Lorie is using long division to find the quotient of x^3 + 6x^2 + 5 and x^2 + x -1, as shown at the bottom of this question.

What mistake did Lorie make?

A. She added an extra term to the dividend.

B. She combined the constants incorrectly in the last step.

C. The second term in the quotient should be 7.

D. The last term in the quotient has an incorrect denominator.

Lorie Is Using Long Division To Find The Quotient Of X^3 + 6x^2 + 5 And X^2 + X -1, As Shown At The Bottom

Answers

Answer 1

Answer:

Option (B)

Step-by-step explanation:

x² + x - 1) x³ + 6x² + 0x + 5 ( x + 5

           - (x³ +   x²  -  x)

                      5x² + x + 5

                    -(5x² + 5x - 5)

                             -4x + 10

Result : [tex]x+5+\frac{-4x+10}{(x^{2}+x-1)}[/tex]

By the comparing the result with the Lorie's solution,

She made a mistake in the last step in which she combined the constant incorrectly.

Therefore, Option (B) will be the answer.


Related Questions

A particle travels along the x axis such that it’s position at time t is given by the function x(t)=2t+t. What is the average speed of this particle over the interval 2

Answers

The required average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is 32 meters/second.

Given that,

A particle travels along the x-axis such that its position at time t is given by,

Function; [tex]\rm x(t)=2t^2+t[/tex]

We have to find,

What is the average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10?

According to the question,

The position of the particle is given by,

[tex]\rm x(t)=2t^2+t[/tex]

The average speed of this particle is determined by differentiating the function with respect to x,

[tex]\rm \dfrac{dx}{dt} = \dfrac{d(2t^2+t)}{dx}\\\\\dfrac{dx}{dt} = 4t + 1 \\\\v(t) = 4t+1[/tex]

Then,

The average speed of the particle over interval 2 is,

[tex]\rm v(t) = 4t+1 \\\\v(2) = 4(2)+1\\\\v(2) = 8+1 \\\\v(2) = 9 \ meter \ per \ second[/tex]

And the average speed of the particle over interval 10 is,

[tex]\rm v(t) = 4t+1 \\\\v(10) = 4(10)+1\\\\v(10) = 40+1 \\\\v(10) = 41 \ meter \ per \ second[/tex]

Therefore,

The average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is,

[tex]\rm v(t) = v(10)-v(2)\\\\v(t) = 41-9\\\\v(t)= 32 \ meter \ per \ second[/tex]

Hence, The required average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is 32 meters/second.

For more details refer to the link given below.

https://brainly.com/question/2292357

Answer:

Very basically, the answer is 3

Step-by-step explanation:

Know this cause Edge 2023

Calculate a point estimate of the mean pull-off force of all connectors in the population (Round the answer to four decimal places (e.g. 90.2353).) g

Answers

Answer:

The answer is "75.627"

Step-by-step explanation:

Please find the correct question in the attached file.

The mean displacement force among all connectors throughout the population calculates the point estimation.

[tex]\bold{ \bar x= \frac{\text{Sum of observation}}{\text{Amount of observations}}}[/tex]

   [tex]= \frac{1966.88}{26}\\\\=75.627[/tex]

Raise to the power: (–2abx)4

Answers

Answer:

(16a^4b^4x^4)

Step-by-step explanation:

You decide to purchase a bond for $500. It pays 5% simple interest per year and matures in 5 years. How much interest will you earn once the bond matures? Round your answer to the nearest dollar.
Do NOT round until you have calculated your final answer.

Answers

Answer:

$625

Step-by-step explanation:

You start with $500

The interest per year is 5% or 500 x 0.05 = $25

If it matures 5 years and each year has an increase of $25 then

Year 1 - $525

Year 2 - $550

Year 3 - $575

Year 4 - $600

Year 5 - $625

Answer:

Step-by-step explanation:

We express the interest rate r in decimal form, so we have r=5%=5100=0.05. The principal is P=500 and the time in years is t=5. So, the interest is I=Prt=(500)(0.05)(5)=$125. The interest earned is $125.

Explain how to use the distributive property to find an expression that is equivalent to 20+16.​

Answers

Step-by-step explanation:

distributive property is a*(b+c) = a*b + a*c

20+16 = 4* (5+4)

I need to solve for n.​

Answers

it’s going to be 286.

I need help please help me out .

Answers

21,540 multiply 359 times 60

A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions the student gets correct. (a) Find P(X = 3). (b) Find P(X > 2). (c) To pass the test, the student must answer 7 or more questions correctly. Would it be unusual for the student to pass? Explain.

