/9 (-2, 2/9)

-1 2/3 (-1, 2/3)

0 2 (0, 2)

1 6 (1, 6)

Step 06: Plot the points and connect them.

The figure below shows the points and the graph.

Done! Your question is solved!

We can add the minutes from 7:20 AM to the next hour (8:00 AM), that is 40 minutes.

Then, from 8:00 AM to 9:00 AM we have 60 more minutes.

Then, from 9:00 AM to 9:49 AM we have 49 additional minutes.

We add all three segments as:

As 60 minutes is 1 hour, 120 minutes is 2 hours. Then, 149 minutes are 2 hours and 29 minutes.

Answer: the time elapsed us 149 minutes (or 2 hours and 29 minutes)

1)

then the solution is

We know that the calculator price (x) was 25 more than 3 times the price of the textbook (y).

This can be represented as:

We also know that the sum of the prices of the two items is equal to $165:

We have to solve this system of equations with the method of substitution.

We can use the first equation, as we have already clear the value of x, to substitute x in the second equation and then solve for y:

With the value of y we can calculate x using the first equation:

Answer: the solution as ordered pair is (x,y) = (130, 35)

Explanation

To find the displacement in cubic feet, divide the volume value by 1728.

Answer: 0.27 cubic feet

To answer this question, we need to find the unit rate in this case. For this, we need to divide the given liters by the hours. Then, we have:

Then, the dairy produces 4.05 liters per hour.

The rate at which turtle can swim is 20 miles per hour or 20 miles in one hour.

For conversion, 1 mile is equal to 5280 foot.

Convert 20 miles per hour in foot per hour.

So answer is 105600 foot per hour.

SOLUTION:

Winston =

Upon simplification, the number of miles wayne walked was 3

Substituting wayne = 3 into the second equation

Wilfred = 2.5

Since Wilfred and Winston walked the same number of miles,

Winston = 2.5

The first drop menu is Wilfred

The second drop menu is 3

The third drop menu is 2.5

The fourth drop menu is faster than.

We have the following sets:

A = {3, 5, 7, 9, 11, 13}

B = {3, 5, 11, 13}

If we look closely, all the elements of B are in A. But each element of A does not belong to B, therefore the statement is totally false.

the amount of money a worker earns is directly proportional to the number of hours worked.at this rate.thag worker makes $104 in an 8 hour shift.weite a direct variation equation that relates the earnings (e) of the worker to the number of hours (n) worked. use the correct lowercase variables given ,and use no spaces​

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form e=kn

In this problem we have

e -----> amount of money a worker earns

n -----> number of hours worked

k is the constant of proportionality

k=e/n

Find the value of k

we have

For n=8 hours, e=$104

sibstitute

k=104/8

k=$13 per hour

The linear equation is

The correct option is Yes, which is option A

Why?

The reason is that the probability that marble is removed from the box does not affect the probability that a marble is drawn from the same box. i.e the two events do not affect each other

The responses to the linear optimization questions are;

Question 1

The optimal daily profit is $380

Question 2

The combination of x and y that yield the optimal value is the option;

x = 0, y = 3

Linear programming is a method by which the optimal solution can be obtained from a model represented mathematically and in which the constraints of the model have linear relationships.

Question 1

Let B represent the number of bear claws, C the almond-filled croissant, F represent the flour, Y represent the amount of yeast and A represent the number of almonds.

The amount of ingredient per each produce is therefore;

B = 6·F + 1·Y + 2·A

C = 3·F + 1·Y + 4A

The amount of ingredient available for the days production is as follows;

Ingredient available; 6600·F + 1400·Y + 4800·A

The constraints are therefore

6·B + 3·C ≤ 6,600

B + C ≤ 1,400

2·B + 4·C ≤ 4800

The maximizing function is therefore;

Profit = 0.2·B + 0.3·F

The equations of the lines are therefore;

B = 1,100 - 0.5·C

B = 1400 - C

B = 2400 - 2·C

The vertices of the feasible region are;

(0, 1100), (600, 800), (1000, 400), 1200, 0)

The values of the maximizing function at the vertices of the feasible region are;

