Mathematics High School

Which of the following expressions is this one equivalent to?
(x^4+2x^3-x-2)÷(x^3-1)

A. 2x-5- (3/x^3-1)
B. x^2+x+1
C. x+2
D. x^2+3x+2
...?

Answers

Answer 1
The answer is C. x+2.


[tex] \frac{ x^{4} +2 x^{3}-x-2 }{x^{3} -1} [/tex]

Rearrange it:
[tex]\frac{ x^{4} +2 x^{3}-x-2 }{x^{3} -1}=\frac{ x^{4} -x+2 x^{3}-2 }{x^{3} -1} =\frac{ x*x^{3} -x*1+2*x^{3}-2*1 }{x^{3} -1}= \frac{x( x^{3}-1)+2(x^{3}-1) }{x^{3}-1} = \\ = \frac{(x^{3}-1)(x+2)}{x^{3}-1} [/tex]

x³ - 1 can be cancelled out:
[tex]\frac{(x^{3}-1)(x+2)}{x^{3}-1} = x+2[/tex]
Answer 2

Answer: x+2. The answer is C.

Step-by-step explanation:

Related Questions

Translate this sentence into an equation.
The product of Raj's score and
6
is
66
.
Use the variable
r
to represent Raj's score.

Answers

Product -> multiplication
product of Raj's score and 6: r x 6
is 66: =66

r x 6 = 66

Final answer:

The sentence 'The product of Raj's score and 6 is 66' translates to the equation 6 × r = 66. By dividing both sides by 6, we find that Raj's score r = 11.

Explanation:

To translate the sentence into an equation, we need to understand the mathematical operation described by the word 'product'.

The product refers to the result of multiplying two numbers.

In this sentence, the product of Raj's score, which we will represent with the variable r, and 6 is given to be 66.

Therefore, the equation representing this relationship is:

6 × r = 66

To solve for Raj's score, you would divide both sides of the equation by 6, which gives you:

r = 66 / 6

Therefore, Raj's score, r, is 11.

given ab/bc = fe/ed find ac

Answers

Well, you can cancel out the b and e, so a/c = f/d.

Then you cancel out a on the left side of the equation by multiplying both sides by 1/a which then gives you c = f/ad.

Hope this helps!

An interior angle of a regular polygon has a measure of 120°. What type of polygon is it? decagon hexagon quadrilateral octagon

Answers

The answer is Hexagon

The correct answer is B. Hexagon

Explanation:

In geometry, a polygon refers to a figure with three or more sides and therefore at least three angles, this includes triangles, pentagons, octagons, etc. Additionally, polygons can include irregular or regular sides and angles.

In the case of hexagons, if a hexagon is regular, this includes six sides of the same length and six angles with the same measure. Moreover, each of the angles is120° considering the total of internal angles in a hexagon is always 720° and therefore 720° divided into six equal angles is equal to 120°.

Therefore, if an interior angle of a regular polygon (figure with equal sides and angles) has a measure of 120° the polygon is a hexagon because the only polygon that can have multiple sides and angles each with 120° and form a regular polygon is the hexagon.

For what values of a and b is the following function is continuous at every x:

-7 x ≤ -3
f(X) = ax-b -3< x < 1
3 x ≥ 1
Find the values is a and b ix f(x) continuous at every x?

Answers

I have a solution here to the same problem but a slight different given:

-1 x<=-1 
ax-b -1<x<1 
2 x>=1 

The solution is as follows:

 f(x) = {-1, x ≤ -1 
...... { ax - b, -1 < x < 1 
...... { 2, x ≥ 1 


Then we must have: 
lim(x-->-1) -1 = lim(x-->-1) ax - b 
==> -1 = -a - b 
==> a + b = 1 

And we must have: 
lim(x-->1) ax - b = lim(x-->1) 2 
==> a - b = 2 

So we need to solve the system of equations given by: 
a + b = 1 
a - b = 2 

After doing so, you should get that: 
a = 3/2 
b = -1/2 

By studying the solution above, you now have the ability to answer the problem on your own! 



By solving a system of equations, we will see that the function is continuous for all values of x if:

a = 2.5b = -0.5.How to make the piecewise-function continuous for every x?

