Use long division to find the quotient below.
(5x5 + 90x² - 135x) + (x+3)
O A. 5x -5x³ + 25x² - 45x
OB. 5x4-15x³ + 45x² - 45x
O C. 5x + 5x³-25x² - 45x
○ D. 5x¹ + 15x³ - 45x² - 45x

Answers

Answer 1

Use long division to the quotient is [tex]5 x^5+90 x^2-134 x+3[/tex]

What is quotient?

A quotient in mathematics is the amount created by dividing two numbers. In mathematics, the term "quotient" is frequently used to refer to the integer portion of a division, as well as to a fraction or a ratio.A fraction's quotient is the whole number that results from simplifying the fraction. The quotient is the fraction's decimal form if the simplified fraction yields a non-whole number.

[tex]\begin{aligned}& \text { Simplify }\left(5 x^5+90 x^2-135 x\right)+(x+3): \quad 5 x^5+90 x^2-134 x+3 \\& \text { Steps } \\& \left(5 x^5+90 x^2-135 x\right)+(x+3)\end{aligned}[/tex]

[tex]Simplify $\left(5 x^5+90 x^2-135 x\right)+(x+3): \quad 5 x^5+90 x^2-135 x+x+3$[/tex]

[tex]=5 x^5+90 x^2-135 x+x+3[/tex]

[tex]Add similar elements: $-135 x+x=-134 x$[/tex]

[tex]=5 x^5+90 x^2-134 x+3[/tex]

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Related Questions

Jaime y rocío están pintando una pared con cubos de pintura idénticos. Si Jaime ha gastado 2/5 de su pintura y rocío,3/5. ¿Quién ha gastado más? ¿Qué cubo de pintura estará más lleno?

Answers

Answer:

Step-by-step explanation:

Rocio ha gastado mas. El cubo de Jaime esta mas lleno.

Rocio gasto otro poco mas porque 3 esta mas grande que 2

the quadtratic expression -3x^2 +6x + 72 will equal zero when x equals

Answers

The values of x is x = 6 Or x = - 4 when the expression - 3x² + 6x + 72 will be zero.

What is a quadratic equaton?

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Here in the problem, we have to find the roots of the quadratic equation

- 3x² + 6x + 72 = 0.

3x² - 6x - 72 = 0.

x² - 2x - 24 = 0.

x² - 6x + 4x - 24 = 0.

x(x - 6) + 4(x - 6) = 0.

(x - 6)(x + 4) = 0.

x = 6 Or x = - 4 are the values of x when the expression will be zero.

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Given:NP=MP,NP PL prove NPL≈MPL

Answers

Please attach a photo so I can assist you!

An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute. At the same​ airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude​ be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.

Answers

By solving a linear equation, it can be calculated that-

The two planes will be in the same altitude after 9 minutes at an altitude of 24300 feet

What is a linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, the linear equation is

Let the time taken by the airplane to meet the same altitude be t minutes

An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute.

So altitude of the first airplane after t minutes = 55800 - 3500t

At the same​ airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.

Altitude of second airplane = 2700t

By the problem,

The linear equation is

55800 - 3500t = 2700t

2700t + 3500t = 55800

6200t = 55800

t = 9 minutes

Altitude = 2700 [tex]\times[/tex] 9 = 24300 feet

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Erica takes out a loan to purchase a car. She borrows 12,000 at 12% annual percentage rate. Complete the statements. The graph is [Drop Down 1]. Erica's loan is a [Drop Down 2] loan. The equation which models this loan is [Drop Down 3]. If Erica pays off the loan in six years, she will have paid [Drop Down 4].

Answers

The graph is that of an exponential function.The equation which models the loan is of: A(t) = 12000(1.12)^t.If Erica pays off the loan in six years, she will have paid $23,686.

What is the exponential function?

An increasing exponential function is modeled as follows:

A(t) = A(0)(1 + r)^t.

The parameters of the exponential function are given as follows:

A(0) is the initial value of the exponential function.r is the growth rate of the exponential function, as a decimal.

She borrows 12,000 at 12% annual percentage rate, hence the initial value and the growth rate are given as follows:

A(0) = 12,000, r = 0.12.

Then the function that describes her loan is given as follows:

A(t) = 12000(1.12)^t.

After six years, the value of the loan is calculated as follows:

A(6) = 12000(1.12)^6 = $23,686.

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show that the picture and board aren't mathematically similar (diagram below)

Answers

Answer:

See below

Step-by-step explanation:

If the figures were similar the corresponding sides would be proportional.

[tex]\frac{10}{12}[/tex] = [tex]\frac{8}{10}[/tex]  This statement would be true if the sides were proportional, but it is not true.  Cross multiply.

