show that (x+1)(x+3)(x+5) can be written in the form ax^3 + bx^2 + cx+ d where a,b,c and d are all positive integers.

Answers

Answer 1

Answer:

x³ + 9x² + 23x + 15

Step-by-step explanation:

Given

(x + 1)(x + 3)(x + 5) ← expand the first pair of factors using FOIL

= (x² + 4x + 3)(x + 5)

Each of the terms in the second factor is multiplied by each of the terms in the first factor, that is

x²(x + 5) + 4x(x + 5) + 3(x + 5) ← distribute the 3 parenthesis

= x³ + 5x² + 4x² + 20x + 3x + 15 ← collect like terms

= x³ + 9x² + 23x + 15 ← in the form ax³ + bx² + cx + d


Related Questions

Estimate the number of school-aged children in the city where the population is approximately 60,000, if 1 of every 10 citizens is a school-aged child. If 500 children can attend each school, about how many schools will the city need?​

Answers

1 out of 10 are school aged.

Divide total population by 10:

60,000 / 10 = 6,000 are school aged.

Each school holds 500, divide school aged by 500:

6,000 / 500 = 12

They would need 12 schools.

The number of schools the city with the population 60,000 requires are 12.

Given that, the number of school-aged children in the city where the population is approximately 60,000.

In population 1 out of 10 are school aged.

Divide total population by 10

60,000/10 = 6,000 are school aged

Each school have 500 children, so the number of schools are

6,000/500 = 12

Therefore, the number of schools the city needs are 12.

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Round the following numbers to 2 decimal places 3526.48502 12.6433 0.2099

Answers

Step-by-step explanation:

3526.49 12.64 0.21

I hope this helps

Answer:

3526.49

12.64

.21

Step-by-step explanation:

1. On the left of the decimal place, take the third number and if it is = to or higher than 5, round the second number up by 1.

3526.485 becomes 3526.49

2. If it is lower than 5, then just leave the second number alone.

12.6433 becomes 12.64

3. If it is a decimal place number, just take the third number and if it is higher than 5, increase the second number.

.2099 becomes .21

f(3) = 6x
Help if you can?!

Answers

Answer: 18


The 3 replaces X
6(3)=18

PLEASE HELP I WILL MARK YOU BRAINLIEST DO PART A AND PART B PLEASE

Answers

Answer:

a)The volume of soil required is 48 ft^3    

b) Trevor has 36 ft^3 of soil

Step-by-step explanation:

The formula a = m – n represents the actual cost, a, of an item with original price m after a coupon for n dollars off is applied. Solve the formula for the amount of the coupon n. A. n = a + m B. n = m – a C. n = a – m D. n = – m – a

Answers

Answer:

n = m - a

Step-by-step explanation:

Given that:

The expression of the formula  a = m - n

where;

a = actual cost of an item

m = original price

n = amount of coupon in dollars

The objective is to solve for the amount of the coupon.

In order to determine the amount of the coupon, we need to make n which is the amount of coupons in dollars the subject of the formula from the given expression.

So if a = m - n

a + n = m

n = m - a

Solve the quadratic equation by completing the square.
x2 + 8x + 19 = 0
What’s the answer ? Math algebra 2

Answers

Answer: x= 4 ± [tex]\sqrt{-3}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex] + 8x + 19 = 0     First subtract 19 from both sides

             -19    -19

[tex]x^{2}[/tex] + 8x           =  -19    Now to complete the square on the left side you will divide 8 by 2 and square the number that you will get and add it to both sides. If you divide 8 by 2 you get 4 and  4 squared is 16 .So add 16 to both sides.

x^2 + 8x + 16 = -19 + 16  Now factor the left side

(x+4)^2 = -3    Take the square root of both sides

(x+4) = ±[tex]\sqrt{-3}[/tex]        

Subtract 4 from both sides

x = ±[tex]\sqrt{-3} - 4[/tex]

A plane is labeled H. 3 horizontal lines are shown. From top to bottom, line k is above the plane and lines n and w are on the plane. Vertical line m cuts through the horizontal lines and the parallelogram. Point x is at the intersection of lines m and n and indicates that m is at a right angle to line n. Lines n and w are parallel to each other. Which statement is true regarding the parallel and perpendicular lines in the diagram? k Parallel to n and w Perpendicular to m k Parallel to n and n Perpendicular to m w Parallel to n and n Perpendicular to m w Parallel to n and wPerpendicular to m

Answers

Answer:

c on edge

Step-by-step explanation:

i just did it

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The correct option is C.

