How much money should be invested every quarter at 9% per year, compounded quarterly, in order to have $3000 in 8 years? (Round your answer to the nearest cent.)

Answer:

x=9

Step-by-step explanation:

To solve for x, you can set up a proportion between the 2 triangles we see.

The small triangle can be written as [tex]\frac{16}{20}[/tex], and the large triangle can be written as [tex]\frac{16+12}{20+2x-3} = \frac{28}{2x+17}[/tex].

Set both proportions equal to each other.

[tex]\frac{16}{20}=\frac{28}{2x+17}[/tex]

Cross multiply and solve for x.

[tex]16(2x+17)=(28)(20)[/tex]

32x+272=560

32x=288

x=9

Answer:

A is correct

Step-by-step explanation:

perimeter is twice the sum of the two adjacent sides

p = 2(x + (2x³ - 3x + 4))

p = 2(2x³ - 2x + 4)

p = 4x³ - 4x + 8

Answer:

6 bananas

Step-by-step explanation:

2 ÷ 0.30 = 6.6 repeating so 6 bananas

Answer:

Step-by-step explanation:

       -(4q+8) + 6q = 12q - 5/6(18q + 6)

Open brackets:

<=>  - 4q - 8 + 6q = 12q - 5/6*18q - 5/6*6

<=>  - 4q - 8 + 6q = 12q - 15q - 5

Put q in one side and non q in one side:

<=> - 4q + 6q - 12q + 15q = 8 - 5

<=> 5q = 3

<=> q = 3/5

Answer:

-0.2

Step-by-step explanation:

pls give me brainliest if possible

Answer:

See image

Step-by-step explanation:

This is to help you practice exponent rules. The rules are short cuts, which are good bc they're faster but bad bc they take away the meaning of the work. If you're trying to remember a rule, think through the meaning. See image.

So, "multiply exponents" and "product of powers" are basic two equivalent phrases! I think the answers on the image should work, but jic if not switch those two.

The Add exponents rule and Subtract are 100% correct.

The expressions are matched to the method needed to evaluate as shown below.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The first expression is 5³ × 5³.

Multiplication rule of exponents states that,

xᵃ × xᵇ = xᵃ⁺ᵇ

That is we add the exponents.

So, 5³ × 5³ = 5³⁺³ = 5⁶

The next expression is (7²)³.

We have the rule, (xᵃ)ᵇ = xᵃᵇ

So, here, multiply the exponents.

(7²)³ = 7⁶

(4x³)⁵

We can write it as,

(4x³)⁵ = 4⁵ . (x³)⁵

That is write is as product of the powers.

Division rule of exponents states that,

xᵃ / xᵇ = xᵃ⁻ᵇ

6⁹ / 6⁵ = 6⁹⁻⁵ = 6⁴

So, subtract the exponents.

Hence the expressions are matched.

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Answer:

Approximately 40,069 days

Answer:

21(3a-2b)

Step-by-step explanation:

Answer:

21(3a-2b)

Step-by-step explanation:

63a - 42b​

21(3a-2b)

Answer:

They were very angry about her helping the colonists.

Step-by-step explanation:

Answer:

  11 million

Step-by-step explanation:

20 -12 +3 = 11

There will be 11 million shares of stock in the treasury.

Answer:

10

Step-by-step explanation:

each tick mark is worth 5

there is the -10, then one to the right is -5, next is 0, next is 5, next one (the one where the x is) 10, next 15, next 20.

Answer:

256, -1024, 4096, -16384

i think that's it

it's being multiplied by -4 (geometric)

Answer:

B. (5,0)

Step-by-step explanation:

hope this helps

Answer:

B. (5,0)

Step-by-step explanation:

Place all the coordinates on the graph and then its pretty much self-explanatory after that. you just see which is closest to the subject. which, in this case, was the school.

Answer:

31.334... years

Step-by-step explanation:

Initial value = $500

r = 1.5%

t = ?

A = (500)[tex]e^{.015*t}[/tex]

I was unsure if the question was asking to express the equations in terms of t =, but i did those steps anyway just in case.

A/500 = [tex]e^{.015*t}[/tex]

ln A/500 = ln[tex]e^{.015*t}[/tex]

ln A/500 = .015*t

ln(A/500)/.015 = t

t = ln(A/500)/.015

To find the amount of time it takes for the account balance to reach $800, we plug in $800 for A in the equation that solves for t.

t= ln(800/500)/.015 = 31.334...(rounded) years

We also could have solved by plugging in $800 into the original equation and then solving for t, but i found it to be easier to find the equation for t prior to solving. Hope this helps!

