Find all roots of y=x^3-64

Answers

Answer 1

Answer:

x = -4i and x = 4i, also x = 4

Step-by-step explanation:

Rewrite y = x^3-64 as y = x^3 - 64.  This can again be rewritten, this time as:

y = (x - 4)(x^2 + 16).

Setting this = to 0, we get x - 4 = 0, whose corresponding root is x = 4, and

x^2 + 16), which has two unequal, imaginary roots:  x = -4i and x = 4i.


Related Questions

2. Which situation leads to a unit cost of $4 per football ticket? (Hint: Find Unit Rate of Each)
A. $6 paid for 2 football tickets
B. $8 paid for 4 football tickets
C. 6 football tickets for $24
D. 10 football tickets for $50

Answers

Answer:

C

Step-by-step explanation:

A. 6/2=3

B. 8/4=2

C. 24/6= 4

D. 50/10=5

solve the equation 18y - 17 = 7 for y

Answers

Answer:

y = 1.3

Step-by-step explanation:

18y - 17 = 7

18y = 7 + 17

18y = 24

y = 24/18

y = 1.3

hope it helps!

Answer:

y=4/3

Step-by-step explanation:

To solve for y, we need to isolate it.

18y-17=7

Let's start by adding 17 to both sides.

18y=24

Next, we can divide both sides by 18.

y=24/18

Simplify.

y=4/3

3(4x+5)=33 What’s the value of x

Answers

Answer:

the answer would be 20

Answer:

x=3/2 or 1.5

Step-by-step explanation:

To solve for x, we have to get x by itself. To do this, perform the opposite of what is being done to the equation.

3(4x+5)=33

First, divide both sides by 3, since 3 is being multiplied by 4x+5

3(4x+5)/3=33/3

4x+5=11

Next, subtract 5 from both sides, since it is being added to 4x

4x+5-5=11-5

4x=6

Divide both sides by 4, since 4 is being multiplied by x

4x/4=6/4

x=6/4

x=3/2 or 1.5

Sarah and Gabriela are at a soccer camp. The length of a soccer practice is 2/3 hour. The coaches have set aside 8 hours for soccer practice. How many soccer practices can the coaches have?

Answers

Answer:

12 soccer practices

Step-by-step explanation:

1 Soccer practice = 2 / 3 hour

We have 8 hours

8 / 2/3

multiply the top and bottom by 3 to get rid of the 3

8 * 3 = 24

2/3 * 3 = 2

24 / 2 = 12

Answer:

One way to answer your problem is by using proportions, and the following method can be done:

Step-by-step explanation:

[tex]\frac{1}{\frac{2}{3}}=\frac{x}{8}[/tex]

Then that reduces to the following:

[tex]\frac{8}{\frac{2}{3}}=x=12[/tex]

So the answer would be 12 practices.

What is the length of a diagonal of a cube with a side length of 1 cm?
StartRoot 2 EndRoot cm
StartRoot 3 EndRoot cm
StartRoot 4 EndRoot cm
StartRoot 5 EndRoot cm

Answers

Answer:

The answer is 3cm

Step-by-step explanation:

The length of a diagonal of a cube with a side length of 1 cm is,

⇒ √3 cm

What is mean by Multiplication?

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

A side length of cube is,

⇒ 1 cm

We know that;

The length of a diagonal of a cube with a side length of a cm is,

⇒ d = √3 × a

Here, a = 1

Hence, The length of a diagonal of a cube with a side length of 1 cm is,

⇒ d = √3 × 1

⇒ d = √3 cm

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ6

Pretty please for a homie

Answers

Slope is -2
_______
Y+4=-2x+8
Y=-2x+4

Given that P(A)=0.5 and P(A and B)=0.4, if A and B are independent events, what is the probability of event B?

