f (x) = 8x^4 – 64

Factor completely

Answers

Answer 1

Answer:

8(x^4 - 8)

Step-by-step explanation:

Factor out an 8, since both 8 and 64 are divisible by 8:

f(x) = 8x^4 - 64

f(x) = 8(x^4 - 8)

So, the equation factored completely is 8(x^4 - 8)

Answer 2

Answer:

[tex]\huge\boxed{f(x)=8(x-\sqrt[4]8)(x+\sqrt[4]8)(x^2+2\sqrt2)}[/tex]

[tex]\huge\boxed{f(x)=8(x-2)(x^2+2x+4)}[/tex]

Step-by-step explanation:

[tex]f(x)=8x^4-64\qquad|\text{distribute}\\\\f(x)=8(x^4-8)=8\bigg[(x^2)^2-\left(\sqrt8\right)^2\bigg]\qquad|\text{use}\ (a-b)(a+b)=a^2-b^2\\\\f(x)=8(x^2-\sqrt8)(x^2+\sqrt8)=8\bigg[x^2-\left(\sqrt[4]8\right)^2\bigg](x^2+\sqrt8)\\\\|\text{use}\ (a-b)(a+b)=a^2-b^2\\\\f(x)=8(x-\sqrt[4]8)(x+\sqrt[4]8)(x^2+\sqrt8)\\\\\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2[/tex]

taking into account the correction from the comment

[tex]f(x)=8x^3-64=8(x^3-8)=8(x^3-2^3)\\\\\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\f(x)=8(x-2)(x^2+(x)(2)+2^2)=8(x-2)(x^2+2x+4)[/tex]


Related Questions

A stack of 3 books weighs 7.8 kilogramh book weighs the s. If eacsame amount, how much does each book weigh?

Answers

Answer:

they each way 2.6 kilograms

A librarian has 16 books that she plans to place in a specific order on her shelf: 7 of them are identical copies of The Shining, 5 of them are identical copies of Carrie, and 4 of them are identical copies of Misery. How many different orders of all 16 of these books are there?

Answers

Answer:

3

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

Find the perimeter or circumference and area of each figure if each unit on the graph measures
1 centimeter. Round answers to the nearest tenth, if necessary.

Answers

Answer:

Circumference of the circle = 17.8 units

Area of the circle = 25.1 square unit

Step-by-step explanation:

Formula to get the circumference of a circle = 2πr

Where r = radius of the circle

Radius of the given circle = Distance between the points A(2, 3) and B(4, 1)

r = [tex]\sqrt{(2-4)^2+(3-1)^2}[/tex]

r = [tex]2\sqrt{2}[/tex] units

Therefore, circumference = 2π(2√2)

                                           = 17.77

                                           ≈ 17.8 units

Area of the circle = πr²

                             = π(2√2)²

                             = 8π

                             = 25.13

                             ≈ 25.1 square unit

What is a constraint in math? For what situations would they be useful?

Answers

Answer:

Constraints are restrictions (limitations, boundaries) that need to be placed upon variables used in equations that model real-world situations. ... Constraints then become necessary to allow the mathematical model to realistically represent the situation. hope this helps!

Step-by-step explanation:

Answer: Constraints are restrictions (limitations, boundaries) that need to be placed upon variables used in equations that model real-world situations. Constraints then become necessary to allow the mathematical model to realistically represent the situation

how do I solve -15+w=6​

Answers

Ans

Add 15 to 6  so w= 21

Step-by-step explanation:

A sailor is 30m above the water in the crow's nest on a sailboat. The sailor encounters an orca surface at an angle of depression of 15 degrees. The crows nest is 20 m horizontally from the bow (front) of the boat. How far in front of the boat is the orca?

Answers

Given :

A sailor is 30 m above the water in the crow's nest on a sailboat.

The sailor encounters an orca surface at an angle of depression of 15 degrees.

The crows nest is 20 m horizontally from the bow (front) of the boat.

To Find :

How far in front of the boat is the orca.

Solution :

Let, distance of boat front from the crow's nest is x.

So,

[tex]\dfrac{30}{20+x}=tan \ 15^{\circ}\\\\x=\dfrac{30}{tan \ 15^{\circ}}-20\\\\x=111.94-20\\\\x=91.94\ m[/tex]

Hence, this is the required solution.

Select the parent function and its graph.

Answers

Answer:

The first one

Step-by-step explanation:

Answer:

first function, second graph

Step-by-step explanation:

got it right in plato :DDD

Tickets to a movie cost $11 for adults and $7 for students. A group of friends purchased 8 tickets
for $76. Write a system of equations to represent the situation. How many adult tickets and
student tickets were purchased
PLEASE HELP ME

Answers

Answer:

5 Adult tickets were purchased and 3 student tickets were purchased.

Step-by-step explanation:

5 Adult tickets were purchased and 3 student tickets were purchased.

Step-by-step explanation:

Write the problem as an equation like this

11x+7x=76

Now make an equation for the number of purchased tickets. Let x be adult and y be students.

x+y=8

Rewrite x + y = 8 as y = -x +8

Substitute y = -x + 8 into the first equation for y.

