hectictar

 -2z + 3 + 7z = -12

Combine like terms.

5z + 3 = -12

Subtract 3 from both sides of the equation.

5z = -12 - 3

5z = -15

Divide both sides of the equation by 5.

z = -15/5

z = -3

6 / 2(1+2)    is     \(\frac62(1+2)\)

and

\(\frac62(1+2)=3(1+2)=3(3)=9\)

Does that help? 

*edit*

If you want \(\frac{6}{2(1+2)}\)

You have to type it like this: 6/(2(1+2)) ...which DOES = 1

Wow Guest, you must eat a lot of really healthy food, like maybe bananas...just as an example.... to keep your brain in tip-top condition 

Thank you very much CPhill ! 

x = length of first piece + length of second piece

tan(63º) = 87 / length of first piece

length of first piece = 87 / tan(63º)

tan(39º) = 87 / length of second piece

length of second piece = 87 / tan(39º)

x = 87 / tan(63º) + 87 / tan(39º)

x ≈ 151.76

There are two ways to wrap the paper around the can.

In case A, the circumference of the can = 19 cm

In case B, the circumference of the can = 29 cm

circumference = π * diameter → diameter = circumference / π

In case A, the diameter = 19 / π ≈ 6.05 cm

In case B, the diameter = 29 / π ≈ 9.23 cm

\(V=\frac43\cdot3.14\cdot8^3 \\~\\ V=\frac43\cdot3.14\cdot512 \\~\\ V\approx 2143.57\)

This looks like the formula for the volume of a sphere with a radius of 8 

.

cos θ = adjacent / hypotenuse

cos 38.1º = x / 37

37 cos 38.1º = x

29.12 feet ≈ x

\(-6 = -\frac1{w+5}\)

Multiply both sides of the equation by (w + 5) .

-6(w + 5) = -1

Divide both sides of the equation by -6 .

w + 5 = 1/6

Subtract 5 from both sides of the equation.

w = 1/6 - 5

Get a common denominator and combine the fractions.

w = 1/6 - 30/6 = -29/6

We want the equation of a line that has a slope of 6.1 and passes through the point (45, 2274.5) ......here, the fuel = x, and the weight of the plane = y

That will be:

y - 2274.5 = 6.1(x - 45)

We could put this into slope intercept form, but it isn't necessary. We just want to know what y is when x = 72. Plug in 72 for x and solve for y.

y - 2274.5 = 6.1(72 - 45)

y = 6.1(72 - 45) + 2274.5 = 2439.2 pounds