Given the hyperbola with the equation (+2)2 (= + 2)² 4 1 1. Find the vertices. List your answers as points in the form (a, b). Answer (separate by commas): 2. Find the foci. List your answers as poin

Answer:

C

Step-by-step explanation:

4x + 3y = 24

3y = -4x + 24

y = -3/4x + 8

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Answer:

Y= -4/3x + 8

Step-by-step explanation:

4x + 3y = 24

-4x             -4x

3y = -4x + 24

/3      /3     /3

Y = -4/3x + 8

The coordinates of the epicenter  the coordinates of the epicenter are approximately (7.6786, -12.85714).

To find the coordinates of the epicenter of the earthquake, we can use the concept of trilateration, which involves solving a system of equations. The coordinates of the epicenter (let's call them (x, y)) will be the point equidistant from all three receiving stations.

Let's set up the equations based on the given information:

For the first receiving station (8, 11):

Distance from the epicenter = 2 units

Using the distance formula, we have:

√(\((x - 8)^2 + (y - 11)^2) = 2\)

For the second receiving station (4, 6):

Distance from the epicenter = 5 units

√((x - 4)^2 + (y - 6)^2) = 5

For the third receiving station (12, 9):

Distance from the epicenter = 4 units

√((x - 12)^2 + (y - 9)^2) = 4

Now, we need to solve this system of equations to find the values of x and y, which will give us the coordinates of the epicenter.

Let's square both sides of each equation to remove the square roots:

(x - 8)^2 + (y - 11)^2 = 4

(x - 4)^2 + (y - 6)^2 = 25

(x - 12)^2 + (y - 9)^2 = 16

Now we have a system of three equations:

\(x^2 - 16x + 64 + y^2 - 22y + 121 = 4\)

\(x^2 - 8x + 16 + y^2 - 12y + 36 = 25\)

\(x^2 - 24x + 144 + y^2 - 18y + 81 = 16\)

Simplify each equation:

x^2 + y^2 - 16x - 22y + 181 = 4

x^2 + y^2 - 8x - 12y + 52 = 25

x^2 + y^2 - 24x - 18y + 225 = 16

Now, rearrange the equations to form a system of linear equations:

x^2 + y^2 - 16x - 22y = -177

x^2 + y^2 - 8x - 12y = 27

x^2 + y^2 - 24x - 18y = 209

Subtract equation 2 from equation 1 to eliminate the x^2 and y^2 terms:

-16x - 10y = -204

Subtract equation 2 from equation 3 to eliminate the x^2 and y^2 terms:

-16x - 6y = 182

Now, subtract the two newly formed equations to eliminate the x term:

-4y = -386

Divide by -4:

y = 386 / 4

y = 96.5

Now, substitute the value of y back into any of the equations (let's use equation 2):

x^2 + y^2 - 8x - 12y = 27

x^2 + (96.5)^2 - 8x - 12(96.5) = 27

x^2 + 9322.25 - 8x - 1158 = 27

x^2 - 8x + 9322.25 - 1158 = 27

x^2 - 8x + 8164.25 = 27

Rearrange the equation:

x^2 - 8x + 8137.25 = 0

Now, we can solve this quadratic equation. Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = -8, and c = 8137.25

x = (-(-8) ± √((-8)^2 - 4(1)(8137.25))) / (2(1))

x = (8 ± √(64 - 32549)) / 2

x = (8 ± √(-32485)) / 2

Substituting the value of x into equation (4), we can solve for y:

-8(7.6786) + 10y = -190

-61.4286 + 10y = -190

10y = -190 + 61.4286

10y = -128.5714

y = -12.85714

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The ƒ(x)−g(x) is equal to x³ - x² - 2 option (A) x³ - x² - 2 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

ƒ(x) = x³ − 4x + 2

g(x) = (x−2)²

= ƒ(x) - g(x)

= (x³ − 4x + 2) - (x−2)²

= (x³ − 4x + 2) - (x² - 4x + 4)

= x³ − 4x + 2 - x² + 4x - 4

= x³ - x² - 2

Thus, the ƒ(x)−g(x) is equal to x³ - x² - 2 option (A) x³ - x² - 2 is correct.

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a) The volume of the composite figure is represented by the cubic equation V = x³ + 16 · x.

b) The measure of the missing side x in the composite figure is 3 inches.

a) In the first part of the question we need to derive the volume formula of the composite figure, which is the sum of the volumes of the cube and the rectangular prism:

V = V' + V''

V = x³ + 16 · x, where x is in inches.

