what is the relationship of the volume of the cube to its edge length?

1/2 because 3 divided by 6 equals 0.5 or 1/2

The complex numbers are [tex]\(5i - 2\)[/tex] and [tex]\(5i + 2\)[/tex], meeting the conditions: sum [tex]\(10i\)[/tex], difference [tex]\(-4\)[/tex], product [tex]\(-29\)[/tex].

Let's denote the two complex numbers as [tex]\(a\)[/tex] and [tex]\(b\)[/tex].

Given:

1. [tex]\(a + b = 10i\)[/tex]

2. [tex]\(a - b = -4\)[/tex]

3. [tex]\(a \times b = -29\)[/tex]

From the first equation, we can isolate one variable in terms of the other:

[tex]\[ a = 10i - b \][/tex]

Now, substitute this expression for [tex]\(a\)[/tex] into the second and third equations:

[tex]\[ (10i - b) - b = -4 \][/tex]

[tex]\[ 10i - 2b = -4 \][/tex]

[tex]\[ 2b = 10i + 4 \][/tex]

[tex]\[ b = 5i + 2 \][/tex]

Now that we have found [tex]\(b\)[/tex], we can substitute it back into the expression for [tex]\(a\)[/tex] to find [tex]\(a\)[/tex]:

[tex]\[ a = 10i - (5i + 2) \][/tex]

[tex]\[ a = 10i - 5i - 2 \][/tex]

[tex]\[ a = 5i - 2 \][/tex]

So, the two complex numbers are [tex]\(5i - 2\)[/tex] and [tex]\(5i + 2\)[/tex]. Both of these satisfy the given conditions.

The two integers between which the cube root of 50 lies are 3 and 4.

To find the two integers between which the cube root of 50 lies, we can start by evaluating the cube roots of consecutive integers until we find the two integers that enclose the cube root of 50.

Let's calculate the cube roots of some consecutive integers:

Cube root of 1: 1

Cube root of 2: 1.25992

Cube root of 3: 1.44225

Cube root of 4: 1.58740

Cube root of 5: 1.70997

Cube root of 6: 1.81712

Cube root of 7: 1.91293

Cube root of 8: 2

Cube root of 9: 2.08008

Cube root of 10: 2.15443

We can observe that the cube root of 50 is greater than the cube root of 27 (which is approximately 3), and less than the cube root of 64 (which is 4). Therefore, the cube root of 50 lies between 3 and 4.

Hence, the two integers between which the cube root of 50 lies are 3 and 4.

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Answer:

6

Step-by-step explanation:

rise = 6

---------------------

run = 1

Rise is the y axis and run is the x axis. You look at the point and first go either up or down to the point you need to stop at. In this case we go down. Run is when you go sideways. Once you reach the line where the point lies, you need to go sideways 1 time to get to the point. Since rise is over run, 6 over 1

Therefore...........

6 over 1 = 6!!!!

Answer:

6

Step-by-step explanation:

Hey there!!

Given equation :

... c(x) = 29x + 54.5

In this equation $54.50 is installation fee and this would remain as a constant. ( This value wouldn't change ).

'x' is represented as the number of months.

The total cost or c(x) is given as $344.50

Getting this into equations :

... 344.50 = 29x + 54.5

Subtracting 54.5 on both sides :

... 29x = 290

Dividing by 29 on both sides :

... x = 10

Hence, the number of months is 10.

Hope my answer helps!!

By manipulating the provided cost function, we find that with $344.50, you can afford 10 months of cable service.

To determine the number of months of cable service you can have for $344.50, you simply need to solve the equation C(x) = 29x + 54.5 = 344.5, where C(x) represents the cost of the service and x is the number of months you are paying for. We can start by subtracting the installation fee (54.5) from both sides of the equation, which gives us 29x = 290. Then, dividing through by 29, we arrive at x=10.

Therefore, you can have cable service for 10 months if you have $344.50.

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Miguel can buy the notebook, pencils, and erasers. This combination ensures he spends his entire $12 budget while acquiring essential school supplies for note-taking, writing, and correction needs.

Miguel's budget is $12. Among the available items, the notebook costs $5, pencils cost $3, and erasers cost $2 each. Considering Miguel's budget, he can afford the notebook, pencils, and erasers with a total cost of $5 + $3 + ($2 x 2) = $12. This exhausts his budget entirely.

Firstly, Miguel can buy the notebook, which is essential for note-taking and organization. Secondly, he can purchase the pencils, providing him with the necessary writing tools. Finally, Miguel can acquire two erasers, offering him the convenience of correcting mistakes. This selection ensures he spends exactly $12 without exceeding his budget.