Answers

Answer:

1)0.2502

2)0.475

3)0.003505

Step-by-step explanation:

Total No. of question n= 10

There are four choices in each question

So, Probability of success [tex]p = \frac{1}{4}[/tex]

Probability of failure q  = [tex]1- \frac{1}{4}=\frac{3}{4}[/tex]

We will use binomial over here

[tex]P(X=x)=^nC_r p^r q^{n-r}[/tex]

1)

[tex]P(X = 3)=^{10}C_3 (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=\frac{10!}{3!7!} (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=0.2502[/tex]

2)  [tex]P(X > 2)=1-P(X\leq 2)[/tex]

P(X>2)=1-(P(X=0)+P(X=1)+P(X=2))

[tex]P(X>2)=1-(^{10}C_0 (\frac{1}{4})^0 (\frac{3}{4})^{10}+(^{10}C_1 (\frac{1}{4})^1 (\frac{3}{4})^9+^{10}C_2 (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]

[tex]P(X>2)=1-((\frac{1}{4})^0 (\frac{3}{4})^{10}+(\frac{10!}{1!9!} (\frac{1}{4})^1 (\frac{3}{4})^9+\frac{10!}{2!8!} (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]

P(X>2)=0.475

3)

[tex]P(X\geq 7)=P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\P(X\geq 7)=^{10}C_7 (\frac{1}{4})^7 (\frac{3}{4})^{3}+(^{10}C_8 (\frac{1}{4})^8 (\frac{3}{4})^2+^{10}C_9 (\frac{1}{4})^9 (\frac{3}{4})^1+^{10}C_{10} (\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=\frac{10!}{7!3!} (\frac{1}{4})^7 (\frac{3}{4})^{3}+\frac{10!}{8!2!} (\frac{1}{4})^8 (\frac{3}{4})^2+\frac{10!}{9!1!} (\frac{1}{4})^9 (\frac{3}{4})^1+\frac{10!}{10!0!}(\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=0.003505[/tex]

spend 54.49 and 79.99. how much in total

Answers

Answer:

25.5

Step-by-step explanation:

Answer:2.25

Step-by-step explanation:

which represents 8(95) using the distributive property to simplify

Answers

Answer:

8*90 + 8*9 = 760

Step-by-step explanation:

Because, 8(95) just means 8 times 95 so you just distribute 8 to 90 and 5.

Which of the following is equal to 7%?
O A. A
O B. 73
O C. 173
O D.
SUBMIT

Answers

7% is equal to 0.007

The decimal equivalent of 7% is, C. 0.07.

What is the percentage?

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

We know, Percentages and decimals are related to each other.

Decimals can be converted into percentages by multiplying them by 100

and vice versa.

Given, We have to find the decimal equivalent of 7%.

The decimal equivalent of 7% is,

= 7/100.

= 0.07.

Q. Which of the following is equal to 7%?

A. 7.

B. 0.7.

C. 0.07.

D. 7%.

learn more about percentages here :

https://brainly.com/question/24159063

#SPJ7

Mackenzie has one candy bar to share equally with her best friend. What portion of the candy bar does Mackenzie give to her best friend.

Answers

Answer:1/2

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation: if each of you get part of the candy bar and you need to share it equally, both of you get 1/2 of it.

If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square. For the uniform electric field normal to the surface, the flux through the surface is____________the area of this surface. Therefore, Φsquare is ________ ϕcircle .

Answers

Answer:

The area of this circle is [tex](\frac{\pi}{2} )[/tex]  the area of the square.

For the uniform electric field normal to the surface, the flux through the surface is electric field multiplied by the area of this surface.

Therefore, Φsquare is [tex](\frac{2}{\pi} )[/tex] ϕcircle

Step-by-step explanation:

Area of the circle is given by;

[tex]A_c = \frac{\pi d^2}{4}[/tex]

Area of the square is given by;

[tex]A_s = L^2[/tex]

relationship between the edge length of the square, d, and length of its side, L,

[tex]d = \sqrt{L^2 + L^2} \\\\d = \sqrt{2L^2}[/tex]

But area of the square , [tex]A_s = L^2[/tex]

[tex]d = \sqrt{2A_s}[/tex]

Then, the area of the square in terms of the edge length is given by;

[tex]A_s = \frac{d^2}{2}[/tex]

Area of the circle in terms of area of the square is given by;

[tex]A_c = \frac{\pi d^2}{4} = \frac{\pi}{2}(\frac{d^2}{2} )\\\\But \ A_s = \frac{d^2}{2} \\\\A_c = \frac{\pi}{2}(\frac{d^2}{2} )\\\\A_c = \frac{\pi}{2}(A_s )[/tex]

For the uniform electric field normal to the surface, the flux through the surface is electric field multiplied by the area of this surface.

