2x3−10x+2/x−4

Using **synthetic division**, the solution to the polynomial fraction expression is; 2x² - 10 + 12/(x - 4)

We are given the **polynomial fraction** as;

(2x³ - 10x + 2)/(x- 4)

This means that we want to divide the polynomial (2x³ - 10x + 2) by (x - 4) using **synthetic division.**

For the divisor, we have x - 4, and that means x - 4 = 0, x = 4

So, we'll be using 4 for the** synthetic division** and we have;

-1 | 2 0 -10 2

× 0 0 10

-------------------------

2 0 -10 12

Now we will form the expression in the form of fraction again;

2x² - 10 + (12/(x - 4))

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I need help on these questions

Question 16

[tex](f(x), g(x))=x^2, (x-9)[/tex]

Note it wants the pair, so you just include the definitions of the functions, not f(x)= and g(x)=Question 17

[tex](f(x), g(x))=\sqrt{x}, 9+\sqrt{x}[/tex]

The **values** for first question are f(x) = x², g(x) = (x - 9) and for **second** question f(x) = √x, g(x) = 9 + √x.

A **function** may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called **independent** variable and output variable is called **dependent** variable. A **composite function** is the one which is written as a **combination** of two function. For two given functions f(x) and g(x) the composite functions are f(g(x)) and g(f(x)). In the first question the composite function is F(x) = (x - 9)². the **parent functions** will be f(x) = x² and g(x) = (x - 9).

in the second question the **composite function** is H(x) = √(9 + √x). The parent functions will be f(x) = √x and g(x) = 9 + √x.

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cost equationcost of producing 7 unitswhat is the break point

**Answer: **

**Part A: C(x) = 0.068x+0.8**

**Part B: 1.28**

**Part C: 9.76**

**Explanation: **

**Part A:**

The cost C equals

cost = revenue - profit

[tex]C(x)=R(x)-P(x)[/tex]which is

[tex]C(x)=0.15x-(0.082x-0.8)[/tex][tex]C(x)=0.15x-0.082x+0.8[/tex][tex]\boxed{C\mleft(x\mright)=0.068x+0.8}[/tex]**Part B:**

**The cost of producing 7 units is found by putting in x = 7 into the above equation. This gives **

**Hence, the cost of producing 7 items is 1,28 million dollars.**

**Part C: **

**To break even, the cost must equal the revenue**

or

[tex]0.15x=0.068x+0.8[/tex]subtracting 0.068 from both sides gives

[tex]0.082x=0.8[/tex]dividing both sides by 0.082 gives

[tex]\boxed{x=9.76}[/tex]which is the break-even point

What is an equation of the line that passes through the point (8,0)(8,0) and is parallel to the line x-4y=20x−4y=20?

The** equation of the line** that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

Given,

The equation of the line: x - 4y = 20

The points which the line passes through, (x₁, y₁) = (8, 0)

We have to find the equation of the line parallel to the given line.

The formula for the **slope intercept form**:

(y - y₁) = m(x - x₁)

m is the slope of the line.

Lets find the slope of the line given.

x - 4y = 20

x = 20 + 4y

x - 20 = 4y

y = (x - 20) / 4

y = 1/4x - 5

Here, slope of the line is 1/4

Now, substitute the slope of the line and (x₁, y₁) in the slope intercept formula to get the equation of line** parallel **to the given line

(y - y₁) = m(x - x₁)

(y - 0) = 1/4(x - 8)

y = 1/4x - 8/4

y = 1/4x - 2

1/4x - y = 2

Therefore,

The **equation of the line **that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

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6. Suppose the class takes a test and the following averages are obtained: mean = 80, median= 90, and mode = 70. Tom, who scored 80, would like to know if he did better than half the class. What is your response?

We know that the mean is 80, the median is 90, and the mode is 70. This means that the majority of students got an 80 on the test.

However, the median is 90, which means half of the class is below 90 where Tom's grade is placed.

Hence, he did not do better than half of the class.Miss sheet,owner of the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40percent markup on selling price what is most that Misu can pay for a comforter?

The **price** that Misu can pay for a comforter based on the markup **percentage** is $103.57.

