**Zeros of a Polynomial**

When a polynomial has a zero at x = a, then its graph 'touches' or 'crosses' the x-axis. If the zero has an even multiplicity (2, 4, 6, etc.), the graph 'bounces' off the x-axis.

We can see the graph crosses the x-axis 4 times and no bouncing occurs, so each zero has a multiplicity of 1.

From left to right, the zeros are:

x = -4 with a multiplicity of 1.

x = -2 with a multiplicity of 1.

x = 1 with a multiplicity of 1.

x = 3 with a multiplicity of 1.

The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function

R(x) = -3x² + 56x

How many hearing aids need to be produced and sold in order to maximize the revenue? (Round to

the nearest whole number.)

The revenue is at a maximum after

- -

The maximum revenue is $

hearing aids are produced and sold.

What is the revenue? (Round answer to the nearest cent.)

The **revenue **is at a** maximum** after **x = 9**

The **maximum** is **$ 261**

**9 hearing aids **are produced and sold.

The **revenue, R(x), **of producing and selling 'x' Awesome Hearing Aids is modeled by the function,

**R(x) = -3x² + 56x**

We need to find the **number of hearing aids** produced and sold in order to maximize the revenue.

We use the differentiation method to find the** maximum** of the function R(x).

Differentiate **R(x)** with respect to x and equate it with 0,

R'(x) = -6x + 56

Then, -6x + 56 = 0

⇒ 6x = 56

⇒ x = 56/6 = 9.33 ≈ 9 [since x is the number of hearing aids]

Now we find the second derivative of R(x) at x = 9.

R''(x) = -6

⇒ R''(9) = -6 < 0

Since R''(9) < 0, the **revenue R(x)** is maximum at x = 9.

So the **maximum revenue** is obtained after **x = 9.**

Therefore **maximum revenue **= R(9) = -3 x 9²+56 x 9 = **$ 261**

**Hearing aids** produced and sold in order to **maximize** the revenue = 9

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b) 150 g of syrup are needed to make 8 flapjacks.

Find the quantity of oats needed to make 16 of these flapjacks.

Based on the fact that 150g of syrup are needed when making 8 **flapjacks**, the **quantity **that is needed to make 16 flapjacks is 300 g.

The quantity of oats needed to make 8 flapjacks is 150 g.

Assuming** direct proportion,** the quantity of oats needed to make 16 **flapjacks **can be found by the formula:

= (Quantity of oats needed for 8 flapjacks x Number of flapjacks to be made) / Number of flapjacks made

Solving for the quantity of **oats** **needed **gives:

= (150 x 16) / 8

= 2,400 / 8

= 2,400 x 1/8

= 300 g

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the equation of a line is y=mx+b. if we know the line passes through (7,8), what does that tell us

The **equation of the line** is given as **y = -2x + 22. **This means that when x is equal to zero, y = 22. M also shows how steep the line is, being the **gradient**.

In order to arrive at a **logical solution**, we must assume the value of the slope as this is not given.

Assuming the slope of the line is -2, we thus can say:

The equation of a line that passes through a point (x₁,y₁) and a slope m is given by

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

Recall that the slope, m = -2

While

Point (x1, y1) = (7, 8)

Hence, the **equation of the line** is:

y-8 = (-2) (x-7)

y-8 = -2x + 14

y = -2x+ 14 + 8

Hence,

y = -2x + 22

Thus, the equation of the line is:**y = -2x + 22**

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A student is purchasing new clothes for the school year. She

can choose any combination of shirts and pants, and she does not

want to spend more than $125. If shirts cost $12.99 each and

pants cost $15.99 each, write an inequality that represents all

possible combinations of x shirts and y pants.

An **inequality** that represents all possible **combinations** of x shirts and y pants is (12.99x + 15.99y) ≤ 125.

Given:

Cost of each shirt = $12.99

Cost of each pant = $15.99

Let's assume the number of shirts is x and the number of pants is y.

Total** cost** of x shirts = $12.99x

Total cost of y pants = $15.99y

Total **cost ** = $(12.99x+15.99y).

Now, she does not want to spend more than $125 which means she can spend equal to or less than 125 dollars.

An inequality that represents all possible **combinations** of x shirts and y pants is,

(12.99x + 15.99y) ≤ 125

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Solve. Todd sold bunches of flowers on a street corner on Friday afternoons. Each bunch sold for $2.75. One Friday he made $71.50. How many bunches of flowers did he sell that day?

**Todd** sold 26 **bunches** of **flowers** on a street **corner** on **Friday** afternoon

The **selling** **price** of each flower bunch = $2.75

**Total** money made by **Todd** on **Friday** = $71.50

**Arithmetic**: The foundational **subject** in mathematics is arithmetic, which covers **operations** with **numbers**. These include **multiplication**, **division**, **addition**, and **subtraction**. One of the **crucial** branches of mathematics, arithmetic serves as the **cornerstone** of the field of **mathematics**.