10(10) ≠ (8)(12)

100≠96

Q9.
Rachel, Samina and Tom share £600 between them.
2
Rachel gets 2/5 of the £600
ima
Samina gets 1/4 of the money that is left over.
Tom gets the rest of the money.
Tom says,
"I would have got more money if we had shared the £600 equally between us."
Is Tom correct?
You must show how you get your answer.

Answers

No. Tom is not correct.

If the money were split equally everyone would've gotten £200.

But, if everyone went by the mentioned distribution, then,

Rachel would get = 2/5 x 600 = £280

Remainder money = 600 - 280 = £320

Samina would get = 1/4 x 320 = £80

Tom would get the remaining money = 600 - (280 + 80)

                                                              = 600 - 360

                                                              =  £240      

Since, £240 > £200, Tom would be incorrect in saying he would have had more money if he had split the money equally.

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Let f(x) be a 4th-degree polynomial function with zeroes 1,-1, and 3-i. If f(0)=20, write the equation in:

a) Factored form

b) Standard form

Answers

The polynomial expression are P(x) = (x - 1)(x + 1)[(x - 3)² + 1] and P(x) = x⁴ - 6x³ + 9x² + 6x - 10

How to determine the polynomial expression?

Factored form

The given parameters are

Degree = 4Zero = 1,-1, and 3-i

There are complex numbers in the above zeros

This means that, the other zero is

Zeros = 3 + i

The equation of the polynomial is then calculated as

P(x) = Leading coefficient * (x - zero)^multiplicity

So, we have

P(x) = (x - 1) * (x + 1) * (x - (3 + i)) * (x - (3 - i))

This gives

P(x) = (x - 1) * (x + 1) * (x - 3 - i) * (x - 3 + i)

Evaluate the products

P(x) = (x - 1) * (x + 1) * [(x - 3)² - (i)²]

So, we have

P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]

P(x) = (x - 1)(x + 1)[(x - 3)² + 1]

The standard form

In (a), we have

P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]

Expand

P(x) = (x² - 1) * (x² - 6x + 9 + 1)

So, we have

P(x) = (x² - 1) * (x² - 6x + 10)

Remove the brackets

P(x) = x⁴ - 6x³ + 10x² - x² + 6x - 10

Evaluate the like terms

P(x) = x⁴ - 6x³ + 9x² + 6x - 10

Hence, the equation is P(x) = x⁴ - 6x³ + 9x² + 6x - 10

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The wholesale price for a chair is $169. A certain furniture store marks up the wholesale price by 16%. Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary.

Need Help!

Answers

The price of the chair in the furniture store is $94.

How to calculate the price of the chair in the furniture store?

Given that the wholesale price for a chair is $169 and that a certain furniture store marks up the wholesale price by 16%.

The price of the chair in the furniture store will be:

= $169 + (16% × $169)

= $169 + $27.04

= $196

The price is $194.

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a surveyor followed a property's legal description by starting at a point of beginning, then following the indicated directions between natural and artificial landmarks to arrive back at the point of beginning, using the method called a) lot-and-block. b) torrens. c) metes and bounds. d) rectangular survey.

Answers

The method which the surveyor followed was the method of metes and bounds.

The surveyor followed a property's legal description by starting at a point of beginning, then following the indicated directions between natural and artificial landmarks to arrive back at the point of beginning, using the method called metes and bounds.

Metes and bounds are the natural markers that define the limits or boundaries of a piece of property. Rivers, roads, stakes, and other natural or artificial markers are examples of metes and bounds landmarks.

A system or method of representing land, real property (as opposed to personal property), or real estate is known as metes and bounds. The technique has been used in England for centuries and is still used to define general boundaries there.

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Please help meee !!!??

Answers

its A

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Jin went to the grocery store and bought bottles of soda and bottles of juice. Each
bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar.
Jin purchased a total of 16 bottles of juice and soda which collectively contain 300
grams of sugar. Graphically solve a system of equations in order to determine the
number of bottles of soda purchased, x, and the number of bottles of juice
purchased, y.

Answers

Answer: x = 6, y = 10; as a point, that would be (6, 10).

Step-by-step explanation:

To do it graphically, you would just graph the equations 25x + 15y = 300 and x + y = 16. Then, you would find the intersecting point.

To do this, you should convert to point-slope format.

15y = -25x + 300 and x + y = 16

1) y = -5/3x + 20 and 2) y = -x + 16

Now, for equation 1, you start at the y-intercept (0, 20) and for every increase of 1 on the x-axis, you decrease -5/3 on the y-axis. To graph this in the software, you click on the point (0, 20) and on another point on the line y = -5/3x + 20. (Any will do, but it should be an integer. (3, 15) works.)

Do the same for equation 2. Start at the y-intercept (0, 16) and decrease 1 for every increase of 1 on the x-axis.

Look for the point(s) where the lines intercept. It is (6, 10). If you have the time, you can verify this algebraically.

