Factor by grouping xy+8y+7x+56

Answers

Answer 1

Factor out y in xy+8y and factor out 7 in 7x+56

y(x+8) + 7(x+8)

(x+8)(y+7)

Answer 2

The expression xy + 8y + 7x + 56 is factored by grouping into (y + 7)(x + 8), by first factoring out the greatest common factors from each grouped pair and then recognizing a common binomial that can be factored out.

The question involves the topic of factorization by grouping, which is a method used in algebra to simplify expressions by finding common factors. The student is asked to factor the expression xy + 8y + 7x + 56. This expression can be factored by grouping in pairs and finding common factors within each group, after which the resulting expressions will also have a common factor that can be factored out.

Step-by-step solution:

Group the terms: (xy + 8y) + (7x + 56).

Factor out the greatest common factor from each group: y(x + 8) + 7(x + 8).

Notice that (x + 8) is a common factor and can be factored out again, which gives us the final factored form: (y + 7)(x + 8).


Related Questions

Sarah owns a car that runs on a mixture of gasoline and ethanol. She can buy fuels that have 85% ethanol or 25% ethanol. How much of each type of fuel should she buy if she wants to fill her 20 gallon tank with a mixture of fuel that contains 50% ethanol?

Answers

Denise needs to buy 25/3 gallons of 85% ethanol and 35/3 gallons of 25% ethanol to have 20 gallons of 50% ethanol.

x | y | 20 gal

use x and y because you don't know how much she needs.


0.85x | 0.25y | 20(0.5)


85% is 85/100 or 0.85, and you need that much of x, same goes for the 25% and 50% mixtures


so now you can make up 2 equations

1) x + y = 20

2) 0.85x + 0.25y= 10 (you get 10 when you multiply 20 by 0.5)


now you can solve for x or y using substitution. first rewrite 1) in terms of x or y:

x+ y= 20 ----> y= 20 - x


now you can substitute 20- x for y in the second equation..

0.85x + 0.25y= 10

0.85x + 0.25(20-x)= 10 distribute here..(0.25 * 20 and 0.25 * (-x) )

0.85x + 5 - 0.25x = 10 combine like terms

0.6x +5 = 10 move the 5 over to the other side

0.6x= 10 -5

0.6x = 5 divide both sides by 0.6

x= 25/3 or 8.3 now you know the amount of x so you can substitue this back into the first equation to find y.


0.85x + 0.25y= 10

0.85(25/3) +0.25y= 10

85/12 + 0.25y= 10

0.25y = 10- 85/12

0.25y= 35/12

y= 35/3 or 11.6


you can check by putting these values into the euations:

1) x+ y= 20

25/3 + 35/3 =20

20= 20 good so far


2) 0.85x + 0.25y= 10

0.85(25/3) + 0.25(35/3)=10

10 = 10 so our values for x and y work

What is 64 ounces in 8 cups as a unit rate

Answers

you have to divide 64 and 8

then you get the answer: 8 ounces per cup


select whether the equation has a solution or not, square root x-2- square root 2x= square root x+2 (a. roots b. no roots)

Answers

The equation is [tex]\sqrt{x-2 \\ \\[/tex] -[tex]\sqrt{2x}[/tex] = [tex]\sqrt{x +2}[/tex]


Solution

Step 1:

Take square on both sides, we get

3x - 2[tex]\sqrt{x-2}[/tex][tex]\sqrt2{x}[/tex] -2 = x +2

Step 2:

Subtract 3x - 2 from both sides, we get

-2[tex]\sqrt{x-2} \sqrt{2x} = -2x + 4[/tex]

Step 3:

Again, square on both sides in order to get rid of the square root from the above equation, we get

[tex]8x^{2}-16x = 4x^{2} -16x +16[/tex]

Now we have to simplify it,

[tex]4x^{2} -16 = 0[/tex]

Step 4:

Now we have to solve this quadratic equation, in order to get the solution.

We get x = 2 and x = -2, When we verifying solution in the original given equation, the solution does not satisfy the equation.

Reason: We get negative number in the square root.

Therefore, it has no Roots.