0.2

0.1

0.8

0.9

Answers

Answer:

0.8

Step-by-step explanation:

He randomly selects a sample of 200 Darwin households. Forty households prefer the new package to all other package designs. The point estimate for this population proportion is

Answers

Answer: The point estimate for this population proportion is 0.2

Step-by-step explanation:

The point estimate for this population proportion is also referred to as the sample proportion. This is also known as the probability of success, p. The formula for determining p is expressed as

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 200

x = 40

p = 40/200 = 0.2

can you please help me out​

Answers

Answer:

fwefwfwfewfwefwefwfew

Step-by-step fweexplanation:

erwrwerw

Two boats started to move towards each other from two boat stations, located 30 miles apart. One boat moved at a speed of 3 miles per hour, the other moved twice as fast. How soon will the boats meet?

Answers

Answer:

The boats will meet in 3.33 hours.

Step-by-step explanation:

The position of each boat can be modeled by a first order equation.

I am going to say that the first boat is at the position 0, and moving in the positive direction with a speed of 3 miles per hour. So

[tex]A(t) = 0 + 3t[/tex]

They are moving in oppositie directions, and initially are 30 miles apart. This means that the second boat starts at the position 30, and moves in the negative direction at the rate of 6 miles an hour. So

[tex]B(t) = 30 - 6t[/tex]

How soon will the boats meet?

This is t when:

[tex]A(t) = B(t)[/tex]

[tex]3t = 30 - 6t[/tex]

[tex]9t = 30[/tex]

[tex]t = \frac{30}{9}[/tex]

[tex]t = 3.33[/tex]

The boats will meet in 3.33 hours.

A dolphin jumped up out of the water and back into the water in a parabolic path. (H) height (t) seconds . H=-8(t-0.5)^2+2 . How long will the dolphin be in the air?

Answers

Answer:

4 seconds

Step-by-step explanation:

using the vertex formula of a quadratic,

[tex]a(x-h)^{2} + k[/tex], where (h,k) is the vertex

[tex]h = -8(t-0.5)^{2}+2[/tex]    h is height and t is time in seconds

the vertex (maximum height) of the dolphin is (h,k) or (0.5, 2)  

Height of 1/2

time of 2 seconds

it will take 2 additional seconds to reach the water again.

this can also be solved using quadratic equation, but since it was already set up in vertex form, i'd use that.

Can someone pls answer this if u do then I love u

Answers

Answer:I think it’s a

Step-by-step explanation:

I believe it’s C. The mean will increase and the median will remain the same.

the graphs of f(x)=-2x and g(x)=(1/2)^x are shown. what are the solutions to thr equation -2x=(1/2)^x? select each correct answer.
-2
-1
2
4

Answers

Answer:

-2

Step-by-step explanation:

hello :

f(x)=-2x and g(x)=(1/2)^x

f(-2)=-2(-2) =4

g(-2)=(1/2)^-2 = 1/2^-2 = 2²=4

A triangle has a base length of (2x - 4) units and a height of (x + 5) units. Write and solve a quadratic equation to determine what value of x gives the triangle an area of 44 square units.

Answers

Answer:

x=6

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

44 = 1/2 (2x-4)(x+5)

Multiply the 1/2 time (2x-4)

44 = (x-2) (x+5)

FOIL

44 = x^2 +5x -2x-10

Combine like terms

44 = x^2 +3x -10

Subtract 44 from each side

0 = x^2 +3x -10-44

0 = x^2 +3x -54

Factor

What two numbers multiply to -54 and add to 3

9*-6 = -54

9+-6 = -3

0 = (x+9)(x-6)

Using the zero product property

x +9 =0    x-6 =0

x = -9          x = 6

The height cannot be negative so x cannot be -9

x=6

A population of rabbits doubles every 60 days according to the formula P=10(2)^t/60, where P is the population of rabbis on day t. What is the value of t when the population is 320

Answers

Answer:

[tex] 320 = 10 (2)^{t/60}[/tex]

If we divide both sides by 10 we got:

[tex] 32 = 2^{t/60}[/tex]

We can apply natural log on both sides and we got:

[tex] ln (32) = \frac{t}{60} ln(2) [/tex]

And solving the value of t we got:

[tex] t = 60 \frac{ln(32)}{ln(2)}= 300[/tex]

So then we can conclude that after t = 300 days we will have approximately 320 rabbits  

Step-by-step explanation:

