(x³ + ³) / (x - y)
Do not include parentheses in your answer.

Answers

Answer 1

The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

Complete question

Simplify the expression: (x³ + (-y)³) / (x - y)

Do not include parentheses in your answer.

How to simplify the expression?

The expression is given as:

[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]

Open the inner bracket

[tex]\frac{x^3 -y^3}{(x - y}[/tex]

Apply the difference of two cubes to the numerator

[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]


Cancel out the common factors

[tex]x^2+xy+y^2[/tex]

Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

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Related Questions

An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic charge if they worked 10 hours in one day?


$450
$400
$550
None of these choices are correct.

Answers

Answer:

$800

Step-by-step explanation:

per hour $40×10hours=$400

$400÷$50=8 times initial fee

8×$50=$400 total initial fee

$400hours fee+$400 initial fee=$800 total payment

Please answer both questions I will give u brainliest if ur right

Answers

first one b 315, second d

Step-by-step explanation:

18*=3*+315

7*+4*=a*

what is the least common multiple of the numbers 8 and 12?
A. 24
B. 8
C. 4
D.96

Answers

The LCM of 18 and 12 is A.24

Answer:

A. 24

Step-by-step explanation:

Least common multiple of 8 and 12 = 24

8× 1 = 8 12×1 = 12

8×2 = 16 12×2=24

8×3 = 24

L.C.M (8,12) = 24

The greatest multiple that occurs in both the multiples of 8 and 12, is 24.

Hence, the least common multiple here is 24.

Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]

Answers

The area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

What is quadrilateral?

It is defined as the four-sided polygon in geometry having four edges and four corners. It has one pair of opposite congruent angles and the diagonals of a kite are perpendicular.

We have a quadrilateral shown in the picture.

The diagonal divides the quadrilateral into two triangles

The area of the quadrilateral = area of the triangle ADC + area of the

                                                   triangle ADB

= (1/2)3.42×4.39 + (1/2)5.44×3.42

= 7.5069 + 9.3024

= 16.80 square units

Thus, the area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

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If the odds on a bet are 7:1 against, what is the probability of winning? Express your answer as a fraction.

Answers

Probability helps us to know the chances of an event occurring. The probability of winning the bet is 0.125.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given the odds on a bet are 7:1, therefore, there are a total of 8 cases out of which only one case is of winning. Thus, the probability of winning the bet will be,

Probability = 1/8 = 0.125

Hence, the probability of winning the bet is 0.125.

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Which graph represents the function​
there are 2 more graphs but it won't add it

Answers

Answer:

[tex]f(x) = 9x^2+9x - 18/3x + 6\\= 9(x^2 + x - 2)/3(x+2)\\= 3(x^2+x-2)/x+2\\= 3(x+2)(x-1)/x+2\\= 3x - 3[/tex]

so y = 3x - 3

since 3x + 6 is on the bottom,

[tex]3x + 6\neq 0\\3x\neq -6\\x\neq -2[/tex]

so this means it should be the graph of y = 3x - 3, but with a hole at (-2, -9)

Which expression is modeled by this arrangement of tiles?

40 positive tiles are broken up into 10 groups of 4 positive tiles.
40 divided by (negative 10)
40 divided by 10
40 divided by 40
40 divided by 40

Answers

Answer:

40 divided by 10

Step-by-step explanation:

Answer:

b

Step-by-step explanation:


Which equation describes the same line as y-5=-2(x+4)

Answers

The same equation is

Let f(t) represent the temperature of a turkey baking in an oven as a function of time (t) in the oven (in minutes). This means time (t) is the independent variable and temperature of the turkey f(t) is the dependent variable. The turkey was in the oven for 360 minutes and then removed. Note that when something is baked in an oven, the temperature of the oven stays constant. The graph of the function is shown below.

Describe the rate of change pattern over each interval of the graph listed below.
a. 0 < t < 345
b. 345 < t < 360
c. t > 360

Explain what is happening in each interval of your graph in terms of the turkey and its temperature, using complete sentences.

Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation.