Answer:

The 31st term is 283

Step-by-step explanation:

The sequence has a common difference therefore, it is an arithmetic sequence

[tex]an = a1 + (n - 1)d[/tex]

a31 = 13 + ( 31-1 ) 9

a31 = 13 + 270

a31 = 283

Answer:

y=-6x+5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-1))/(0-1)

m=(5+1)/-1

m=6/-1

m=-6

y-y1=m(x-x1)

y-(-1)=-6(x-1)

y+1=-6(x-1)

y=-6x+6-1

y=-6x+5

Answer:

67 hamburgers

Step-by-step explanation:

In order to find the answer to this question, you must do the following equation:

44÷2/3. The answer to this is 66.

Then, you add 1 to 66, because 2/3 divided by 2/3 = 1!

So, the cook can make 67 hamburgers.

Answer:

BDE

Step-by-step explanation:

Answer:

m = —1/3

Step-by-step explanation:

There are two clear points shown on the graph

point 1: (0;3)

point 2: (6;1)

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

[tex]m = \frac{1 - 3}{6 - 0} [/tex]

[tex]m = - \frac{2}{6} [/tex]

[tex]m = - \frac{1}{3} [/tex]

Answer:

mmmmmmm

Step-by-step explanation:

n

Daisy will cover a total area of 647.625 square feet, if she uses all of the bags of mulch.

The amount of mulch is given as:

[tex]Bag = 2\frac 34[/tex]

The area covered by each bag is given as:

[tex]Area = 235.5ft^2[/tex]

If she uses all bags, the total area covered by the bags is:

[tex]Total = Bag \times Area[/tex]

So, we have:

[tex]Total = 2\frac 34 \times 235.5ft^2[/tex]

Rewrite the fraction as an improper fraction

[tex]Total = \frac {11}4 \times 235.5ft^2[/tex]

This gives

[tex]Total = \frac {2590.5}4 ft^2[/tex]

[tex]Total = 647.625 ft^2[/tex]

Hence, she will be able to cover a total area of 647.625 square feet

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Answer:

It seems like the answer would be 21 students.

Step-by-step explanation:

5 times 3 is 15 so 15 girls

2 times3 is 6 so 6 boys

15+6=21

I hope this helps :))

The population of earth growing in logistic pattern will be helpful because it will help the human population to grow gradually to approach the carrying capacity of earth and without making any burden on it.

In logistic growth the population at first increases at slow rate and then at high then it stops when resources start depleting.

When population on earth will follow the logistic growth pattern, the people leaving can have enough resources to use, and it will in a way can a make a better community without war or disturbance.

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Answer:

1399/200 699.5%

Step-by-step explanation:

1. 6.995 is already a decimal.

2. As a fraction it is [tex]\frac{1399}{200}[/tex] and as an improper fraction it would be 6  [tex]\frac{199}{200}[/tex].

3. As a percent it would be 669.5%.

Answer:

000

Step-by-step explanation:

000

Answer:

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]

Step-by-step explanation:

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = \lim_{x\to 0^+} \tan(x) - \lim_{x\to 0^+} \frac{1}{x^2} $[/tex]

and

[tex]$\lim_{x\to 0^+} \tan(x) = \tan(0) = 0$[/tex]

[tex]$\lim_{x\to 0^+} \frac{1}{x^2} = +\infty$[/tex]

Therefore,

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]

The angle relationship and their reasons are:

The angle pairs are formed based on their relative positions. The following shows each angle relationship and their reasons:

∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are  equal based on the vertical angles theorem.

∠KFE and ∠FEJ are alternate interior angles, therefore, they are  equal based on the alternate interior angles theorem.

∠LFG and ∠FEJ are alternate exterior angles, therefore, they are  equal based on the alternate exterior angles theorem.

∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.

∠DEJ and ∠EFL are corresponding angles, therefore, they are  equal based on the corresponding angles theorem.

∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.

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Answer: x=4

Step-by-step explanation:

1/2x+8=10

Subtract 8 from 10

Multiply 2 to 2

x=4

Step-by-step explanation:

1/2(10)+8=

1/20+8=

161/20=

8.05

Answer:

y=42/15x+8

Step-by-step explanation:

We can get the change in height with 50-8, or 42. Now we divide, so 42/15. I'm assuming this is a slope question, so it would be y=42/15x + 8. Let me know if this is the way you want the answer.

Answer:

x=8+(number of feet/number of months)

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = 8(14) - 5(14 - 5 - 2) = 77 m²

Answer:

77m (squared)

Step-by-step explanation: