The product of (x+p)(x+q) can be written as x^2+(p+q)x+pq.
An intermediate step in this multiplication is
x^2+px+qx+pq=x^2+(p+q)x+pq.
Explain why px+qx=(p+q)x.
I'm Really confused please help!

Answers

Answer 1

Answer:

[tex]px+qx=(p+q)x[/tex] by taking out the common factors.

Step-by-step explanation:

It is given that the product of [tex](x+p)(x+q)[/tex] is [tex]x^2+(p+q)x+pq[/tex].

Given expression is

[tex](x+p)(x+q)[/tex]

Using distributive property, we get

[tex]x(x+q)+p(x+q)[/tex]

[tex]x(x)+q(x)+p(x)+p(q)[/tex]

[tex]x^2+qx+px+pq[/tex]

In middle terms px and qx the highest common factor is x. So taking out common factor from middle terms we get

[tex]x^2+x(q+p)+pq[/tex]

It can be written as

[tex]x^2+x(p+q)+pq[/tex]

Therefore, [tex]px+qx=(p+q)x[/tex] by taking out the common factors.


Related Questions



Find the area of the pentagon.
A) 107 inches2
B) 116 inches2
C) 150 inches2
D) 182 inches2

Find the area of the pentagon.
A) 107 inches2
B) 116 inches2
C) 150 inches2
D) 182 inches2

Answers

Answer:

A

Step-by-step explanation:

Answer:

A) 107 inches2

Step-by-step explanation:

4*16= 64

64/2 = 32

9+16 = 25

25/2 = 12.50

12.50*6 = 75  

32 + 75 = 107

Got it right in USA TESTING

help please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

4 feet by 3 feet

Step-by-step explanation:

I hope this helped you out

Find the length of arc KN.
can a genius help me??please​

Answers

Answer:

Length KN = 2π/3 = 2.094

Step-by-step explanation:

Length KN = (mKN/360)2πr

Length KN = (40/360)2π3

Length KN = (1/9)6π

Length KN = 6π/9

Length KN = 2π/3 = 2.094

Which fraction is equivalent to 15/30
A 3/4
B 2/4
C 3/5
D 5/6

Answers

Answer:

2/4

Step-by-step explanation:

2/4ths because 15/30 is 1/2 which isn’t on here but 2/4th is equal to 2/4

50 POINTS HELP ASAP

Answers

its 10 points not 50 Gzz

Answer:

its 10 points not 50

Step-by-step explanation:

What factors do 6 and 12 have in common?

Answers

Answer:

6x^2 im pretty sure thats whats its asking for

Step-by-step explanation:

The product of Jack's age and Florence's age is 266. Jack is 14 years
old. How old is Florence?

Answers

Answer:

19

Step-by-step explanation:

you divide 266 by 14

Answer:

19

Step-by-step explanation:

266 ÷ 14 = 19

need answer asap!!!!!!!!!!!

Answers

Answer:

126 degrees

Step-by-step explanation:

A straight line makes a 180 degree angle. Since we know one side is 54, just subtract 54 from 180.

Does the function model exponential growth or decay?
h(t) = 0.25 - 1.5t
A.) growth
B.) decay

Answers

Answer: it’s growth

Step-by-step explanation:

Please help
Find answer Asap and I will mark as brainliest!!

Answers

Answer:

3 units.

Step-by-step explanation:

If you view the triangle face in halves, the bottom leg is  units as 8/2 = 4. The hypotenuse is 5 units given in the centre of the triangular prism. You can then use the Pythagorean theorem to calculate that the height is 3.  

The height is 3 units

I will give you all five stars ⭐⭐⭐⭐⭐

Answers

Answer:

B

Step-by-step explanation:

Seeing as the change is consistent within the vertices, this would be correct.

Two different sports teams are doing fundraising to be able to afford their uniforms. The softball team needs to raise $318.12 between the twelve girls on the team. The hockey team needs to raise $391.92 between the 24 boys on the team. If each player raises the same amount of money, does each softball player or hockey player need to raise more? How can estimation help you solve?

Answers

Answer: A softball player will need to raise more.

Step-by-step explanation:

The softball team needs to raise $318.12 among the twelve girls on the team. Each softball player needs to raise:

$318.12 ÷ 12 = $26.51

The hockey team needs to raise $391.92 among the 24 boys on the team. Each hockey player will raise:

$391.92 ÷ 24 = $16.33

A softball player will raise $26.51 while a hockey player will raise $16.33. Therefore, a softball player will need to raise more.

A rectangle has a height of 7a^2 and a width of a^4+5a^2+4.

Express the area of the entire rectangle.