Here we have the piecewise function:

f(x) = -7            if x ≤  -3

f(x) = a*x- b     if -3 < x < 1

f(x) = 3             if  1 ≤ x

The piecewise function will be continuous only if the values at the limits where we have jumps (at x = -3 and x = 1) are the same in both pieces of the function.

This means that we must have:

f(-3) = -7 = a*(-3) - b

f(1) =  3 = a*1 - b

Then we have a system of equations:

-7 = -3a - b

3 = a - b

To solve this, first, we isolate one of the variables in one of the equations, I will isolate b in the second one to get:

b = a - 3

Now we can replace that in the other equation to get:

-7 = -3a - (a - 3)

Now we can solve this for a.

-7 = -4a + 3

-7 -3 = -4a

-10/-4 = a = 2.5

Then the value of a must be 2.5, to get the value of b we use:

b = a - 3 = 2.5 - 3 = -0.5

So the solution is a = 2.5, b = -0.5.

If you want to learn more about systems of equations, you can read:

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need help answer is not 3.14
The circumference, or perimeter, of a circle can be found by multiplying its diameter by 3.14. What is the circumference of a circle that has a diameter of inch?
Express your answer as a decimal.plz

Answers

Final answer:

The circumference of the circle with a diameter of inch is 3.14 inch.

Explanation:

The circumference of a circle can be found by multiplying its diameter by π (pi). In this case, the diameter of the circle is given as inch. To find the circumference, we need to multiply the diameter by π.

Circumference = Diameter × π

Since the diameter is inch, the circumference of the circle is ( inch) × π = inch × π = 3.14 inch.

What are all the factor pairs for 30?

Answers

there are 3
the number 5 number 3 and 2

Initially, Heather has $125 in her savings account. At the end of each week, she deposits $25 into her account.

What is a explicit rule for amount of money Heather has after n weeks?

Answers

An explicit rule for amount of money Heather has after n weeks would be 25n because this is the amount she is depositing indefinitely after n weeks.
125+25n=new weekly total

start at 5 1/2 add 1 1/5

Answers

5 1/2 = 5 5/10 and 1 1/5 = 1 2/10. 5 5/10 + 1 2/10=
6 7/10

A(n) _____ is a segment that is formed by the intersection of two faces

Answers

I believe it is called an "edge"

Answer:

The answer is Edge. A segment that is formed by the intersection of two faces is called an EDGE.

Step-by-step explanation:

A segment that is formed by the intersection of two faces is called an EDGE.

An edge is defined as a type of line segment, that joins two vertices in a polygon, polyhedron etc. In a  polytope, an edge is a line segment between faces.

In the situation, simple interest is calculated yearly. how much interest was earned? drag and drop the answer into the box. principal: $12,000; time: 3 years; interest rate: 15%; interest: ?

Answers

I=prt,,i=12000*3*0.15=5400

The amount of interest earned is $5,400

From the question,

We are to calculate the simple interest earned

Interest can be calculated by using the simple interest formula

I = PRT

Where I is the interest

P is the principal

R is the rate

T is the time

From the question

P = $12,000

R = 15%

T = 3 years

∴ Interest,

I = $12000 × 15% × 3

I = $12000 × 0.15 × 3

∴ I = $5400

Hence, the amount of interest earned is $5,400

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20,000 is what percent of 80,000

Answers

the percent of 20,000 is 25 because if you turn 20,000 and 80,000 into 2 and 8 its easy.so its 2 4 6 8  if u divide 100 into 4 it becomes 25 %

Which of the following best represents the average speed of a fast runner?

10 meters per second

10 miles per minute

10 centimeters per hour

10 kilometers per second

Answers

10 meters per second is the correct answer

Here's why:
10 miles per minute is 600mph

10 centimeters per hour is
0.000062mph

10 kilometers per hour is 22369mph

Answer:

D

Step-by-step explanation:

kilo is faster than meters

5.7n + 4.1 = 2.96

What is n Im thinking -32

Answers

5.7n = 2.96-4.1
5.7n = -1.14
n= -1.14/5.7
n = -0.2

Which of the following measurements is the most accurate for a pellet with a mass of 3.25 grams?
a.
3 grams
b.
3.20 grams
c.
3.27 grams
d.
3.50 gram

Answers

the nearest value of the mass is 3.27 grams
it s near 3.25
answer is c

Answer:

the nearest value of the mass is 3.27 grams

it s near 3.25

answer is c

how to factor polynomial
u^2+uv+v^2

Answers

this polynomial can't be factored further. the three terms have nothing in common that make it factorable--you can't take anything out of all three terms.

however, if you perhaps mistyped and meant u² + 2uv + v², you would be able to factor it into (u + v)(u + v).

