4+3 +3 + 10 + 5 = 25
What is the average value?

The solutions to x^3 = 5 - 5i in polar form are √50cis(-π/12), √50cis(4π/3), and √50cis(5π/12).

To find the solutions to the equation x^3 = 5 - 5i in polar form, we can start by converting the complex number 5 - 5i into polar form.

The magnitude (r) of the complex number can be found using the equation r = √(a^2 + b^2), where a is the real part and b is the imaginary part. In this case, the magnitude is √(5^2 + (-5)^2) = √(25 + 25) = √50.

To find the argument (θ), we can use the equation θ = tan^(-1)(b/a), where b is the imaginary part and a is the real part. In this case, the argument is tan^(-1)(-5/5) = tan^(-1)(-1) = -π/4.

Therefore, the complex number 5 - 5i in polar form is represented as √50cis(-π/4).

To find the solutions to x^3 = 5 - 5i, we can take the cube root of both sides of the equation. Using De Moivre's Theorem, we can express the cube root of the complex number in polar form as the cube root of the magnitude raised to the power of 3, and the argument divided by 3.

Therefore, the solutions to x^3 = 5 - 5i in polar form are:

a. √50cis(-π/12)

e. √50cis(4π/3)

i. √50cis(5π/12)

Answer:

[tex] \sqrt[6 ]{50} cis( \frac{7\pi}{12} ) \sqrt[6]{50} cis( \frac{23\pi}{12} ) \sqrt[6]{50} cis( \frac{5\pi}{4} )[/tex]

Answer:

Length = 32 ft

Width = 10 1/3 ft

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

9,862 times 2/2 = 9862 so that doesn't work

but 9,862 times 4/2 = 19724 and that is greater than 9,862.

Answer: D) 9,862 * [tex]\frac{4}{2}[/tex]

Step-by-step explanation: If a number is not greater than one, then the number will actually decrease. Let's turn [tex]\frac{4}{2}[/tex] into a decimal.

4 ÷ 2 = 2

9,862 * 2 = 19,724

I hope this helps!

This results in the total amount of 7/8 ounce of green paint used.

The amount of green paint that Candita used for drawing seven green lines on her painting can be represented by the expression 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8. Each 1/8 ounce of green paint is used for one green line, and she draws a total of 7 green lines. So, we simply add up seven times the fraction 1/8.

The sum can be calculated as:

Which equals:

This is the total amount of paint she used to draw all the green lines.

Answer:

Scaling

Step-by-step explanation:

Scaling was the type of transformation used on f(x), such that:

[tex]g (x) = 2 \cdot f(x)[/tex]

Answer:

A. 30.27

Step-by-step explanation:

Answer:

the answer is A.

Step-by-step explanation:

Answer:

[tex]x = 14.8[/tex]

Step-by-step explanation:

As these triangles are similar, every side and angle corresponds and this is key to calculating this equation.

First, look at the side that is labeled [tex]x + 8[/tex] and find the corresponding side on the other triangle. Write this out as a fraction as shown below. Now find two corresponding sides that are both marked (the base lines) and write them out as a fraction as well (note that which ever triangle you are solving for, it's numbers will go on the top of the fraction)

[tex]\frac{x + 8}{36} = \frac{38}{60}[/tex]

We want to get the [tex]x[/tex] by its self and at the moment it is divided by 36. To remove the 36, we need to multiply both sides of the equation by 36

36 x [tex]\frac{x + 8}{36} = \frac{38}{60}[/tex] x 36

This cancels out both the 36s on the left leaving us with

[tex]x + 8 = \frac{38}{60}[/tex] x 36

all that needs to happen now is to remove the +8 so we are just left with [tex]x[/tex]. to do this, just subtract 8 from both sides and we are left with

[tex]x = \frac{38}{60}[/tex] x 36 - 8

calculate 38 ÷ 60 x 36 - 8 = 14.8

∴ [tex]x = 14.8[/tex]

I hope this was helpful and not too long :-)

Answer:

k = 9

Step-by-step explanation:

n = 3, so substitute 3 for n in the equation

k = 3(3)

k = 9

Answer:

-7 and 6

Step-by-step explanation:

You can solve this problem by setting up a system of equations. Lets call the first number x, and the second number y. Now:

x*y=-42

x+y=-1

You can subtract y from both sides of the second equation to get x=-y-1, which you can then substitute into the first:

(-y-1)*y=-42

-y^2-y=-42

y^2+y-42=0

Solving the quadratic equation:

(y-6)(y+7)=0

y=-7 or 6

x= 6 or -7

When one of the numbers is -7, the other is 6, and when it is 6, the other is -7. Hope this helps!