What is a line segment?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. A line segment is a straight line with finite length, and thus, has two endpoints(points on either end).

The diagram for the given condition can be made as shown below. Now, from the image, the following conclusion can be made,

The two lines w and n are parallel to each other.The line m is perpendicular to n, this is because the angle between the two lines is equal to 90°. The two lines k and line n are also parallel to each other.

Further, if all the options are observed.

A.) k Parallel to n and w Perpendicular to m

The first half of the given statement is correct but the second half of the equation is completely wrong. Therefore, not the correct option.

B.) k Parallel to n and w Perpendicular to m

The first half of the given statement is correct but the second half of the equation is completely wrong. Therefore, not the correct option.

C.) w Parallel to n and n Perpendicular to m

Since both the parts of the statement are correct, therefore, it can be concluded that the given statement is correct.

D.) w Parallel to n and w Perpendicular to m

The first half of the given statement is correct but the second half of the equation is completely wrong. Therefore, not the correct option.

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-5 -10=10 I need help urgently!!

Answers

Answer:

5

Step-by-step explanation:

-5 minus -10 = 5

l m a o i used a calculator. Is ur problem even -5 minus -10?

Answer: x - 15

It would be x - 15 x - 5 - 10 = x - 15 - x (subtract x from both sides)(simplify) -5 - 10 = -15= x - 15 = -15

Sarah's birthday is in 3 weeks how many days away is Sarahs birthday explain.

Answers

3 x 7 = 21
Her birthday is in 21 days because there are 7 days in 1 week so you multiply the number of weeks by how many days in a week there is

Answer:

21 days

Step-by-step explanation:

There a 7 days in a week, and there a 3 weeks so you would just multiply 7*3 which equal 21. Hope this helped.

please help needed asap!!

Answers

Answer: 55

Step-by-step explanation:

90+x+15+3x-5=180

Combine like terms

100+4x=180

Subtract 100 from both sides

4x=180

Divide by 4

X=20

Insert into equation

3(20)-5

=55

What is 10 to the -6th powert 10^-6 a. 0.000001 b. 100000 c. 1000000 d. 0.0000001 Easy points for you guys

Answers

Answer:

The answer is D

Step-by-step explanation:

When the exponent is negative then you go in to decimals

Answer:

since its a negative number you need to to go to the decimals> therefore the answer would be (D)

0.75a=-9 Please show workkkkk

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = - 12}}}}}[/tex]

Step-by-step explanation:

[tex] \star{ \sf{ \: \: 0.75a = - 9}}[/tex]

Divide both sides by 0.75 . Thenafter, Calculate it

[tex] \hookrightarrow{ \sf{ \frac{0.75a}{a} = \frac{ - 9}{0.75}}} [/tex]

[tex] \hookrightarrow{ \boxed{ \sf{a = - 12}}}[/tex]

The value of a is -12

Hope I helped!

Best regards!

~ TheAnimeGirl

Solve for x in simplest form. 7=8/5 (3x+5)

Answers

Answer:

7=8/5 (3x+5)

or (7*5)= 24x + 40

or 24x = -5

x = -5/24

Step-by-step explanation:

Point L is on line segment KM . Given KM = 5x + 10 , LM = 4x , and KL = 3x , determine the numerical length of KL

Answers

Answer:15

I know Bc I got it wrong that was the answer

I need help fast please!!!

Answers

Answer:

the answer is 3  

Step-by-step explanation:

What is the midpoint of AB?

Answers

Answer:

-4

Step-by-step explanation:

It’s -4

Answer:

(-4,-0.5)

Step-by-step explanation:

Newton is thinking of a 6-digit number in which all of the digits are the same. The value of the digit in the thousands place is 8,000. What is Newton's number?

Answers

Answer:

Newton’s number is 888888

Step-by-step explanation:

Here, we want to write the Digit in which Newton is thinking of.

The information we have at hand is that, there are 6 numbers which are the same in this digits.

