Write the cubic functions in factored form and standard form. Zeros: x = -3, x = 0, x = 1

Answer:

To find the slope of a line, we can use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Given the points (0,-10) and (-4,-11), we can plug these coordinates into the formula:

slope = (-11 - (-10)) / (-4 - 0) = -1 / -4 = 1/4

So, the slope of the line that passes through the points (0,-10) and (-4,-11) is 1/4.

Step-by-step explanation:

Given that EF = 2x, FG = x + 1, and EG = 4, we can use the information provided to find the value of EF.

Since EG = 4, we know that EF + FG = EG.

so, 2x + (x + 1) = 4

Solving for x, we get:

3x + 1 = 4

3x = 3

x = 1

Now we can substitute this value back into the equation for EF:

EF = 2x

EF = 2(1)

EF = 2

So, EF = 2

It is not possible to find the value of FG if the information provided is not correct and it's missing a part of the equation, Therefore I'm unable to find the value of FG.

The mean period of the oscillation is 1.257 s and the standard deviation is 0.123 s.

To find the mean and standard deviation of the data, we can use the following formulas:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest

Standard deviation = [tex]\frac{\sqrt{((sum of (data point - mean)^{2}) } \\}{number of data points - 1}[/tex]

First, let's find the mean:

Mean = (1.88 + 0.97 + 1.43 + 1.26 + 1.61 + 1.19 + 1.17 + 1.28 + 1.25 + 1.48) / 10

Mean = [tex]\frac{12.57}{10}[/tex]

Mean = 1.257

The mean is 1.257.

Next, let's find the standard deviation:

Standard deviation = ([tex]\sqrt{(((1.88 - 1.257)^{2}+(0.97 - 1.257)^{2} (1.43 - 1.257)^{2}+(1.26 - 1.257)^{2}+(1.61 - 1.257)^{2}}[/tex][tex]+\sqrt{+(1.17 - 1.257)^{2}+(1.28 - 1.257)^{2}+(1.48 - 1.257)^{2}}[/tex])/9

Standard deviation =[tex]\sqrt{\frac{0.134}{9} }[/tex]

Standard deviation = [tex]\sqrt{0.015}[/tex]

Standard deviation = 0.123

Therefore, the mean period of the oscillation is 1.257 s and the standard deviation is 0.123 s (sample standard deviation).

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Answer:

Step-by-step explanation:

a. To find out how much floor space each box will cover, we need to multiply the volume of the box by the height of the stack of items. The volume of the box is x3 + 10x2 + 29x + 20 cubic units and the height of the stack of items is x + 5 units. So the floor space covered by each box is (x3 + 10x2 + 29x + 20) * (x + 5) square units.b. To find the maximum number of boxes Darren can place on the floor of the storage unit, we need to divide the total floor area of the storage unit by the floor space covered by each box. The total floor area of the storage unit is x* + 5x° + x7 _ 20x - 14 square units and the floor space covered by each box is (x3 + 10x2 + 29x + 20) * (x + 5) square units, then we can divide the total floor area by the floor space covered by each boxx* + 5x° + x7 _ 20x - 14 / (x3 + 10x2 + 29x + 20) * (x + 5) = maximum number of boxesc. To find out how much of the floor space is not covered by a box, we can subtract the floor space covered by the maximum number of boxes from the total floor area of the storage unit.Total floor area - floor space covered by the maximum number of boxes = remaining floor space.Please note that this is a polynomial equation and the solution will be different depending on the value of x.

a) Floor space of each box = ([tex]x^3 + 10x^2 - 29x + 20[/tex]) / (x + 5)

b) Maximum number of boxes = ([tex]x^4 + 5x^3 + x^2 - 20x - 14[/tex]) / (([tex]x^3 + 10x^2 - 29x + 20[/tex]) / (x + 5))

c) Uncovered floor space = [tex]x^4 + 5x^3 + x^2 - 20x - 14 - ((x^3 + 10x^2 - 29x + 20) / (x + 5) * Maximum number of boxes)[/tex]

We have a storage unit with a given floor area and boxes with specified volumes and heights.

We'll determine the floor space each box covers, the maximum number of boxes Darren can place on the floor, and how much floor space is left uncovered when he places the maximum number of boxes without overlap.

a) Floor space covered by each box:

To find the floor space covered by each box, we divide the volume of the box by its height. This gives us the area each box covers on the floor.

The floor space of each box can be calculated by dividing its volume by its height.

The volume of each box is given by the expression [tex]x^3 + 10x^2 - 29x + 20[/tex], and its height is x + 5. Therefore, the floor space covered by each box can be represented as:

Floor space of each box = Volume of the box / Height of the box

Floor space of each box = [tex](x^3 + 10x^2 - 29x + 20) / (x + 5)[/tex]

b) Maximum number of boxes Darren can place:

To find the maximum number of boxes Darren can place on the floor, we need to divide the total floor area by the floor space covered by each box.