Profit, P = 0.2×1100 + 3×0 = 220

At point (600, 800), P = 0.2×800 + 0.3×600 = 340

At point (1000, 400), P = 0.2×400 + 0.3×1000 = 380

At point (1200, 0), P = 0.2×0 + 0.3×1200 = 360

Question 2

Maximize $3·x + $15·y

Subject to the following constraints;

2·x + 4·y ≤ 12

5·x + 2·y ≤ 10

x, y ≥ 10

The equations are therefore;

4·y ≤ 12 - 2·x

y ≤ 3 - 0.5·x...(1)

5·x + 2·y ≤ 10

2·y ≤ 10 - 5·x

y ≤ 5 - 2.5·x...(2)

x ≥ 10, y ≥ 10

The coordinates of the vertices of the feasible region are;

(0, 3), (1, 2.5), and (2, 0)

The values of the maximizing function are therefore;

At (0, 3), M = $3 × 0 + $15 × 3 = $45

At (1, 2.5), M = $3 × 1 + $15 × 2.5 = $40.5

At (2, 0), M = $3 × 2 + $15 × 0 = $6

The combination of x and y that yield the optimum is therefore;

(x, y) = (0, 3)

x = 0, and y = 3

Learn more about linear optimization or programming here:

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Explanation

Step 1

remember

Step 2

solve

Given:

The unpaid balance after the 26 payments is $3,733.55.

Therefore, the interest for payment 27 will be

Evaluating

Hence, the interest for payment 27 is $522.70.

Answer:

Interior angle = 81°; exterior angle = 99°.

Step-by-step explanation:

For triangle XYZ:

Angle X and its exterior angle form a straight line.

Angles on a straight line sum to 180°.

Therefore:

⇒ (4g + 13)° + (3g + 48)° = 180°

⇒ 4g + 13 + 3g + 48 = 180

⇒ 7g + 61 = 180

⇒ 7g + 61 - 61 = 180 - 61

⇒ 7g = 119

⇒ 7g ÷ 7 = 119 ÷ 7

⇒ g = 17

To find the measure of ∠X and its exterior angle, substitute the found value of g into the angle expressions:

⇒ m∠X = (4(17) + 13)°

⇒ m∠X = (68 + 13)°

⇒ m∠X = 81°

⇒ exterior angle to ∠X = (3(17) + 48)°

⇒ exterior angle to ∠X = (51 + 48)°

⇒ exterior angle to ∠X = 99°

Therefore:

Answer: C

Step-by-step explanation: did the practice test!

12.5% as a decimal is 0.125.

To convert a percentage in to a decimal, we divide the percentage by 100:

Answer

The statement istrue.

Natural numbers are also whole numbers.

Explanation

Natural numbers are counting numbers.

They are the numbers that are numerically used to count things.

Hence, all natural numbers (counting numbers) are whole numbers.

Hope this Helps!!!

The equation for a hyperbola that opens up and down has the following general form:

Where the foci of the hyperbola are located at (h,k+c) and (h,k-c) with c given by:

And asymptotes with slopes given by a/b and -a/b.

The hyperbola with the equation that we have to find has these two foci:

This means that:

So we get h=3, k=2 and c=√26.

The slope of the asymptotes have to be 5 and -5 which means that:

Using the value of c we have:

So we have two equation for a and b. We can take the first one and multiply b to both sides:

And we use this in the second equation:

We divide both sides by 26:

Which implies that b=1. Then a is equal to:

Now that we have found a, b, h and k we can write the equation of the hyperbola. Then the answer is:

Given:

Let's differentiate the equation.

To differentiate since -8 is constant with resppect to x, the derivative will be:

Where:

derivative of ln(x) with respect to x = 1/x

Thus, we have:

ANSWER:

Solution:

Given the equation below

Applying the completing the square method

Where the general form of a quadratic equation is

For the completing square method,

Where

The number that should be added to both sides of the equation to complete the square is

Hence, the number is 9 (option B)

We can rewrite the next equations in the slope-intercept form:

The first equation:

The second equation:

As we can see, the slope of the first line is m = -3/4, and the slope of the second line is m = -2. Then, since the slope is different, these lines are not parallel (Option C).