Four students were asked to write an expression which has terms that have a greatest common factor of ab. The expressions provided by the students are shown below.


Michelle
16 a + 3 b

Naomi
18 a b c minus 13 a b c

Olivia
20 a b minus 14 a b c

Peyton
15 a b c + 14 a b

Which student wrote the correct expression?
Michelle
Naomi
Olivia
Peyton

Answers

Answer 1

Answer:

D.) Peyton

Step-by-step explanation:

If m is any integer, then gcd(a + m⋅b, b) = gcd(a, b). If m is a positive common divisor of a and b, then gcd(a/m, b/m) = gcd(a, b)/m. The GCD is a multiplicative function in the following sense: if a1 and a2 are relatively prime, then gcd(a1⋅a2, b) = gcd(a1, b)⋅gcd(a2, b). Factoring out the GCF is the first step in many factoring problems. Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common. Step 2: Factor out (or divide out) the greatest common factor from each term.

Answer 2

Answer:

peyton is correct because she is the only one with ab even in her awnser

Step-by-step explanation:


Related Questions

Why do you think adding and subtracting polynomial expressions is like adding and subtracting
expressions?

Answers

Answer:

Polynomials are closed under addition and subtraction, which is fancy mathspeak that means that whenever we add or subtract two polynomials, we always get another polynomial. In that way, they behave a lot like the numbers you're probably already familiar with. Adding and subtracting:

Two integers gives you another integerTwo rational numbers gives you another rational numberTwo real numbers gives you another real number

And it works the same with polynomials!

Determine if the following statements are true or false. If true give a reason or cite a theorem and if false, give a counter example.

a. If {a _n} is bounded, then it converges.
b. If {a _n} is not bounded, then it diverges.
c. If {a _n} diverges, then it is not bounded

Give an example of divergent sequences {a _n} and {b _n} such that {a _n + b _n} converges

Answers

Answer:

a. False the series [tex]\sum\limits_{i=1}^\infty (-1)^n[/tex]is bounded but does not converge

b. False, xₙ = n + (-1)ⁿ⁻¹(n - 1) does not diverge to infinity but it is not bounded for n ≥ 1

c. False some bounded sequences are divergent

An example of divergent sequences, aₙ, and bₙ, such that aₙ + bₙ converges is [tex]a_n = \sum\limits_{n} \dfrac{1}{n} , \, b_n = \sum\limits_{n} \dfrac{-1}{n}[/tex]

[tex]\sum\limits_{n} \dfrac{1}{n} + \sum\limits_{n} \dfrac{-1}{n}[/tex] is convergent

Step-by-step explanation:

absolute value of -93​

Answers

The absolute value will be the positive version of the number
absolute value of -93 will be 93

Answer:

93

Step-by-step explanation:

The absolute value is just how far from away from zero a number is.

The time it takes to charge the battery of a cell phone is directly proportional to the charge of the battery.
The equation, y = 0.21x, is used to approximate the time it takes to charge the battery of a cell phone.
Cell Phone Battery Charge
100
70
60
Bettery Charge (%)
SON
40
BO
20
NON
Time (AM)
Approximate how long it will take the battery to charge to 100%.
4 hours
7 hours
6 hours
5 hours
Please help me

Answers

12.1+0.21x=100.23
That is the answer

Name this net pattern.

Answers

Answer:

triangular pyramid

Step-by-step explanation:

help me with this please!!! :)

Answers

Answer:

C. 4x-4

Step-by-step explanation:

If you divide by 4 on the left side you get...

16x/4 - 16/4

4x - 4

We are dividing by 4 because it was factored out of the expression.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded annually, how much total interest will she earn in 10 years?

Answers

If you use the formula you would get $3992.77 in 10 years

Tara has a large box of treats that weighs 9.0 pounds. She uses the large box of dog treats to make smaller bags, each containing 0.6 pound of treats. How many smaller bags of dog treats can Tara make?

Answers

Answer:

Step-by-step explanation:

So, she has a box of treats that weighs 9.0 pounds.

She's using those treats to make smaller bags, each having 0.6 pounds of treats.

How many smaller bags can she make?

