Which of the following expressions are equivalent to (x+y)^2? There may be more than one correct answer

Answers

Answer 1

The equivalent expressions are:

[tex](x+y)^2 = x^2+2xy+y^2[/tex]

[tex](x+y)^2 = x(x+y)+y(x+y)[/tex]

[tex](x+y)^2 = (x+y)(x+y)[/tex]

[tex](x+y)^2=(y+x)^2[/tex]

Solution:

We have to find the equivalent expression for the given expression

Given expression is:

[tex](x+y)^2[/tex]

First equivalent expression:

Let us first use the algebraic identity

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Therefore,

[tex](x+y)^2 = x^2+2xy+y^2[/tex]

Second Equivalent expression:

From above we get,

[tex](x+y)^2 = x^2+2xy+y^2[/tex]

2xy can be rewritten as xy + xy

Thus we get,

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

Group the terms we get,

[tex]x^2+2xy + y^2 = (x^2+xy)+(xy+y^2)[/tex]

Factor out "x" from first bracket and "y" from second bracket

[tex]x^2+2xy+y^2 = x(x+y)+y(x+y)[/tex]

Thus the equivalent expression is:

[tex](x+y)^2 = x(x+y)+y(x+y)[/tex]

Third equivalent expression:

[tex]\text{We know that } a^2 = a \times a[/tex]

Therefore,

[tex](x+y)^2 = (x+y)(x+y)[/tex]

Fourth equivalent expression:

By commutative property we know that,

[tex]a + b = b + a[/tex]

Therefore,

[tex](x+y)^2=(y+x)^2[/tex]

Thus the equivalent expressions are found


Related Questions

Which expression is equivalent to 12/15?
A. 25÷12
B. 12÷25
C. 12÷1/25
D. 25÷1/12



Answers

Answer:

None of the answers are correct, because 12/15=4/5, it's equivalent to 12 divided by 15.

Step-by-step explanation:

how do you solve -4(2z+6)-12=4?

Answers

Answer: -8z-40

Step-by-step explanation:

-4(2z+6) = -8z-24

-8z-24-12=-8z-36

-8z-36=4 (you have to move 4 to the other side of the equal sign so 4 becomes -4)

-8z-40

Answer:

z= - 5

Step-by-step explanation:

−4(2z+6)−12=4

Step 1: Simplify both sides of the equation.

−4(2z+6)−12=4(Distribute)

−8z+−24+−12=4

(−8z)+(−24+−12)=4(Combine Like Terms)

−8z−36=4

Step 2: Add 36 to both sides.

−8z−36=4

−8z=40

Step 3: Divide both sides by -8.

−8z=40

z=−5

I hope that this will help

On square JKLM below if J is located at (-2,5) and K is located at (2,2) what is the slope of LK

Answers

Answer:

Slope= -3/4

Step-by-step explanation:


A plane was traveling from Florida to Canada. It flew 5 hours and went 1895km what was it’s velocity?

Answers

The velocity of plane is 379 kilometer per hour

Solution:

Given that, plane was traveling from Florida to Canada

It flew 5 hours and went 1895 km

To find: Velcoity

The velocity can be found by dividing the distance traveled by time taken

[tex]velocity = \frac{distance}{time}[/tex]

Here in this sum,

distance = 1895 km

time = 5 hours

Substituting the values in formula,

[tex]velocity = \frac{1895}{5}\\\\velocity = 379[/tex]

Thus velocity of plane is 379 kilometer per hour

What is 28 divided by 3 in fraction form

Answers

9 and 1/3 (simplified form)

The number 28 is divided by the number 3 in fraction form is  9 1/3.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The number 28 is divided by the number 3.

This can be written in fraction form as 28/3.

Now, 3×9 = 27.

Therefore, 28/3.

= 9 1/3.

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It takes 9 minutes to fill an empty aquarium of a depth of 3/5 meters. What is the unit rate in minutes per meter?

Answers

Answer:

The rate is 15 minutes per meter.

Step-by-step explanation:

It takes 9 minutes to fill a depth of [tex]\frac{3}{5}[/tex] meters.

Filling  [tex]\frac{3}{5}[/tex] meters take 9 minutes time.

Filling 3 meters of the aquarium takes [tex]5\times9[/tex] = 45 minutes time (Multiplying by 5 both the numbers).