Answer: b) No roots

write the number of laps completed per minute

Answers

laps per minute by:

- Mai- 12/3 = 4 laps

- Lena- 48/6= 8 laps

- Susan- 30/5= 6 laps

thus, the person who drove fastest was Lena, who drove 8 laps per minute.

Least common factor of 17 and 6

Answers

That will be 1, since 17 can only be factored by itself and 1

Even though 6 can be factored by 3 and 2, the least common factor between 17 and 6 will be 1.

Hello there,

The correct answer is 2 the (LCM) or Least common factor of 17 and 6 is 2

If my answered helped you understand more greatly please mark me as brainliest thank you and have the best day ever!

estimate 19 precent of 41

Answers

19% turns into 20%

20%*41=8.2

Have a nice day.

A horizontal plane passes through a cone that has a horizontal base.

Which figure or figures can be produced? Select all that apply.

Answers

If the horizontal plan passes through the cone that have horizontal base, the shaped form will be circular.


B AND C I THINK BUT IM NOT SURE

Mrs. Travis rode her bike 17.8 miles the first week, 21.5 miles the second week, and 13.4 miles the third week. The rest of her mileage was in the final week of the month. Her total mileage for the month was 62.9 miles.

Answers

She rode her bike 10.2 mile the final week.

You simply just add all of the numbers together & subtract from 62.9 then get 10.2.

Hopefully this helps! :-)


Tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers? It's participation so I just have to have an answer, it doesn't have to be right. Read comments for solution.

Answers

Let

n-------> the lesser even number

n+2----> the greater even number

we know that

[tex]3(n+2)=(n-10)[/tex]

Solve for n

[tex]3n+6=n-10[/tex]

Combine like terms

[tex]3n-n=-10-6[/tex]

[tex]2n=-16[/tex]

[tex]n=-8[/tex]

so

[tex]n=-8\\n+2=-8+2=-6[/tex]

therefore

the answer is

the lesser even number is [tex]-8[/tex]

the greater even number is [tex]-6[/tex]

Find the equation of the line that is parallel to y=-x+9 and contains the point (7,-13).

Answers

y=-x-6 is the answer.

The equation of the line that is parallel to y = -x + 9 and passes through the point (7, -13) is y = -x - 6.

Now, we want to find the equation of a line that is parallel to this given line and passes through the point (7, -13). Since the new line is parallel, it will have the same slope of -1. Let's denote the equation of the new line as y = mx + b. We know the slope (m = -1), and we have a point (7, -13) that the line passes through. We can use this information to find the value of b.

To find b, we can plug in the coordinates of the point (7, -13) into the equation y = -x + b:

-13 = -1 * 7 + b

Now, solve for b:

b = -13 + 7

b = -6

Therefore, the value of b is -6.

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angle A and angle B are complementary angles. if the measure of angle B is 29 degrees, what is the measure of angle A?

Answers

Angle A measures 61 because complementary angles are angles that added together make a 90 degree angle

The measure of angle A is 61 degrees.

Given that

Angle A and angle B are complementary angles.

If the measure of angle B is 29 degrees.

We have to determine

The measure of angle A?

According to the question

The measure of angle A is determined in the following steps given below.

When adding the two complementary angles the sum of the angle is equal to 90 degrees.

[tex]\rm \angle A + \angle B = 90[/tex]

The measure of angle B is 29 degrees.

Then,

The measure of angle A is,

[tex]\rm \angle A + \angle B = 90\\\\\rm \angle A + 29= 90\\\\\rm \angle A =90-29\\\\\rm \angle A =61[/tex]

Hence, the measure of angle A is 61 degrees.

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What is the following sum? 5(3sq root x)+9(3sq root x)

Answers

[tex]Domain:\ x\geq0\\\\5\sqrt[3]{x}+9\sqrt[3]{x}=(5+9)\sqrt[3]{x}=14\sqrt[3]{x}[/tex]

Functions can be defined using graphs, tables, and ordered pairs. Define the domain and range of a function.

The domain is the output and the range is the input.

The domain is any x-value used and the range is all numbers.

The domain is all numbers and the range is any x-value used.

The domain is the input and the range is the output.