From the information, the **Bedspread** shop knows his customers will pay no more than $145 for a comforter Misu wants a 40** ****percent** markup on selling price.

Let the selling **price** be represented as x. Based on the information given, this will be illustrated as:

x + (40% × x) = 145

x + 0.4x = 145

1.4x = 145

**Divide**

x = 145/1.4.

x = 103.57

The selling **price** will be $103.57.

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help meeeeeeeeeeeeeeeeeeeeeeee pleaseeeeee

**Answer:**

**it would be 600**

The table shows the number of restaurants in five different cities Cities numbers of restaurants Carlsbad 489 potters vale 261 little hath 282 edgbaston 216 barrow 317 how many more restaurants are there in Carlsbad than in barrow?

To answer this question, we will use the next table (obtained from the Question Tab):

**City -------- Number of restaurants **

Carlsbad 489

Potter Valley 261

Little Heath 282

Edgbaston 216

Barrow 317

If we want to know how many more restaurants there are in Carlsbad than in Barrow, we need to subtract the number of restaurants in Barrow from Carlsbad as follows:

[tex]489-317=172[/tex]*From the table, we have that in Carlsbad there are 489 restaurants, while there are 317 in Barrow*.

We can check this as follows:

**In summary, we can say that there are ****172**** more restaurants in Carlsbad than in Barrow.**

The elephants at the zoo eat 3 1/6 buckets of bananas each day. The zookeeper bought 6 1/3 buckets of bananas. How many days will the bananas last?

Write your answer as a fraction or as a whole or mixed number.

The bananas will last 2 days at the zoo (found by **division**).

According to the question,

We have the following information:

The elephants at the zoo eat [tex]3\frac{1}{6}[/tex] buckets of bananas each day. The zookeeper bought [tex]6\frac{1}{3}[/tex] **buckets** of bananas.

Now, first we will find the number of days taken in eating 1 bucket of bananas.

[tex]3\frac{1}{6}[/tex] buckets = 1 day

Now, we will convert this** mixed fraction** into simple fraction.

19/6 buckets = 1 day

1 bucket = 1/(19/6) days

1 bucket = 6/19 days

Now, we have the total **number **of buckets as [tex]6\frac{1}{3}[/tex].

Now, after converting this mixed fraction, we have:

19/3 buckets

1 bucket = 6/19 days

19/3 buckets = (6/19)*(19/3)

19/3 buckets = 2 days

2 is a** whole number.**

Hence, the given buckets of bananas will last 2 days.

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Construct a triangle with the given measures. Label all sides and angle measurements. 1. 4 cm, 6cm

Answer: **angle = 33.7° ; angle =56.3 ° ;side AC = 7.2cm.**

Given the two sides measurement,

• Assuming that the other side represent x and the other side represent y,( 4cm;6cm) , and that we are drawing a right angle triangle .We can constuct a triangle as follows :

• We can find the value of side h by using Pythagorean theorem:

[tex]\begin{gathered} \text{ h = }\sqrt[]{x^2+y^2}\text{ } \\ \text{where x = 4}cm\text{ and y = 6}cm\text{ , } \\ \therefore\text{ h = }\sqrt[]{4^2+6^2} \\ \text{ = 7.2 }cm \end{gathered}[/tex]• Subsequently, we will find angle angle , as shown in the diagram above as follows:

[tex]\begin{gathered} \text{For angle }\beta \\ Tan\text{ }\beta\text{ = opposite /adjacent } \\ \text{Tan }\beta\text{ = }\frac{AB}{BC\text{ }} \\ Tan\text{ }\beta\text{ = }\frac{6}{4} \\ \beta\text{ = }\tan ^{-1}(\frac{6}{4}) \\ \text{ =56.3}\degree \end{gathered}[/tex]• Since we have angle ,= 56.3 °, ,we can find, angle :

,• + + 90° = 180 °,....(angles in a triangle adds up to 180°)

∴ = 180° -90° -56.3°

** =33.7°**

a line contains the point ( -3, -1 ) and has a slope of 1/3. which equation represents this line?

