One side of a rectangle is 7 inches longer than another side. If the longer side of this rectangle decreases by 3 inches, and the shorter side increases by 2 inches, the area of the new rectangle equals the area of the original rectangle. Find the dimensions of the original rectangle.

Step-by-step explanation:

Slope=9

i)

[tex]y−y1=m(x−x1)[/tex]

When line is parallel

y+5=9(x-6)

y+5 = 9x - 54

When line is perpendicular

y+5=-1/9(x-6)

9(y+5)= -1(x-6)

9y + 45 = -x+6

Answer: 21 ft

Step-by-step explanation:

Answer: Would the total be 20 Students? What exactly is the question

Step-by-step explanation:

10 + 10 = 20

Answer:

length is 12 feet and the width is 6 feet

Step-by-step explanation:

w=width  l=length

l=2w

2l+2w=36ft

4w+2w=36ft

6w=36ft

w=6ft

l=2*6=12ft

Answer:

A washer and dryer cost a total of $964 . The cost of the washer is three times the cost of the dryer. Find the cost of each item.

Answer: 96$

Answer:

The washer costs $723 and the dryer $241.

Step-by-step explanation:

Represent the cost of the washer by w and that of the dryer as d.

Then w = 3d.

Since w + d + $964, we get 3d + d = $964, or 4d = $964, or d = $241.

Three times that is $723.

The washer costs $723 and the dryer $241.

Answer:

firast divide it by the nearest decimal, then convert your answer into simplest form and you will have your answer.

Step-by-step explanation:

Answer:

can you guys please teach me how to do that

Answer:

x=4/5

Step-by-step explanation:

Add 18 to both sides and simplify

17 weeks and she'll have $5 extra.

Answer:

18πm

Step-by-step explanation:

The area is πr^, so to find just the radius, take the square root of 81.

This means the radius is 9, and because the formula for the circumference is 2πr, simply double it and multiply by π to get 18π.

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The increase in monthly amortization has result of higher interest rate is $349.86.

We have given ,the smiths were just approved for a 25 year mortgage at an 11% fixed rate. if they had not filed bankruptcy in the past, they could have gotten a rate of 7%.

We have to calculate the mortage value when loan amount is,$128,000,

[tex]A = P \times ((r(1+r)^n)/((1+r)^n-1))[/tex]

A = is the amortization

P = is the principal

r = is the rate

n = is the period

We have to compute for the amortization using the 11% interest rate.

[tex]A = $128000 \times ((0.11(1.11)^{25})/((1.11)^{25}-1))[/tex]

[tex]A = \$1,254.54[/tex]

When we  solve manually, the answer should be divided by 12 because it was on a monthly basis.

Next we have to compute for the amortization using the 7% interest rate.

[tex]A = $128000 \times ((0.07(1.07)^25)/((1.07)^25-1))[/tex]

[tex]A = $904.68[/tex]

When solve manually, the answer should be divided by 12 because it was on a monthly basis.

Therefore, the increase in monthly amortization has result of higher interest rate is $349.86.

To learn more about the amortization visit:

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Answer:

Step-by-step explanation:

To determine a volume, you need a volume formula.

Volume:

[tex]\Longrightarrow:\sf{V=l*w*h}[/tex]

Multiply these numbers from left to right.

[tex]\sf{7.1m*5.2m*3.4m=\boxed{\sf{125.5m^{3}}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Step-by-step explanation:

This equation is known as slope-intercept form.

Parts of the slope-intercept form equation:

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

m represents the slope.

b represents the y-intercept.

In the equation, [tex]-\frac{1}{2}[/tex] is in the placement of m.

We can conclude that [tex]-\frac{1}{2}[/tex] is our slope.

Learn more about the slope of a line:

Answer:

I would think that It is the first one but if it is not trust the other people

Step-by-step explanation:

The earned income is $80,000 and the capital income is $5,000. Then the correct option is B.

A profit in the value of an asset then an investor can make a profit by selling an asset. Then selling price of an asset must be greater than the cost of an asset.

Padraig is a financial advisor.

He earned a salary of $80,000 last year and sold stocks for $5,000.

A salary of $80,000 is known as earned income because of employment bases.

$5,000 is a capital gain because this is obtained from the selling of stocks.

The income gained by the interest income, rental income, or dividend income is known as passive income.

More about the capital income link is given below.

https://brainly.com/question/14103167

Answer: Both of these events are more likely.

Step-by-step explanation:

Since we have given that

Probability that she is getting injured playing volleyball = 0.1

Probability that she is getting injured playing soccer is given by

Since we need to compare both the probabilities so, for this we first need to change the second probability in decimal form.

So,

since both the events have same probability.

Hence, Both of these events are more likely.Step-by-step explanation:

Answer:

0.0332

Step-by-step explanation:

Min put too many zeros in front of 33.2. 33.2 with 3 zeros in front is 0.0332

Answer:

47

Step-by-step explanation:

Determine if the sequence is arithmetic or geometric.

The difference between each term in the sequence is constant, so this is an arithmetic sequence.