For this case we have the following function:

[tex] P(t) = 10 (2)^{t/60}[/tex]

Where P is the population of rabbis on day t. And for this case we want to find the value of t when P =320 so we can set up the following equation:

[tex] 320 = 10 (2)^{t/60}[/tex]

If we divide both sides by 10 we got:

[tex] 32 = 2^{t/60}[/tex]

We can apply natural log on both sides and we got:

[tex] ln (32) = \frac{t}{60} ln(2) [/tex]

And solving the value of t we got:

[tex] t = 60 \frac{ln(32)}{ln(2)}= 300[/tex]

So then we can conclude that after t = 300 days we will have approximately 320 rabbits  

Ethan has partially filled the prism with 8 unit cubes. How many more cubes does he need to fill the prism completely A:10 B:15 C:19 D:21 Help me please!!!???!

Answers

Corrected Question

Ethan has partially filled the prism with 8 unit cubes.

A rectangular prism with length, height, and width of 3.

How many more cubes does he need to fill the prism completely?

Answer:

(C)19

Step-by-step explanation:

First, we determine the volume of the rectangular prism

Volume of a rectangular prism = Length X Height X Width

=3 X 3 X 3=27 cubic units

Volume of the Cube=1 cubic unit

The number of unit cubes that will fill the rectangular prism = 27

Ethan has partially filled the prism with 8 unit cubes, we subtract 8 from 27 to determine the number left to fill the prism

27-8=19.

Therefore, Ethan will need 19 more cubes to fill the rectangular prism.

The correct option is C

f(n)=93+4(n-1) Complete the recursive formula of f(n)

Answers

Answer:

f(1) = 93

f(n) = f(n - 1) + 4

Step-by-step explanation:

The recursive formula for an arithmetic sequence is given as:

f(1) = a

f(n) = f(n - 1) + d

where a = first term and d = common difference

An arithmetic sequence is in the form:

f(n) = a + d(n - 1)

where a = first term and d = common difference

The common difference in f(n) = 93 + 4(n-1) is 4.

The first term is 93.

The recursive formula is therefore:

f(1) = 93

f(n) = f(n - 1) + 4

Answer:

f(1)=93

f(n)=f(n-1)+4

Step-by-step explanation:

As you can see in the picture, the initial value is 93, which is why it's the first part of the equation. The 4 is multiplying the (n-1) part in the equation and as we complete the recursive formula of N, you have to put the numbers in the correct order.

What is the value of 98.84 divided by 14​?

Answers

Answer:

7.06

Step-by-step explanation

i just searched for calculator put in the problem

Hope that helps :)

Please I need help with this one

Answers

Answer:

$0.60

Step-by-step explanation:

What type of correlation is shown by the graph?

Answers

Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

Which of the following functions is not linear?

Answers

Answer:

D. y = 8x² + 8x + 4

Step-by-step explanation:

The equation of a linear function is in form:

[tex]y=mx+b[/tex]

We have:

[tex]\bold{A.}\\\\y=8(x+8)+4(x+8)\qquad\text{use the distributive property}\\\\y=8x+64+4x+32\qquad\text{combine like terms}\\\\y=12x+86\to m=12,\ b=86\\\\\bold{linear\ function}[/tex]

[tex]\bold{B.}\\\\y=\dfrac{\sqrt8}{8}x-4\to m=\dfrac{\sqrt8}{8},\ b=-4\\\\\bold{linear\ function}[/tex]

[tex]\bold{C.}\\\\y=\dfrac{1}{8}x+8\to m=\dfrac{1}{8},\ b=8\\\\\bold{linear\ function}[/tex]

[tex]\bold{D.}\\\\y=8x^2+8x+4\\\\\bold{not\ linear\ function}\\\\\text{because is}\ x^2\\\\\text{It's a quadratic function}[/tex]

Which points are Coplanar and noncollinear. ?

Answers

Answer:

Non-collinear points: These points, like points X, Y, and Z in the above figure, don't all lie on the same line. Coplanar points: A group of points that lie in the same plane are coplanar. Any two or three points are always coplanar. Four or more points might or might not be coplanar.

