Factor this expression completely and then place the factors in the proper location on the grid. Note: Place factors alphabetically in the grid! mr + ns - nr - ms

Answers

Answer 1

Greetings!

Find the GCF by Grouping.
[tex]mr+ns-nr-ms[/tex]
[tex]mr-ms-nr+ns[/tex]
[tex]m(r-s)-n(r-s)[/tex]
Find the GCF.
[tex](r-s)(m-n)[/tex]
This is the furthest you can factor.

Hope this helps.
-Benjamin

Answer 2

Answer:

(m-n)(r-s)

Step-by-step explanation:

We will factor this by grouping. First we rearrange the terms so the m's are together and the n's are together:

mr-ms+ns-nr

Next we group the first two and the last two:

(mr-ms)+(ns-nr)

The GCF of the first group is m; factor this out:

m(r-s)+(ns-nr)

The GCF of the second group is n; factor this out:

m(r-s)+n(s-r)

We want to have the same thing in both sets of parentheses; to do this, we will multiply the second factor by -1:

m(r-s)+-n(r-s)

Factoring out the term now in common, r-s, we have

(r-s)(m-n) = (m-n)(r-s)

Related Questions

If the length of the rectangle is twice the width and the perimeter of the rectangle is 30 cm find its area

Answers

Lets let width=x meters.
Length is twice the width, twice meaning two times and we know that the width is x so length = 2x.
The perimeter is the sum of all the sides or width + width + length + length which is equal to x + x + 2x + 2x by substituting x for width and 2x for length. We know that x is really 1x since 1 times anything is that anything.
So the perimeter can be written as 1x + 1x + 2x + 2x which we are told is equally 42 meters. We reduce the equation by collecting all terms that have the same variables so we get (1 + 1 + 2 + 2 )x = 42. Adding the collected terms together we get 6x = 42. Now we solve for x by dividing both sides of the equation by six. Whatever we do to one side we have to do to the other so the equation remains balanced. So 6x divide by 6 is 1x or we can just say x, and 42 is divided 6 giving us 7. So x = 7. Going back to our original stated facts width = x = 7 and length = twice the width or 2x = 2 (7) =14. So
width = 7 meters
legth = 14 meters

We can double check this since we know the formular for the perimeter = width + width + length + length = 7 + 7 + 14 + 14 = 42.

A jet travels 510 miles in 2 hours. At this rate, how far could the jet fly in 15 hours? What is the rate of the speed of the jet?

Answers

First, find how much distance is covered in 1 hour

510/2 = 255.

Multiply 1 hour distance covered by 15

255*15=3825 miles

Hope I helped :)

In a class of 10, there are 2 students who forgot their lunch.

If the teacher chooses 2 students, what is the probability that both of them forgot their lunch?

Answers

Answer:2/10

Step-by-step explanation: 10 students, 2 of them forgot their lunch. So 2/10 of the students will be chosen by the teacher

Evaluate the function f(x)=−4x−3 f(x)=−4x−3 for x=−6x=−6.

Answers

what does x equal?? for the questions

How to solve the second equation

Answers

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} y = &{{ -0.02}}x^2&{{ +1}}x&{{ +6}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{1^2}{2(-0.02)}~~,~~6-\cfrac{1^2}{4(-0.02)} \right) \\\\\\ (\stackrel{\textit{how far ahead it went}}{25}~,~\stackrel{\textit{how high it went}}{18\frac{1}{2}})[/tex]

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} y = &{{ -0.01}}x^2&{{ +0.7}}x&{{ +6}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{0.7^2}{2(-0.01)}~~,~~6-\cfrac{0.7^2}{4(-0.01)} \right) \\\\\\ (\stackrel{\textit{how far ahead it went}}{24\frac{1}{2}}~,~\stackrel{\textit{how high it went}}{18\frac{1}{2}})[/tex]

Eric and his work crew have 50 trees o plant. In 8 hours today, they planted 40 trees. If the work at the same rate tomorrow, how long will it take to finish planting the trees?

Answers

it will take them 1 hour and 25 minitues to plant 10 trees tomorrow

Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
Alexander thought the equivalent quarterly interest rate would be 2%. Is Alexander correct? If he is, explain
why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your
answer. i need to show my work and everything

Answers

The reason he is NOT correct is because a quarterly rate refers to 1/4 of a year. 7/4 does mot equal 2. it only equals 1.75, so his quarterly interest would be 1.75%.

