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4 years ago

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By decreasing each dimension by 1 unit, the area of a rectangle decrease from 40 square feet (on the left) to 28 square feet (on

the right). find the percent of decrease in area,

1 answer:

Anettt [7]4 years ago

8 0

<span>The was a 30% decrease in area. You started with 40 sq ft and ended up with 28 sq ft. So you lost 40 - 28 = 12 sq ft. Now you need to figure out what percentage of 40 is 12. For that you just simply divide 12 / 40 = 0.30 And to convert 0.30 from a decimal to a percentage, just multiply by 100. 0.30 * 100 = 30%</span>

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3 years ago

Which of the following equations is equivalent to y=logx?

ElenaW [278]

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3 years ago

Read 2 more answers

What is the x-coordinate of the point of intersection for the two lines below?

Brut [27]

Answer:

From the graph, it is clear that the point of intersection is:

(x, y) = (-4, -1)

And the x-coordinate of the point of intersection for the two lines is:

x = -4

Step-by-step explanation:

As we know that the solution of the system of equations is the point of intersection. Let us solve it.

Given the system of equations

$\begin{bmatrix}2x+y=-9\\ 2x-5y=-3\end{bmatrix}$

solving the system of equations

subtracting 2x+y = -9 from 2x-5y = -3

$2x-5y=-3$

$-$

$\underline{2x+y=-9}$

$-6y=6$

so

$\begin{bmatrix}2x+y=-9\\ -6y=6\end{bmatrix}$

solving for y

$-6y=6$

Divide both sides by -6

$\frac{-6y}{-6}=\frac{6}{-6}$

$y=-1$

$\mathrm{For\:}2x+y=-9\mathrm{\:plug\:in\:}y=-1$

$2x-1=-9$

$2x=-8$

Divide both sides by 2

$\frac{2x}{2}=\frac{-8}{2}$

$x=-4$

Thus, the x-coordinate of the point of intersection for the two lines below will be:

$x=-4$

Also, the graph is attached.

From the graph, it is clear that the point of intersection is:

(x, y) = (-4, -1)

And the x-coordinate of the point of intersection for the two lines is:

x = -4

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3 years ago

Someone please solve x+5>20

Aloiza [94]

Answer:

x>15

Step-by-step explanation:

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3 years ago

How long will it take for $2500 to double if it is invested at 6% annual interest compounded 6 times a year? Enter exact calcula

12345 [234]

Answer:

Part 1) $t=11.610\ years$

Part 2) $t=11.552\ years$

Step-by-step explanation:

Part 1) we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06\\n=6$

substitute in the formula above

$5,000=2,500(1+\frac{0.06}{6})^{6t}$

$2=(1.01)^{6t}$

Apply log both sides

$log(2)=log[(1.01)^{6t}]$

$log(2)=(6t)log(1.01)$

solve for t

$t=log(2)/[6log(1.01)]$

$t=11.610\ years$

Part 2) we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06$

substitute in the formula above

$5,000=2,500(e)^{0.06t}$

$2=(e)^{0.06t}$

Apply ln both sides

$ln(2)=ln[(e)^{0.06t}]$

$ln(2)=(0.06t)ln(e)$

$ln(2)=(0.06t)$

$t=ln(2)/(0.06)$

$t=11.552\ years$

3 0

3 years ago