In order to fill 1 meter of the aquarium it will take [tex]\frac{9\times5}{3} = 15[/tex] minutes (Dividing by 3 both the numerical values).

Answer:

The rate is 15 minutes per meter.

Step-by-step explanation: please give brainliest

Which expressions are equivalent to 4^-3 / 4^-1

Choose two answers

A. 4^1 / 4^3

B. 1/4^2

c. 4^3 x 4^1

d. (4^-1)^-3

Answers

Answer:

The answer is A and B

Step-by-step explanation:

Because 4 to the power of -3 divided by 4 to the power of -1 switched (Like when there is a negative exponent you move the number or variable to the other side of the fraction) and scince both have a negative number you switch both. and 1-3 is -2 so you switch it to the bottem and put a 1 at the top.

                                         ^^Hope this helps!

Final answer:

The expressions equivalent to 4^-3 / 4^-1 are 1/4^2 and (4^-1)^-3.

Explanation:

In the subject of mathematics, the given expression is 4^-3 / 4^-1. To simplify this expression, you need to understand two rules of exponents:

The rule a^-n = 1/a^n, which says that a negative exponent indicates the reciprocal of the positive exponent, andWhen you divide numbers with the same base, you should subtract the exponents.

Applying these two rules, 4^-3 / 4^-1 = 4^-3 * 4^1 = 4^(1 - 3) = 1/4^2.

Another way to simplify the expression is to use the rules of exponents to rewrite each part independently. 4^-3 = 1/4^3 and 4^-1 = 1/4. Therefore, 4^-3 / 4^-1 = (1/4^3) / (1/4) = 4, which is equivalent to (4^-1)^-3.

Therefore, the equivalent expressions are (B) 1/4^2 and (D) (4^-1)^-3.

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What multiplied by 3 equals 15 but added by 3 equals 18

Answers

Answer:

15

Step-by-step explanation:

I think you meant “then added by 3” because that means the answer is 5 because there is no such number in you question

What is the answer to
6(3x-5)-7x=25

Answers

Answer:

I believe the answer to this question is: X=5.

Need help picture is displayed

Answers

Answer:

x= 40°

Step-by-step explanation:

Please see attached picture for full solution.

Key concepts:

- Corresponding angles are equal to each other

- The sum of the angles in a triangle add up to 180°

What is area of this shape

Answers

Answer:

132 ft squared

Step-by-step explanation:

One way is to divide the shape into a rectangle and a triangle, by drawing a vertical line.

This gives a rectangle that is 9 by 11, so has area 99.

The triangle has a base of 11 and height of 15 - 9 = 6.

So the area of the triangle = 1/2 x b x h = 1/2 x 11 x 6 = 33

So the total area is 99 + 33 = 132.

The ratio of boys to girls in a class is 3:5. There are 32 students in the class. How many more girls than boys are there?

Answers

Answer:

There are 8 more girls than boys.

Step-by-step explanation:

First, find how many girls and boys are in the class. Add the two parts of the ratio together, 3 and 5 to get 8. Then divide 32 by 8 to get 4. Since the total number of students in the class is 4 times the ratio of boys to girls, multiply both sides of the ratio by 4. You then get 12 boys : 20 girls. You can check this by adding 12 + 20 to get 32. Next, subtract the number of girls from the boys. 20 - 12 = 8. Therefore, there are 8 more girls than boys.

there are 8 girls more than boys

Total ratio = 8

Number of students = 32

Number of boys = 3/8 × 32= 12

Number of girls= 5/ 8 × 32= 20

Girls are more than boys with = (20-12)=8

Therefore there are 8 girls more than boys

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How to explain how to graph the problem y=10x+15

Answers

If x=0
Y=10*0+15
Y=15
If y=0
0=10x+15
10x=-15
X=-1.5
So we have (-1.5;15)
Then try to draw like this ( the picture is just a example)

cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 at the end of 3 years. what is the smallest amount, to the nearest pound she can invest

Answers

Answer:

The smallest amount is [tex]\£6,911[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1[/tex]  

substitute in the formula above

[tex]8,000=P(1+\frac{0.05}{1})^{1*3}[/tex]  

solve for P

[tex]8,000=P(1.05)^{3}[/tex]  

[tex]P=8,000/(1.05)^{3}[/tex]  

[tex]P=\£6,910.70[/tex]  

Round to the nearest pound she can invest

The smallest amount is [tex]\£6,911[/tex]

i need help asap i am almost done

Answers

So tendizvehcusvhdn 35291/273842

BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

A bag of corn chips contains 1,596 calories. The bag contains 12 servings.

