Simply this equation 2(x-7)=-4

The polynomial is f(x) = x³ - 12x² + 64x + 128

Given,

The polynomial has 4, 4-4i, and 4+4i as its roots.

f(-1) equals -255

We have to find a polynomial of degree 3.

If x = 4 is a root, then:

(x - 4) is a factor of the polynomial.

If x = 4 - 4i is a root,

Then,

(x - 4 + 4i) is a factor of the polynomial.

If x = 4+4i is a root.

Now,

(x - 4 - 4i) is a factor of the polynomial.

All the three roots are of the same polynomial.

So,

The polynomial is the product of these factors.

f(x) = k(x - 4) (x-4+4i) (x-4-4i)

f(x) = k(x - 4) [(x-4)² - (4i)²]

f(x) = k(x- 4) [x² + 16 - 8x + 16]

f(x) = k(x - 4) [x² - 8x + 32]

f(x) = k[x³ - 8x² + 32x - 4x² + 32x - 128]

f(x) = k[x³ - 12x² + 64x + 128]

Now find "k", we know that f(-1) = -255.

f(-1) = k[(-1)³ - 12(-1)² + 64(-1) + 128]

-255 = k[-1 - 12 - 64 + 128]

-255 = k × -255

k = 1

That is, the polynomial is f(x) = x³ - 12x² + 64x + 128

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Answer:

the answer is 2 and one fourth

Step-by-step explanation:

because the 3s cancel out

The boxes of candy sold by Roger are 29/30.

According to the question,

We have the following information:

Roger sold 1/3 as much candy as Sally sold.

Sally sold [tex]2\frac{9}{10}[/tex] boxes of candy.

Now, first we will convert the boxes of candy sold by Sally from the mixed fraction.

(More to know: there are three kinds of fraction: mixed fraction, proper fraction and improper fraction. We need to change mixed fraction in most of the cases to solve the questions further.)

We have:

29/10

Now, we know that the boxes of candy sold by Roger is 1/3 of 29/10.

So, we have the following expression:

[tex]\frac{1}{3}* \frac{29}{10}[/tex]

29/30

Hence, the boxes of candy sold by Roger is 29/30.

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2, 4, 5, 10 and 20 cast members were possible attendees at the celebration.

The acting teacher provided 20 biscuits and 40 carrot sticks as refreshments in light of this.

What are the factors?

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

2, 4, 5, 10, and 20 make up the factors of 20 and 40.

Additionally, the number of cast members must be greater than one and a divisor of 20 and 40.

Therefore, there could be 2, 4, 5, 10, or 20 cast members.

Therefore, 2, 4, 5, 10 and 20 cast members may have attended the celebration.

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The experimental design which is used in the study is Completely randomized design.

Completely Randomized design may be defined as a technique in which all the solutions are assigned at random so that each questions receive all the possible solutions. According to the question we know that the sample size is 100 volunteers who are suffering from chronic pain. Now, out of the 100 volunteers, 50 males and 50 females are chosen. Further out of the 50 males, 25 males are randomly assigned to the treatment group while the other 25 males are assigned to a control group. Since, the treatments are randomly assigned completely, each of the volunteers have an equal chance of receiving the treatments.

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Answer: 18 combinations

Step-by-step explanation: you want to multiply the amount of ice cream flavors by the amount of children to be able to find the amount of possible combinations. so, 6 children x 3 flavors of ice cream = 18 different combinations. 6 x 3 = 18

In order to find 5a-3b, lets find 5a. This is given by

Similarly, -3b is given by

Then, by substituting our results into the expression 5a-3b, we get

This can can be done by adding entry by entry, that is

Therefore, the answer is

Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.

Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).

Here the ΔCED and ΔPOR,

∠CED=∠POR

Side PR=CD

Side ED=PO

by using SAS rule,

ΔCED≅ΔPOR

Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.

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ANSWERS

1. Domain: all real values

2. Zeros: 0 (with multiplicity 2) and 3

3. Not periodic. Symmetric about the point (1, 2)

4. Positive for x < 3; negative for x > 3

5. f → ∞ as x → -∞; f → -∞ as x → ∞

6. none

EXPLANATION

1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.

2. To find the zeros of the function, we have to solve,

First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,

So, we have,

In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.

Hence, the zeros are 0 and 3. 0 has multiplicity 2.

3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).