In essence, Miguel makes a balanced and practical choice, covering both writing and correction needs within the constraints of his budget. This strategic allocation of funds allows him to maximize the utility of his $12 while obtaining a variety of essential school supplies.

the answer to your question is D

Answer:  the correct option is

(D) (-7, -1), 6 units.

Step-by-step explanation:  We are given to find the co-ordinates of the center and the length of the radius of the following circle :

[tex]x^2+y^2+14x+2y+14=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the STANDARD equation of a circle with center at the point (h, k) and radius of length r units is given by

[tex](x-h)^2+(y-k)^2=r^2.[/tex]

From equation (i), we have

[tex]x^2+y^2+14x+2y+14=0\\\\\Rightarrow (x^2+14x+49)+(y^2+2y+1)+14-49-1=0\\\\\Rightarrow (x+7)^2+(y+1)^2-36=0\\\\\Rightarrow (x+7)^2+(y+1)^2=36\\\\\Rightarrow (x-(-7))^2+(y-(-1))^2=6^2.[/tex]

Comparing the above equation with the standard equation of a circle, we get

center, (h, k) = (-7, -1)  and radius, r = 6 units.

Thus, (D) is the correct option.

Assuming that the question is "11 times 6" rather than "11x times 6". The answer would be 66.

The equation for this problem is: 11 + (11 x 6) - 11)

"11 more than" means you would add 11 to the next equation. "11 less than" means you would subtract 11 from the following equation.

According to Order of Operations, you would start with the expressions in the parenthesis. So we would start with "11 x 6", which is 66. Then the expression would become 11 + (66 - 11). We would do the expression the parenthesis, "66 - 11", and we would get the answer 55. The expression would become 11 + 55, and 11 + 55 is 66.

The arithmetic statement '11 more than 11 less than (11x6)' first requires you to do the multiplication, resulting in 66, then subtract 11 to get 55, and finally add 11 to get 66.

The mathematical statement "11 more than 11 less than (11x6)" is an arithmetic problem that requires several steps to solve. Firstly, compute the values in brackets. You must multiply 11 by 6, which results in 66. The next step is to understand what '11 less than' means. It means to subtract 11 from 66, which gives you 55. Then you interpret the last part of the statement: '11 more than', which means you add 11 to that 55. This finally gives you a sum of 66.

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OK.

Let g(x) = ax²

We have the point (3, 1).

Substitute x = 3 and g(x) = 1:

1 = a(3²)

9a = 1    |divide both sides by 9

a = 1/9

Therefore your answer is

[tex]g(x)=\dfrac{1}{9}x^2=\left(\dfrac{1}{3}x\right)^2[/tex]

The fraction that is equivalent to 2/-6 would be -2/6 because they both equal -.03333 or -1/3.

Ohhh your in K12, here i got you let me do the equation and i promise ill be right with you.

Answer:

20 cm

Step-by-step explanation:

ik its looks like a different question your is just a shorter question but its the same

If 4 - 3 + 5 = -6 + 8 + 4 is a mathematically correct statement, then both sides should end up with the same number:

4 - 3 + 5 = -6 + 8 + 4     Original statement.

1 + 5 = -6 + 8 + 4     You can do this in any order, but I start by doing the 4 - 3.

6 = -6 + 8 + 4     Finish simplifying the left side.

6 = 2 + 4     Combine the -6 and 8.

6 = 6     Finish simplifying the right side.

Because both sides are equal to each other, the sentence must be true.

Therefore, the sentence is true because when simplified, the statement is 6 = 6.

Hope this helps! :)

EDIT: Just incase anyone is curious, both this way and the way the other guy used both work, as they both prove that both sides are equal.

Two factors of 64 that add up to 12 are 8 and 4.

8 x 8 is 64 so its a factor of 64

16 x 4 is 64 so its a factor of 64

8 + 4 = 12

Answer:

Given equation of the line,

[tex]y=\frac{4}{7}x-2[/tex]

If x = 0,

[tex]y=\frac{4}{7}(0) - 2=0-2=-2[/tex]

Thus, the line intercepts y-axis at (0,-2)

If y = 0,

[tex]0=\frac{4}{7}x-2\implies 2=\frac{4}{7}x\implies x=\frac{14}{4}=3.5[/tex]

Thus, the line intercepts x-axis at (3.5,0)

By joining these two points in the graph,

We will get the graph of the given line ( shown below )

The graph of the function y = 4/7x - 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 4/7x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

-270

Step-by-step explanation:

The value closest to zero on the number line is greatest because all of the values are negative which is less than zero. -270 is closer to 0 than the other values.

Answer:

It is A the first quadrant

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Profit means increase in money.

So, then the answer would be +650 because the person is gaining money, not losing it.

If the person was losing it, then the answer would be -650.

I hope that this helped you! :) Comment if u have any questions.