50 points please help asap

Answers

The domain is set of all real numbers and the range is y ≥ -4

How to determine the domain and the range of the function?

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

The equation is given as

g(x) = |x + 4|

The domain

The above equation is an absolute value equation

An absolute value equation can take any value as its input

This means that the domain is the set of all real numbers

When represented as an interval, we have

The domain is (-∝, ∝)

Also, we have

-∝ < x < ∝

Hence, the domain is the set of all real numbers

The range

Here, we have

g(x) = |x + 4|

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-4, 0)

Remove the x value

y = -4

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

[-4, ∝)

Another representation is

y ≥ -4

So, the range is y ≥ -4

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Write the linear equation in slope intercept form

Answers

The given linear equation (1/3)x+ y=2 in the slope-intercept form is

y=(-1/3)x+2.

Explain about slope-intercept form?

Where m is the slope and b is the y-intercept, the slope-intercept form is represented as y = mx+ b. By utilizing y=mx+ b, a line is typically simple to graph. The point-slope form and standard form of linear equations are further types. Example 1: A line with a slope of 1/2 and a y-axis crossing at (0, -3). Calculate the line's equation. It is y = x/2 - 3 that determines the line's equation. Example 2: Determine the equation utilizing the y-y-intercept axis's and the horizontal line's slope intercept formula (0, 8).

Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+ b allow us to build an equation for that line.

Given linear equation is:

(1/3)x+ y=2

The following is the slope-intercept form of the given linear equation:

y=(-1/3)x+2

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The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to
clean 2 hamster cages.
Complete the table.
Minutes
15
Cages cleaned 2 4
Graph the data from the table.
Cages cleaned
20
18
16
14
12
10
8
30 55

90
8 10

Answers

The complete table will be;

Minutes              15   30

Cages cleaned   2    4

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.

Now,

Since, The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.

Hence, By definition of proportion we get;

Let the time to clean 4 hamster cages = x

So, We get;

⇒ 15 / 2 = x / 4

⇒ 15×4 / 2 = x

⇒ 30 = x

⇒ x = 30

Thus, It take 30 minutes to clean the 4 hamster cages.

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write a system of three linear equations with three variables each that has the unique solution . write your equations in standard form. use the variables , , and with non-zero coefficients.

Answers

the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.

2x + 3y + 4z = 30

3x + 4y + 5z = 45

5x + 6y + 7z = 75

The first equation is 2x + 3y + 4z = 30. The coefficients for the variables are 2, 3 and 4 which are all non-zero, meaning that this equation has a unique solution.

The second equation is 3x + 4y + 5z = 45. The coefficients for the variables are 3, 4 and 5 which are all non-zero, meaning that this equation also has a unique solution.

The third equation is 5x + 6y + 7z = 75. The coefficients for the variables are 5, 6 and 7 which are all non-zero, meaning that this equation also has a unique solution.

Therefore, the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.

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mathematics-help-dilate-

Answers

The dilated figure is plotted and attached and the coordinates is written as

preimage            image

A (-4, 3)               A; (-8, 6)

B (3, 2)                B' (6, 4)

C (-4, 0)               C' (-8, 0)

How to find the coordinates of the dilation

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we have

preimage                           image

A (-4, 3)   → (-4 * 2, 3 * 2) →   A' (-8, 6)

B (3, 2)    → (3 * 2, 2 * 2)  →    B' (6, 4)  

C (-4, 0)  → (-4 * 2, 0 * 2) →    C' (-8, 0)

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(a) Calculate the simple interest collected by a bank if $1500 is loaned for 3 years at 8% per annum.
(b) What amount of money did the borrower actually pay the bank?
(c) What amount of money was paid monthly?

Answers

Answer:

Step-by-step explanation:

(a)Given:

Principal Amount=$1500

Time = 3 years

Rate of Interest = 8% per annum

Find:

Simple Interest=?

According to the formula of  simple interest

Simple Interest=Principal x Time x Rate of Interest

i.e., SI=PRT

      SI= 1500 X 3 X 8/100

      SI= $360

Therefore, the simple interest for the principal amount of the loan $1500 in 3 years at a rate of 8% per annum will be $360.

(b) According to the formula:

Total Amount= Principal Amount + Simple Interest

i.e., Total Amount = $1500+$360

      Total Amount = $1860

Therefore, the loan amount the borrower will pay the bank is $1860.

PLEASE HELP WITH THIS PROBLEM

Answers

Answer:

y -2 = 2(x +7)y -2 = -1/2(x +7)

Step-by-step explanation:

You want equations of lines parallel and perpendicular to y = 2x -1 through the point (-7, 2).

Slope

The given equation is written in slope-intercept form:

  y = mx + b

where m = 2, and b = -1.

The slope of the line is m, the x-coefficient. For the given line, the slope is 2.