Which of the following rational functions is graphed below?
O A. F(X) =
2x
x(x - 2)
B. F(x) =
1
x(x - 2)
C. Fix) =
1
x(x - 2)
D. F(x) =
x + 1
(x + 2)(x +0)

Answers

Answer:

Huh? I'm not sure what you're asking try C

Answer:

B. f(x) = 1/x(x - 2)

Step-by-step explanation:

The graphed function has two vertical asymptotes.

The functions A and D have degree 1 on the numerator and degree 2 on the denominator, so finally having degree 1, have one vertical asymptote, therefore discounted.

We are left with B and C.

Function B has vertical asymptotes 0 and -2.

This is matching the graph, correct

Function C has vertical asymptotes 0 and 2

This is not matching the graph, incorrect

See the attached to confirm

cupcakes for a bake sale. He can bake 45
cupcakes in one hour. Which inequality shows the minimum number of hours that Hannah must bake to make at least 250
cupcakes?

Answers

Answer:

About 5 to 5.5 hours

Step-by-step explanation:

Get out of my swamp!

Determine the roots of the following function of the quadratic formula:
x^2-5x-4=0

Answers

Answer:

4,1

Step-by-step explanation:

(x-4)(x-1)

x=4 or x=1

The answer is 4,1
-------------------------11

Find y if the line through (5, 2) and (7, y) has a slope of 4.

Y=___

Answers

Answer:

5

Step-by-step explanation:

45 degrees and 6 find each variable
Will mark brainliest

Answers

Answer:

[tex]x = y = 3\sqrt{ 2[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find x and y

The given triangle has 45 degrees as one of its angles, and it is also a right angle triangle.

For this kind of parameter, the opposite = the adjacent

i.e. x = y

Apply Pythagoras theorem

[tex]x^2 + y^2= 6^2[/tex]

Substitute x for y

[tex]y^2 + y^2= 6^2[/tex]

[tex]2y^2= 36[/tex]

Divide by 2

[tex]y^2 = 18[/tex]

Take square root

[tex]y = \sqrt{18[/tex]

[tex]y = \sqrt{9 * 2[/tex]

Split

[tex]y = \sqrt{9} *\sqrt{ 2[/tex]

[tex]y = 3*\sqrt{ 2[/tex]

[tex]y = 3\sqrt{ 2[/tex]

[tex]x = y = 3\sqrt{ 2[/tex]

Solve this system of equations:
y = x - 4
y = 6x - 9
Show your work in the text box below.
also Write your answer as an ordered pair.

Answers

Answer:

y=-3 x=1 (1,-3)

Step-by-step explanation:

y=x-4

y=6x-9

y+4=x

y+9=6x

difference = 5

x+5=6x

x=1

y=-3

1,-3

What is the volume of a rectangular prism with a height of 6 m, a length of 4 m, and a
width of 2 m?

Answers

48

Volume = length x width x height
4(2) = 8
8(6) = 48

Express as a difference: a+5

Answers

Ax5 a➗5 and a-5

................

The expression expressed as a difference is (a - 2) - (-7).

We have,

We can express a + 5 as a difference by subtracting a suitable term from it.

One way to do this is to subtract 2 and add 2, like this:

a + 5 = a + 5 - 2 + 2   (adding and subtracting 2)

     = (a - 2) + 7     (rearranging)

Now,

We can express a + 5 as the difference between a - 2 and -7, like this:

a + 5 = (a - 2) - (-7)

Thus,

The expression expressed as a difference is (a - 2) - (-7).

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A system of inequalities is shown below.
y < -1
2x - y < 2
In which quadrants is the solution set of the system?

Answers

Answer:

C

I may be wrong sorry if I am

Answer:

The answer is C

Step-by-step explanation:

Since they both have a negative y and Quardant 4 has a positive x

Someone helllppppppppppoppppoop

Answers

Answer:

The answer is 2..............

Evaluate: x + (x2 - xy) - y
if x = 5 and y = 4

Answers

the answer to this is -9

When x = 5 and y = 4, the expression [tex]x + (x^2 - xy) - y[/tex]  evaluates to 6.