The maximum number of boxes Darren can place is determined by dividing the total floor area, given by [tex]x^4 + 5x^3 + x^2 - 20x - 14[/tex], by the floor space covered by each box. We already calculated the floor space of each box as [tex](x^3 + 10x^2 - 29x + 20) / (x + 5)[/tex]. Now, we'll perform the division:

Maximum number of boxes = Total floor area / Floor space of each box

Maximum number of boxes = [tex](x^4 + 5x^3 + x^2 - 20x - 14) / ((x^3 + 10x^2 - 29x + 20) / (x + 5))[/tex]

c) Uncovered floor space with maximum number of boxes:

To find the uncovered floor space when Darren places the maximum number of boxes without overlap, we subtract the total floor area covered by the boxes from the total floor area of the storage unit.

The floor space not covered by boxes can be determined by subtracting the total floor area covered by the boxes from the total floor area of the storage unit.

We already know the total floor area of the storage unit is [tex]x^4 + 5x^3 + x^2 - 20x - 14[/tex], and we calculated the floor space covered by each box in part (a). The maximum number of boxes Darren can place was determined in part (b). Now, we'll perform the subtraction:

Uncovered floor space = Total floor area of storage unit - (Floor space of each box × Maximum number of boxes)

Uncovered floor space =[tex]x^4 + 5x^3 + x^2 - 20x - 14 - ((x^3 + 10x^2 - 29x + 20) / (x + 5) * Maximum number of boxes)[/tex]

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Complete Question

Darren is placing shipping boxes in a storage unit with a floor area of

[tex]x^4+5x^3+x^2-20x-14[/tex] square units. Each box has a volume of  [tex]x^3+10x^2-29x+20[/tex].

cubic units and can hold a stack of items with a height of x + 5 units.

a) How much floor space will each box cover?

b) What is the maximum number of boxes Darren can place on the floor of the storage unit?

c) Assume Darren places the maximum number of boxes on the floor of the storage unit, with no overlap. How much of the floor space is not covered by a box?

According to the angle addition postulate, the measure of ∠ABD, that contains BC is 162°.

We have to determine according to the angle addition postulate, the measure of ∠ABD, that contains BC.

Measure of ∠ABC =  120° and measure of ∠CBD = 78°.

As we know that the sum of all angle is 360°.

So; ∠ABC + ∠CBD + ∠ABD = 360°

Now putting the value

120° + 78° + ∠ABD = 360°

Simplify

198° + ∠ABD = 360°

Subtract 198° on both side, we get

∠ABD = 162°

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The diagram of the question is:

The fraction 19/8 on the graph is located between the integers 2 and 3, exactly at the decimal 2.375.

A fraction is converted to decimal applying a proportion, which is the division of the numerator of the fraction by the denominator of the fraction.

The fraction in this problem is given as follows:

19/8.

For which:

Hence the equivalent decimal is given as follows:

19/8 = 16/8 + 3/8 = 2 + 0.375 = 2.375.

Which is between 2 and 3 on the number line.

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The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

If the cost of the favors is:

$13.5 < $14 < $15 < $20

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

All of the party favors cost more than $13.

This means,

Cost = x

x > 13

Now,

If the following are the cost of the favors:

$13.5, $14, $15, and $20

The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

13.5 < 14 < 15 < 20

Thus,

The least expensive will be the lowest cost among the cost greater than $13.

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-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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15 + 6t >= 63

t >= (63 - 15) / 6

t >= 4.5

t >= 5 (since t must be a whole number of minutes)

So the possible numbers of minutes Kaitlin could add water are 5, 6, 7, 8, ... (any whole number greater than or equal to 5). This can be written as t >= 5.

The total payment will be $90 + $15x and the job would have to be 1/15 hour long for the payment to cancel out Wanda's expenditures.

What is Fraction?

Fraction is a mathematical expression that represents a part of a whole. It is written as a ratio of two numbers, where the first number is the numerator and the second number is the denominator. For example, 1/2 is a fraction that represents one-half of a whole.

The total cost of equipment and employee wages for a business is the sum of the cost of the equipment and the cost of the employee's wages, which is calculated by multiplying the employee's hourly wage by the number of hours worked.

To determine how much the job would pay, we need to calculate the total cost of the equipment and the server's wages.

The cost of the equipment is $89 and the server's wage is $16 per hour.

To calculate the total cost of the server's wages, we need to know how long the job is. Let x be the number of hours the server works.