A flock of Canadian geese migrated 1623 miles in 28 days. What was the average rate at which these geese traveled in miles per day?

Answers

It's asking for miles/day (miles per day) meaning you would divide the number of miles by the number of days. So divide 1623 by 28.
1623/28=57.964

six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the probability that exactly one girl and two boys will recite awards? express your answer as a percent

Answers

The probability that exactly one girl and two boys will receive awards is 75%.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that there are:-

6 girls

4 boys

Probability of 1 girl being chosen: 1/6

Probability of 1 boy being chosen: 1/4

Probability of another boy being chosen: 1/3

1/6 = 0.17 x 100% = 17%

1/4 = 0.25 x 100% = 25%

1/3 = 0.33 x 100% = 33%

17% + 25% + 33% = 75%

Therefore the probability that exactly one girl and two boys will receive awards is 75%.

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You invested $2,300 in a stock. Your account now has a value of $2,643. Your percentage gain on the investment (rounded to the nearest percent) was:

a)0%
b)5%
c)10%
d)15%

Answers

I hope this helps you

Answer:

15%

Step-by-step explanation:

 

Suppose you are determining the growth rate of two species of plants. Species A is 12 cm tall and grows 2 cm per month. Species B is 10 cm tall and grows 3 cm per month. Which system of equations models the height of each species H(m) as a function of months m.

H(m ) = 12 + 2m
H(m ) = 3 + 10m
H(m ) = 2 + 12m
H(m ) = 3 + 10m
H(m ) = 12 + 2m
H(m ) = 10 + 3m
H(m ) = 2 + 12m
H(m ) = 10 + 3m

Answers

First one has initial height of 12 cm and on that inicial height we add 2cm each month which can be written as 2m + 12

Second one has initial height of 10 cm and grows 3cm per month which can be written as 3m + 10

Now we just have to find those expressions in offered equations to find answer.

We can see that system of equations is:
H(m) = 12 + 2m
H(m) = 10 + 3m

or third pair.

Phil gets a commission of 25% on all sales. He sold $1500.00 worth of goods. What was the amount of his paycheck?

Answers

Well let me tell you that this problem calls for multiply. So what you need to do is multiply 
1500 x 0.25 = 375.00
Hope this is what you were looking for

375.00

Good luck on your quiz


Due to a leak, the amount of water in a pool is decreasing by 5858 gal every hour.

What is the total change in the number of gallons of water in the pool after 3434 h?

Enter your answer in the box as a simplified fraction.

Answers

Here is the solution to the given problem above.
Given the the amount of water in a pool is decreasing 5/8 gallon every hour.
And what would be the change in the number of gallons after 3/4 hour. So what we are going to do is just to multiply 5/8 by 3/4. And the result would be 15/32. The total change in the number of gallons of water in the pool after 3/4 hour would be 15/32 gallons.

Is the system of equations is consistent, consistent and coincident, or inconsistent?

y=−3x+12y=−6x+2

Answers

Final answer:

The system of equations given is y=-3x+12 and y=-6x+2. Comparing their slopes and y-intercepts, the slopes are different and the y-intercepts are different too. Hence, the system is consistent.

Explanation:

The system of equations given is y=-3x+12 and y=-6x+2. To determine whether these equations are inconsistent, consistent, or consistently coincident, we must compare their slopes and y-intercepts. If the slopes are the same (-3 and -6 are not similar) and the y-intercepts are different (12 and 2 are not equal), then the system is inconsistent. If the slopes and the y-intercepts are identical, then the system is consistent and coincident. Otherwise, if the slopes are different, which is the case in this scenario, the system is consistent.

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Your $1000 investment in an energy stock doubles. Your $1000 investment in a tech stock drops in half. What was the total return on the two investments?

