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3 years ago

7x - 2 = 5x + 12 Solve for x

Mathematics

1 answer:

Alinara [238K]3 years ago

4 0

X=7

7x-2=5x+12
+2. +2
7x=5x+14
-5x -5x
2x=14
÷2 ÷2
x=7

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Helen is putting a fence around her flower garden, which is in the shape of half of a circle and a rectangle. If the semicircle

erastova [34]

Answer:

Part 1) Helen will need 38 feet of fencing

Part 2) The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) The approximate distance around half of the circle is 11 feet

Step-by-step explanation:

Part 1) How much fencing will Helen need?

Find out the perimeter

we know that

The perimeter of the figure is equal to the sum of three sides of the rectangular section plus the circumference of a semicircle

$P=2L+W+\frac{1}{2}\pi D$

we have

$L=10\ ft\\W=7\ ft\\D=7\ ft\\\pi =\frac{22}{7}$

substitute

$P=2(10)+7+\frac{1}{2}(\frac{22}{7})(7)$

$P=20)+7+11=38\ ft$

therefore

Helen will need 38 feet of fencing

Part 2) What is the perimeter around the three sides of the rectangular section of the garden?

$P=2L+W$

we have

$L=10\ ft\\W=7\ ft$

substitute

$P=2(10)+7$

$P=20+7=27\ ft$

therefore

The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) What is the approximate distance around half of the circle?

Find the circumference of semicircle

$C=\frac{1}{2}\pi D$

we have

$D=7\ ft\\\pi =\frac{22}{7}$

substitute

$C=\frac{1}{2}(\frac{22}{7})(7)$

$C=11\ ft$

therefore

The approximate distance around half of the circle is 11 feet

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3 years ago

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Answer: 3/7

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Midwest Water Works estimates that its WACC is 10.45%. The company is considering the following capital budgeting projects.Assum

irinina [24]

Answer:

Don't accept A-G

Accept only A-E

Step-by-step explanation:

The company would those projects with a return of return equal to or higher than its cost of capital of 10.45%

Project A with a 12% return is acceptable.

Project B with a 11.5% rate of return is also acceptable

Project C has a rate of return of 11.2% , hence acceptable.

Project D has 11% rate of return and it is therefore acceptable.

Project E has 10.7% return rate and it is acceptable.

Project F has a lower rate of return of 10.3%, hence rejected, as well as projects G

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3 years ago

Write each fraction as a decimal 4/50

Len [333]

4/50 as a decimal is .08
Divide 4 by 50

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3 years ago

Which is the equation of a circle with its center at (-4,2) and a radius of 4?

Snowcat [4.5K]

Answer:

(x +4)^2 + (y-2)^2 = 16

Step-by-step explanation:

We can write the equation for a circle with the formula

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

We know the center is at (-4,2) and the radius is 4

(x- -4)^2 + (y-2)^2 = 4^2

(x +4)^2 + (y-2)^2 = 16

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3 years ago