Therefore, the total cost of the server's wages is $16x

The job pays a base of $90 in addition to $15 per hour that the server works. So the total payment is

90 + 15x

To cancel out Wanda's expenditures, The total payment should be equal to the total cost of the equipment and the server's wages. So, we can set up the equation:

$90 + $15x = $89 + $16x

To solve for x, we can subtract $89 from both sides:

$15x = $1

Finally, we can divide both sides by 15

x= 1/15

So, the job would have to be 1/15 hours long for the payment to cancel out Wanda's expenditures.

It should be noted that this answer is not realistic, since time cannot be expressed in fractions of hours. Also, the job payment would be enough to cover the costs but not to generate any profit for Wanda.

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Answer:

y = (-5/6)x - (5/3)

Step-by-step explanation:

The equation of a line in point-slope form is y - y1 = m(x - x1) where (x1,y1) is a point on the line, and m is the slope of the line.

Given that the line passes through the point (6,-8) and has a slope of -5/6, the equation of the line is:

y - (-8) = (-5/6)(x - 6)

y + 8 = (-5/6)x + (-5/6) * 6

y = (-5/6)x - (5/3)

Answer:

(6,-5)

Step-by-step explanation:

(y-y1)=m(x-x1)

(y--8)=-5/6(x-6)

6y=-5x+2

Answer:

B

because if yiy multiple all those you get somewhere around 390 and then you round the number it is 390

The zeros of the function f(x)=x²-8x+15 are x = 3 and x = 5. Option A

From the information given, we have that the quadratic equation is given by the function;

f(x)=x²-8x+15

Using the factorization method, we have to multiply the coefficient of x² by the constant 15

Then move further to find the pair factors of 15 that add up to -8

Substitute the value, we get;

x² - 5x - 3x + 15

Pair the expression

(x² -5x) - (3x + 15)

factorize

x(x -5) - 3(x-5)

Then,

x - 3

x = 3

And

x = 5

Hence, the values are 3 and 5

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a) The graph of the parabola opens downwards.

b) The point for axis of symmetry is x = -3.

c) The points of vertex for the parabola is (-3,-3).

d) There is no x-intercept and only one y-intercept, y = - 7.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

The graph of a parabola is given.

a) The parabola is starting from -∞ and is rising and then it is falling downwards towards the +∞.

Therefore, the parabola opens downwards.

b) The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The parabola is symmetrical about x = -3.

Therefore, the axis of symmetry is x = -3.

c) There is a pivotal point in every parabola. To put it another way, it has a turning point where it either goes from "growing" to "decreasing" or vice versa. The vertex of the parabola is the name given to that pivotal point.

Here, the parabola turns at point (-3,-3).

Therefore, the points of vertex is (-3,-3).

d) The x-intercept is when the graph of parabola crosses the x-axis. In this case the parabola is drawn below the x-axis so there is no x-intercept.

The y-intercept is when the graph of parabola crosses the y-axis. In this case the parabola crosses the y-axis once at y = -7.

Therefore, the y-intercept is y = -7.

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Answer:

-4

Step-by-step explanation:

3x + 9 = 2x + 5

Collect like terms

3x - 2x = 5 - 9

x = -4

Answer: 342.55

Step-by-step explanation:

689.45 - 346.90 = 342.55

or

346.90 + 342.55 = 689.45

Answer:

Stacy needs to sell at least 23 prints in order for her revenue to equal her expenses.

Explanation: To calculate the total expenses, we need to add the fixed cost of equipment ($38) to the variable cost of each print ($2.5). So the total expenses per print is $2.5 + $38 = $40.50. To calculate the number of prints needed to break even, we divide the total expenses by the revenue per print. 40.50 / 12 = 3.375 which is approximately 3.4 and if we round it up to 4 ,then we will get 4*12 = 48 and this is less than the fixed cost of 38. So, we need to increase the number of print to 23 in order to her revenue to equal her expenses.

Step-by-step explanation:

The cc of each that should be mixed are 73.33 and 146.67

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

Using x and y as the variables, we have the following equations:

x + y = 220

0.14x + 0.08y = 220 * 10% = 22

So, we have

x + y = 220

0.14x + 0.08y = 22

Make y the subject

y = 220 - x

So, the second equation becomes

0.14x + 0.08(220 - x) = 22

This gives

0.14x - 0.08x + 17.6 = 22

Evaluate the like terms

0.06x = 4.4

This gives

x = 73.33

Recall that

y = 220 - x

So, we have

y = 220 - 73.33

y = 146.67

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Complete question

A pharmacist needs 220cc of a solution with a 10% concentration of medicine. They have one solution with 14% concentration and another solution with 8% concentration. How many cc of each should be mixed? etup an equation and solve.