4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,

For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.

Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.

Hence, is the function is positive for x < 3 and negative for x > 3.

5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.

Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.

6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.

Answer:

Step-by-step explanation:

It is a representation of the functional relation with dependent and independent variables, normally, x- independent and f(x) - dependent variable.

We can write the given function as:

The Nya will pay $46.42 for the sweater. The decimal equivalent of a 20 percent discount is 0.20. To calculate the savings in dollars, multiply the decimal discount by the item's price. For instance, if the item's original price is $24, you would multiply 0.2 by that amount to get $4.80.

We have been given that Nya wants to buy a sweater that had an original price of $55. The sweater is now discounted 20%.

the price of sweater after20% discount is 55-20% of 55

The price of the sweater after discount =55-(20/100*55)

The price of the sweater after discount=55-(0.20*55)

The price of the sweater after discount=55-11

The price of the sweater after discount=44

SO  The price of the sweater after discount is $44

Now let us find the price of sweater after adding 5.5% sales tax

The price of sweater after sales tax =44+(5.5/100*44)

The price of sweater after sales tax=44+(0.055*44)

The price of sweater after sales tax=44+2.42

The price of sweater after sales tax=46.42

$46.42 is paid for sweater after sales tax

Hence, The Nya will pay $46.42 for the sweater.

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When seen as a function, a relationship exists between a set of inputs and outputs.

The number of bricks in the chimney exists 900.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Simply described, a function is an input-output connection where each input is coupled to exactly one output range, codomain, and domain are included in each function. A function exists generally denoted by f(x) where x exists the input.

Let x be the number of bricks in the chimney. The work done exists the rate multiplied by the time.

Using w = rt, we get

[tex]$x=\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5[/tex]

Expanding the above equation, we get

[tex]$\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5: \quad \frac{19 x}{18}-50$[/tex]

x = (19x / 18) - 50

Multiply both sides by 18

[tex]$x \cdot 18=\frac{19 x}{18} \cdot 18-50 \cdot 18[/tex]

Simplifying the above equation,

x × 18 = 19x - 900

Subtract 19x from both sides

x × 18 - 19x = 19x - 900 - 19x

Simplifying the above equation, we get

-x = -900

Divide both sides by -1

[tex]$\frac{-x}{-1}=\frac{-900}{-1}[/tex]

x = 900

Therefore, the value of x exists 900.

The complete question is:

Bricklayer Brenda would take nine hours to build a chimney alone, and bricklayer Brandon would take  hours to build it alone. When they work together, they talk a lot, and their combined output decreases by  bricks per hour. Working together, they build the chimney in  hours. How many bricks are in the chimney?

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Question: Write the system of linear equations represented by the augmented matrix to the right use W, X, Y and Z for the variables :

Solution:

An augmented matrix is equivalent to a system of linear equations. In this case, the given matrix is represented by the following system of linear equations:

-1 w - 3x +5y +2z = 13

0w + 1x + 3y + 0z = 10

0w + 0x +y - 1z = 3

1w - 3x + 0y + 0z = -2

this is equivalent to:

w - 3x +5y +2z = 13

x + 3y = 10

y - z = 3

1w - 3x = -2

So that, the correct answer is:

w - 3x +5y +2z = 13

x + 3y = 10

y - z = 3

1w - 3x = -2

Answer:

9*X+5*3.25

Step-by-step explanation:

So, total 9 person; 4 person have their own shoe.

Cost for game = 9*X;

Cost for shoe = 5*3.25;

So the total cost = 9*X+5*3.25

Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9

1) Given that an oatmeal cookie has these proportions, let's set a pair of ratios to get that:

Answer:

x = 20

Step-by-step explanation:

X = 20 Because the values are Corresponding Angles This means that they are congruent

By taking the quotient between the average depth of the oceans, we conclude that the atlantic ocean is 3.251 times deeper.

We know that the average depth of the arctic ocean is 3.953x10^3 feet and the average depth of the atlantic ocean is 1.2851x10^4 feet

Notice that both of these are in scientific notation.

To see how many times deeper is the atlantic ocean than the artic ocean we need to take the quotient between the average depth of the atlantic ocean and the average depth of the arctic ocean, this gives:

(1.2851x10^4)/(3.953x10^3) = (1.2851/3.953)*(10^4/10^3)

= 0.3251*(10^1) = 3.251

The atlantic ocean is 3.251 times deeper than the artic.