How many calories are in each serving of corn chips?

Enter your answer in the box.

____calories

Answers

Step-by-step explanation:

A bag of calories=1,596

calories in each serving of corn chips=?

1,596/12=133

"133 calories are present in each serving of corn chips."

Final answer:

Each serving of corn chips contains 133 calories.

Explanation:

To find the number of calories in each serving of corn chips, we need to divide the total number of calories in the bag by the number of servings.

Calories per serving= Number of servings/Total calories in the bag

​Calories per serving= 12servings/1,596calories= 133

In conclusion each serving of the corn chips contributes 133 calories to the overall caloric content of the bag.

This calculation allows you to find the caloric content per serving, providing a helpful metric for individuals managing their calorie intake.

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can you guys help me out.​

Answers

Answer:

y = -21

Step-by-step explanation:

4(u+4) please help me

Answers

Answer:

4u+16

Step-by-step explanation:

first multiply the outside bumber(in this case its 4) by each of the numbers and variables inside. (making u turn into 4u) and ( making 4 turn into 16 bcs 4x4=16

i need help please i’m confused and i need the answers

Answers

Answer:

first C then B

Step-by-step explanation:

The distance Raphael needs to travel goes down by time. Therefore the y-value (the amount of distance) will go down as the x-value (the amount of time) will go up. So C.

The speed of the rollercoaster is increasing as time goes by. Therefor the y-value (the speed) will go up and the x-value (the amount of time) will also go up. So B.

Time is almost always moving forward so you can almost always assume x will go up.

19=8+y solve for y? pleas ehelp me answer

Answers

Answer:

Step-by-step explanation:

8+?=19

19-8=11

Y=11

Final answer:

To solve the equation 19 = 8 + y for y, you subtract 8 from both sides which gives you y = 11.

Explanation:

The equation provided, 19 = 8 + y, is a simple linear equation where you are solving for the variable y. To find the value of y, you need to isolate y on one side of the equation.

Here is the step-by-step process:

Start with the original equation: 19 = 8 + y.

To isolate y, you need to get rid of the 8 on the right side of the equation. You can do this by subtracting 8 from both sides of the equation.

Subtracting 8 from both sides gives us: 19 - 8 = y.

Simplify the left side: 11 = y.

Therefore, y equals 11.

Juan and Raj cut up a banana to put on cereal. Juan puts 17 of the banana on his bowl of cereal, and Raj puts 25 ​ of the banana on his bowl of cereal.

What fraction of the banana did Juan and Raj put on their cereal altogether?

Answers

Question:

Juan and raj cut up a banana to put on cereal. juan puts 1/7 of the banana on his bowl of cereal, and raj puts 2/5 ​ of the banana on his bowl of cereal.

what fraction of the banana did juan and raj put on their cereal altogether?

a. 2/35 banana

b. 3/12 banana

c. 3/7 banana

d. 19/35 banana

Answer:

Juan and Raj altogether put 19/35 banana

Solution:

Given that, Juan and Raj cut up a banana to put on cereal

[tex]fraction\ of\ banana\ put\ by\ Juan = \frac{1}{7}\\\\fraction\ of\ banana\ put\ by\ Raj = \frac{2}{5}[/tex]

We have to find the fraction of banana put by Juan and Raj altogether

This means, we have to add both the fractions

[tex]fraction\ of\ banana\ put\ altogether = fraction\ of\ banana\ put\ by\ Juan + fraction\ of\ banana\ put\ by\ Raj[/tex]

[tex]fraction\ of\ banana\ put\ altogether = \frac{1}{7} + \frac{2}{5}\\\\\text{Cross multiply to simplify }\\\\fraction\ of\ banana\ put\ altogether = \frac{1 \times 5 + 2 \times 7}{7 \times 5}\\\\fraction\ of\ banana\ put\ altogether = \frac{5+14}{35}\\\\fraction\ of\ banana\ put\ altogether = \frac{19}{35}[/tex]

Thus they put [tex]\frac{19}{35}[/tex] of banana by Juan and Raj altogether

How many solutions does y=-2x+4 have

Answers

infinite solutions for this
infinite solutions if can have

Which answer describes the type of sequence? 1, 2, 4, 8, 16, . . .