Now let’s look at the other information. The value of the thousand figure is 8,000. What this practically means is that the digit at the thousand place is simply 8.

Since all the digits are same, the digit he is thinking of will be 888888

describe the discontinutiy for the function f(x)= x^2+5/x-5

Answers

Answer:

f(x) = x² + 5 / x - 5

There is infinite discontinuity at x = 5. At this value, the graph becomes undefined because the denominator is 0.

how many strawberries will Maria need if she has three smoothies​

Answers

Answer:

how many dose she have

Step-by-step explanation:

Answer: 18 strawberries

Maria puts 6 strawberries in each smoothie she makes. She makes 3 smoothies altogether how many strawberries does Maria use in the smoothies? (i’m guessing is the real question)

Well she needs to put 6 strawberries in EACH of the 3 smoothies. The easiest way to find the answer is to multiply! 6 • 3 = 18! So, I hope this helps!

Explain how solving -7y > 161 is different from solving 7y > -161

Answers

there are different negatives and positives

Answer:

Sample response:

Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>

Does anyone know the answer to this?
18t + (3b)t + 75

Answers

18+(3b)t+753(6t+bt+25

what's -2 divided by -2

Answers

Answer:

1

Step-by-step explanation:

simple math..

-2/(-2) = 1
2/2=1 if you have one - is -1, but if you have both negative than two minuses make positive

If 7p-4=8 , what is the value of p?

A)7/12

B)7/4

C)12/7

D)4/7

Answers

C) 12/7

Sol:-

7p=8+4

ஃ p=12/7.

Hope it helps you!!

Step-by-step explanation:

7p=8+4

7p=12

p=12/7

the correct answer is option A

Find the value of x of this triangle.​

Answers

Answer:

12x

Step-by-step explanation:

Answer: x = 35°

Step-by-step explanation:

A triangle adds up to 180°. Therefore, the equation to find the value of x is 110+2x = 180.Subtract 110 on both sides. 2x = 70Divide by 2 on both sides. x = 35°

what's the square root of 1/36?

Answers

0.27... repeating :)

The square root of the number is A = 1/6 = 0.16667

Given data ,

Let the first number be represented as p

where the value of p = 1/36

Now , the square root of the number is expressed as

A = √p

The radical form of a number refers to expressing a number using a radical symbol (√) to represent a root.

It is used to express the roots present in the number.

So , A = √( 1/36 )

On simplifying , we get

A = 1/6

On further simplification , we get

A = 0.166667

Hence , the square root is A = 1/6 = 0.16667

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The table shows conversions of common units of length.

Approximately how many inches are in 2500 millimeters?

Please hurry up with your answer!!

Answers

Answer:

98.4252

Step-by-step explanation:

This is because 1 millimeter is 0.0393701 inches;2,500 millimeters =0.0393701 multiply 2,500=98.4252.

Answer:

It’s would be 98

Step-by-step explanation:

Have a good rest of your day:)

Shania is making an apricot drink for her 4 friends and needs 1/9 of a gallon of water to make the apricot drink. How much of the gallon of water will be in each of the 4 drinks?

Answers

answer:

4/9ths of a gallon

step-by-step explanation:

1/9×4 .change whole number to fraction: 1/9×4/1. multiply the numerators and the denominators together. 1×4 and 9×1. 1×4=4 and 9×1=9 so the answer is 4/9

Why might you expect most absolute value equations to have two solutions? Why not three or four?

Answers

Answer:

If the absolute value expression is not equal to zero, the expression inside an absolute value can be either positive or negative. So, there can be at most two solutions. Looking at this graphically, an absolute value graph can intersect a horizontal line at most two times.

Give the center and radius of the circle.
x2 + y2 = 25
(2.3) r=5
(0.0) r=5
(0,0) r=25
(3.2) r=25

Answers

Answer:

x=√−y2+25 or x=−√−y2+25

Step-by-step explanation:

x2+y2=25

Step 1: Add -y^2 to both sides.

x2+y2+−y2=25+−y2x2=−y2+25

Step 2: Take square root.

x=√−y2+25 or x=−√−y2+25

Answer:

x=√−y2+25 or x=−√−y2+25

Solve the following inequality in the simplest form: 8(−x−2/3)−1≥7

Answers

The answer is as in pic
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