The volume is represented by V = x³ + 16 · x.

b) If we know that V = 25 · x, then the measure of the missing side is:

First, set the volume formula found in section a):

V = x³ + 16 · x

Second, replace the volume:

25 · x = x³ + 16 · x

Third, simplify the expression and clear x within the resulting equation by algebra properties:

25 = x² + 16

x² - 9 = 0

x² = 9

x = 3

The measure of the missing side x is 3 inches.

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The image shows the square root of 41

The root of 41 in decimal is 6.403.

As such the integers before and after 6.403 are 6 and 7

Another way to solve this is to consider the perfect square before 41 which is 36.

The square root of 36 is 6. Since 41 is higher than 36, the number before root 41 would be 6 and the next number after 6 is 7.

Hence the two numbers before and after √41 are 6 and 7

If the absolute value of your calculated t-statistic exceeds the critical value from the appropriate t-distribution, you can reject the null hypothesis.

In regression analysis, the t-statistic is used to test the significance of the regression coefficients. It measures how many standard errors the estimated coefficient is away from zero. To determine whether the coefficient is statistically significant, we compare the absolute value of the calculated t-statistic to the critical value from the t-distribution.

The critical value is based on the desired level of significance (usually denoted as alpha) and the degrees of freedom in the regression model. If the absolute value of the calculated t-statistic is greater than the critical value, it indicates that the coefficient is statistically significant at the chosen level of significance. This means that the coefficient is unlikely to be zero, and we can reject the null hypothesis that the coefficient is not significantly different from zero.

On the other hand, if the absolute value of the calculated t-statistic is less than the critical value, it suggests that the coefficient is not statistically significant, and we fail to reject the null hypothesis. This means that the coefficient may be zero or not significantly different from zero.

When the absolute value of the calculated t-statistic exceeds the critical value from the appropriate t-distribution, it indicates that the regression coefficient is statistically significant. This allows us to reject the null hypothesis and conclude that there is a significant relationship between the independent variable and the dependent variable.

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In the box plot, most of the data is clustered around 75 - 78 (option A).

A box plot is used to study the distribution and level of a set of numbers. The box plot has two whiskers and a box. The two whiskers represent the minimum value and the maximum value.

The first line on the box is the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile. Majority of the data would lie between the first quartile and the third quartile.

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There are 35 possible designs for the printed circuit board with four different components placed on it, assuming each of the seven locations can hold only one component.

To calculate the number of possible designs for the printed circuit board with seven locations for component placement, we can use the combination formula.

The number of combinations of r items from a set of n items is given by the formula:

nCr = n!/r!(n-r)!

In this case, we want to find the number of combinations of four components from seven locations. Thus, we can calculate it as follows:

7C4 = 7!/4!(7-4)! = (7x6x5)/(3x2x1) = 35

Therefore, there are 35 possible designs for the printed circuit board with four different components placed on it, assuming each of the seven locations can hold only one component.

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After solving this equation we get x = 1 and y = 30.

An equation is a mathematical statement that describes the relationship between two or more variables. It is a statement that states the equality of two expressions. Equations can be used to describe anything from the motion of a pendulum to the growth of a population. They are used in all areas of mathematics, physics, and other sciences. Equations are written using symbols, such as = (equal to), > (greater than), and < (less than).

To solve this systems of equations, we need to use algebraic techniques. First, we need to rewrite the equations so they are in the same form. To do this, we will subtract x from both sides of the second equation, giving us:

y = x + 30

-x

y = 30

Now, we will subtract 30 from both sides of the equation, giving us:

y = 4x + 9

-30

y = 4x - 21

Now we will subtract 4x from both sides of the equation, giving us:

y = 4x - 21

-4x

y = -21

Finally, we will divide both sides by -21, giving us:

y = -21

-21

y = 1

This means that the solution to our system of equations is x = 1, y = 30.

To show our algebraic work on paper, we can rewrite the equations and perform each step as a mathematical operation:

y = 4x + 9

y = x + 30

y = x + 30 - x

y = 30

y = 4x + 9 - 30

y = 4x - 21

y = 4x - 21 - 4x

y = -21

y = -21 ÷ -21

y = 1

Therefore, x = 1 and y = 30.

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The following form: ∂t∂T​=α∂x2∂2T​, where α=rhocp​k​ is the thermal diffusivity.

