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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