Answers

This is a geometric sequence.

Each new term is found by multiplying the last term by 2

1*2 = 2

2*2 = 4

2*4 = 8

2*8 = 16

and so on

Therefore the common ratio is r = 2.

The starting term is a = 1

The general nth term is [tex]a*(r)^{n-1} = 1*(2)^{n-1} = 2^{n-1}[/tex] where n is an integer (aka whole number) and n starts at n = 1.

Write the slope-intercept form of the equation of the line that passes through the given points: (-4, -2) and (3, -1)

Answers

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}}\implies \cfrac{-1+2}{3+4}\implies \cfrac{1}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{\cfrac{1}{7}}[x-\stackrel{x_1}{(-4)}]\implies y+2=\cfrac{1}{7}(x+4) \\\\\\ y+2=\cfrac{1}{7}x+\cfrac{4}{7}\implies y=\cfrac{1}{7}x+\cfrac{4}{7}-2\implies y=\cfrac{1}{7}x-\cfrac{10}{7}[/tex]


[tex]1 \frac{3}{5} + \sqrt{4} [/tex]

Answers

Step-by-step explanation:

Check out the pic, if it doesn't help you can ask me whichever part you don’t understand

Please help with this problem

Answers

Measure of one of the vertical angle is 156°

Solution:

The measure of angles given are (x + 104)° and 3x°.

The given angles are vertical in order.

If two lines meet at a point, then the angle formed in vertical positions are equal.

That is vertically opposite angles are equal.

⇒ 3x° = (x + 104)°

⇒ 3x° = x° + 104°

Subtract x° on both sides of the equation to equal the expression,

⇒ 3x° – x° = x° + 104° – x°

⇒ 2x° – x° = 104°

⇒ 2x° = 104°

Divide both sides of the expression by 2, we get

x° = 52°

Substitute x° = 52° in one of the vertical angle.

3x° = 3 × 52° = 156° (or)

x° + 104° = 52°+ 104° = 156°

Hence the measure of one of the vertical angle is 156°.

math question thanks if you help!

Answers

Answer:

- 12

Step-by-step explanation:

The rate of change is measured by the slope m of the data

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 2) and (x₂, y₁ ) = (5, - 26) ← 2 ordered pairs from the table

m = [tex]\frac{-26+2}{5-3}[/tex] = [tex]\frac{-24}{2}[/tex] = - 12

Rate of change = - 12

-2x+y=-12, 3y- 2x=-12

Answers

Answer:

x = 6

y = 0

Explanation:

−2x+y=−12;3y−2x=−12

Rewrite equations:

−2x+y=−12;−2x+3y=−12

Solve −2x+y=−12 for y

−2x+y=−12

−2x+y+2x=−12+2x(Add 2x to both sides)

y=2x−12

Substitute 2x−12 for y in −2x+3y=−12

−2x+3y=−12

−2x+3(2x−12)=−12

4x−36=−12 (Simplify both sides of the equation)

4x−36+36=−12+36 (Add 36 to both sides)

4x=24

Divide both sides by 4

4x / 4 = 24 / 4

x = 6

Substitute 6 for x in y=2x−12

y=2x−12

y=(2)(6)−12

y=0 (Simplify both sides of the equation)

set equal as -2x+y=3y-2x isolate the variables as -2y = 0. y=0. substitute back in as -2x+0=-12. divide both sides by -2. 6=x.

anyone wanna help out?​

Answers

Answer:

To find out the length of AB you are trying to figure out how long it is

If B is at 45, and A is at 16

You need to figure out how far it is from 16 to 45

In order to do this the easiest way, you would go 45-16

45-16=29

AB=29

Hope this helps ;)

A homeowner has two people to mow his land. Person A is able to mow the land in 2 hours by herself. Person B is able to mow the land in 3 hours by himself. What would be the amount of time is will take for both persons A and B to mow the lawn together?

Answers

Answer:

1 1/2 hours

Step-by-step explanation:

divide 3/2 and whatever you got is your answer

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