11x+7(-x+8)=76

11x+(-7x)+56=76

solve for 11x+(-7x)

4x+56+76

subtract 56 from both sides

4x=20

Divide both sides by 4

X=5

x + y = 8

5 + y = 8

y = 3

5 Adult tickets were purchased and 3 student tickets were purchased.

5 adult tickets and 3 student tickets were purchased.

What are system equations?

A finite set of simultaneous equations are called system equations.

Let, they purchased x tickets for adults and y tickets for students.

Therefore, system equations are:

x + y = 8 ----- equation 1

11x + 7y = 76----- equation 2

From equation 1,  we get: x = (8 - y)

Now, substituting the value of x in equation 2, we get:

11 × (8 - y) + 7y = 76

⇒ 88 - 11y + 7y = 76

⇒ 88 - 76 = 4y

⇒ 4y = 12

⇒ y = 3.

Therefore, putting the value of y in equation 2, we get: x = (8 - 3) = 5.

Hence, 5 adult tickets and 3 student tickets were purchased.

Learn more about system equations here: https://brainly.com/question/24065247

#Tag #SPJ2

You are making a scale drawing with a scale of 2 in. = 17 ft. Explain how you find the length of the drawing of an object that has an actual length of 51 ft.

Answers

Answer:

17/2 = 8.5

1 inch = 8.5 feet

51/8.5 = 6 inches

Step-by-step explanation:

HI :)

Answer:

51 divided by 17 = the answer

Step-by-step explanation:

if each 2 in. is 17 ft, you are looking for how many inches 51 feet would be.

15 points! Please I need some help this is due ...

Answers

Answer:

The answer above is correct

hi so I need help with my math the question says use the long division algorithm to find the decimal value of the fraction -1/4​

Answers

Answer:

uhm well I'm not sure what you mean by algorithm but just think it like this :

Step-by-step explanation:

think of 1/4 as a quarter and it says the negative

so -.25

Liam earned $1,200 in 2 weeks at his job. Matthew earned $1,450 in 4 weeks at his job. Which explains who earned more per week? A. Liam earned more per week because in 2 weeks he earned $250 more than Matthew earned in 4 weeks. B. Liam earned more per week because in 2 weeks he earned almost the same amount as Matthew earned in 4 weeks. C. Matthew earned more per week because in 4 weeks he earned $250 more than Liam earned in 2 weeks. D. Matthew earned more per week because he worked twice as many weeks as Liam worked.

Answers

Answer:

B. Liam earned more per week because in 2 weeks he earned almost the same amount as Matthew earned in 4 weeks.

Step-by-step explanation:

 in this problem we want to find who earns more between Liam and Mathiew

given

Liam earned $1,200 in 2 weeks

Matthew earned $1,450 in 4 weeks

Another way to find out who earns more per week is to find their weekly earns

for Liam earned $1,200 in 2 weeks

in a week he will earn= 1200/2

=$600 per week

for Mathew earned $1,450 in 4 weeks

in a week he will earn= 1450/4

=$362.5 per week

In a week Liam earns more

Two thirds of 148 seventh
graders buy their lunch at
school. How many students
is this?

Answers

Answer:

if you round, its 99. if you ignore the decimal, its 98

Step-by-step explanation:

2/3 of 148 is 98.66

which system of linear inequalities is represented by the graph​

Answers

Answer:

WOAH CALM DOWN JAMAL

Step-by-step explanation:

Answer:

y < x-2 and y > x+1

Step-by-step explanation:

Please help look at the screenshot

Answers

Answer:

Step-by-step explanation: 40 newtons to the right

Answer: 40 Newton’s

Which of the following is an example of direct variation?
y= cx
xy = c
y = czx
y= cx/z​

Answers

Answer: Choice A) y = cx

The 'c' is the constant of variation

For example, if c = 2, then y = 2x is a direct variation. Whatever x is, we double it to get y. As x increases, so does y. As x decreases, then so does y. Both x and y increase/decrease together.

Direct variation equations always go through the origin, and they are always linear. The 'c' plays the role of the slope. You can think of y = cx as y = mx+b where b = 0 in this case and c = m.

A man basic wage for a 40-hour weekly is $160.00. He is paid $5.00 per hour for overtime . If he works 6 1/2 hours over time in a certain week his wage for that week is

Answers

107.50 + 160.00= how much he will make

Which one?
A. B. C. or D?​

Answers

Answer: D 3sqrt2

Step-by-step explanation:

6x3=18

Sqrt of 18 = 3sqrt2

Option d is the answer

IVE BEEN TRYING TO GET THE ANSWER FOR THIS WITH A PICTURE AND KEYBOARD PLEASE HELP (It’s a picture)

Answers

Answer:

Step-by-step explanation:

Luke is a dog walker. He gets $10 per day for walking his neighbor's dogs. He recently snapped his surfboard and wants to buy a used surfboard for $325. If he has $142 in the bank, how many days will he have to walk the dogs to earn enough for the board?