Finding the **number** of flower **bunches** sold by **Todd**:

**Number** of **bunches** sold by **Todd** = Total **money** made by **Todd**/Selling **price** of each flower **bunch**

= 71.50/2.75

= 26

**Number** of **bunches** sold = 26

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A coin is weighted so that there is a 58% chance that it will come up "heads" when flipped. The coin is flipped four times. Find the probability of getting two "heads" and two "tails". Round your answer to four decimal places.

P(A) =Probability of heads

P(B) = Probability of tails

P(B)= 1 - P(A) = 1 - 58 = 42%

The events are independent, so, let's assume that we flip the coin and the first two results are heads, so:

P(A) =0.58

Now, let's assume the last two results are tails so:

P(B) = 0.42

Therefore:

[tex]\begin{gathered} P(A\cap A\cup B\cap B)=P(A)\cdot P(A)\cdot P(A)+P(B)\cdot P(B) \\ P(A\cap A\cup B\cap B)=0.58\cdot0.58+0.42\cdot0.42=0.3364+0.1764=0.5128 \end{gathered}[/tex]The height of Debbie is 85 centimetres. The height of Leo is 90 centimetres. Write the height of Debbie as a fraction of the height of Leo. Give your answer in its simplest form.

To write the height of **Debbie **as a fraction of the height of **Leo **in its simplest form is this: 17/18.

Writing one figure as a **fraction **of another can be done by representing the figures as numerators and denominators. In this case, what we will have is 85/90. That is the **height **of Debbie divided by the height of Leo.

To express this fraction in its simplest form will mean dividing the figures until they can no longer be divided. Using 5 as a common factor for dividing, we can conclude that the **simplest **form of the **answer **is 17/18.

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Question

Solve: n- 5/11=-1/3

N=?

**Answer: 26/33**

**Step-by-step explanation:**

**Step-by-step explanation:**

app called maple calculator

Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?

CORRECT ANSWERS ONly

**Answer first evening she received 130 second evening she received 520 third evening she received 1300 **

**Step-by-step explanation: that's the right one for shure i worked it out **

Find the greatest common factor of thefollowing monomials:10x^3y^3 32xy^2

The greatest common factor between the monomials can be determined as,

[tex]\text{GCF}(10x^3y^3,32xy^2)=2xy^2[/tex]**Thus, the above expression gives the required greatest common factor.**

nine sales representitives for a company are to br chosen at random to participate in a training program. the company has twelve sales representatives, three in each of four regions. what is the probability that the nine sales representatives chosen to participate in the training program will be from only three of the four regions?

The **probability **is 6/70.

What is **probability ?**

**probability** is concerning about numerical description is how likely is an event is occur or how likely it is true.

Sol-

way will be selecting 84 out of eight since representative so 84 which is equal to at 70. And we need that we since we are things. There are two things representing the regions, so the four selected sales representatives are from only two off the regions. So if we select to sales representative from the two regions while we select de o sales representative from the other two regions, so four is it to selected from the four and to select from the two region and to select from two regions on day zero selected from the two regions and they're selected from the two regions. So is equal to four factorial over two factorial, two factorial times two factorial over to Victoria, zero factorial times too times Sorry, that was two factorial over to factory a factory times two factorial zero factorial two factorial which is equal to six for the

Thus,

**probability ** is 6/70 which is equal toe open toe eight 57.

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The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .

For the **coordinates **and their **weights**, the weight average is 5

The given parameters are:

Coordinate 3 has a weight of 1

Coordinate 6 has a weight of 2

The **weight average **is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

Substitute the known values in the above equation

So, we have the following equation

Weight average = (3 * 1 + 6 * 2)/(1 + 2)

Evaluate the **product **in the above equation

So, we have the following equation

Weight average = (3 + 12)/(1 + 2)

Evaluate the **sum **in the above equation

So, we have the following equation

Weight average = (15)/(3)

Evaluate the **quotient **in the above equation

So, we have the following equation

Weight average = 5

Hence, the **weight average **of the **coordinates **is 5

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**Complete question**

The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .

Find the weighted average.

2x(3x-4)-3x(5x+6)

Can somebody help explain how to get the awnser for this like step by step!

By using **basic algebra** we get x = 0 and x =[tex]\frac{-26}{9}[/tex]

**Algebra** is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like** addition**, **subtraction**,** multiplication**, and **division** are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic equation is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when **operations **such as addition, subtraction, multiplication, division, etc. are done on variables and constants.

