You want to build a cement walk around a 24 ft x 49 ft garden
If we let x = the width of the cement walk, then the outside dimensions of the walk will be
(24 + 2x) and (49 + 2x)
The garden itself will not be covered with cement, so the equation for the area of the walk...

Let A, B, and C = the three different teams.
Then:
A + B + C = 110
and we know that
B = A - 10
C = B - 5
so substituting into the first equation, we have
A + (A - 10) + (A - 10) - 5 = 110
combine like terms and solve:
3A...

Let R = number of radios
Let P = the price she paid for each radio
R*P = 1400 so P = 1400/R
and
(R-7)*(P+10) = 1400
substitute for P
(R - 7)*(1400/R + 10) = 1400
and multiply
1400 -(7)(1400)/R + 10R - 70 = 1400
multiply...

You can use the midpoint formula, knowing the midpoint between two points (x1,y1) and (x2,y2) has the coordinates
[(x1 + x2)/2, (y1 + y2)/2]
Substituting what we are given, we get:
(2 + x2)/2 = 5 and (5 + y2)/2 = 1
so,
2...

First, see that 80 liters of a 20% kool aid solution has 16 liters of kool aid, since 80x20% = 16
Now, we're going to add an amount of 59% kool aid to produce a total concentration of 30% kool aid.
So you can set it up as a proportion. Let x = number of liters...

To solve this equation, manipulate the numbers so that the base numbers are the same. Since 4 = 2^2 we can rewrite this as:
2^3x = (2^2)^(x+2)
Expanding the exponent gives:
2^3x = 2^(2x+4)
Now that both bases are the same, we see that
3x = 2x+4
Solving...

To solve this equation for x, we should simplify and then combine like terms.
Notice that the second term, 8x/x, simplifies to 8 since x/x = 1, so we can rewrite the equation as:
4-8+1 = 8/x+1
Combining the constant terms gives:
-3 = 8/x +1
To get the x...

Notice that you can factor a 2 from the numerator to get
[2(x^2 + 2x +1)]/(x^2 + 3x +2)
Next, we factor both numerator and denominator to get
[2(x+1)(x+1)]/(x+1)(x+2)
Cancelling (x+1) from both numerator and denominator gives
[2(x+1)]/...

We have:
A = [2 -3
-2 5]
2B = [8 6x
0 -2]
So A + 2B = [2+8 -3+6x
-2+0 5-2]
or
[10 -3+6x
-2 ...

Since you are give three zeros, we know we have a 3rd degree polynomial. Recall that we factor a polynomial in the form of:
(x-a)(x-b)(x-3) = 0
where a, b, and c are the zeros of the function.
Thus, your function factors as:
(x+5)(x+1)(x-2) = 0
Doing this...

x = 8
To solve, first distribute the left side of the equation to get:
4x - 4 = 28
Next, add 4 to both sides of the equation:
4x - 4 + 4 = 28 + 4
4x = 32
Finally, divide both sides by 4:
4x/4 = 32/4
x = 8