To calculate the common difference, subtract one term from the next term:

14.5 - 8 = 6.5

21 - 14.5 = 6.5

27. 5 - 21 = 6.5

34 - 27.5 = 6.5

40.5 - 34 = 6.5

So the common difference is 6.5

To find the next term in the sequence, add 6.5 to the last term given:

40.5 + 6.5 = 47

Answer:

140

Step-by-step explanation: all you have to do is add all the numbers then multiply those by 4 then you will get 140

Answer:

That's just the way of the world

Somewhere in the world, they think they're working for themselves

They get up everyday to go to work for someone else

And somebody works for them and, so, they think they got it made

But they're all just working to get paid the very same

And so, they keep on twiddlin' them thumbs.

Answer:

well its two

Step-by-step explanation:

but A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's expand the given expression ~

[tex]\qquad \sf  \dashrightarrow \: - 3y( {y}^{4} + 2 {y}^{3} - 5 {y}^{2} - y + 4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: ( - 3y \cdot {y}^{4} ) + ( - 3y \cdot2 {y}^{3} ) + ( - 3y \cdot - 5 {y}^{2} ) + ( - 3y \cdot - y) + ( - 3y \cdot4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 3{y}^{5} - 6{y}^{4} + 1 5 {y}^{3} + 3{y}^{2} - 12y[/tex]

Answer:

y = x+2

Step-by-step explanation:

y = mx +c

y-intercept is +2

so y = mx + 2

the slope of the line is one across one up so

y = x+2

Answer:

Step-by-step explanation:

At y-intercept, x =0

So, from the graph, y-intecept = b = 2

Equation of the line: y =mx +b

y = mx + 2

Choose any point on the line and substitue in the above equation and we get the slope(m)

(-2 ,0)

0 = m*(-2) + 2

0 = -2m + 2

-2 = -2m

-2/-2 = m

m= 1

Equation of the line: y = x + 2

Answer:

D. 60

Step-by-step explanation:

Height = constant / width

30 = c / 2

2* 30 = 60

c = 60

12 = c / 5

12 * 5 = 60

c = 60

10 = c / 6

10 * 6 = 60

c = 60

Answer:

The answer is B. 1/4^8

Step-by-step explanation:

Every time the power it to the negative it inverse it.

An example, 2^-2 = 1 / 2^2

So, 4^-8 = 1 / 4^8

Answer:

Perimeter = 30 in

Step-by-step explanation:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute given values into the formula and solving for a:

⇒ a² + 12² = 13²

⇒ a² + 144 = 169

⇒ a² = 25

⇒ a = 5 in

Therefore, perimeter = a + b + c

                                   = 5 in + 12 in + 13 in

                                   = 30 in

Final Answer:

[tex]\fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

Step by Step explanation:

Data achieved from diagram:

The given triangle is a right angle triangle

Hypotenuse of triangle = 13 in.

Base of triangle = 12 in.

To find:

Perimeter of triangle = ?

Solution:

We need length of all three sides (Altitude) of triangle,

let's find out the measure of length of Altitude using Pythagoras theorem!

[tex]{Hypotenuse}^2 = {Base}^2 + {Altitude}^2 \\ {13}^{2} = {12}^{2} + {A}^{2} \\ {A}^{2} = 169 - 144 \\ {A}^{2} = 25 \\ {A} = \sqrt{25 } \\ \fbox{A = 5 \: in.}[/tex]

Now we have all three sides of triangle,

[tex]perimeter \: of \: triangle = Hyp. + Base + Alt. \\perimeter \: of \: triangle = 13 + 12 + 5 \\ \fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

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Answer:

the first

Step-by-step explanation:

the first and the second set both multiply out correctly to the original expression, but -2x² is of greater dimension than -2x.

#1

Change of base formula is given by

[tex]\\ \rm\Rrightarrow log_ab=\dfrac{log_db}{log_da}[/tex]

#2

Two most common bases are

As general logarithm has base 10 and natural has base e hence these two are most used

#3

We use e as base

[tex]\\ \rm\Rrightarrow log_23[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{log_e3}{log_e2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{ln3}{ln2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1.0986122886681}{0.6931471805599}[/tex]

[tex]\\ \rm\Rrightarrow 1.6[/tex]

Answer:

112

Step-by-step explanation:

So, we know that a triangle's sides must add up to have a sum of 180. If you add up your given lengths and you should get 47, not including x. Then if you look at the left side/the one without a given length and it should be identical to the 21, so you know that side is 21. So now add 21 to 47, you should get 68. Finally, you subtract 68 from 180 like this: 180-68, and it should equal 112. So you're answer is 112.

By using the exponential growth equation, we will see that the population triples after 5.83 months.

We know that the initial population of bunnies is 820, and it grows at a rate of 20.75% per month, then we can write the exponential growth as:

P(t) = 820*(1 + 20.75%/100%)^t

P(t) = 820*(1 + 0.2075)^t

Where t is the time in months.

Then we need to find the value of t such that the population triples, so we actually need to solve:

(1 + 0.2075)^t = 3

If we apply the natural logarithm to both sides, we get:

ln((1 + 0.2075)^t) = ln(3)

t*ln(1.2075) = ln(3)

t = ln(3)/ln(1.2075) = 5.83 months.

So, after 5.84 months, the population of bunnies will triple.

If you want to learn more about exponential functions, you can read:

https://brainly.com/question/11464095