Jack divided his fortune of $92,000 into 8 equal parts. He gave 4 parts to his wife, 1 part to his son and divided the remaining 3 parts equally among 5 charities.
How much more money did his son get than each charity?

Answer:

1

Step-by-step explanation:

note that i² = - 1

Thus

[tex]i^{8}[/tex]

= i² × i² × i² × i²

= - 1 × - 1 × - 1 × - 1

= 1 × 1

= 1

The value of complex number is 1. Therefore, the option B is the correct answer.

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.

The given complex number is i⁸.

We know that, i²=-1

Now, i⁸ can be written as i²×i²×i²×i²

= -1×(-1)×(-1)×(-1)

= 1

Therefore, the option B is the correct answer.

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Answer:

X = 6

Step-by-step explanation:

Look at the attachment

First, I need to decide what equation this is like.

I believe this is y=mx.

We know that x is typically the input, and m is the constant function.

Y is the output.

So the original function may have been y=200x.

The only difference is now we've been given something to apply to the equation, in place of x.

2. Imagine a cloning machine. Whatever you put in, you get a copy of, and the original thing you put in. Its function would be y=2x. Let's pretend we decided to put three things in; 3 would go where x is.

Y would be the result of 3 copies and their originals, or 2(3).

(6=2(3))

Now, when someone else decides to use the cloning machine, they may put any number in, but the only properties that will change are y and x, not m.

The function will remain y = 2x. Any number could go in place of x, and multiplying x by 2 will give you the y. As long as you have a different value for x, the y will never be the same.

3. So now we have an understanding of what it means, we see that we have been given an x value to insert; an input.

A more practical example could be someting with money. This won't be entirely realistic, because we are dealing with a fraction of a number and another large number.

4. I decided to go with flour. I wanted the 200 to represent pennies, or cents. Before I landed on this, I looked up the cost of flour per pound. I found that the average is .43 dollars, which isn't terribly close to two dollars. But maybe the flour is high quality, so we can stick with that.

5. Seeing that this equation, y=200x, means we are charging 200 cents, or two dollars, we can write a problem from here.

Sylvia is in charge of selling home-harvested flour from an organic farm. She charges two dollars per pound of flower. Today, her next-door neighbors hope to buy a ninth of pound of flour, and they insist on paying with pennies. How many pennies do they need to pay for their order?

Let me know if this helped, or if you have any questions!

Answer: c < -3

Step-by-step explanation: To solve for c in this inequality, your goal is the same as it would be you were solving an equation, to get c by itself on one side of the inequality.

Since 2 is being added to c, subtract

2 from both sides of the inequality.

On the left, the +2 and -2 cancel out

and on the right, -1 - 2 is -3.

So we end up with c < -3.

I have also graphed this for you below.

Answer:

3.5

Step-by-step explanation:

0 1 1 3 3 3 4 5 7

median= 3

Q1= 1

Q3= 4.5

4.5-1= 3.5

Answer:3.5

0,1,1,3,3,3,4,5,7

Answer:

7500

Step-by-step explanation:

3*1975=5925

5925/.79=$7500

Answer:

5175

Step-by-step explanation:

1975*3=5925

5925/79%=7500 (Take one zero off)

750

5925-750=5175

The Company will pay 5175 in total. But 1725 per each person going.

The value of x is 13. Therefore, option B is the correct answer.

Given that, EF=7x+9, FG=3x+4 and EG=143.

A line segment is a part of a line that connects two points which are considered to be its endpoints. It is the distance between two points that can be measured.

Now, EG=EF+FG

⇒143=7x+9+3x+4

⇒10x+13=143

⇒10x=130

⇒x=13

The value of x is 13. Therefore, option B is the correct answer.

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Answer:

(D)

Step-by-step explanation:

Equivalent expressions are expressions that have equal values

The equivalent expression of [tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex] is [tex]\sqrt{\frac{8x}{3}}[/tex]

The expression is given as:

[tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex]

Represent the expression as a quotient

[tex]\sqrt{8x^2 } \div \sqrt{3x} = \sqrt{\frac{8x^2}{3x}}[/tex]

Evaluate the quotient

[tex]\sqrt{8x^2 } \div \sqrt{3x} = \sqrt{\frac{8x}{3}}[/tex]

Hence, the equivalent expression of [tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex] is [tex]\sqrt{\frac{8x}{3}}[/tex]

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[tex] (2.3 \times 10^1) \times (7 \times 10^6)[/tex]

[tex](2.3 \times 7) \times (1 {0}^{1} \times {10}^{6} )[/tex]

[tex]16.1 \times {10}^{1 + 6} [/tex]

[tex]16.1 \times {10}^{7} [/tex]

The product of the given numbers is 1.61 × 10⁸.