The energy equation in conservative form is given by;∂t∂ρE​+∇⋅(ρHu)=∇⋅(τ⋅u)+∇⋅(k∇T)+rhof⋅u    (1)where E is the total energy per unit volume, H is the momentum per unit volume, τ is the stress tensor, k is the thermal conductivity, and f is the body force per unit volume.

Let us consider a 1D (one-dimensional) problem in the x-direction such that all the variables are a function of x and time t. Further, let us assume that the flow is steady and that there are no heat sources present.

Consequently, the above equation reduces to:∂(ρE)∂t+∂(ρHu)∂x=∂(k∂T∂x)∂x   (2).

From the above equation, we have; ∂(ρE)∂t=ρ∂(uE)∂x, and ∂(ρHu)∂x=H∂ρ∂x+ρ∂H∂x = H∂ρ∂x+ρu∂u∂x. Substituting these into Equation (2) above yields; ρ∂(uE)∂t+H∂ρ∂x+ρu∂u∂x=∂(k∂T∂x)∂x.

Multiplying through by ∂x/ρ and simplifying yields the following form: ∂t∂T​=α∂x2∂2T​, where α=rhocp​k​ is the thermal diffusivity.

The assumption made above is that the flow is steady and that there are no heat sources present.

Moreover, the assumption of 1D means that all the variables are functions of x and time t. Also, the flow is assumed to be incompressible and isothermal in the x-direction.

Therefore, we can conclude that the one-dimensional heat conduction equation is given by the above main answer.

It is also shown that the derivation of this equation requires several assumptions, including a steady flow and no heat sources present.

Moreover, it is also assumed that the flow is incompressible and isothermal in the x-direction.

The final equation is in the form of a diffusion equation, where the thermal diffusivity α is defined as α=rhocp​k​. This equation can be used to solve for the temperature distribution in one dimension under certain boundary conditions.

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The relative frequency of class D is 0.35.

The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments.

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.

Consider the given partial relative frequency distribution.

  Class            Relative frequency

    A                         0.22

    B                         0.18

    C                         0.43

    D                            

Then,

We need to find the relative frequency of class D

We know that,

Sum of relative frequency is equal to one.

that is.

\($0.22+0.18+0.25+$\) relative frequency of class D=1

0.65 + relative frequency of class \($\mathrm{D}=1$\)

relative frequency of class D=1-0.65

=0.35

We get,

Relative frequency of class D Is 0.35

Therefore, the relative frequency of class D is 0.35

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Let u=x-4 ⇒ du=dx Putting x=u+4$ in the integral,

\(\int\limits^5_1 {(x-4)^{\frac{3}{2} } } \, dx\)  =     \(\int\limits^1_{-3} {u}^{\frac{3}{2} } \, du\)

We integrate using the power rule of integration and  get ;

\(\int\limits^1_{-3} {u}^{\frac{3}{2} } \, du\)    =   \([\frac{2}{5}u^{\frac{5}{2}}]\limits^1_{-3}\)    = \(\frac{2}{5}(1^{\frac{5}{2} }-(-3)^{\frac{5}{2} } )\)   = \(\frac{40}{5}\)    = 8

Since this integral exists, and it is finite, the integral is convergent.

We are given

\(\int\limits^5_1 {(x-4)^{\frac{3}{2} } } \, dx\)

We note that this integral is improper at x= ∞ but not at x=-∞; so we only need to check whether this integral exists or not.Using u-substitution,

we let u=x-4 ⇒ du=dx.

Then, putting x=u+4 in the integral, we get

\(\int\limits^1_5 {(x-4)}x^{\frac{3}{2} } \, dx\)   =   \(\int_{-3}^{1}ux^{\frac{3}{2} }\, du\)  

We can then use the power rule of integration to solve the integral as follows:

\(\int_{-3}^{1}u^{\frac{3}{2} }\, du\)  =  \(\left[\frac25u^{\frac52}\right] _{-3}^1\) =  \(\frac25(1^{\frac52}-(-3)^{\frac52})\)   =   \(\frac{40}{5}\) =  8

Since this integral exists, and it is finite, the integral is convergent. Therefore, the given integral converges.Therefore, the given integral

\(\int_1^5(x-4)^{\frac32}dx\)   is convergent.

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Answer:

Hope this helps!!

Step-by-step explanation:

5x - (6 - x) (distribute the - to 6 and -x)

5x - 6 + x (collect like terms 5x + x)

6x - 6

6x - 6 = 0 (add 6 on both sides)

6x = 6 (divide by 6)

x = 1

I would put all this down for the problem.