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For the figure to be a parallelogram, then y must be equal to 12

Here, we want to get the value of y for which the the quadilateral must be a parallelogarm

Mathematically, the diagonals of a parallelogarm bisects each other

That means the lengths on either sides are equal

Mathematically, we can get two equations as follows;

Answer:

Since all triangle angles sum to 180 then we can say

2x + 3x + 7x = 180

12x = 180

x = 15

There fore the angles are

2 * 15 3 * 15 and 7 * 15 or

30 45 and 105

Those 3 total 180 degrees

Step-by-step explanation:

The value of x is 40 and the value of y is 25.

What is consecutive interior angles?

Pairs of angles that are between two lines and on the same side of the line that cuts through the two lines are referred to as consecutive internal angles. According to the theorem, if two lines are parallel, then successive interior angles are supplementary to one another.

Angles that add up to 180 degrees are referred to as supplementary angles.

As we know that the sum of three angles of triangle is 180 degrees.

So from the first figure we get,

2x + x + y + y + 10 = 180

3x + 2y = 170          ...(1)

From the second figure we get,

4x - y + x + 5 = 180         (Since they are consecutive interior angles)

5x - y = 175             ...(2)

After solving equation (1) and (2), we get

x = 40 and y = 25

There the value of x is 40 and the value of y is 25.

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The quadrilateral in the picture is a square since all four sides are equal.

The angles are all equal and all are right angles.

Clearly, the quadrilateral is a square.

Answer:

  y = -1/3x +1

Step-by-step explanation:

You want the slope-intercept form equation of the line through the points (-3, 2) and (-9, 4).

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x)

  m = (4 -2)/(-9 -(-3)) = 2/-6 = -1/3

The y-intercept is given by the formula ...

  b = y1 -m(x1)

  b = 2 - (-1/3)(-3) = 1

The slope-intercept equation of the line is ...

  y = mx +b

  y = -1/3x +1

The Number of small and large boxes shipped are 10 and 5 respectively.

Large boxes :

Volume = 18 cubic feets

Let number of large boxes = b

Small boxes :

Volume = 10 cubic feets

Number of small boxes = 2b

Total volume shipped = 190 cubic feet

To obtain total volume shipped :

(Number of small boxes × volume of small boxes) + (Number of large boxes × volume of large boxes

Writing as a system of equation :

(10 × 2b) + (18 × b)

20b + 18b = 190 cubic feets

38b = 190

b = 190 ÷ 38

b = 5

Hence,

Number of large boxes = 5

Number of small boxes = 2(5) = 10

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1) Considering that x is for pounds of apples and y is a total cost of an apple let's find the cost per pound of the apples, given that the y=2.57x +4.5

Let's turn that function into an equation

0=2.57x +4.5 Subtract 2.57x from both sides

-2.57x=4.5 Divide both sides by -2.57

x=-1.75

2) So if no one pie crust is sold, there is going to be a loss of $-1.75, according to that equation.

Therefore, we can infer that the cost per pound of the apples is $1.75

The graph for the given equation is plotted below.

The given equation is y=3x-4.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Put x=0, 1, 2, 3, 4,....in the given equation and solve for y

When x=0, y=-4

When x=1, y=-1

When x=2, y=2

When x=3, y=5

Plot the coordinates (0, -4), (1, -1), (2, 2) and (3, 5) on the graph.

Therefore, the graph for the given equation is plotted below.

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The scale factor K = 0.9 is smaller than 1, so this is a reduction.

If we have a dimension L, a change of scale of scale factor K gives the new length: K*L

Then:

if K > 1, we have an enlargement.

if K = 1, we have a preservation (nothing changes)

if  0 < K < 1, we have a reduction.

In this case, we have K = 0.9, this is smaller than 1, so we have a reduction.

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Answer:

Exterior angle = 20 degrees

Interior angle = 160 degrees

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

Explanation:

The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,

exterior = (1/8)*(interior)

That rearranges to

interior = 8*(exterior)

Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle

The two must add to 180 to form a straight line.

interior + exterior = 180

8x + x = 180

9x = 180

x = 180/9

x = 20 is the measure of the exterior angle

8x = 8*20 = 160 is the measure of the interior angle

Note how 160+20 = 180 to verify our answers.