Answers

Answer:

a. When the time is greater than 0, but less than 345 minutes, the temperature of the turkey is increasing at roughly a linear rate.

b. When the time ranges from 345 to 360 minutes, the temperature of the turkey stays constant, at 165 degrees.

c. When the time is greater than 360 minutes, the temperature of the turkey decreases.

Needa line segment has endpoints P(-8,7) and Q(6,-3). What is the midpoint of the segment?

Answers

Answer:

1/2(6-8), 1/2(-3+7)=-1,2

Answer: C - (-1, 2)

Step-by-step explanation:

please help me asap :)

Answers

Answer:

They are not similar because corresponding sides are not proportional.

Explaination

Condition for similarity of two triangles -

The ratio of corresponding sides should be equal.

Condition for congruence of two triangle -

Any of the following -

Side side side

side angle side

angle angle

angle side angle

Find the 7th term in the
sequence
-, -1, -5, -25, . . .
Hint: Write a formula to help you.
1st term. Common Ratio (desired term - 1)
Enter

Answers

Answer: -15625

Step-by-step explanation:

The explicit formula for the sequence is

[tex]a_{n}=-1(5)^{n-1}\\\\\implies a_{7}=-1(5)^{7-1}=\boxed{-15625}[/tex]

urgent algebra 2 help please

Answers

Answer:

y = 4x - 5

Step-by-step explanation:

y = mx + b

By putting above values in equation (i)

-1 = 4 (1) + b

-1 = 4 + b

-5 = b

b = -5

y = 4x - 5

please help! write D u E and D n E using interval notation.

Answers

Part 1

[tex]D \cup E[/tex] denotes the union of the two sets (in other words, all the elements in both sets).

This means it is [tex](-\infty, 4) \cup [7, \infty)[/tex]

Part 2

[tex]D \cap E[/tex] denotes the elements shared between both sets.

This means the answer is [tex](4, 7][/tex]

A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?


The difference is only 0.04, but that is still a significant change.


The margin of error is quite small compared to the change year over year, so it is a significant issue.


The change of 0.09 is not a lot and thus should be ignored.


The margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored.

Answers

The correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.

What is the margin of error(MOE)?

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

We have:

A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C.

As the value of MOE is 0.13 degrees

It is a serious problem because the margin of error is quite narrow in comparison to the shift from year to year.

Thus, the correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.

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There are 10 USB drives in a box and 3 are defective. Two drives are to be selected, one after the other. What is the probability of selecting a defective USB followed by another defective USB?

Answers

[tex]|\Omega|=10\cdot9=90\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6.7\%[/tex]

the density of some steel is7.98gm/cc.how much does 60cc weigh?​

Answers

Substituting into the formula d=m/v,

[tex]7.98=\frac{m}{60}\\\\m=\boxed{478.8 \text{ gm}}[/tex]

what is next number in pattern 7, 11, 2, 18, -7

Answers

Answer:

the answer is -7+-25=-32

pls help oooooooooooo

Answers

Answer:

110

Step-by-step explanation:

Suppose lines EH and BD are parallel:

Angle <GFE and angle <ABC are supplementary so their sum is equal to 180

2x + 10 + x  + 20 = 180 add like terms

3x + 30 = 180 subtract 30 from both sides

3x = 150 divide both sides by 3

x = 50

We are asked the value of <ACD

<ABD and <ACD are also supplementary so we can find the value od <ACD:

x + 20 + <ACD = 180 we know x = 50 so we can replace x with that

50 + 20 + <ACD = 180

70 + <ACD = 180 subtract 79 from both sides

<ACD = 110

Suppose f(x)=x²+4 and g(x)=2x+1.
Find the value of f(-2)g(-2).