Answers

Answer: 0.25 or 25%

Explanation:

1) The first stock will double its value ⇒ new value = $1,000 × 2 = $2000

2) The second stock wil dropt to half ⇒ new value = $ 1,000 / 2 = $500

3) Total value of the investments after the change of the values: $2,500 + $ 500 = $ 2,500.

4) Return on investment = benefit / investment

5) benefit = new value - investment = $2,500 - $2000 = $ 500

6) Return on investment = $500 / $2,000 = 0.25

Which you can also represent in percent form: 0.25 = 25%.

Translate the following statement into an inequality: Five less than a number is at least nine.

Answers

The given statement translates to the inequality x - 5 ≥ 9.

To do this, we first need to interpret ‘a number’ as a variable, which we can call x. ‘Five less than a number’ means we subtract five from our variable, expressed as x - 5. ‘At least nine’ indicates that the value should be greater than or equal to nine, which in inequality form is ( ≥ 9 ). Therefore, the complete inequality that represents the given statement is x - 5 ≥ 9.

A survey was given and here are the results "Number responding less than 1 week"
Gender - X N
Males - 71 411
Females - 64 253

a) Construct a 95% confidence interval for the difference in the proportions of males and females at this university. Who would respond less than one week?

b) does there appear to be evidence of a difference in the proportions of men and women at this university who would respond less than 1 week. Provide statistical justification

Answers

p2 = 71/411 = 0.1727
p1 = 64/253 = 0.2530

(p1 - p2) = 0.2530 - 0.1727 = 0.0803
SE = sqrt{[p1(1 - p1)/n1] + [p2(1 - p2)/n2]} = sqrt{[0.2530(1 - 0.2530)/253] + [0.1727(1 - 0.1727)/411]} = sqrt(0.000747 + 0.0003476) = sqrt(0.001095) = 0.0331

Therefore, 95% confidence interval for the difference in the proportions of males and females at this university who would respond less than one week = (p1 - p2) + or - 1.96(SE) = 0.0803 + or - 1.96(0.0331) = 0.0803 - 0.0648 to 0.0803 + 0.0648 = 0.0155 to 0.1451

b.) Yes.

An apartment requires an initial deposit of $500 + $400 per month for rent.

Let C be the total cost of
the apartment.

Which shows the equation for the total cost for x number of months?

Answers

C = $400 X x (months rented) + $500

Please I really don't get this. Can someone please help me?

There are ten shirts in your closet, four blue, three green, and three red. You randomly select a different shirt each day. You wear a blue shirt Monday, Tuesday, and Wednesday.

Answers

It's a probability problem to find the odds of picking a green or red shirt out of the 10 shirts on Thursday, Friday and Saturday since you have randomly already know you have picked a blue shirt on the other days. Probability = Number favorable outcomes / total number of outcomes

Answer:

It's a probability problem to find the odds of picking a green or red shirt out of the 10 shirts on Thursday, Friday and Saturday since you have randomly already know you have picked a blue shirt on the other days. Probability = Number favorable outcomes / total number of outcomes

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Step-by-step explanation:

Nam has a beginning balance of $815 in her checking account. She writes a check for $210 and has a debit transaction of $525. What is her new balance?

$125

$80

$1550

$120

Answers

Nam's new balance is $80

Answer:the answer is ($80)

Step-by-step explanation:i took the test on k12 online school

plz give me bianleast it helps oh lot thank you

List the fractors of 35 is this number prime or composite

Answers

35 is a composite number. 35=5×7. 

Answer: Composite

Step-by-step explanation: To see if 35 is a prime number or a composite number, let's first start by finding the factors of 35.

To find the factors of 35, begin by dividing 35 by 1 which gives us 35. This means that 1 and 35 are factors.

Next, since 35 is not divisible by 2, 3, or 4, we divided 35 by 5 which gives us 7. This means that 5 and 7 are factors.

Next, since 35 is not divisible by 6, we divide 35 by 7 which gives us 5. Notice that 7 and 5 are repeat factors and once we hit repeat factors, this means that all other factors we try will repeat.

Therefore, the factors of 35 are 1, 5, 7, and 35.

Since 35 has more than two factors, it's called a composite number.

How do you find the perimeter and area?

Answers

Perimeter by adding lengths of each single side. That's just addition.

Area - depends on geometric shape, a lot of formulas. All about multiplication.
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