Answers

The domain is the input and the ramge is the output.

Domain = x Range = y

You cant say that the domain/range is ALL NUMBERS you can only say it is and x/y value.

Input = x. Output = y

True or False? In a two-column proof, the left column states your reasons.

Answers

False because the left is statement in the right is reason

False becuase wat you picked is definitley wrong

Victoria drove 211⁄2 miles in 2⁄3 of an hour. What was her speed?      A.) 32 1/2 miles per hour B.) 32 1/3 miles per hour C.) 32 3/4 miles per hour D.) 32 1/4 miles per hour

Answers

change each to improper fractions

21 1/2 = (2*21 +1)/2 = 43/2

2/3 = 2/3

43/2  divided by 2/3    

copy dot flip

43/2 * 3/2

129/4 = 32 1/4

Answer:

Speed of Victoria, [tex]v=32\dfrac{1}{4}\ miles/hour[/tex]

Step-by-step explanation:

It is given that,

Distance covered by Victoria, [tex]d=21\dfrac{1}{2}\ miles=\dfrac{43}{2}\ miles[/tex]

Time taken, [tex]t=\dfrac{2}{3}\ hour[/tex]          

Speed (v) of Victoria is given by total distance divided by total time taken. It is given by :

[tex]v=\dfrac{d}{t}[/tex]

[tex]v=\dfrac{\dfrac{43}{2}\ miles}{\dfrac{2}{3}\ hour}[/tex]

[tex]v=\dfrac{129}{4}\ miles/hour[/tex]

or

[tex]v=32\dfrac{1}{4}\ miles/hour[/tex]

So, the speed of Victoria is [tex]32\dfrac{1}{4}\ miles/hour[/tex]. Hence, this is the required solution.

explain in words how to find the product of -4(-1.5) on the number line

Answers

Multiplying Negatives odd # of negatives means negative answer. even means positive answer.

-4(1.5) Change both to improper fractions

-4/1(6/5) Multiply

-24/5  Simplify

-4 4/5   THE END

Final answer:

To find the product of -4(-1.5) on the number line, start from zero, move 4 units to the left due to the negative sign, and then move 6 units (4 x 1.5) to the right because of the negative multiplied by a negative rule. The result is 6.

Explanation:

To find the product of -4(-1.5) on the number line, you would follow a few steps. First, choose your starting point on the number line. In this case, the starting point would be zero.

Next, because the first number is negative, move 4 units to the left from zero. Since the second number is also negative, it changes the direction. So multiply by 1.5 in the opposite direction, which means moving to the right on the number line.

However, as it's a decimal multiplication you need to move 1.5 times or multiply the distance you moved when you moved 1 unit 4 times. It's like taking 1.5 steps to the right for each of the 4 steps we initially moved to the left. In the end, you will end up 6 units to the right of 0. Thus, the product of -4 and -1.5 is 6.

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of the 125 guests invited to a wedding, 104 attended the wedding. what percent of the invited guests attended the wedding?

Answers

The answer is 83.2%, Hope this helps

What is the value of y 10 18 2y+4 10+2x

Answers

10 = 2y + 4
6 = 2y
y = 3

18 = 10 + 2x
8 = 2x
x = 4

Answer:

[tex]y=3[/tex]

Step-by-step explanation:

Given figure is a rectangle.

In a rectangle , opposite sides are equal

to find out y we equate the opposite sides 10 and 2y+4

[tex]10=2y+4[/tex]

Subtract 4 from both sides

[tex]10-4=2y+4-4[/tex]

[tex]6= 2y[/tex]

Divide both sides by 2

[tex]y=3[/tex]

What is the equation of the verticl line through (5,2)?

Answers

It's a vertical line so it runs straight up and down. We need to simply find what x equals. The answer would be x = 5

Final answer:

The equation of a vertical line passing through the point (5,2) is x = 5. This type of line has an undefined slope and is defined by its x-coordinate, not dependent on the y-coordinate.

Explanation:

The equation of a vertical line that passes through the point (5,2) can be determined by understanding that a vertical line has an undefined slope and does not depend on the y-coordinate for its location on a coordinate plane. Instead, a vertical line's location is solely determined by its x-coordinate. Therefore, the equation of a vertical line that passes through (5,2) will have the same x-coordinate for all its points. This means that the equation for the vertical line through (5,2) is simply x = 5.