Answer:

x=125    y=130

Step-by-step explanation:

I believe if you add 50+75 you get x

50+75=125

And if you subtract 180 from 50 you get y

180-50= 130

The reason being is because the two numbers inside the triangle add up to the number outside of the triangle "x". Then you would subtract 180 from 50 because that is a supplementary angle meaning it adds up to 180 to get the number on the outside of the triangle "y".

Hope this helped!

The equations that have x = -2 as their solution are B and C

How to find the solution x  = - 2

A. 4x=4+2x

4x - 2x = 4

2x = 4

x = 4 / 2

x = 2

B 2(x+5)=x+8

2x + 10 = x + 8

2x - x = 8 - 10

x = -2

C.  5+3x=-1

5 + 1 = - 3x

6 = -3x

x = -2

D 3x-5=1

3x = 5 + 1

3x = 6

x = 2

E  19=2(x-6)+3

19 = 2x - 12 + 3

19 = 2x - 9

19 + 9 = 2x

28 = 2x

x = 28/2

x = 14

The equations where x=-2 is a solution are 5+3x=-1 , 2(x+5)=x+8

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The value of y of the given rhombus is; y = 7

The parallel sides of a rhombus or even parallelogram are always equal to each other and as a result in this case, the parallel sides are equal. Thus;

3y - 12 = 5y - 26

Rearrange to get;

5y - 3y = 26 - 12

2y = 14

y = 14/2

y = 7

Thus;

Length of side of rhombus = 3(7) - 12

= 21 - 12

= 9

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Total cost c as a function of x is $94000 + 11.2x.

A company invests $94,000 for equipment to produce a new product. each unit of the product costs $11.40 and is sold for $17.98.

let x be the number of units produced and sold.

now,

Number of units = x

so,

c(x)= $94000 + 11.2x

Equation

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Function

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

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The proportional relationship is option D. The graph of the relationship is given below.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

A relationship is proportional if y = kx, for some constant k.

Consider the last table.

x −2   1   2   3

y −6   3  6   9

When x = -2, y = -2 × 3 = -6

When x = 1, y = 1 × 3 = 3

When x = 2, y = 2 × 3 = 6

When x = 3, y = 3 × 3 = 9

So this is a proportional relationship with constant of proportionality k = 3.

Hence the table shown in the last option is the proportional relationship.

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The expression for the area of a rectangle is A = L * W, where L is the length and W is the width.

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The point of intersection of the diagonals of the rhombus with vertices is (3, -5)

Function is a type of relation, or rule, that maps one input to specific single output.

When a relation is given in the form of ordered pairs, the first element of each ordered pair is the member of domain set and second element is the member of range set.

Given the rhombus with vertices:

(-1,2), (3,4), (5,8), and (1,6)

The domain is:

{1,3,5,1}

Rhombus is a parallelogram in which diagonals bisect each other, we can see there is repetition in domain i.e. 1 is twice in the set, the given relation is not a function.

Hence, the point of intersection is (3, -5)

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The median of the dataset is 9.

Median is a measure of central tendency that is used to determine the number that is at the center of a dataset. The dataset has to be arranged in either ascending or descending order.

The data set arranged in ascending order : 6, 7, 7, 8, 10, 14, 15, 15

Median = (n + 1) / 2 = (8 + 1) / 2 = 9/2 = 4.5th number = (10 + 8) / 2 = 18/2 = 9

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Answer:2216 feet

Step-by-step explanation:

Badwater Basin is below sea level, so already we know that the 284 should be a negative number since it is below sea level. Mount McKinley is above sea level, so that number stays as a positive number. Now we can put these two number into an equation to solve, which would be 2,500 + (-284).

Note that the parenthesis are only there so you know that the number is negative, you don't need to solve anything.

Since adding a negative to a positive number is the same as subtraction, we can simplify it to look a little less confusing. You only need to solve 2,500 - 284 , which then equals 2216 ft.

Hope this helps you!

Answer:

To solve the equation (4x - 24) + x = 14, we can start by combining like terms on the left side of the equation:

4x - 24 + x = 14

Next we'll add the x terms together and the constants together:

5x - 24 = 14

Then we'll add 24 to both sides to get all the x terms on one side:

5x = 38

Finally we'll divide both sides by 5 to find the value of x:

x = 7.6

So the solution to the equation is x = 7.6

The average rate of change from 2014 to 2017 is 554.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given:

f(x) = 12,000[tex](1.036)^x[/tex]

Year              2008  2011      2014    2017    2020

Population  12,000 13,343 14,836 16,498 18,344

Now, the average rate of change from 2014 to 2017

= f(2017)- f(2014)/(2017- 2014)

=  12,000[tex](1.036)^{2017[/tex] -  12,000[tex](1.036)^{2014[/tex]/3

= 1662/ 3

= 554.

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