Answers

7a^6 + 35 a^4 + 28a^2

Find the value of X

X=

Part B

Find the measure of RPS

A. 45

B. 36

C. 60

D. 64

Answers

Answer:

x=8

RPS = 36

Step-by-step explanation:

QPS = 180

The two angles that form QPS

QPR + RPS = 180

7x+88 + 3x+12 = 180

Combine like terms

10x+100 =180

Subtract 100 from each side

10x = 180-100

10x = 80

Divide by 10

x =80/10

x = 8

RPS = 3x+12

        = 3(8)+12

         24+12

        36

Find the missing angle measurements

Answers

Answer:

The angle for the top of the triangle is 79. For the right corner would be 56. Then going to the bottom of the blue triangle vertice would be 75. The missing angle next to that one would be 55/

Step-by-step explanation:

Find the value of x and y

Answers

Answer:

x=24 y=19

Step-by-step explanation:

2y=y+19

y=19

2x-8=x+16

x=16+8

x=24

Answer:

x = 24

y = 19

Step-by-step explanation:

Set the expressions with the x-variables together, and the y-variables together, like so:

2x - 8 = x + 16

Subtract x from both sides:

x - 8 = 16

Add 8 to both sides:

x = 24

Solving for y:

2y = y + 19

Subtract y from both sides:

y = 19

A triangle has angles that measure 59°, 48°, and 73°. What kind of triangle is it?

Answers

Answer: it is an isosceles triangle

Step-by-step explanation:

all three angles are lower than 90 degrees. if the angles were all higher than 90 degrees the triangle would be considered obtuse.  even though all the angles are lower than 90 degrees, it would also be considered acute.

PLEASE HELP 35 POINTS!!!!!!


In two or more complete sentences discuss the advantages and disadvantages of investing in a 529 plan versus investing in a money market account.

Answers

Answer:

Step-by-step explanation:

A 529 plan (Qualified tuition plan) is a tax-advantaged savings plan for future education costs while a money market account refers to a investment or a deposit with a financial institution that earns interest based on the current rates.

Money market deposit accounts are better choices than 529 plan for money you might need to tap at a moment’s notice to cover an emergency or an unexpectedly large expense. They pay higher interest than ordinary savings accounts and give you immediate access to your money

While in 529 savings plan, If you don’t use the money invested for college tuition, you will be penalized 10 percent when you withdraw the money to use it for something else. In addition, both your state and the federal government will tax the earnings on your account in your current tax bracket.

The basic advantage of 529 plan over money market account is the tax-advantage that is the amount invested or withdrawn is tax free. It also has high return and funds from it can be used for another beneficiary who is a qualified family member. Whereas the disadvantage is that the 529 plan is a specified fund for future education purposes. This makes it restricted as the fund can not be transferred for a different use. Unlike the money market account whose use is not restricted. It can be withdrawn to meet diverse financial needs including education. More so, funds in the money market account are insured and can be easily accessed.

In essence, the 529 plan is a specific investment while a money market account is more general in nature.

Answer:

im grounded bc i cheated with this

Step-by-step explanation:

Help ASAP please ! Explain too if you can

Answers

Answer:

B

Step-by-step explanation:

180-118=42 so angle c=42

add 42 +76 =138

in a triangle all degrees ad up to 180 so

subtract 138 from 180=42

Answer:

B) 42 degrees

Step-by-step explanation:

If we're looking for the measure of angle E, we need to know the measures of angles D and C too. (Otherwise we just have nothing to work with.)

So they already give us angle D's measurement, which is 76; we just have to find the smaller angle at C and then solve for E. If this doesn't make sense, just look at C; there's a big angle (118) and a small one that we don't know. We have to find the small one.

Well at C there's just a straight line, so we can assume that the big angle and the small angle add up to 180 degrees, because straight angles are always 180 degrees.

Now to get the small angle, we can take 118 away from 180 to get 62, which will be the measure of the smaller angle. (Comment if you don't know why I did this.)

Now that we know two out of three measures in the triangle, we can find the measure of angle E. All triangles' angles add up to 180 degrees, so we can take away 76 (measure of D) and 62 (measure of small C) from 180 to get the measure of E: 180 - 76 - 62 = 42

So the measure of angle E is 42.

Can someone helpppppppppp

Answers

Answer:

A

Step-by-step explanation:

The reason it is A is because

It goes in biggest to lowest A B C D

C and B don't follow that so we are left with A and D

In answer D   C and B are too close in percentage therefore it cannot be D

Therefore your answer is A

Hope this helped!

Which statement about the credibility of this source is most accurate ? A.

Answers

Answer:

C. The source is credible because it contains facts and information that are accurate.

Step-by-step explanation:

The statistics(60%) used provide facts on the topic that make the source credible

100 to anyone who can answer all of these !!!

Answers

Answer:

24yrds is (a) 24.12yrds is (b) 64yrds is (c) And that's all i can do, don't get mad at me please.

Step-by-step explanation:

What is the value of s?
units
0
5
В
8
15
S
D

Answers

Consider the triangle ABD,

Here,

AB = 5

BD = 15

AD = s

As we know,

In a triangle, the sum of lengths of two sides is greater than the third side.