To evaluate the expression [tex]x + (x^2 - xy) - y[/tex] when x = 5 and y = 4, we substitute the given values into the expression and perform the

calculations:

[tex]x + (x^2 - xy) - y\\x= 5 + (5^2 - 5*4) - 4\\x= 5 + (25 - 20) - 4\\x= 5 + 5 - 4\\x= 10 - 4\\x= 6\\[/tex]

It's crucial to remember that the expression in question is not an equation that represents a graph, nevertheless. It is merely an algebraic expression that, given the values of "x" and "y," evaluates to a single value. We need an equation that connects 'x' and 'y' and specifies the relationship between them if we are to construct a graph.

Therefore, when x = 5 and y = 4, the expression [tex]x + (x^2 - xy) - y[/tex] evaluates to 6.

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Correct Question is:

Evaluate:  [tex]x + (x^2 - xy) - y[/tex] if x = 5 and y = 4.

Ms. Reiger’s students found a total of 16 bird feathers. The line plot shows the lengths, in inches, of the bird feathers found by the students
Look at the line plot, and then select the two correct statements about the bird feathers.
The difference between the lengths of the shortest feather and the longest feather is 318 inches.
A. The difference between the lengths of the shortest feather and the longest feather is 238 inches.
B. The combined length of the two longest feathers is 828 inches.
C. The combined length of the shortest feather and the longest feather is 738 inches.
D. The combined length of the shortest feather and the longest feather is 618 inches.

Answers

Answer:

i need the picture to answer the question, sorry. but if you give me the picture im happy to answer it

Step-by-step explanation:

A business school is conducting a study to investigate whether a students’ scores on a placement test can be used to predict students’ starting salaries. Based on a random sample of 200 graduates of the business school, a 98 percent confidence interval for the slope of the linear regression line relating placement scores and starting salary is calculated to be (315,336). Assume the conditions for inference are met.

Which of the following is a correct interpretation of the confidence interval?

a. There is a 98 percent probability that the slope of the population regression line is between $315 per point and $336 per point.
b. Ninety-eight percent of the time, a 10-point increase in placement score will result in an average increase between $3,150 and $3,360 in starting salary.
c. We are 98 percent confident that a 10-point increase in placement score will result in a predicted increase in starting salary of between $3,150 and $3,360.
d. We are 98 percent confident that predicted starting salaries will be between $315,000 and $336,000.
e. We are 98 percent confident that the regression equation can be used to make accurate predictions for placement scores between 315 and 336.

Answers

Answer:

The answer is C

Step-by-step explanation:

I did it on college board

The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $85,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $8,700.

The Mean Corporation's statisticians would like to construct a hypothesis test for the population mean annual profit earned by health-drink franchises. A random sample of 50 franchises was chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $82,441.

The hypotheses that were used by the statisticians were

Null hypothesis: population mean = 81,000, Alternative hypothesis: population mean > 81,000 and the test statistic was found to be 1.29 (to 2 decimal places).

Required:
Calculate the p-value for this test, giving your answer as a decimal to 4 decimal places.

Answers

Answer:

The p-value is approximately 0.9015  

Step-by-step explanation:

The statistic parameters are;

The population mean, μ₀ = $85,000

The population standard deviation, σ = $8,700

The size of the sample, n = 50

The sample mean annual profit, [tex]\bar x[/tex] = $82,441

The null hypothesis, H₀: μ = 81,000

The alternative hypothesis, Hₐ: μ > 81,000

Given that n > 30, a z-test is used

The test statistic ≈ 1.29

Therefore, we have;

[tex]z=\dfrac{\bar{x}-\mu_0 }{\dfrac{\sigma }{\sqrt{n}}} = 1.29[/tex]

From the z-score, the p value for a test statistic of 1.29 = 0.90147 which is 0.9015 after rounding up to 4 decimal places

For what value(s) of k will the relation not be a function?
#1: A = {(k^2, 16), (4k, 32)}
#2: B = {(k^2-5k, 10), (k+7, 4)}
#3: R = {(k^3-5k^2+3k, -5), (-k, 4)}
#4: S = {(|k+1|+2, 4), (8, 7)}
Will give 100 points and Brainliest!

Answers

Answer:

See below

Step-by-step explanation:

The relation is not a function when x -value is same but y- values are different.