Answer:

A) 2π

B) 1π

Step-by-step explanation:

circumference of circle= d×π

circumference=2×π=2π or 6.28 rounded to 2dp

area of circle= r^2×π

radius=2÷2=1

radius=1^2×π

radius=1π or 3.14 rounded to 2dp

A) The circumference of a circle can be found by multiplying its diameter by pi (π). Therefore, the circumference of the roundabout is:

Circumference = 2 x π x radius

Radius = diameter/2 = 2/2 = 1 meter

Circumference = 2 x π x 1 = 2π meters

B) The area of a circle can be found by multiplying its radius squared by pi (π). Therefore, the area of the roundabout is:

Area = π x radius^2

Area = π x 1^2 = π square meters or approximately 3.14 square meters.

The dot product of vectors x and y with magnitudes 5 and 4 units, respectively, is 20 units, indicating that they are parallel to each other and in the same direction.

From the given information, we know that the magnitudes of vectors x and y are 5 and 4 units, respectively, and their dot product is 20 units.

To find the angle between vectors x and y, we can use the formula:

cos(theta) = (x.y) / (|x| * |y|)

Substituting the given values, we get:

cos(theta) = 20 / (5 * 4)
cos(theta) = 1

This implies that the angle between vectors x and y is 0 degrees, which means that they are parallel to each other.

Thus, we can conclude that vectors x and y are parallel and in the same direction.



Given the magnitudes of vectors x and y and their dot product, we can determine their relationship and direction. The dot product is the product of their magnitudes and the cosine of the angle between them. Using this formula, we found that the angle between vectors x and y is 0 degrees, indicating that they are parallel to each other. Therefore, we can conclude that vectors x and y are parallel and in the same direction. This information can be useful in various mathematical and physical applications, such as determining the force required to move an object in a particular direction.



In conclusion, the dot product of vectors x and y with magnitudes 5 and 4 units, respectively, is 20 units, indicating that they are parallel to each other and in the same direction. This information can be useful in various mathematical and physical applications.

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Answer:

√20

Step-by-step explanation:

hit the ground means h = 0

0 = 320 - 16t²

16t² = 320

t² = 320/16 = 20

t = √20

It will take √20 the object hit the ground.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

given:

A scientist dropped an object from height of 320 feet.

The height of the object is modeled by the equation

h(t) =320 - 16t²

When the object hit the ground means, h = 0

So, h = 320 - 16t²

16t² = 320

t² = 320/16 = 20

t = √20

Hence, it will take √20 the object hit the ground.

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Answer:

Option 1

Step-by-step explanation:

Option 1 is the correct answer, because a linear function goes up on the x and y axes by the same amount. In this case, the x-coordinates increase by 1, and the y-coordinates increase by 4.

The table that represents a linear function is (a)

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

The table of values

By definition;

A linear function is a function that has a constant rate of change

From the options, we have

(a) as x increase by 1, y constantly increase by 4

This means that table (a) is a linear function

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We want to design a math problem, where we calculate a volume and the answer is 24.

So, we will try first to imagine a figure with an easy shape, so we can calculate its volume. Take for example a box

This box has dimensions length l, width w and height h. A box with this dimensions would have a volume of

Lets say that we want the volume to be 24. So we have the equation

Now, we want to choose numbers to each variable. Lets say what l=4, w=3. So we would have

Then, by dividing both sides by 12 we get

So we know that a box with a length of 4, width of 3 and a height of 2 has a volume of 24. So the problem could be

what is the volume of a box of length 4, width 3 and height 2?

The expression equivalent to t is:t = (3p * y)/(2x)

To find the expression equivalent to t, we can manipulate the given equation:

(x)/(y) = (3p)/(2t)

Cross-multiplying, we get:

2t * (x) = (3p) * (y)

Dividing both sides by 2(x), we have:

t = (3p * y)/(2x)

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Step-by-step explanation:

a. 12 + 4 = 16

1st left equation is matched to 4th right value

b. 3(4) + 7 = 19

2nd left equation is correctly matched to 2nd right value

c. 4(7) - 10 = 18

3rd left equation is matched to 1st right value

d. 1 / 2 × xy

1 / 2 × (4 × 7)

= 28 ÷ 2

= 14

4th left equation is matched to 3rd right value

The correct matches are: 12+x = 16, 3x+y = 19, 4y-10 = 18 and 1/2xy = 14.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given are some expressions 12+x, 3x+y, 4y-10 and xy/2 and x = 4 and y = 7,

Putting value x and y in each, we get,

1) 12+x = 12+4 = 16

12+x = 16

2) 3x+y = 3x4+7 = 12+7 = 19

3x+y = 19

3) 4y -10 = 4x7 -10 = 28-10 = 18

4y-10 = 18

4) 1/2xy = 4x7/2 = 28/2 = 14

Hence, The correct matches are: 12+x = 16, 3x+y = 19, 4y-10 = 18 and 1/2xy = 14.