So,

[tex]5 + 15 > s[/tex]

[tex]15 + s > 5[/tex]

[tex]s + 5 > 15[/tex]

Now,

To satisfy the equation, the value of s can possibly be 11, 12, 13, 14, 15, 16, 17, 18, 19

Answer: the value of s is 17 units

Step-by-step explanation: youre welcome

Need Help Please, Stressing out :( and Thank you:)

Answers

Answer:

please don't be stressed :)

2. c

Step-by-step explanation:

2. if 1,000 is one kilogram then 1,412 = 1.412.

sorry i could only answer 1 but hope this helps

I think it is C, if I’m wrong, I’m really sorry !

4) The diameter of a circle is 32m. The radius is represented by 4(x + 2).
Part A: Write an equation you can use to find the value of x.
Part B: What is the value of x?

Answers

Answer:

The value of x is 2

Step-by-step explanation:

Diameter = 2r -------------------------------------------------------------------(1)

where r is the radius

The value of the diameter = 32 m   and  radius is given to be 4(x+2)

substitute the above into equation (1)   and then solve for x

32  =  2 [ 4(x + 2)]

first open the inner bracket

32 = 2[4x + 8}

then open the outer bracket

32 = 8x + 16

subtract 16 from both-side of the equation

32 - 16 = 8x +16 - 16

16 = 8x

Divide both-side of the equation by 8

16/8  = 8x/8

2 = x

x = 2

Therefore, the value of x is 2

many organize a classroom party. there are 20 of cold drinks at the party, 13 of which contain diet Pepsi, what is the probability that randomly selected drink will be a diet Pepsi? answer key

Answers

Answer:

so its either 13/20

Step-by-step explanation:

if you get this wrong sorry:(

The answer is 13/20

Explanation:
20 is the denominator because it is how many drinks there are in total. 13 is the numerator because that’s how many are Diet Pepsi’s and you cannot simplify this. That’s why the answer in 13/20.

P.S whenever you can simplify this you should :)

Write the equation of the circle P graphed below.

Answers

(1,-4) the fourth axis i think is (+,-) the ex is one away from the origin and the y is 4 steps away from the origin

Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/16 miles apart and arranged in a
square grid (see map). They are both standing at the corner of 6th avenue and L street. Doug can run at an average speed of 30
mi/hr through the streets of Salt Lake, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the corner of
10th avenue and Estreet. who would win and why?

Answers

No map given but it shouldn't matter.

E is the 5th letter, L the 12th.

Start at S(6,12).  End at E(10,5)

The vector between them, E-S=(4,-7)

Each unit is 1/16 of a mile, though that probably doesn't matter that much.

Doug has to stay on the grid, so has to run |4|+|7|=11 units.  At 30 mi/hr that takes (11/16)/30 =  0.022916 hours.

Bert can go diagonally, so flies √(4²+7²)=√65 ≈ 8.06 units.  At 20 mi/hr that takes (8.06/16)/20 = 0.025194 hours.

Answer:  Doug wins

Why? Because it's quicker to cover 4+7 at 30 mph than it is to cover √(4²+7²) at 20 mph.  That is, Doug is 1.5 times faster and the 1.5 times the diagonal distance is more than the grid distance.

Answer:

Doug wins. He finishes in 1.38 minutes. Bert takes 1.51 minutes.

Step-by-step explanation:

Each city block is a square 1/16 mile by 1/16 mile.

From 6th Av and L Street to 10th Av and E Street, they need to go 4 avenues and 7 streets over. These two distances along blocks are the legs of a right triangle. The right triangle has legs of length 4 * 1/16 mile and 7 * 1/16 mile.

leg1 = 4 * 1/16 mile = 0.25 mile

leg2 = 7 * 1.16 mile = 0.4375 mile

The hypotenuse of the right triangle can be calculated by the Pythagorean theorem.

a^2 + b^2 = c^2

(0.25 mile)^2 + (0.4375 mile)^2 = c^2

c = 0.50389

The direct distance from one corner to the other is 0.50389 miles.

The bird travels this distance since the bird can fly above the streets.

The dog has to travel along the legs of right triangle by running in the streets and avenues. The dog travels 0.25 mile + 0.4375 mile = 0.6875 miles

Now we need to see what takes less time:

Bird: distance of 0.50389 miles at 20 mph, or

Dog: distance of 0.6875 miles at 30 mph

We start with the formula for speed:

speed = distance/time

s = dt

Now we solve it for time:

st = d

t = d/s

Time equals distance divided by speed.

Now we find the times for the bird and for the dog.

Bird:

t = d/s = (0.50389 mi)/(20 mi/h) = 0.02519 hours = 1.51 minutes

Dog:

t = d/s = (0.6875 mi)/(30 mi/h) = 0.0229 hours = 1.38 minutes

The bird takes 1.51 minutes, and the dog takes 1.38 minutes.

The dog takes less time to get there, so the dog wins.

Can someone help me with this? ;^;

Answers

Answer:

The mode would be 10

Step-by-step explanation:

Because it is there more than the others

hope this helps! =D

Answer:

10

Step-by-step explanation:

What number is the opposite of 98?

Answers

Answer:

-98

Step-by-step explanation:

hope this is right

Answer:

-98

Step-by-step explanation:

a negative number is the opposite of a positive number

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