Scientific notation is a way of writing a large number or small number with many digits in a simpler form using the power of 10.

For example, 30,000 can be written as 3 × 10⁴.

Given that,

We have to multiply the numbers (2.3 x 10¹) (7 x 10⁶).

The numbers in scientific notation uses exponents.

So we have to use the product rule of exponents here.

(2.3 x 10¹) (7 x 10⁶) = (2.3 × 7) × (10¹ x 10⁶)

                              = 16.1 × (10¹ x 10⁶)

We have the product rule, xᵃ . xᵇ = xᵃ⁺ᵇ

So the product is,

(2.3 x 10¹) (7 x 10⁶) = 16.1 × (10¹⁺⁶)

                              = 16.1 × 10⁷

                              = 1.61 × 10⁸

Hence the product in scientific notation is 1.61 × 10⁸.

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Answer:

[tex]y^{-4}\cdot y^3=y^{-1}[/tex].

Step-by-step explanation:

The given expression is

[tex]y^{-4}\cdot y^3[/tex]

We have to simplify the above expression. in form of [tex]y^n[/tex].

Using property of exponents, we get

[tex]y^{-4}\cdot y^3=y^{-4+3}[/tex]      [tex][\because a^ma^n=a^{m+n}][/tex]

After addition of exponents, we get

[tex]y^{-4}\cdot y^3=y^{-1}[/tex]

Therefore, [tex]y^{-4}\cdot y^3=y^{-1}[/tex].

Answer:

54 in^2

Step-by-step explanation:

9*12/2=54 in^2

Answer:

54

Step-by-step explanation:

The formula is 1/2*base*height which is 1/2*12*9. This is equal to 54.

hope this helps:)

Answer:

story 1

Step-by-step explanation:

because it says 2 higher than -2 so -2+2 is 0

Inverse operations are an operation that undoes each other. For example, addition and subtraction, multiplication and division, squares and square roots.

For example, we have the equation:

2 + 2 = 4

The inverse of this equation is:

4 - 2 = 2

Best of Luck!

===========================================================

Explanation:

The half-life is 35 hours. This means every 35 hours, the amount of the substance is cut in half. If we started with 100 grams, then 35 hours later, we will have 50 grams. Then another 35 hours later we will then have 25 grams, and so on.

In this case, we start with 904 grams and follow this sequence:

904, 452, 226, 113, ...

Each term is cut in half. Going from term to term it takes 35 hours each. The third term 226 is the result of waiting two half-lives, which is 2*35 = 70 hours that have elapsed total.

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

If you want to use a formula, then it would be

[tex]y = A*\left(\frac{1}{2}\right)^{x/H}[/tex]

where,

H = half-life duration (in this case, it is 35)

A = starting amount (which is 904 in this case)

x = amount of time that has elapsed (we will plug in x = 70)

y = final amount after x units of time has elapsed

note that x and H must have the same time unit. Both are in terms of hours in this case.

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

So we will plug A = 904, x = 70, H = 35 into the formula to get...

[tex]y = A*\left(\frac{1}{2}\right)^{x/H}\\\\y = 904*\left(\frac{1}{2}\right)^{70/35}\\\\y = 904*(0.5)^{2}\\\\y = 904*(0.25)\\\\y = 226\\\\[/tex]

We see that x = 70 leads to y = 226. This means after 70 hours, there is 226 grams of the material left.

Answers and Step-by-step explanations:

Let's look at the first row:

cost = _______ + _______ * (monthly payment)

The first blank should be the "down payment" because this is the initial, constant value that is paid. The second blank should be the "number of months" because this way, when multiplied by the actual amount each payment is (monthly payment), then we get the total amount paid during those months.