List an example of two events that are independent. (b) list an example of two events that are dependent. (a) list an example of two events that are independent. choose the correct answer below.
a. a father having hazel eyes and a daughter having hazel eyes
b. selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck
c. rolling a die twice
d. not putting money in a parking meter and getting a parking ticket (b) list an example of two events that are dependent. choose the correct answer below.
a. tossing a coin and getting a head, and then rolling a six-sided die and obtaining a 6
b. selecting a ball numbered 1 through 12 from a bin, replacing it, and then selecting a second numbered ball from the bin
c. rolling a die twice
d. drawing one card from a standard deck, not replacing it, and then selecting another card

Answers

When two events are dependent, this means that one event cannot occur without the other, or simply put the two events are connected to each other in one way or the other.

When two events are independent, this means that the two events can occur separately, with one event having no effect on the occurrence of the other.

Therefore the dependent and independent events are as follows:

Independent event:

c. rolling a die twice

The outcome of the first die does not affect the outcome of the second die, hence independent.

Dependent event:

d. drawing one card from a standard deck, not replacing it, and then selecting another card

By the act of not replacing the drawn card, we are changing the probability of selecting another card, hence dependent.

Reuben drove 576 miles in 8 hours.
At the same rate, how long would it take him to drive 936 miles?

Answers

13 hours should be your answer. divide 576 by 8. divide 936 by your answer

Reuben's driving rate is 72 miles per hour. At this same rate, it would take him 13 hours to drive 936 miles.

To determine how long it would take Reuben to drive 936 miles at the same rate, we first need to find his driving rate. Reuben drove 576 miles in 8 hours. To find his rate, we divide the distance by the time:

Rate = Distance / Time

Rate = 576 miles / 8 hours = 72 miles/hour

Next, we use this rate to find out how long it will take him to drive 936 miles:

Time = Distance / Rate

Time = 936 miles / 72 miles/hour = 13 hours

Thus, it would take Reuben 13 hours to drive 936 miles at the same rate.

The endpoints of a diameter of a circle a(-1,1) and b(3,3). what is the length of the radius

Answers

If we determine the distance from one point to the second point, we get the length of the diameter. This is calculated through the equation,

D= sqrt ((x2 – x1)^2 + (y2 – y1)^2)

Substituting the known values,

D = sqrt ((-1 – 3)^2 + (1 – 3)^2)

D = 4.47

The length of the radius is half that of the diameter. Hence, the radius is,

R = 4.47 /2 = 2.236

Answer: r = 2.24

Given that f(a+b)= f(a) + f(b) and f(x) is always positive, what os the value of f(0)?

Answers

This is a strange question, and f(x) may not even exist. Why do I say that? Well..

[1] We know that f(a+b) = f(a) + f(b). Therefore, f(0+0) = f(0) + f(0). In other words, f(0) = f(0) + f(0). Subtracting, we see, f(0) - f(0) = f(0) or 0 = f(0).

[2] So, what's the problem? We found the answer, f(0) = 0, right? Maybe, but the second rule says that f(x) is always positive. However, f(0) = 0 is not positive!

Since there is a contradiction, we must either conclude that the single value f(0) does not exist, or that the entire function f(x) does not exist.

To fix this, we could instead say that "f(x) is always nonnegative" and then we would be safe.

A rectangular swimming pool with a flat bottom is 20 feet by 12 feet. How long will it take to fill the swimming pool to 5 feet if water is being pumped into the pool at 30 cubic feet per minute?
A) 8 minutes
B) 40 minutes
C) 67 minutes
D) 120 minutes

Answers

Hi,

The answer to this question is going to be

20 feet * 12 feet * 5 feet
= 20 * 12 * 5 feet ^3
= 1200 feet^3

1200 feet^3 / (30 feet^3 / minute)
= (1200 / 30) minutes
= (120 / 3) minutes
= 40 minutes

Hoped I Helped

Convert 7 4/7 to a mixed decimal and rounded to the nearest thousandth.

Answers

you got to divide four by seven. You get 0.571, as thousandths are three decimal places out. you add 7 to it and get 7.571

PLEASE HELP ASAP!! Will give brainliest!

Answers

1/2n + 3/4n = 1/2 ...multiply by common denominator 4

2n + 3n = 2

5n = 2

n = 2/5

So... n = 2/5

I hope this helped! : )
Please rate and thank!

Each digit in the division example has been replaced with the same letter throughout (r stands for remainder) the digits used were 1, 2, 3, 4, 5, 7, and 9 find the numbers clue u is 5

Answers

Final answer:

This is a cryptarithm problem where every unique letter represents a unique digit. Given that 'u' equals 5, we would navigate the problem by dividing numbers out front and subtracting the exponents.

Explanation:

This question is about a form of a cryptarithm. Cryptarithms are mathematical puzzles where the digits are replaced by letters of the alphabet or other symbols. If the same letter appears more than once, it represents the same digit each time. Your question implies that each letter corresponds to a unique digit and that division is involved. Therefore, we need to figure out which numbers are represented by the remaining letters. You've already been given that 'u' represents 5. Since there isn't a complete problem provided, I can't offer a step by step guide on how to solve it. However, I can suggest to you to start the cryptarithm solution by dividing numbers out front and subtracting the exponents.