#1

k^2 = 4kk = 0, k = 4

#2

k^2 - 5k = k + 7k^2 - 6k = 7k^2 - 6k + 9 = 16k - 3 = 4 ⇒ k = 7k - 3 = -4 ⇒ k = -1

#3

k^3 - 5k^2 + 3k = -kk^3 - 5k^2 + 4k = 0k(k^2 - 5k + 4) = 0k = 0, k = 1, k = 4

#4

|k + 1| + 2 = 8|k + 1| = 6k = 5, k = -7

An Olympic swimmer competes in the same events during each long course swim season. A swimmer currently
competing on the United States Women's Olympic Swim Team, will swim her best events each year with the hope of
continuous Improvement. The following table is a record of the swimmer's best times for the 100 meter freestyle event,
measured In long course meters.
Long Course Recorded
Season Best Time
2005 2:33.42
2006
2:24.81
2007
2:10.93
2008
2:03.45
2009
1:58.67
2010
1:59.17
1:55.06
2011
2012
1:55.82
2013
1:54.81
2014
2:00.03
1. Create a scatter plot representing the data displayed in the table.
2. Use the scatter plot to determine whether there is positive, negative or no correlation between the data values.
3. Write a conclusion statement regarding the data and the rate of change present in the line of best fit. Do not actually
calculate the slope or write the equation for the line of best fit.

Please help me
Will give brainly
Just give me the answer to 2 and 3
I already have 1
I just need 2 and 3
Please and thank you
Please answer this

Answers

Answer: Equation for the line of best fit is given by f(x)=-4.28402x+0.0875

Step-by-step explanation: like what you just put in your picture

Long Course Season Recorded Best time

2005 2:33.42

2006 2:24.81

2007 2:10.93

2008 2:03.45

2009 1:58.67

2010 1:59.17

2011 1:55.06

2012 1:55.82

2013 1:54.81

2014 2:00.03

-Since we can see from the scatter plot that it has negative correlation.

Equation for the line of best fit is given by f(x)=-4.28402x+0.0875

- This is what I can give you I see some people do this work before and when I see it I just take note and I think it was the answer...

- Hope this help :)

find the measure of angle a.

Answers

Answer:

<A=50

Step-by-step explanation:

85+x+55+x+50=180

2x+190=180

2x=180-190

2x=-10

x=-5

A=x+55

A=-5+55

A=50

A< 50 because i said so

Work out the number of cubes in the cuboid

Answers

20 cubes in the cuboid

there are 15 peices of fruit in a bowl and 6 of them are apples what percentage of the peices of fruit are apples​

Answers

Answer:

40%

Step-by-step explanation:

6/15 = 0.4

0.4x100 = 40%

how many people in the town of summit have jobs if there are 9,255 people in the town and 1/3 of them are employed? simplify the fraction if possible ​

Answers

Answer:

divide 9,255 divide 1/3 and you will get your answer hope this helps :)))

Step-by-step explanation:

In the town of Summit, 3,085 people have jobs. If there are 9,255 people in the town and 1/3 of them are employed.

To find the number of people in the town of Summit who have jobs, we can multiply the total population by the fraction representing the employed individuals.

Total population = 9,255 people

Fraction employed = 1/3

Number of people employed = Total population * Fraction employed

Number of people employed = 9,255 * (1/3)

To simplify the fraction (1/3), we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case.

Dividing 1 and 3 by 1, we get:

1/1 = 1

3/1 = 3

So, the simplified fraction is 1/3.

Continuing the calculation:

Number of people employed = 9,255 * (1/3)

Number of people employed = 9,255 / 3

Number of people employed = 3,085

Therefore, in the town of Summit, 3,085 people have jobs.

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7 Select the correct answer. A scientist is trying to predict the reglors of the world most likely to see a decrease in natural resources from population changes. Based on the evidence in the graph, what should the scientist conclude? ​

Answers

Answer:

A

Step-by-step explanation:

Jessie started a record collection with 8 records. Each week he added 3 records to his collection. Riley started her record collection with 23 records. Each week she gave away 2 records.

a) Write an equation to represent the number of records in Jessie's collection based on the number of weeks he has been collecting records.

Answers

3 per week + blank=8              Step-by-step explanation: brainly plz

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