Ф = E.A

Flux through the surface of the circle is given by;

[tex]\phi _{circle} = E.(\frac{\pi d^2}{4})[/tex]

Flux through the surface of the square is given by;

[tex]\phi _{square} = E.(\frac{d^2}{2} )\\\\\phi _{square} =E.(\frac{d^2}{2} ).(\frac{\pi}{2} ).(\frac{2}{\pi} )\\\\\phi _{square} =E.(\frac{\pi d^2}{4} ).(\frac{2}{\pi} )\\\\\phi _{square} =(\phi _{circle}).(\frac{2}{\pi} )[/tex]

Therefore, Φsquare is [tex](\frac{2}{\pi} )[/tex] ϕcircle

If the circle has the same diameter as the edge length of the square, then the area of this circle is [tex]\rm \dfrac{\pi }{2}[/tex] the area of the square

The uniform electric field is normal to the surface, the flux through the surface is the electric field multiplied by the area of this surface.

Φsquare is [tex]\dfrac{2}{\pi}[/tex]  ϕcircle

Given

If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square

For the uniform electric field normal to the surface, the flux through the surface is____________the area of this surface.

Therefore, Φsquare is ________ ϕcircle .

1. If the circle has the same diameter as the edge length of the square, then the area of this circle is ___________the area of the square.

The area of the circle is;

[tex]\rm Area \ of \ circle = \dfrac{\pi d^2}{4}[/tex]

The area of the square is;

[tex]\rm Area \ of \ square = a^2[/tex]

The relationship between the edge length of the square, d, and length of its side a is;

[tex]\rm d = \sqrt{a^2+a^2}\\\\d = \sqrt{2a^2}\\\\d = \sqrt{2} a[/tex]
The area of the circle in terms of the area of the square is;

[tex]\rm Area \ of \ circle = \dfrac{\pi }{2} \ Area \ of \ square[/tex]

If the circle has the same diameter as the edge length of the square, then the area of this circle is [tex]\rm \dfrac{\pi }{2}[/tex] the area of the square.

2. The uniform electric field is normal to the surface, the flux through the surface is the electric field multiplied by the area of this surface.

Ф = E.A

3. Flux through the surface of the circle is given by;

[tex]= \rm E\dfrac{\pi d^2}{4}\\\\=\dfrac{2}{\pi }[/tex]

To know more about Flux click the link given below.

https://brainly.com/question/5932170

Guys pls help if I don’t know if I’m correct

Answers

Answer:

Yes u are correct

Colin invests £1200 into his bank account.
He receives 5% per year simple interest.
How much will Colin have after 3 years?
Give your answer to the nearest penny where appropriate.

Answers

Gshhebehbebe hebebeb bebebeb benenne hwbebeb hebebvecehalonw wine wow. Nennen

Which expression is equivalent to |-5| + |-3|

Answers

Answer:

5+3

Step-by-step explanation:

5+3

Answer:

5+3=8

Step-by-step explanation:

Samantha is training for a race. The distances of her training runs form an arithmetic sequence. She runs 1 mi the first day and 2 mi the seventh day.

a. What is the explicit definition for this sequence?



b. How far does she run on day 19?

Answers

B Because how far does she runs on day 19

If adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 70beats per minute and 82beats per minute.

Answers

This question is incomplete.

Complete Question

Assume that females have pulse rates that are normally distributed with a mean of u = 76.0 beats per minute and a standard deviation of 12.5 beats per minute. If 1 adult female is randomly selected, find the probability that her pulse rate is between 70 beats per minute and 82 beats per minute. The probability is (Round to four decimal places as needed.)

Answer:

0.3688

Step-by-step explanation:

The formula for calculating a z-score when given a random sample of numbers is is z = (x-μ)/σ/√n

where x is the raw score,

μ is the population mean, and

σ is the population standard deviation.

mean = 76.0 beats per minute and a standard deviation = 12.5 beats per minute.

n = number of random samples = 1

For 70 beats per minute

z = 70 - 76/12.5/√1

z = -0.48

Probability value from Z-Table:

P(x = 70) = 0.31561

For 82 beats per minute.

z = 82 - 76/12.5/√1

z = 0.48

Probability value from Z-Table:

P(x = 82) = 0.68439

The probability that her pulse rate is between 70 beats per minute and 82 beats per minute.

P(x = 82) - P(x = 70)

0.68439 - 0.31561

= 0.36878

≈ 0.3688

Just the picture, Geometry.

Answers

∠2 = ∠3 ( vertically opposite angles )

= 112° = 112°

= ∠3 = ∠7 ( corresponding angles )

Therefore , m∠7 = 112° .

What is 1.6 + 4x > 14.

Answers

Answer:

Simplifying

1.6 + 4x = 14

Solving

1.6 + 4x = 14

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.6' to each side of the equation.