A parallel line will have the same slope: 2.

A perpendicular line will have the opposite reciprocal slope: -1/2.

Point-slope equation

When you have a point and slope, it is useful to use the point-slope form of the equation for a line:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

For both of the desired lines, the point is (h, k) = (-7, 2). Using this point and the above slopes, we have ...

equation of parallel line: y -2 = 2(x +7)equation of perpendicular line: y -2 = -1/2(x +7)

two stores sell identical sandwich rolls in different size packages, store A sells a six pack for $5.28 store B sells a four pack for $3.40, which store offers the better per-roll price

Answers

Store B offers better $0.85 per-roll price than store A.

What is division?

One type of operation is division in mathematics. The phrases or numbers are divided into the same number of components during this operation.

Given, two stores sell identical sandwich rolls in different size packages.

Store A sells a six-pack for $5.28.

To find the unit price,

we take division of 5.28 with number 6.

The unit price of sandwich roll for store A,

= 5.28 / 6

= $0.88

To find the unit price of sandwich roll for store B,

we take division of 3.40 with number 4.

= 3.40 / 4

= $0.85

And $0.85 < $0.88.

Therefore, Store B offers better per-roll price.

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-2(2x-3)=-22 i dont get it

Answers

Divide both side by -2
2x-3=11

Move constant
2x=11+3

Simplify
2x=14

Solution
X=7
-2(2x - 3) = -22
-4x + 6 = -22
-4x = -22-6
-4x = -28
X = 7

Another way:
-2(2x - 3) = -22
2x - 3 = -22/-2
2x - 3 = 11
2x = 11+3
2x = 14
X = 7

a mistake was made in the steps shown to simplify the expression. which step includes the mistake?

Answers

The step in which there is a problem is the operation in step 4. option C

Where is the mistake?

In this question, we are expected to solve the problem in a number of steps. We know that in mathematics, the solution to a given problem can only be worked out through a number of steps that can help us to be able to know what the correct solution of the problem ought to be.

In this case we have a simplification problem. It should be know that the acronym of BODMAS has to be called to mind here and that is;

BracketOfDivisionMultiplicationAdditionSubtraction

Mathematical operations would have to be carried out in this order else there would be a mistake in it. We can see that the addition in step 4 before division did not follow the principle of BODMAS thus that step is wrong.

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Luis typically eats 4 1/4 ounces of fruit each day. Today he ate his usual amount. Write each answer as a fraction and as a decimal. Use bar notation is necessary.

Answers

Answer:

Fraction: 4 1/4 = 17/4

Decimal: 17/4 = 4.25

Step-by-step explanation:

a poll shows that of all voters approve of the mayor's work. on three separate occasions a pollster selects a voter at random. what is the probability that on exactly one of these three occasions the voter approves of the mayor's work?

Answers

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

What is the binomial distribution formula?

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

Missing Information

The proportion of voters that approve the mayor's work is of 70%.

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What is the total cost of the rental is Dana drives the car for 15 miles?

Answers

The total cost of the rental if Dana drives the car for 15 miles is $90.2

How to determine the total cost?

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

C = 73.25 + 1.13m

Where

m = number of miles

This means that

m = 15

SO, we have the following equation

C = 73.25 + 1.13 * 15

Evaluate

C = 90.2

Hence, the total cost is $90.2

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"Dana and her family are going to Six Flags Great America the sum- mer after her Sophomore year. She is excited, because she will be doing all driving: After doing some complicated analysis, she calcu; lates that it will cost a certain amount per mile to pick up everyone and drive to the park, plus flat amount for everyone's admission tickets. The equation below models the total cost, €,and the variable m represents the number of miles driven: C = 73.25 + 1.13m

20
Write "less" or "greater" in the blank.
972 is
than 792

Answers

Answer:greater

Step-by-step explanation:

Answer:

972 is greater than 792.

Which expression is equivalent to 10d+d-2d?
d+8
9d9d
1+8d1+8d
11d11d
pls help

Answers

Answer: 9d

Step-by-step explanation:

10d+d-2d = 9d

A random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%. the test statistic is?

Answers

Answer:

Step-by-step explanation:

Sorry if this is different, but based on what I read, here is the answer.

100 x 0.85 = 85

therefor it is 85%, which is significantly more than 80%

On a team,8 girls and 5 boys devoted a total of 87 points. The difference between the number of points scored by the 8 girls and the number of points scored by the 5 boys is 57. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and boy

Answers

Answer:

Girls: 7 points each

Boys: 11 points each

Step-by-step explanation:

Josiah began earning an allowance each day. At the end of 6 days he buys a video game that costs $150 and has $102 left over. How much money does he earn each day in allowance

Answers

Answer:

42

Step-by-step explanation:

150+102=252

252/6=42

150+102=252 (allowance over six days)
252/6=42 (allowance per day)
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