Step-by-step explanation:

What happens if b = 0 in the general exponential function() = a
b
?

Answers

Answer:

It stays a zero or it turns into whatever the b or a is

Step-by-step explanation:

Help me it’s urgent

Answers

Answer:

∠GHJ and ∠IHJ

Answer:

[-10, 10]

This is an absolute value problem and numbers within the brackets are always seen as positive. [-10] = 10   and [10] = 10

Step-by-step explanation:

Could some one plz help me with this question
P.S ignore the answer choices their wrong

25 Points

Answers

Answer:

A

Step-by-step explanation:

The formula for this type of interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where A is the total amount, P is the initial investment, x is the interest rate, n is the amount of times that the investment is compounded a year, and t is the amount of years. Plugging in the numbers given, you get:

[tex]A=1800(1+\frac{0.025}{2})^{2\cdot 12}=[/tex]

[tex]1800(1.0125)^{24}\approx 2425.23[/tex]

Now, she invests this into a new account, and you can set up the following equation:

[tex]A=2425.23(1+\frac{0.04}{12})^{12\cdot 7}=[/tex]

[tex]2425.23(1.0033333)^{84}\approx 3207.40[/tex], or option A.

Hope this helps!

Myra is a scientist and needs 45 gallons of a 16% acid solution. The lab is currently stocked only with a 20% acid solution and a 10% acid solution. Myra will need to mix how many gallons of the 20% solution and how many gallons of the 10% solution to have what she needs.

Answers

Answer:

The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons

Step-by-step explanation:

Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:

x + y = 45

The concentration of acid of the final solution is:

0.2*x + 0.1*y = 45*0.16

0.2*x + 0.1*y = 7.2

Therefore we have a system of equation:

x + y = 45

0.2*x + 0.1*y = 7.2

We need to multiply the first equation by -0.1:

-0.1*x -0.1*y = -4.5

0.2*x + 0.1*y = 7.2

We now sum both equation:

0.1*x = 2.7

x = 2.7/0.1 = 27 gallons

y = 45 - 27  = 18 gallons

Brianna and Ava go to the movie theater and purchase refreshments for their friends. Brianna spends a total of $39.00 on 2 bags of popcorn and 2 drinks. Ava spends a total of $174.50 on 8 bags of popcorn and 10 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.

Answers

Answer:

2p + 2d = 39 ____________(1)

8p + 10d = 174.50 _________(2)

Price of one drink is $9.25

Step-by-step explanation:

Let the price of a bag of popcorn be p.

Let the price of a drink be d.

Brianna spends a total of $39.00 on 2 bags of popcorn and 2 drinks. This implies that:

2p + 2d = 39 ____________(1)

Ava spends a total of $174.50 on 8 bags of popcorn and 10 drinks. This implies that:

8p + 10d = 174.50 _________(2)

We now have two system of equations which we can use to find the price of a bag of popcorn and drink:

2p + 2d = 39 ____________(1)

8p + 10d = 174.50 _________(2)

Multiply (1) by 4 subtract from (2):

 8p + 10d = 174.50 _______(2)

- 8p + 8d = 156    __________(1)

        2d = 18.50

=>       d = $9.25

The price of one drink is $9.25

The graph of f(x)= x is translated 3 units down to form the graph of g(x). Which of the following is g(x)
Answers :
A: g(x)= -3x
B: g(x)= 3x
C: g(x)= x - 3
D: g(x)= x + 3

Answers

Answer:

I'll edit the answer and try to answer it, but where is the graph?

Answer:

C: g(x)= x- 3

Step-by-step explanation:

translated 3 units down means you go 3 down on the y-axis. Therefore it is g(x)= x-3

The question on the bottom

Answers

Answer:

9th grade student=33.3%, unit 7=45%

Step-by-step explanation:

27,9, 3, ...
Find the 6th term.

Answers

Answer: .1

Step-by-step explanation: divide all the numbers by three. 27 ÷ 3 = 9

9÷3= 3

3÷3= 1

1÷3= .3

.3 ÷3 = .1

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