27.5 number of games Archie and kel will finish nonstop from 9:00 am to 2:30 pm.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

Archie and kel takes an average of 12 minutes to finish one game.

now calculating the total time being between 9:00 am to 2:30 pm = 330 minutes

Now, the number of games Archie and kel will finish in this 330 minutes will be calculated by dividing 330 minutes by 12 minutes :

330/12 = 27.5 games

Therefore,  27.5 number of games Archie and kel will finish nonstop from 9:00 am to 2:30 pm.

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we know that

Unit Rate is the ratio of two measurements in which the second term is one

so

to find the unit rate divide [tex](5/8)[/tex] by [tex](1/4)[/tex]

[tex]Unit\ rate=\frac{(5/8)}{(1/4)}= \frac{5}{8}*4= \frac{2.5}{1} =2.5 \frac{ft^{2}}{hour}[/tex]

therefore

the answer is

The unit rate is [tex]2.5 \frac{ft^{2}}{hour}[/tex]

Answer:

2/5

Step-by-step explanation: multiply then break down the fraction

Answer:

n= -4

Step-by-step explanation:

First we have to find the equation of line which passes through (6,3) and (8,4).

Then we have to pass this line through the point (n , -2).

we know, equation of line passing through (x1,y1) and (x2,y2) is

[tex]\frac{x-x1}{x1-x2}=\frac{y-y1}{y1-y2}[/tex]

So, the equation of line passing through (6,3) and (8,4) is

[tex]\frac{x-6}{6-8}=\frac{y-3}{3-4}[/tex]

or, [tex]\frac{x-6}{-2} =\frac{y-3}{-1}[/tex]

multiplying both sides by  -2

x-6=2(y-3)

or, x-6=2y-6

or, x-2y=6-6

or, x-2y=0

Now, we have to pass this line through  (n,-2)

So, using the point in the line, that is using  x=n  , y=-2

we get

n-2(-2)=0

or, n+4=0

or, n=-4

Answer:

Step-by-step explanation:

Given that the line passes through

(6,3), (8,4), and (n,-2).

We have to find the value of n.

Let us name the points as A, B and C in that order

Slope of AB = slope of BC since all 3 points lie in the same line

To find slope of AB:

Slope = (y2-y1)/(x2-x1) = (4-3)/(8-6) = 1/2

To find slope of BC:

Using the same formula slope = (-2-4)/(n-8) = -6/(n-8)

The two slopes are equal.

Hence 1/2 = -6/(n-8)

n-8 = -12

n = -4

4

9

16

25

36

49

64

81

100

(more than 6, oops)

Hello!

The approximate volume of the cylinder is the second option: 59.3 [tex]ft^{3}[/tex]

V = [tex]\pi r^{2} h[/tex]

V = 3.14 * 3^2 * 2.1

V = 3.14 * 9 * 2.1

V = 59.346 [tex]ft^{3}[/tex]

Final answer:

Explanation of calculating the volume of a cylinder with given radius and height using the formula V = πr²h.

Explanation:

The volume of a cylinder can be calculated using the formula V = πr²h. Given a radius of 3 feet and a height of 2.1 feet, when plugged into the formula with π = 3.14, the volume is approximately 19.74 cubic feet.

Answer:

179/180

Step-by-step explanation:

Step One

Find the prime factors of 18 and 20

18:3*3*2

20: 2 * 2 * 5

Step Two

You need two 2s two 3s and one 5 for the common denominator

The common denominator is 2 * 2 * 3 * 3 * 5 = 180

Step Three

Put the two fractions over 180

[tex]\dfrac{17*10}{10*18} + \dfrac{1*9}{10*18}[/tex]

[tex]\dfrac{170}{180} + \dfrac{9}{180}[/tex]

179/180

Jocelyn answered 76% of the questions correctly on her test. To find the percentage of questions Jocelyn answered correctly, we can use the following formula: Percentage = (Number of Correct Answers / Total Number of Questions) × 100

Given that Jocelyn got 19 out of 25 questions correct, we can plug these values into the formula:

Percentage = (19 / 25) × 100

Now, let's calculate the percentage:

Percentage = 0.76 × 100

Percentage = 76

Jocelyn answered 76% of the questions correctly on her test.

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Answer:

Step-by-step explanation:

Given that in the  town of Clover, 3 out of 5 citizens who are eligible to bit did so in the fall election.

A) No of citizens =400

Assume the same proportion as given holds good here

the number of citizens that voted in the fall election=[tex]\frac{3}{5} (400) \\= 240[/tex]

B) Assume the same proportion as given holds good here

No of citizens that voted in the fall election=180

Total no of citizens = [tex]\frac{5}{3} (180)\\=300[/tex]

Using partial quotients is a method of dividing where you break the DIVIDEND into sections that are easy to divide