**Given:**

Slope = 1/3

Contain the point = ( -3,-1 )

**Find-:**

The equation of a line.

**Explanation-:**

The general equation of a line is:

[tex]y=mx+c[/tex]Where,

[tex]\begin{gathered} m=\text{ Slope} \\ \\ c=\text{ y-intercept} \end{gathered}[/tex]Given the slope is 1/3, then the equation of the line become.

[tex]\begin{gathered} m=\frac{1}{3} \\ \\ y=mx+c \\ \\ y=\frac{1}{3}x+c \end{gathered}[/tex]The value of y-intercept is:

The point (-3,-1) contains the line so its satisfied the equation.

[tex]\begin{gathered} (x,y)=(-3,-1) \\ \\ \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{3}x+c \\ \\ -1=\frac{1}{3}(-3)+c \\ \\ -1=-1+c \\ \\ c=-1+1 \\ \\ c=0 \end{gathered}[/tex]So equation of line become:

[tex]\begin{gathered} y=mx+c \\ \\ y=\frac{1}{3}x+0 \\ \\ y=\frac{1}{3}x \\ \\ 3y=x \\ \\ x-3y=0 \end{gathered}[/tex]The final equation of line is:

[tex]x-3y=0[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

What is the correct formula for the volume of a cone? Is the correct answer option A B or C?

The formula for the volume of a cone is a third of the product of pi, its height h and the square of its radius r. Then, it is:

[tex]\frac{1}{3}\pi r^2h[/tex]Answer: C

the sum of two consecutive natural number is 36 find the number

The correct answer is 18 because we need to divide 36 by 2 and it comes 18.

So, simply if we add 18 to itself comes 36.

So, simply if we add 18 to itself comes 36.

How many inches are in 4 feet 6 inches?

6 inches

54 inches

46 inches

48 inches

**Answer:**

54 inches

**Step-by-step explanation:**

There are 12 inches in 1 foot

12in = 1ft

There are 4 feet and 6 inches

If you break it down its 4×12

4 × 12 = 48

Add 6 inches

48 + 6 = 54

Therefore the answer would be 54 inches

Your welcome <3

3.Justify each step of the solution by stating the name of the property that was used to get to each step.Given: Step 1: 1.________________________________Step 2: 2. _______________________________Step 3: 17x = 403. _______________________________Step 4: 4. _______________________________Answer:

We are given the following equation:

[tex]2(10-13x)+9x=-34x+60[/tex]In the first step we will use the distributive property on the left side:

[tex]20-26x+9x=-34x+60[/tex]In step 2, we will add like terms on the left side using associative properties of addition and subtraction and we will subtract 20 from both sides, we get:

[tex](20-20)+(-26x+9x)=-34x+(60-20)[/tex]Solving the operations we get:

[tex]-17x=-34x+40[/tex]In step 3 we will add 34x to both sides, this is the inverse additive inverse:

[tex](-17x+34x)=(-34x+34x)+40[/tex]Solving the operations:

[tex]17x=40[/tex]In step 4, we divide both sides by 17, this is the division property of equality:

[tex](\frac{17x}{17})=\frac{40}{17}[/tex]Solving the operations:

[tex]x=\frac{40}{17}[/tex]El área de un sector circular de un círculo con radio igual a 8cm y ángulo central igual a 56° es aproximadamente

The sectorial **area** of the circle is equal 31.3cm^2

The formula for the b of the **sector** of a circle is /360o (r2) where r is the radius of the circle and is the angle of the sector.

Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the sector angle subtended by the arc at the center, in degrees, and 'r' is the radius of the circle.

Data;

Radius - 8cmangle = 56 degreesThe area of the sector can be calculated using the formula given

[tex]A = \frac{\theta }{360} * \pi r^2[/tex]

Substituting the values into the formula;

[tex]A = \frac{\theta }{360} * \pi r^2\\A = \frac{56}{360}* \pi * 8^2\\A = 31.27cm\\A = 31.3cm^2[/tex]

The area is equal 31.3cm^2

Translation:

The area of a circular sector of a circle with radius equal to 8cm and central angle equal to 56 degrees.