2x(3x-4)-3x(5x+6)

[tex]6x^{2} -8 -15x^{2} -18x\\-9x^{2} -26x = 0\\9x^{2} +26x = 0\\x(9x +26)=0\\x = 0\\ x = \frac{-26}{9}[/tex]

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Solve the system[tex]\begin{bmatrix}4x-2y=8\\ 3x+y=2\end{bmatrix}[/tex]

The** value **of** x= 1.2 **and the value of** y = -1.6**

Given two equations

[tex]4x-2y=8[/tex]

[tex]3x+y=2[/tex]

Since there are** two equations** and** two unknowns** we can solve the equations by **arithmetical methods.**

Initially multiply second equation by 2 and add it it to first equation.

[tex]3x+2y=2[/tex] × 2

[tex]6x+2y=4[/tex]

Now **adding** this to equation 1

[tex]4x-2y=8 + 6x+2y=4[/tex]

[tex]10x=12[/tex]

[tex]x=1.2[/tex]

To get y value **substitute **x value in any of the equation

[tex]4(1.2)-2y=8[/tex]

[tex]-2y = 3.2[/tex]

[tex]y = -1.6[/tex]

Therefore** x and y values** are 1.2 and [tex]-1.6[/tex] respectively.

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Find the value of x that makes line u parallel to line v

**Answer:**

**x = 10**

**Step-by-step explanation:**

the angles shown are *corresponding angles*

*corresponding angles are equal*

12x - 4 = 10x + 16

subtract 10x from both sides

2x - 4 = 16

add 4 to both sides

2x = 20

divide both sides by 2

**x = 10**

How many seven-digit numbers are there when 0 and 8 cannot be the leading number?

There are_____such seven-digit numbers.

**Answer:**

With the restrictions that 0 or 8 cannot be the leading digit, the leading digit can be one of [1, 2, 3, 4, 5, 6, 7, 9] = 8 choices.

The other six digits can be one of [1, 2, 3, 4, 5, 6, 7, 8, 9, 0] = 10 choices each.

Therefore, there are:

8*10*10*10*10*10*10 = 8*10^6 = 8,000,000 7-digit numbers under the given restrictions.

**Step-by-step explanation:**

hope this helps

a 4x³ - 6x² + 4 para x = -2, 3 y 1.

3

**For value 4x³- 6x² + 4 is**

**If para x = -2 **

4x³ - 6x² + 4

=4(-2)³ - 6(-2)² + 4

=4(-8) - 6(4) + 4

=-32 - 24 + 4

=**-52**

**If para x = 3**

=4x³ - 6x² + 4

=4(3)³ - 6(3)² + 4

=4(27) - 6(9) + 4

=108 - 54 + 4

=**58**

**If para x = 1**

4x³ - 6x² + 4

=4(1)³ - 6(1)² + 4

=4 - 6 + 4

=**2**

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Point A is at (-1, -9) and point B is at

(2, 4).

What is the midpoint of line segment AB?

-9-8-7 -6 -5 -4 -3 -2

The most appropriate form of** midpoint** of **line segment** will be given by-

Coordinate of **midpoint **of AB = ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])

**What is midpoint of a line segment?**

At first, it is important to know about** section formula**. Let the coordinate of end point of a** line segment** is ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]) respectively. Let another line intersects the line in the ratio m : n. Coordinate of point of intersection =[tex](\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m + n})[/tex].

If m = n =1, we get the coordinate of **midpoint.**

Coordinate of **midpoint** = [tex](\frac{x_1+y_1}{2}, \frac{x_2, y_2}{2})[/tex]

**Midpoint** of a **line segment** is that point which is equidistant from both the end points.

Here,

Coordinate of A = (-1, -9)

Coordinate of B = (2, 4)

Coordinate of **midpoint** of AB = ( [tex]\frac{-1 + 2}{2}, \frac{-9 + 4}{2}[/tex])

= ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])

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Please answer this question, I need help.

**Answer:3 8 10**

**Step-by-step explanation:**

Find the difference.

(-9ab-4a+8) - (-2ab+4)

Enter the correct answer.

**Answer:**

-7ab-4a+4

**Step-by-step explanation:**

simplify the expression

hope this helped

have a great day ^^

Find the recursive formula. 2, 32, 62, 92, ...

**Answer:**

122

**Step-by-step explanation:**

2+30 =32

32+30=62

62+30=92

**Answer:**

Use the formula

**Step-by-step explanation:**

I hope it helps

If 4−5=−12 and y = 3, what is x ?

