In order to solve equations like these, you need to move all terms involving the variable on one side, and all the numeric constants on the other side.

To do so, we can add/subtract the same quantity to both sides.

For example, we can add 5.2 to both sides to get

$-0.7+2.8+5.2=-3.14x-5.2+5.2 \iff -0.7+2.8+5.2=-3.14x$

Then, we can add all the terms on the left hand side, and we have

$-0.7+2.8+5.2=-3.14x \iff 7.3=-3.14x$

Finally, we can divide both sides by -3.14:

$\dfrac{7.3}{-3.14} = \dfrac{-3.14x}{-3.14} \iff x = -\dfrac{7.3}{3.14}$

In order to check the solution, we have to plug the value we found for x in the initial equation:

$-0.7+2.8=-3.14x-5.2 \iff -0.7+2.8=-3.14\cdot \left(-\dfrac{7.3}{3.14}\right) -5.2 \iff -0.7+2.8 = 7.3-5.2 \iff 2.1=2.1$

which is clearly true.

6 0

3 years ago

A basket of laundry is being separated. Divide 48 pieces into 2 clothing groups so the ratio is 1 to 3

KiRa [710]

$\bf 48\qquad 1:3\qquad \cfrac{1}{3}\qquad \qquad \cfrac{1\cdot \frac{48}{1+3}}{3\cdot \frac{48}{1+3}}\implies \cfrac{1\cdot 12}{3\cdot 12}\implies \cfrac{12}{36}$

btw, don't put the shirts in the same bundle as the socks, you may end up with an unwanted perfume.

3 0

3 years ago

If 16 cups equals one gallon than one 1/4 gallon equal cups

hoa [83]

Well...this is a proportion problwm. for every 16 cups I have 1 gallon, so I can write that as:

16 cups
-----------
1 gallon

this value will be proportional to 1/4 a gallon equal "so many" cups. let's equal the unknown about of cups to x.

16 cups______ x cups
-----------.... = ..... ----------
1 gallon _____ 1/4 gallons

I can cross multiply to find x.

1 gallon • x cups = 16 cups • 1/4 gallons

16 times 1/4 is the same as 16/4, which equals 4.

1 gallon • x cups = 4 cups gallons

divide both sides by gallons

x cups = 4 cups

so! 1/4 of a gallon equals 4 cups.

8 0

4 years ago

The net of a pyramid is shown below:

Stells [14]

Answer:

245 square inches

Step-by-step explanation:

4(1/2×7×14)+(7×7)

4 0

3 years ago