Answer:

Four times a number less 6 is 8 more than twice that number. find the number. Denote that number: a, we have:

a x 4 - 6 = a x 2 + 8

=> a x 2 = 6 + 8 =14

=> a = 14/2 = 7

Hope this helps!

:)

Answer:

The answer is a

Step-by-step explanation

2x2 - 4x + 2 will be a polynomial

(4x + 6) + (2x² - 8x - 4)

= 4x + 6 + 2x² - 8x - 4

= 2x² + (4x - 8x) + (6 - 4)

= 2x² - 4x + 2

And it is polynomial (it has more than 1 term)

Answer:

A. [tex]2x^{2} - 4x + 2[/tex] ; will be a polynomial

Step-by-step explanation:

(4x + 6) + (2x² - 8x - 4)

= 4x + 6 + 2x² - 8x - 4

= 2x² + (4x - 8x) + (6 - 4)

= 2x² - 4x + 2

Polynomial (it has more than 1 term)

Hope that help!

There is a negative correlation in the data set, Option B is correct.

As per the question, it is to be determined which correlation is shown in the scatterplot.

The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis.

Here,
In the scatter, plot the graph of the points shows a decline while moving on the positive x-axis. Thus the negative correlation is plainly going down, starting at the top left and moving down to the bottom right.

Thus, there is a negative correlation in the data set, Option B is correct.

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Answer A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

hope this helps!

The descriptions that can define more than one triangle is

a) angle measurements of 35°, 35°, and 110°

b) angle measurements of 40°, 60°, and 80°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now  the measurements of the triangle are

a)

angle measurements of 35°, 35°, and 110°

A triangle must have length sides that fulfil the Triangle Inequality Theorem and interior angles that add up to 180 degrees.

When two triangles are comparable, their corresponding sides have a proportionate ratio and their corresponding angles have a congruent relationship.

So , several triangles with the same internal angles are possible

b)

angle measurements of 40°, 60°, and 80°

Now , several triangles with the same internal angles are possible

Hence , the triangle is solved

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The descriptions that can describe more than one triangle are:

Angle measurements of 35°, 35°, and 110°

Side lengths of 6 ft, 8 ft, and 10 ft

The descriptions that can describe more than one triangle are:

Angle measurements of 35°, 35°, and 110°: This set of angles can form more than one triangle because the sum of angles in a triangle is always 180°. So, even though two angles are equal (35° each), their combination with a larger angle (110°) allows for multiple triangle constructions.

Side lengths of 6 ft, 8 ft, and 10 ft: This set of side lengths satisfies the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Thus, there are multiple triangles possible with these side lengths.

Question

Which descriptions can describe more than one triangle? Select two options.

side lengths of 6 ft, 8 ft, and 10 ft

angle measurements of 35, 35, and 110°

angle measurements of 30°, 40, and 50°

angle measurements of 40°, 60°, and 80°

side lengths of 4 cm, 6 cm, and 9 cm

Answer:

1.) In 529 plan, Your account earns interest and you can contribute as much as you want. But Your investment options are limited and the money must be used for college

2.) While in money market account, the account pays higher interest than traditional savings accounts, but limited to writing no more than three checks a month. Some banks limit your cash withdrawals.

Step-by-step explanation:

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.

Answer:

one

Step-by-step explanation: you cant simplify the equation so that both sides can be divided to get the same equation, if you graph it theres not a parabola so the only thing left is one.

Answer:

One solution

Step-by-step explanation:

To solve this problem, isolate x.

1/2(x + 12) = 4x - 1

Dividing 1/2 from both sides, we get x + 12 = 8x - 2

Subtracting 12 from both sides, we get x = 8x - 14

Subtracting 8x from both sides, we get -7x = -14

Dividing -7 from both sides, we get x = 2

Since this problem is able to be solved with only one answer, there is one solution: x = 2.

Answer:

0 ≤ x ≤ 4

Step-by-step explanation:

we are asked to find all the values of x such that y>0.

for y>0, this means that we will only consider the portion of the graph that is above the x - axis (i.e the part of the graph above y=0)

By observation, we can see that the graph is only above the x-axis between the interval  0 ≤ x ≤ 4  (which is the answer to your question)

Answer:

The last graph

Step-by-step explanation:

In the first and third one the labels are switched. And the minutes should be on the x axis while the hours should be on the y axis.

The second one is incorrect because it literally says that 0 minutes= 0.5 hour

Answer:

A (the first graph on edge)

Step-by-step explanation:

Looking at the graph, we can see that the graph that has the line pass through (30, .5) is going to be the correct one.