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Solve the following linear equation using equivalent equations to isolate the variable. Express your answer as an integer, as a simplified fraction, or as a decimal number rounded to two places.

**ANSWER**

**EXPLANATION**

We want to solve the given linear equation:

[tex]-6u=\frac{-6}{5}[/tex]To do this, divide both sides of the equation by -6 to isolate u and simplify:

[tex]\begin{gathered} \frac{-6u}{-6}=\frac{-6}{5}\cdot\frac{1}{-6} \\ \Rightarrow u=\frac{1}{5} \end{gathered}[/tex]That is the solution to the linear equation.

Select the correct answer.

What is the product of (7) (-16)(-7) (-1)?

A.

B.

-7

9

B. -16

C. -

D. 192

The product of (7) (-16)(-7) (-1) is - 784 by using simple **multiplication**.

Finding the **product** of two or more numbers in **mathematics** is done by multiplying the numbers. It is one of the **fundamental operations** in mathematics that we perform on a daily basis. The symbols for multiplication are a cross (x), an asterisk (*), and **dot** (.). You seem to utilize the cross a lot when you write in your notebooks. In both **algebra** and computer languages, the asterisk and dot are symbols (higher mathematics).

7 × -16 = -112

-112 × -7 = 784

784 × -1 = -784

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72.7% to nearest 10th percent

**Answer:**

72.7% to nearest 10th percent would be** 73%!**

**Step-by-step explanation:**

Hope it helps! =D

Sjsjsjshsxjxhxhxhxhzh27272727

The population of a town over the past 10 years can be represented with the equationy = 2450(1.07)? What is the rate of change?A) 1.07%B 2450C 7%D.0796

Let's begin by identifying key information given to us:

The population is represented by the equation:

[tex]y=2450\mleft(1.07\mright)[/tex]We will compare the equation for the population with the general exponential growth equation, we have:

[tex]\begin{gathered} f(x)=a(1+r)^x \\ where\colon \\ f(x)=exponential\text{ }growth\text{ }function \\ a=initial\text{ }amount \\ r=growth\text{ }rate \\ x=number\text{ }of\text{ }time\text{ }intervals \end{gathered}[/tex]Comparing, we have:

[tex]\begin{gathered} f(x)\Rightarrow y \\ a=2450 \\ (1+r)=1.07\Rightarrow r=1.07-1=0.07 \\ \Rightarrow r=0.07=7\text{\%} \\ \\ \\ \end{gathered}[/tex]**Therefore, the rate of change is 7%. Hence, C is the answer**

How many zeroes are in the product of 40 x 107? O A. 6 B. 7 O C. 8 O D. 9

We need to count the number of zeros in a number multiplied by a power of 10. Which is shown below:

[tex]40\cdot10^7[/tex]The power of 10 will add a certain number of zeros, which is equal to the expoent of the power, in this case it's 7, but there is one more zero which is present in the "40", therefore the total number of zeros will be 8.

Point DD is located at (-6,-5)(−6,−5) on the coordinate plane. Point DD is reflected over the xx-axis to create point D'D ′ . What ordered pair describes the location of D'?D ′ ?

The **ordered pair** that describes the location of N is (2,6)

Given:

N's **coordinates** are: (-2,-6)

Point N ′ is produced by reflecting point N over the y-axis.

By reflecting point N' over the x-axis, the final point N" is produced.

x , y = -x , y

N(-2 -6) = N'(2 6)

To locate the** ordered pair** describing where N" is located.

Point N's coordinates are (-2,-6). Point N ′ is produced by **reflecting** point N over the y-axis.

x , y = -x , y

N(-2 -6) = N'(2 6)

The** resultant point** N" is created by reflecting point N' over the x-axis.

The **ordered pair** for point N" is therefore (2,6) gives its location.