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Final answer:

The question involves substituting the given number for a letter in a division problem and then solving it. It's a step-by-step process of trial and error.

Explanation:

In this problem, you are asked to find the numbers that replace the same letter throughout a division problem. Given that 'u' is 5, you know that wherever 'u' appears in your division equation, you can replace it with 5. Solve the division problem accordingly. Do not forget, each distinct letter represents a distinct number. It is a process of trial and error until you come up with the right numbers that fit the equation and abides by the division rules.

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round 999.999 to the nearest tenth

Answers

999.9

to the left of the point you start with tenths then hundredths and so on

Answer: 1000
Reasoning:
For the number 999.999, the 0.9 is the tenth's digit.
Since the next number is 5 or greater, we round the 0.9 up. Now 0.9 rounded up is 1, so that takes away the decimals and adds one to the ones place value.
Since we are adding 1 to 9, it becomes 10, meaning the following 9 becomes a ten as well.
All said and done, it becomes 1000 from the rounding.

A city has 7204 recycle bins. The city gives half of the recycle bins to it's citizens. The rest of the recycle bins are divided into 23 equal groups for city parks. How many recycle bins are left over?

Answers

The number of recycle bins that the city gives to citizens:
7204 : 2= 3602
The number of recycle bins is left:
7204 - 3602= 3602
The largest number of bins that can be given in each group:
3602 : 23 = 156 (residual: 14)
=> There are 14 bins left over.

Calc Question :fuel cost Please help me.

Answers

Disclaimer, I'm in pre-ap algebra 2, not calc lol. But based on common knowledge + a quick google search, I'm fairly certain this is the right answer.

So, first you need to find how many gallons the car uses per year.
Since x is the number of gallons, this would be 15000/x.

Now, you need to multiply however many gallons the car used by 2.95 to get the cost, C.
C=2.95(15000/x) is your function for this problem.
However, this can also be written as C=[tex] \frac{44250}{x} [/tex].

Let's fill in the row for C first.
Starting with 10 mpg.
44250/10
4425

So the first value should be 4425. Keep on doing this for the rest.

Now for dC/dx, this means rate of change in C caused by a change of the value x.
Starting with 10 mpg.
-4425/10
-442.5

So in the end, the table should look like this (approximating to decimals)
[tex] \left[\begin{array}{cccccccc}x&10&15&20&25&30&35&40\\C&4425&2950&2212.5&1770&1475&1264.29&1106.25\end{array}\right] [/tex]
[tex] \left[\begin{array}{cccccccc}\\dC/dx&-442.5&-196.67&-110.635&-70.8&-49.17&-36.12&-27.66\end{array}\right] [/tex]

The driver who gets 15 mpg would benefit more because
(-44250/16)/16 = -172.85
(-44250/36)/36 = -34.14

The driver with 15 mpg saves much more money than the driver with 35 mpg.

Once again, not fully certain if that is correct, but the answer seems logical to me, and I did google a bit to check it.

Solve the inequality
7x ≥ -7

a. x ≤ -1
b. x > -14
c. x ≥ -1
d. x ≥ 14

Answers

7x ≥ -7

Divide both sides by 7 to get x by its self....

x ≥ -1 is the answer ..

To check substitute the -1 for x in the inequality..

7(-1) ≥ - 7
- 7 ≥ -7

It is correct because - 7 is greater than or EQUAL TO -7

Answer:

A: x ≥ -1

its rightc bc

How do you verify that a hexagon formed by A=(0,0), B=(2,1), C=(3,3), D=(2,5), E=(0,4) and F=(-1,2) is equiangular? (I already know that it is equilateral)

Answers

The solution is attached. This is the only way I could verify if it is equiangular.

Final answer:

To verify that the hexagon is equiangular, calculate the slopes and angles of all sides using the coordinates of the vertices.

Explanation:

To verify that a hexagon is equiangular, we need to show that all interior angles of the hexagon are congruent. We can calculate the angles using the coordinates of the vertices A, B, C, D, E, and F.

Calculate the slope of each side of the hexagon. For example, for side AB with points A(0,0) and B(2,1), the slope is (1-0)/(2-0) = 1/2.Use the slope to find the angle using the formula arctan(slope). For side AB, the angle is arctan(1/2) = 26.57 degrees.Repeat steps 1 and 2 for all sides of the hexagon.If all six angles are equal, then the hexagon is equiangular.

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Robert climbed 775 steps in 12 1/2minutes. how many steps did he average per minute?