Answers

Answer:

10$

Step-by-step explanation:

Arianna is packing scented candles and candle holders into gift boxes. She has 84 candles and 48 holders, and each box must contain both items. She puts the same number of candles in each box, and the same number of holders in each box. What is the maximum number of gift boxes Arianna can pack, and how many scented candles and candle holders will each box have?

Answers

Answer:

Step-by-step explanation:

If she has 84 candles and 48 holders, we can write out the factors of both values as shown

For candles

84 = 2×2×3×7

84 = 12×7

For 48

48 = 2×2×2×2×3

48 = (2×2)×(2×2×3)

48 = 4×12

48 = 12×4

From both factors, we can are that 12 common to both of them. This means that the maximum number of gift boxes Ariana can pack is 12

The other factors will give the amount of scented candles and candle holders that each box will have. This means that each box will have 7scented candles and 4 holders.

Simplify.

xb2aaayx3yyb3xxabby4x2

Answers

Answer:

is that even a real equation?

Uh, I don’t believe this can be simplified...

if y =32 when x =8 find y when x =30

Answers

Answer:

y = 120

Step-by-step explanation:

If y = 32 when x = 8, then y is 4 times the number of x. If x = 30, then (4)30 = 120.

John bought a new TV. The tag in the shop said it cost £299 + VAT.
If VAT is charged at 20%, how much did he pay (to the nearest penny)?​

Answers

Answer:

59.8

Step-by-step explanation:

20÷100×299

0.2×299

59.8

A market stall has 13 bags of apples, and 11 loose apples on display. In
total there are 141 apples at the stall. How many apples are in each bag?

Answers

Answer:

10 apples

Step-by-step explanation:

141-11 is 130. it says there are 11 loose apples on display. in total, there are 130 apples in the bag

we know that there are 13 bags of apples. so 130/13 is 10. there are 10 apples in each bag

(?)^2-3(?)=-2 can anyone solve this

Answers

Answer: x = 1 or x = 2

Sub in x for ?:

x^2-3x = -2 (Move all the terms to one side, and set the equation to equal 0)

x^2-3x+2 = 0 (Factor the simple trinomial by finding two numbers that multiply to 2 and add to -3)

x^2-x-2x+2 = 0 (Factor the expression)

x(x-1)-2(x-1) = 0 (Group like terms)

(x-1)(x-2) = 0 (Solve for x by setting each term equal to 0)

x-1 = 0

x = 1

x-2 = 0

x = 2

∴ x = 1 or x = 2.

solve for x please ​

Answers

Answer: 53°

Step-by-step explanation: If two parallel lines are cut by

a transversal, then same-side interior angles are supplementary.

So if we know one of our angles measures 127,

our other angle will measure 180 - 127, which is 53.

So x is 53 degrees.

Remember, whenever you have two parallel lines cut by a transversal,

same-side interior <'s are supp. or the sum of their measures is 180 degrees.

if 22,x,y,31 are in ap. find the values of x and y​

Answers

Answer:

x = 25, y = 28

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 22 and

a₄ = a₁ + 3d = 31 , that is

22 + 3d = 31 ( subtract 22 from both sides )

3d = 9 ( divide both sides by 3 )

d = 3

Thus

x = 22 + 3 = 25

y = 25 + 3 = 28

In American football, the ball is punted by dropping and kicking it before it hits the ground. The height ht of the football above the ground in meters t seconds after being punted is affected by gravity and by the punter's kick, and can be represented as the difference of two functions: at=4.9t2, which specifies the effect of gravity on the height of the ball, and vt=13.7t+0.5, which specifies the effect of the punt on the ball. With these two functions, ht=vt-at, how high above the ground was the ball when it was punted?

Answers

Answer:

The ball was 0.5 m above the ground before it was punted.

Step-by-step explanation:

Since at = 4.9t² specifies the effect of gravity on the height of the ball, and vt = 13.7t + 0.5 specifies the effect of the punt on the ball, the height ht of the ball above the ground after the punt is  ht=vt-at

ht = 13.7t + 0.5 - 4.9t². To find the height ht above the ground at which the ball was punted, we insert t = 0 which is the start time of the punt into the equation for ht. So with t = 0, ht becomes

ht = 13.7t + 0.5 - 4.9t²

ht = 13.7 × 0 + 0.5 - 4.9 × 0²

ht = 0 + 0.5 - 0

ht = 0.5 m

So the ball was 0.5 m above the ground before it was punted.

Which data values are outliers?
71, 96, 110, 112, 114, 114, 121, 127, 135, 175, 180

Answers

Answer:  71, 175, 180

Step-by-step explanation:

Find the interquartile range. 127- 112 = 23   Multiply by 1.5 = 34.5

Add to the mean  114 + 34.5 = 148.5  

Subtract from the mean  114 - 34.5 = 79.5

Any number greater than 148.5 or less than 79.5 is considered an outlier

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