Answer:

x=0, x=-4

Step-by-step explanation:

Answer:

x=0, x=4

Step-by-step explanation: yes

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes, a rectangle.

We know that the area of a rectangular shape is

Area =length x width

Since we don't have any specific data regarding Nathan's plot of land

Let's assume some figure for better understanding

Say the length is 18m

And the width is 12m

Area = 18*12

Area= 216m²

Answer:

its B on edge

Step-by-step explanation:

Answer:

a. Account 1: 1 year Account 2: 10 years

b. Account 1: 2 years Account 2: 30 years

c. The first account grows exponentially, while the second one grows at a linear rate. Therefore, over time the first account tends to surpass the second one in value.

Step-by-step explanation:

The first account can be modeled by using a compounded formula with 100% rating, since it doubles every year. The formula is shown below:

M = C*(1 + r)^t

Where M is the final amount, C is the initial amount, r is the interest rate and t is the elapsed time. If r = 1, then it doubles every year, so we have the following expression for the first account:

M = 200*(2)^t

While the second acount grows at a steady rate of $100, therefore it can be modeled by the initial amount added by the growth rate multiplied by the elapsed time as shown below:

M = 1000 + 100*t

a. The first acount take 1 year to double, since it doubles every year.

In order for the second acount to double it needs to reach M = 2000, so we have:

2000 = 1000 + 100*t

100* t = 2000 - 1000

100*t = 1000

t = 10

It will take 10 years to double.

b. The first account will double again in 1 more year, so 2 years total.

The second account will need to reach M = 4000, therefore:

4000 = 1000 + 100*t

100*t = 4000 - 1000

100*t = 3000

t = 30

It'll take 30 years total for the second account to double again.

c. Since the first account grows exponentially it grows at a faster rate in comparison to the second one that grows linearly over time. Therefore over time the first account tends to surpass the second one in value.

In this exercise we will have to use the knowledge of finance to calculate the income time in this way we can say that:

a. [tex]Account 1: 1 year \\Account 2: 10 years[/tex]

b. [tex]Account 1: 2 years\\ Account 2: 30 years[/tex]

c. The first account grows exponentially, while the second one grows at a linear rate.  

Then writing the yield formula as:

[tex]M = C*(1 + r)^t[/tex]

Where:

If r = 1, then it doubles every year, so we have the following expression for the first account:

[tex]M = 200*(2)^tM = 1000 + 100*t[/tex]

a. In order for the second acount to double it needs to reach M = 2000, so we have:

[tex]2000 = 1000 + 100*t100* t = 2000 - 1000100*t = 1000t = 10[/tex]

b. The second account will need to reach M = 4000, therefore:

[tex]4000 = 1000 + 100*t100*t = 4000 - 1000100*t = 3000t = 30[/tex]  

c. Since the first record of finances evolve exponentially it become larger at a faster rate distinguished to the second individual that evolve linearly over opportunity. Therefore over opportunity the first fees be apt to outdo something or someone the second individual fashionable advantage.

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Answer:

C

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

The graph of the problem is plotted using Asymptote and attached.

From the graph:

There are a total of 20 families.

Average Number of Pets

[tex]=\dfrac{6*0+3*1+3*2+6*3+1*4+1*5}{20} \\\\=\dfrac{36}{20}\\\\=1.8[/tex]

The average number of pets per family is 1.8.

Answer:

1.8

Step-by-step explanation:

The bar chart tells us that:

6 families each have 0 pets,

3 families each have 1 pet,

3 families each have 2 pets,

6 families each have 3 pets,

1 family has 4 pets, and

1 family has 5 pets.

The total number of pets in all these families is (6 ∙ 0) + (3 ∙ 1) + (3 ∙ 2) + (6 ∙t 3) + (1 ∙ 4) + (1 ∙ 5) = 36. The number of families is 6 + 3 + 3 + 6 + 1 + 1 = 20. Therefore, the average number of pets per family is 38/20 = 1.8.

Answer:

20/18

Step-by-step explanation:

Answer:

1 1/3

Step-by-step explanation:

Answer:

This would be a negative

Answer:

Negative because it says ¨below zero¨ clarifying it is, indeed, a negative.

Answer:

See explanation

Step-by-step explanation:

To find the percentage of a number, multiply the number by the decimal form of the percentage.

To find the decimal point of a percentage, remove the percent sign, then move the decimal point two spaces to the left. For example, 25% becomes 0.25.

Now, let's move on to solving the problems.

1. 0.22 * 198 = 43.56 (option #4)

2. 0.07 * 980 = 68.6 (option #2)

3. 0.15 * 75 = 11.25 (option #3)

4. 0.45 * 62 = 27.9 (option #1)