Answers

1162 is the awnser i believe

What’s the reciprocal of 7/2a

2a/7

-2a/7

7/2a

-7/2a

Answers

The reciprocal of a number (also called the multiplicative inverse) means 1/this number or (This number)^-1

So, to get the reciprocal of 7/2a, you need to divide 1 by this number as follows:
reciprocal = 1 / (7/2a) = 2a/7

The answer is : 2a/7

PLESEEE HELP I WILL GIVE THE BRAINLIEST TO THE BEST ANWSERS
Which word sentence represents the equation?

6(x + 3) = 42

A)The sum of 3 and six times some number is 42.

B)Three plus 3 times some number is 42.

C)Six times some number plus 3 is 42.

D)Six times the sum of a number and 3 is 42.

What is the solution set for 3x + 2 = 14, given the replacement set {1, 2, 3, 4} ?

A)x = 1B)x = 2C)x = 3D)x = 4

Answers

The answer to the first question is D.)

The 6 in front of the parentheses modifies both 'x' and 3

The answer to the second question is D.)

When you plug 4 into the equation, you get 14

3(4) + 2 = 14
12 + 2 = 14
14=14

Hope this helps!

the answers are D and D.

A shop has a sale that offers 20% off all price. On the final day they reduce all the sale prices by 25%. Linz buys a radio on the final day. Work out the overall percentage reduction on he price of the radio.

Answers

hmmmm is not very clear if the 25% is just 25% of the original price, or of the reduced price, but let's assume is of the reduced price.

say the original price is "x", 20% off that, means the sale price is 80% of the original price, or (80/100) * x, or 0.8x.

then Linz shows up on the last day, and she's got 25% off from that price plus a beanie baby and a free garden hose.

so if the price is reduced by 25%, then the sale price is just 75% of whatever it was, but it was already reduced to 0.8x, what is 75% of 0.8x?

(75/100) * 0.8x, or 0.75 * 0.8x, which is 0.6x, now 0.6 * 100 is 60 to change it to percentage format, or 60% overall percentage reduction from the original price.

Final answer:

To calculate the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. The second discount of 25% off reduces the price by 25/100 = 0.25. The overall percentage reduction is 40%.

Explanation:

To find the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. So, the price after the first discount is 1 - 0.2 = 0.8 times the original price. The second discount of 25% off reduces the price by 25/100 = 0.25. So, the final price after both discounts is 0.8 * (1 - 0.25) = 0.8 * 0.75 = 0.6 times the original price.

To calculate the overall percentage reduction, we can subtract the final price from the original price, divide by the original price, and multiply by 100. The overall percentage reduction is ((1 - 0.6) / 1) * 100 = 40%.

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To take a taxi , it cost $3.00 plus an additional $2.00 mile traveled. you spent exactly $20 on a taxi, which includes the $1tip you left. how many miles did you travel?

Answers

Let's break it down.
You spent $20. Plus the $1 tip.
20 - 1 = 19
$19 is how much you spent without the tip
The cost for the taxi ride itself is $3
19 - 3 = 16
$16 is how much you spent without the ride cost + tip
You spent $2 for every mile traveled.
16/2=8

You traveled 8 miles

Write a decimal number that, then round to the nearest tenth, is 0.3.

Answers

0.34 could round down to o.3

vertical angles are opposite angles with the same vertex
true or false

Answers

true
Vertical angles are opposite angles with the same vertex

An air cargo plane can transport as many as 15 regular shipping containers. One supersize container takes up the space of 3 regular containers.

Answers

An air cargo plane can transport as many as 15 regular shipping containers. One super-size container takes up the space of 3 regular containers. Write an inequality to model the number of regular and super-size containers the plane can transport.

Let the number of regular containers the plane can transport be x and the number of super-size containers the plane can transport be y, then

Given that one super-size container takes up the space of 3 regular containers, i.e. y = 3x and that the capacity of the plane is 15 regular containers.

When the ship is not carrying any super-sized container, it can carry up to 15 regular containers and when the ship is not carrying any regular containers it can carry up to 5 super-sized containers.

Therefore, the inequality to model the number of regular and super-size containers the plane can transport is given by

x + 3y ≤ 15

The length of a rectangle is four times its width. If the perimeter is at most 100 centimeters, what is the greatest possible value for the width? Question 17 options:

Answers

if l=4w:
l=40, w = 10
40+40+10+10=100cm
anything bigger isn't allowed, so the width is 10cm

A baker wants to put 3 3/4 pounds of apples in each pie sge makes. She purchased 52 1/2 pounds of apples. How many pies can she make?

Answers

52.5 / 3.75 = 14

She can make 14 pies.

divide 52 1/2 pounds by 3 3/4 pounds

52 1/2 / 3 3/4 = 14

she can make 14 pies

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