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Can I please get answer for a and b. I just need the answers. Thanks

When we have a function and want to evalueate it for some "x", we just substitute every "x" with the value in parenthesis. So, to evaluate f(a + 2), we have x = a + 2, so we need to substitute every "x" in the function with a + 2:

[tex]f(a+2)=(a+2)^2-2(a+2)+1[/tex]Now, to simplify, we first need to use the distributive property on the second parenthesis and evaluate the binomial in the first:

[tex]f(a+2)=a^2+4a+4-2a-4+1[/tex]Now, we group the like-terms and add them:

[tex]\begin{gathered} f(a+2)=a^2+4a-2a+4+4+1 \\ f(a+2)=a^2+2a+1 \end{gathered}[/tex]For yhe other one, Let's do each term and then make the substraction:

[tex]\begin{gathered} f(a+h)=(a+h)^2-2(a+h)+1 \\ f(a+h)=a^2+2ah+h^2-2a-2h+1 \\ f(a+h)=a^2+h^2+2ah-2a-2h+1 \end{gathered}[/tex][tex]f(a)=a^2-2a+1[/tex]So:

[tex]\begin{gathered} f(a+h)-f(a)=a^2+h^2+2ah-2a-2h+1-(a^2-2a+1) \\ f(a+h)-f(a)=a^2-a^2+h^2+2ah-2a+2a-2h+1-1 \\ f(a+h)-f(a)=h^2+2ah-2h \end{gathered}[/tex]One year ago, Anne could run a mile in m minutes. Since then, her time hasdecreased by 16%. Write two different expressions that represent the number ofminutes it now takes Anne to run a mile, and show or explain why the expressionsare equivalent.

We know that

• Anne could run a mile in ,m, minutes.

,• Now, time has decreased by 16%.

The following expressions represent the number of minutes She uses to run a mile now.

[tex]\frac{16}{100}\cdot m[/tex]This expression represents 16% of *m* in fraction form.

This expressed represents 16% of *m *in decimal form.

Both expressions are equivalent because they refer to the same percentage 16%. That is 0.16 and 16/100 are equivalent to 16%

Dalia's living room is 12 feet long and 10 feet wide. Her dining room

is also 10 feet wide. Write two equivalent expressions that each

represent the combined area of the two rooms.

10ft

12 ft-

Living

Room

xft-

Dining

Room

(120 + 10x) sq. feet or 10(12+x) sq. feet will be the combined **area** of the two rooms.

the given dimensions of the living room are given as follows,

length =12

width/breadth =10

thus the **area** of the living room will be,

length x breadth, i.e.

=12 x 10

=120 sq. feet

the given dimensions of the dining room are given as follows,

length= x

width/breadth=10

thus the **area** of the dining room can be calculated as

length x breadth

=10x sq. feet

Now, to calculate the combined **area** of both the rooms, we have to add the **area** of the dining room and the **area** of the living room,

that is,

(120 + 10x) sq. feet

What is **area**?

The **area** is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

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Find the vertex of the parabola y=2x^2+8x+7.

Hi i hope this helps you out

2. Math on the Spot Solve each equation.

A. 3n+ 1 = 19

B. 21 = -2p - 5

A.

[tex]3n =19 - 1 \\ 3n = 18 \\ \frac{3n}{3} = \frac{18}{3} \\ n = 6[/tex]

B.

[tex]21 + 5 = - 2p \\ 2p = - 26 \\ \frac{2p}{2} = \frac{26}{2} \\ p = 13[/tex]

HOPE THIS HELPS.

PLEASE HURRY

What is the value of the expression 45x − 16 if x is equal to −6?

**Answer:**

-286

**Step-by-step explanation:**

45(-6)-16

= -270 - 16

= -286

**Step-by-step explanation:**

45x - 16

x = -6

45(-6) - 16

-270 - 16

-286

Hope this helps! :)

Find g(x), where g(x) is the reflection across the y-axis of f(x) = -9x - 4.

Write your answer in the form mx + b, where m and b are integers.

g(x) =

**Answer: **[tex]9x-4[/tex]

**Step-by-step explanation:**

Reflecting across the y-axis means [tex]f(x) \longrightarrow f(-x)[/tex].

[tex]g(x)=-9(-x)-4=9x-4[/tex]

please help meeee i am lost

**Answer:**

The sum of a sequence is known as a series. Thus means a harmonic series is infinite with no limit

2x 1 over 5 - 3x +2 over 4
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