Substituting y=3 in 4x-5y=-12 we get:

[tex]4x-5\cdot3=-12.[/tex]Simplifying the above equation we get:

[tex]4x-15=-12.[/tex]Adding 15 to the above equation we get:

[tex]\begin{gathered} 4x-15+15=-12+15, \\ 4x=3. \end{gathered}[/tex]Finally, dividing the above equation by 4 we get:

[tex]\begin{gathered} \frac{4x}{4}=\frac{3}{4}, \\ x=\frac{3}{4}\text{.} \end{gathered}[/tex]**Answer:** If 4x-5y=-12 and y=3 then:

What equation would you set up to solve for X?

A-bc^7 is the answer

A company XYZ issued 30 year bonds with 10% annual coupon rate at their par value of $1000 in 2010. The Bonds had a 7% call premium, with 5 years of call protection. Today XYZ called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued in 2010. Briefly explain why the investor should or should not be happy.

1. Tha rate of return is 11.12%

2. The **investor** will not be happy in case the market interest rates fall

n is NPER 5 (called back in 5yrs)

Coupon **payment** / PMT = 1000 * 10% = 100,

Purchase **price** PV (PV is entered as a negative value) -1000

Called for value is **FV** Call premium is 7% hence FV = 107% * 1000 = 1070

You can use the RATE **function** in excel

Rate(nper, PMT, PV,FV, Type)

RATE(5,100,-1000,1070)

= 11.12%

The investor was promised a fixed **return** rate of 10%, but since the bond was called after 5 years, the actual return was 11.12%, so the investor had good reason to be pleased.

In the event that **market interest** rates decline, the investor will not be pleased because, had the **bond** not been called, he would have continued to receive his fixed 10% coupon payments of $100 per year.

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what is -5 x (- 3/9)

Answer:

Step-by-step explanation:

−5(−3/9)

Divide

-5x(-1/3)

Multiply

−5x(−1/3)

x 5/3

combine multiple terms into single fraction

5x/3

What’s the frequency?

The total **frequency **of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.

So, the frequency for 5 classes:

Frequency of 67: 4Frequency of 68: 6Frequency of 69: 4Frequency of 70: 4Frequency of 71: 1The total frequency of these particular 5 classes will be:

4 + 6 + 4 + 4 + 1 = 19Therefore, the total **frequency **of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.

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Please help me out, I need to turn it in in 15 mins

What is their rate of change (speed) in Section D (Hours 7-10)? Remember to include units.

**Step-by-step explanation:**

I assume the hours are also in units of 2.

that means in D the distance is -20 miles in 10 hours or

-20 miles / 10 hours = -2 miles / hour

Find the circumference of a circular swimming pool with a radius of 8.5 yards. Use 3.14 as an approximation for pie. Round your answer to the nearest whole yard. Enter only the number.

**Answer:**

53 yards

**Step-by-step explanation:**

Hello!

The **circumference formula** of a circle is [tex]C = 2\pi r[/tex], where C is the **circumference**, and r is the **radius**.

Given that pi is 3.14, solve for the **circumference.**

The circumference of the circle is 53.38, but **rounded** to the **nearest** **whole** **yard** would be **53 yards**.

Sales of SUVs (sport utility vehicles) in the United States (in millions) for the years 1990-1999 can be modeled by the quadratic equation shown below.y = 0.016x^2 +0.124x +0.787Here x = 0 represents 1990, x = 1 represents 1991, and so on. Use the model to approximate sales in 1995, Sales in 1995 were approximately ____ million SUVs.(Round to the nearest tenth as needed.)

**The sales in 1995 were approximately 1.8 millions.**

**Explanation:**

Since x = 0 is 1995, x = 1 is 1991 and so on, if we want to find the approximate amount of sales, we need to evaluate the expression for x = 5:

[tex]y=0.016x^2+0.124x+0.787[/tex][tex]\begin{gathered} y=0.016\cdot5^2+0.124\cdot5+0.787 \\ y=0.016\cdot25+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=1.807 \end{gathered}[/tex]**To the nearest tenth, the sales of SUV were approximately 1.8 millions**

Is trangle ABC ~ trangle XYZ ? if so , what sequence of transformation maps trangle ABC to XYZ

You have the figurew ABC with the following vertices:

**A(-2,-4)**

**B(0,-1)**

**C(2,-4)**

First, multiply all points by 2 (this is the first transformation)

**A => A'(-4,-8)**

**B => B'(0,-2)**

**C => C'(4,-8)**

Next, translate the previous points 6 units upward (which means add 6 units to each y-coordinate).

**A' => X(-4,-2)**

**B' => Y(0,4)**

**C' => Z(4,-2)**

as you can notice, with the previous transformation you obtain the vertices X, Y, and Z and form the figure XYZ.

**Answer: a dilation by and a translation **

**Step-by-step explanation: just did on edge**

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Write and equation of the line parallel to the given line that contains C C(4,3) ; y=-2x+5
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