This equation is different from the conventional y = mx + b, which defines a straight line with a slope m and y-intercept b. In the case of a vertical line, the slope is undefined, and therefore, the standard linear equation cannot be applied. Instead, the equation is independent of y and is expressed only in terms of the constant x-value of the vertical line.

Sam thinks of a number n. He multiplies his number by 7 and then he adds 3 to the result. His final answer is 45. Write down an equation for this information
Solve the equation and find the number n.

Answers

N x 7 +3 = 45


N = 6    Hope this helps.

Hi GueenSilia,

Answer: (n x 7) + 3

45 - 3 = 42

42 / 7 = n

n x 7 + 3 = 45

----------------------------

42 / 7 = 6

6 x 7 = 42

42 + 3 = 45

n = 6

1. There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. How many different combinations of players are possible?

2. There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. If the selection is random, what is the probability of selecting a team of 5 girls and 5 boys? what is the decimal?

Answers

Answer:  1.  286 different combinations of players are possible.

2.  The probability of selecting a team of 5 girls and 5 boys is [tex]\frac{63}{143}[/tex] and the decimal is 0.4405...

Step-by-step explanation:

1.  Number of girls is 6 and number of boys is 7.

So, the total number of players = 6+7 = 13

A team of 10 players is to be selected from the class.

So, the total possible number of different combinations of players will be:  [tex]^1^3C_{10} = \frac{13!}{10! (13-10)!}=\frac{13*12*11*10!}{10!*3!}= \frac{13*12*11}{6}=286[/tex]


2.   Number of girls is 6 and number of boys is 7.

The possible number of teams by selecting 5 girls and 5 boys will be:  [tex]^6C_{5}\times ^7C_{5} =6\times 21= 126[/tex]

and the number of total possible teams of 10 players [tex]= ^1^3C_{10} =286[/tex]

Thus, the probability of selecting a team of 5 girls and 5 boys [tex]=\frac{126}{286}= \frac{63}{143}[/tex] or [tex]0.4405...[/tex]

round 457.395 to 2 decimal places

Answers

The answer is: 457.40
457.40 is the answer.

Write a decimal that is 1 Tenth of 0.9.

Answers

0.09

-hope this helps

the equation y=0.5x represents the distance Henry hikes,in miles,over time in hours.The graph represents the rate that Clark hikes. Determine which hiker is last

Order from least to greatest 4/5 3/4 0.88

Answers

from least to greatest the order is 3/4, 4/5, 0.88
3/4, 4/5, 0.88. convert them all into decimals and it will be easier

If f(x)= 6x+7, determine the value of f(m)

Answers

[tex]<b>HEY THERE!![/tex]

Question:- If f(x)= 6x+7, determine the value of f(m)

Solution:-

In theis question you have to substitute x with m so wherever is x put m

=> f(m) = 6m+7

HOPE IT HELPS YOU.

1. Suppose you invest $500 at 10% interest, compounded annually. After 5 years, how much money would you have in your account? Remember, the formula is A = P(1 + r)t.

2. If you invest $100 at 2% interest, compounded every 2 years, what would your balance be after 6 years?


4. Two friends are going on a road trip and are downloading podcasts to listen to on the drive. They choose two podcasts. They download A episodes of Podcast A, and B episodes of Podcast B. Each episode of Podcast A is x minutes long, and each episode of Podcast B is y minutes long. Tell what the following expressions represent in the situation.
a. Ax + By
b. A + B

Answers

Solution 1:

The compound interest formula to be used here is given by:

[tex]A=P(1+r)^{t}[/tex]

Now we are given:

P=$500

r=10% or 0.1

t=5 years

Plugging them in the formula ,

[tex]A=500(1+0.1)^{5}[/tex]

A=$802.255

Answer : After 5 years I will have $802.255 in my account.