1.6 + -1.6 + 4x = 14 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0

0.0 + 4x = 14 + -1.6

4x = 14 + -1.6

Combine like terms: 14 + -1.6 = 12.4

4x = 12.4

Divide each side by '4'.

x = 3.1

Simplifying

x = 3.1

Step-by-step explanation:

help me idk what it is​

Answers

the answer is the bottom one on the first row

it should be the top right answer.
4, 7, 8, 10, 11, 13, 15, 15, 22, 28 is the data set in order.
By finding the median, it would be 12, since 11+13=24/2=12
The first quartile would be 8, because between 4-11, 8 is in the middle
Then the third quartile would be 15, repeating the same process except with 13-28

So basically the answer is the top right choice. With a median of 12, first quartile 8, third quartile 15

An object is moving at a speed of 2 feet every 8.5 minutes. Express this speed in meters per hour.

Answers

Answer:

67 meters per hour

Step-by-step explanation: becasue i need pints

muggsy weigh 5/7 as much as his friend bruno. bruno weighs 125 lb. how many does muggsy weigh?

Answers

Answer:

Muggsy weighs 89 2/7 lbs.

wilma buys a new game that is priced at 43.89. She gets successive discounts of 15% followed by 5% off on the game. The purchase price of Wilma's game is what percentage of the original price?

Answers

Answer:

C

Step-by-step explanation:

Edge 2020

Answer:

c edg

Step-by-step explanation:

2x2 + x + 5 = 0 i don’t know how to do this please help

Answers

9514 1404 393

Answer:

  x = -0.25+√2.4375i or -0.25-√2.4375i

Step-by-step explanation:

The quadratic formula works for this. The quadratic equation ...

  ax² +bx +c = 0

has solutions given by the quadratic formula:

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Your equation ...

  2x² +x +5 = 0

has coefficients a=2, b=1, c=5, so the quadratic formula tells you the solutions are ...

  [tex]x=\dfrac{-1\pm\sqrt{1^2-4\cdot2\cdot5}}{2\cdot2}=\dfrac{-1\pm\sqrt{-39}}{4}\\\\x=\left\{-\dfrac{1}{4}+\dfrac{\sqrt{39}}{4}i, -\dfrac{1}{4}-\dfrac{\sqrt{39}}{4}i\right\}[/tex]

The decimal equivalents are ...

  x = -0.25+√2.4375i   or   -0.25-√2.4375i . . . . . . the 'i' is outside the radical

I need help on this I will give brainlist help it will mean a lot this is my last math problem help me!​

Answers

Answer:

the second one

Step-by-step explanation:

i did it in my head and double checked :)

Answer:

Store Z has the best sale price of $28

Step-by-step explanation:

Starting Price = $35

Store X offers 15% off = only 5.25$ off (0.15 * 35 = 5.25, 35 - 5.25 = 29.75) Final Price = $29.75

Store Y offers $5 off = only 5$ off (35 - 5 = 30) Finaly Price = $30

Store Z offers 1/5 off = only 7$ off (1/5 = 0.20, 0.20 * 35 = 7, 35 - 7 = 28) Final Price = $28 (BEST PRICE)

Anyone good with matrixes and matrices? please help me i need help with 10 questions and I need to raise my grade ASAP please

Answers

Answer:

what questions need to be done? We need to know the problems before we answer them. :/

Suppose the equation of line t is y = x. Which shows the graph of A'B'C' for Rt?

Answers

Answer:

A'(1, -1), B'(-1, 1), C'(-1, -1)

Step-by-step explanation:

Coordinates of the vertices of the given triangle ABC are,

A(-1, 1), B(1, -1), C(-3, -1)

We have to find the new coordinates of these vertices after reflection across y = x,

Rule for the reflection of a point across a line, (y = x) is,

(x, y) → (y, x)

Following the given rule of transformation,

A(-1, 1) → A'(1, -1)

B(1, -1) → B'(-1, 1)

C(-3, -1) → C'(-1, -3)

PLEASE HELP!
How do you calculate the cost of repaying a car loan

Answers

Answer:

Multiply and divide

Step-by-step explanation:

Answer:

To determine how much you can expect to pay in finance charges over the life of the loan, multiply the Monthly Payment Amount by the Number of Payments, minus the Amount Borrowed. This should give you the Total Amount of Finance Charges that you can expect to pay.

Step-by-step explanation:

Hope This Helps probably not but here!

Which figure represents the image of parallelogram LMNP after a reflection across the line y = x?

Answers

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. This gives you such reflection rule:

From the diagram:
L(3,1), M(4,3), N(5,3) and P(4,1).
Using the reflection rule, you can find coordinates of image points:
L'(1,3), M'(3,4), N'(3,5) and P'(1,4).
As you can see, these are coordinates of vertices of the figure C.
Answer: correct choice is option 3 - figure C.

Answer:

Quick answer option C

Step-by-step explanation:

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