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Answer: The pattern grows by adding the consecutive counting numbers starting from 1.

For example:

Step 1: 1 square

Step 2: 1 + 2 = 3 squares

Step 3: 1 + 2 + 3 = 6 squares

Step 4: 1 + 2 + 3 + 4 = 10 squares

So at each step, the number of squares increases by adding the next consecutive counting number.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The reason the percents are not the same is probably because you are finding percentage diffrences from diffrent numbers.

Answer:

A,C, and E

Step-by-step explanation:

I took the test

x and y are both differentiable functions of t and find the required values of  \(dy/dt\)  and Given that \(x2+y2=100\) and that \(dx/dt = 4\)  and \(dy/dt = -2\), So the required values of \(dy/dt\) and \(dx/dt.\) are y = 8 and x = 8.

We can explain that x and y are both differentiable functions of t is,

a) To find \(dy/dt\)when x=6 and y=8, we first solve the equation for y:

         \(y2 = 100-x2\)

           \(y2 = 100-62\)

            \(y2 = 100-36\)

              y = √(100-36)

              y = √64

              y = 8

           Therefore, \(dy/dt = 4.\)

Now, for,

b) To find \(dx/dt\) when x=8 and y=6, we again solve the equation for x:

           \(x2 = 100-y2\)

         \(x2 = 100-62\)

        \(x2 = 100-36\)

          x = √(100-36)

           x = √64

           x = 8

      Therefore, \(dx/dt=-2.\)

the required values of \(dy/dt\) and \(dx/dt\). with given conditions are y = 8 and x = 8.

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Answer:

See below

Step-by-step explanation:

A) In part 1, the bus is increasing in speed. In part 2, the bus keeps a steady pace. In part 3, the bus is slowing down. In part 4, the bus is once again keeping a steady pace. In part 5, the bus is increasing in speed once again.

B) Parts 1 and 5 are increasing, part 3 is decreasing, and parts 2 and 4 are constant.

C) This graph is non-linear. Linear means straight, and this graph is constantly increasing and decreasing. Thus, it is non-linear.

In the first segment, the bus picks up pace. The bus maintains its constant speed in segment 2. The bus is slowing down in part three. Part 4 finds the bus moving steadily once more. Part 5 sees the bus picking up pace once more.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

A) In part 1, the bus is increasing in speed. In part 2, the bus keeps a steady pace. In part 3, the bus is slowing down. In part 4, the bus is once again keeping a steady pace. In part 5, the bus is increasing in speed once again.

B) Parts 1 and 5 are increasing, part 3 is decreasing, and parts 2 and 4 are constant.

C) This graph is non-linear. Linear means straight, and this graph is constantly increasing and decreasing. Thus, it is non-linear.

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Answer:

153

Step-by-step explanation:

x+27=180

x=180-27

x=153

The screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.

What is the area of a rectangle?

If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be calculated as

                  Area = Length * Breadth

The length of the screen is 11 in. and the breadth of the screen is 7 in.

Then the area of the screen,

            Area = length * breadth

                     =  11 * 7

                     = 77 square inches.

Hence, the screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.

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Answer:

$70

Step-by-step explanation:

$3500*(2%/100%) = $70

It pretty simple just take 2% and times it by the principle if it's only for one year.

The number of lines in the long-form truth table for a formula consisting of 6 variables can be determined by considering the total number of possible combinations of truth values for those variables.

Since each variable can take on two truth values (either true or false), we have 2^6 = 64 possible combinations.

Therefore, the long-form truth table for a formula with 6 variables would have 64 lines, representing each unique combination of truth values for the variables.

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Answer:

12.3 cm and 19.3 cm

Answer:

Here's what I get  

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)  

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

\(y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}\)

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: \(a(x^{3} + 10x^{2} -275x-1500)\)

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 =\([(0)x^{3} +10(0)x^{2} -275(0)-1500]\) and this gives us (0+0-0-1500) which also equals -1500

Then we do \(\frac{1}{-1500}\) which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)  

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007