Solution 2:

The formula for compound interest here is given by:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Here interest is compounded after every two years, so n=2

r=2% or 0.02

t=6 years

P= $100

Plugging these into the formula:

[tex]A=100(1+\frac{0.02}{2})^{2*6}[/tex]

[tex]A=100(1+0.01)^{12}[/tex]

[tex]A=100(1.01)^{12}[/tex]

A=$112.683

Answer: The balance after 6 years would be $112.683.

Solution 4:

In this situation:

a. Ax+By

Ax represents duration of Podcast A episodes

By represents duration of Podcast B episodes

Ax+By represents total duration of Podcast A and Podcast B songs.

b. A+B

A+B represents total number of episodes of Podcast A and Podcast B.

A mattress store charges 7% sales tax and a 50 delivery fee

Answers

We are given function f(a) = 1.07a for total amount including sales tax.

g(b) = b+50 total cost including delivery.


We need to write function g(f(a)).

g(f(a)) = g of f(a).

We need to substitute function f(a) in g(b) function for b.

g(f(a)) = g(1.07a) = 1.07a +50.

Therefore,  g(f(a)) = 1.07a +50.

We are given mattress price a = $1125.

In order to find the total cost including delivery charges, we need to plug a= 1125 in the above function 1.07a +50.

Plugging a= $1125, we get

g(1125) = 1.07a +50 = 1.07*1125 +50 = 1203.75 +50 = 1253.75.

Therefore, total cost including delivery charges is $1253.75.

Answer:

g(f(a)) = 1.07a +50.

Total cost including delivery charges is $1253.75.

factorise 2p^2 - p - 10
(2p squared)

Answers

2p² - p - 10 = 0

2 = a

- 1 = b

- 10 = c

To factor, find two numbers that multiply to equal a·c and also that have a sum of b

2p² + 4p - 5p - 10 = 0

2p (p + 2) - 5 (p + 2) = 0

Answer: ( 2p - 5 ) ( p + 2 ) = 0

What is 0.8 divided by 0.6 and what would it be if I round it to the nearest hundred

Answers

Final answer:

0.8 divided by 0.6 is 1.33333... which, when rounded to the nearest hundredth, is 1.33. The rounding should be done to the nearest hundredth as 'rounding to the nearest hundred' typically does not apply to decimals.

Explanation:

To calculate 0.8 divided by 0.6, we simply perform the division:

0.8 ÷ 0.6 = 1.33333...

When we round this to the nearest hundredth, we look at the third decimal place. Since it's 3, we do not round up the second decimal place. Thus, 1.33333... rounded to the nearest hundredth is 1.33.

Rounding numbers and understanding division are fundamental skills in mathematics. They are essential for various applications, such as converting fractions to percentages or when dealing with metrics and customary units.

However, the question asked to round to the nearest hundred, which seems to be a typographical mistake, because we usually round numbers to the nearest hundredth or to the nearest hundred as a whole number, but not to the nearest hundred as a decimal. Assuming it's a typo and meant the hundredth, the result is 1.33. Otherwise, 1.33 rounded to the nearest hundred as a whole number is simply 100 (since this is the closest hundred to 1.33).

Which area is greatest?
a. b=4, h=3.5
b. b=0.8, h=20
c. b=6, h=2.25
d. b=10, h=1.4

Answers

the answer is b because to find the area of something you have to do Base(b) multiplied by the Height(h) and the area of B was 16

A: 14

B: 16

C: 13.5

D: 14

Final answer:

Answer Is Option(b.) :-To find the greatest area among the given rectangles, calculate the area of each rectangle by multiplying the base by height. The greatest area is of rectangle b.

Explanation:

The subject matter of this question involves finding the area of rectangles. In mathematics, the area of a rectangle is calculated by multiplying its base (b) by its height (h), represented as A = b x h. In this question, you are given four different rectangles (a, b, c, and d) with varying base and height values. You need to calculate the area for each and determine which one is the greatest:

For rectangle a, the area is b x h = 4 x 3.5 = 14 For rectangle b, the area is b x h = 0.8 x 20 = 16 For rectangle c, the area is b x h = 6 x 2.25 = 13.5 For rectangle d, the area is b x h = 10 x 1.4 = 14

After calculations, you can see that rectangle b has the greatest area.

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