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3 years ago

What is the value of m in the equation 1/2m - 3\4n = 16 , when n = 8?

1 answer:

8 0

1/2m -3/4n = 16

solve your system of equations.

n=8: (1/2)(m)+((−3)/4)(n)=16

Solve n=8 for n:

Substitute (8) for n in 1/2m+−3/4n=16:

1/2m+−3/4n=16

1/2m+−3/4(8)=16

1/2m−6=16(Simplify both sides of the equation)

1/2m−6+6=16+6(Add 6 to both sides)

1/2m=22

1/2m1/2 = 22 / 1/2(Divide both sides by 1/2)

m=44

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

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Wanda took out a personal loan for $16,000 at 9% simple interest how much interest will she pay after 5 years?

alekssr [168]

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olganol [36]

You would simply have to plug in, or substitute, the given values in the equations.

So, H=-5, W=2 and the problem is 4h-3w

To plug them in, your new equation would be 4(-5)-3(2) and simplify. So it becomes -20-6 which = -26.

And -26 would be your answer.

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