So, we have:

cost = (down payment) + (number of months) * (monthly payment)

Now for the second row, we just plug in numbers and variables:

335 = 50 + 6 * p

Finally, we can solve for p:

335  = 50 + 6p

6p = 285

p = $47.50

Answer:

Cost = down payment + no. of monthly payments × monthly payment

335 = 50 + 6 × p

285 = 6p

p = 47.5

Answer:

752 bellow sea just did that

Answer:

Its 752 below see level!

Step-by-step explanation:

I am doing the assignment right now and got it right!, if you want can you guys mark brainliest that would help a lot!!

Answer:

185.68 for perimeter

1652.16 for area

Step-by-step explanation:

Please give me brainliest i hope you do well.!

Answer:

What is the length of Side X Z?

✔ 5

What is the length of Size Y Z?

✔ 6

The length of side XZ is 5 units.

The length of side YZ is 6 units.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To find the length of side XZ, we can use the distance formula, which is:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Substituting the coordinates of X (-2, 4) and Z (3, 4), we get:

[tex]d(XZ) = \sqrt{(3 - (-2))^2 + (4 - 4)^2}\\= \sqrt{5^2 + 0^2}\\= \sqrt{25}\\= 5[/tex]

The length of side XZ is 5 units.

To find the length of side YZ, we can again use the distance formula with the coordinates of Y (3, -2) and Z (3, 4):

[tex]d(YZ) = \sqrt{(3 - 3)^2 + (4 - (-2))^2}\\= \sqrt{0^2 + 6^2}\\= \sqrt(36)\\= 6[/tex]

The length of side YZ is 6 units.

Thus,

The length of side XZ is 5 units.

The length of side YZ is 6 units.

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Answer:

363

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 92 and d = - 85 - (- 92) = - 85 + 92 = 7 , thus

[tex]a_{66}[/tex] = - 92 + (65 × 7) = - 92 + 455 = 363

Answer:

363.

Step-by-step explanation:

We see that each term increases by 7.

This is an arithmetic sequence with first term (a1) = -92  and the common difference (d) is 7.

an = a1 + (n - 1)d

a66 = -92 + (66 - 1)7

= -92 + 455

= 363.

Answer:

85%

Step-by-step explanation:

He  hit it 17/20

We want that as a percent

Multiply by 5/5

17/20*5/5 = 85/100

Percent means out of 100

85%

Answer:

85

Step-by-step explanation:

P(hit) = 17/20 × 100

85%

Answer:

is there supossed to be a picture?

Step-by-step explanation:

Answer:

Can you please give us a picture!

Step-by-step explanation:

Answer:

Yes, lines CD & AB are perpendicular

Step-by-step explanation:

AB slope: y = -12/8x + 7

CD slope: y = 6/9x - 6

Once the slopes are simplified:

AB: -3/2

CD: 2/3

Hope this helps!

Answer:

Step-by-step explanation:

Rule for the transformations has been given as,

[tex]T_{(5, -0.05)o\text{R}(0, 180)}(x,y)[/tex] defines the rules as the translation by 5 units right and 0.5 units down followed by rotation of the triangle by 180° about the origin.

In other words,

Rule for translation:

F(x, y) → F"(x + 5, y - 0.5)

Followed by the rotation of 180° about the origin,

Rule of rotation,

F"(x', y') → F'(-x, -y)

Following these rules coordinates of the new triangle F'G'H' can be obtained.

Answer:

d. no solution

Step-by-step explanation:

y=2x-3

2x=y-3

y=2x+3

Since these are two distinct parallel lines (same slope), they will never meet. Hence, no solution

Answer:

No solution :)

Step-by-step explanation:

Answer:

D. run

Step-by-step explanation:

The slope is given by

m = (y2-y1)/ (x2-x1) =  rise/ run

The change in the x coordinates is the run

Answer:

a) At what time does Bethan arrive home from school?

The answer would be C) 15:30

b) What distance does Siobhan travel each day when going to school and back?

The answer would be D) 16km

Step-by-step explanation:

Answer:

D.)The two variables are the number of crackers and the number of calories.

Step-by-step explanation:

The number of crackers is the independent variable, and the number of calories is the dependent variable.

The point (6, 42) is on the line

The number of crackers are graphed on the x-axis, and calories are graphed on the y-axis.