Answers

Answer: -24

Step-by-step explanation:

I am assuming you want the value of (f × g)(-2)

[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]

[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]

8 × -3 = -24

f(x)= 2x^3 + 6x^2 -5x - 3, g(x)= 3x-4 find (f-g)(x)

Answers

The difference in the given functions is 2x^3 + 6x^2 -8x + 1

Difference of functions

Given the following function a shown

f(x)= 2x^3 + 6x^2 -5x - 3

g(x)= 3x-4

Take the difference

(f-g)(x) = f(x) - g(x)

Substitute

(f-g)(x)  = 2x^3 + 6x^2 -5x - 3 - (3x - 4)

Expand

(f-g)(x)  = 2x^3 + 6x^2 -5x - 3 - 3x + 4

(f-g)(x) = 2x^3 + 6x^2 -8x + 1

Hence the difference in the given functions is 2x^3 + 6x^2 -8x + 1

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NEED HELP ASAP !!!

Simplify: √16r
O 47²
O 473
87²
O 8-3

Answers

Answer:

4 r^3

Step-by-step explanation:

sqrt ( 16 r^6 )    = sqrt ( 4^2 * (r^3)^2  )    =   4 r^3

5 ice creams cost 6.50 pounds. How much do 11 ice creams cost​

Answers

Answer:

14.30

Step-by-step explanation:

6.50/5=1.3

so one ice cream is 1.30 pounds

1.30X11=14.3

so 11 ice creams is 14.30 pounds

2.
Julia grows flowers in a garden that is the shape of a rectangle. The side lengths of
the garden are shown in the diagram.
5½⁄2 feet
3 feet
Which of these is equal to the area of the garden? Select all that apply.
A. 8
square feet
1
B.
5
feet x 3 feet
2
C.
151/11
square feet
D. 16
16¹ square feet
E. 5 feet +
11/12
F. (5 feet x 3 feet) +
foot + 3 feet
for
foot

Answers

The area of the rectangular garden given the length and width is 16 1/2 square feet

Area of the gardenLength = 5 1/2 feetWidth = 3 feet

Area of a rectangular garden = length × width

= 5 1/2 feet × 3 feet

= 11/2 × 3

= 33/2

= 16 1/2 square feet

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Let −5, 3 be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.

Answers

The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

What is the Pythagoras theorem?

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have (−5, 3) be a point on the terminal side of θ.

Perpendicular = -5

Base = 3

From Pythagoras' theorem:

Hypotenuse² =  (3)² + (-5)²

Hypotenuse = √34

cosθ = 3/√34

cscθ = -√34/5

tanθ = -5/3

Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

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Hey I need help with statistics

Answers

What’s your question?

Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.

Which is the equation for y?

Answers

Answer:

y = -t

Step-by-step explanation:

Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

parametric equation of line passing through a point (a₁, b₁, c₁)

   and parallel to a vector <a, b, c> is given by :

   x =a₁ + at ,   y = b₁ + bt   ,   z = c₁ + ct

now according to question:

given -

point, P(1, 0, -3)

line,   x = −1 + 2t , y = 2−t, and z = 3+3t.

so from the line the vector is=  <2, -1, 3>

now using above formula,

equation of line is =   x = 1 + 2t , y = −t, and z = -3+3t.

we have to solve for 'y' only,

⇒ y = -t    (answer)

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Can you please help meee

Answers

Answer: y = 4x + 5/4

Step-by-step explanation: Plug in the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept, and such that m, b ≠ 0.

Christine splits 4/5 pounds of candy with 5 people. What is the unit rate in pounds per person. In simplest form

Answers

Answer:

4/25

Step-by-step explanation:

4/5 ÷ 5 = 4/5 × 1/5 = 4/25

A phone company offers a monthly cellular
phone plan for $25. The plan includes 250
anytime minutes, and charges $0.20 per minute
above 250 min. Write a piecewise-defined
function for C(x), the cost for using x minutes in
a month.

Answers

The function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

What is a function?

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Given that:-

A phone company offers a monthly cellular phone plan for $25. The plan includes 250 anytime minutes and charges $0.20 per minute above 250 min.

The cost of the 250 minutes is $25 and if the time extends from 250 minutes then the function will be expressed in the form of.

C(x) = 25 + 0.2 (x)

Here C(x) is the total cost and the x is in minutes.

Hence the function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

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