hectictar

-3(m - 2)   =   21

Divide both sides of the equation by   -3   .

m - 2   =   21 ÷  -3

m - 2   =   -7

Add 2 to both sides of the equation.

m   =   -7 + 2

m   =   -5

1.

area of old rectangle = L * W

area of new rectangle = (1.5) * L * (1.5) * W

area of new rectangle = 2.25 * L * W

area of new rectangle = 2.25 * area of old rectangle

area of new rectangle = 2.25 * 112 cm²

area of new rectangle = 252 cm²

2.

\(\angle{STU}=\frac12\,\cdot\,\overset{ \frown}{SU} \\~\\ 64^{\circ}=\frac12\,\cdot\,\overset{\frown}{SU} \qquad \text{ Multiply both sides of the equation by 2.} \\~\\ 128^{\circ}=\overset{\frown}{SU}\)

3.

\(m\overset{\frown}{HJ}=180^{\circ}-101^{\circ}=79^{\circ}\)

Also, I noticed the 281º in the bottom right of the circle.

\(m\overset{\frown}{HJ}=360^{\circ}-281^{\circ}=79^{\circ}\)

\(\frac{E}{e}=\frac{R+r}{R-r}\)

Multiply both sides of the equation by  (R - r)  .

\((R-r)\,*\,\frac{E}{e}=R+r\)

Distribute the   \( \frac{E}{e} \)  .

\(R*\frac{E}{e}\,-\,r*\frac{E}{e}=R+r\)

Add   \( r*\frac{E}{e} \)   to both sides of the equation.

\(R*\frac{E}{e}=R+r+r*\frac{E}{e}\)

Subtract R from both sides of the equation.

\(R*\frac{E}{e}-R=r+r*\frac{E}{e}\)

Factor out an   r   on the right side.

\(R*\frac{E}{e}-R=r(1+\frac{E}{e})\)

Divide both sides of the equation by   \( (1+\frac{E}{e}) \)  .

\(\frac{R*\frac{E}{e}-R}{1+\frac{E}{e}}=r\)

volume of sphere = volume of cylinder

\(\frac43\,*\,\pi\,*\,6^3=\pi\,*\,6^2\,*\,h \\~\\ \frac43\pi\,*\,216=36\pi\,*\,h \\~\\ 288\pi=36\pi\,*\,h \\~\\ \frac{288\pi}{36\pi}=h \\~\\ 8\,\text{meters}=h\)

Hahaha! I never heard that one before! 

how to simplify     tan² x - sin²x     to     tan²x * sin²x

tan² x - sin²x

= sin²x / cos²x    -  sin²x cos²x / cos²x

= [ sin²x - sin²x cos²x ] / cos²x

= [ sin²x ( 1 - cos²x ) ] / cos²x

= [ sin²x (sin²x) ] / cos²x

= sin²x / cos²x * sin²x

= tan²x * sin²x

My guess is the second choice:

" It implies that instead of plentiful possessions, there were widespread lack. "

There are 8 candies in the bowl.

2 of them are orange.

3 of them are strawberry.

The rest are pineapple.

How many are pineapple?

The probability is just

(number of pineapple candies) / 8

I know this isn't exactly the answer, but I hope it helps.

You can treat the negative like it is a negative one that is being multiplied by the fraction.

For example....

\(-\,\frac58=(-1)\,*\,(\frac58)\)

Then...just divide the fraction inside the parenthesees like normal.

\((-1)\,*\,(\frac58)=(-1)\,*\,(0.625)\)

And multiplying the negative one makes it

\((-1)\,*\,(0.625)=-0.625\)

Do you have a specific problem you need help on?