Cindy Let the first angle be designated as A and the second angle as B. There are two critical pieces of information provide. 1. The two angles are supplementary. This means that they add up to 180 degrees. This can be expressed in...
Sheicia: Let's look at this problem step by step. At the start, Alice has x tapes. Bill has x+10 tapes (in other words, "10 more tapes than Alice"). Once Alice has given Bill 15 of her tapes, Alice now has x-15 tapes remaining...
Lauren It would be much easier to describe the triangle expressed in the problem statement, if it could be drawn. In any case, the triangle discussed has 3 angles of 114 degrees (BAC), 45 degrees (ACB), and 21 degrees (ABC). (The 3rd angle of 21 degrees...
Ma Let's take the 1st expression: a7b8+a5b6-a3b2 Notice that all three of the terms have variables a and b raised to different powers. The Greatest Common Factor of GCF is determined by selecting the lowest power for each variable across all...
Heather: In this problem, you shouldn't be confused by the log3 since we know that when the log3 a = log3 b, then very simply a must be equal to b. In this problem a=3x-6 and b=2x+1 So: 3x-6=2x+1 3x-2x=1+6 ...
Angela: Since the pool is rectangular in shape, we know that the Volume=Length*Width*Depth. In this problem, we know that 10 inches needs to be added to the depth of the pool (note that 10 inches is equal to 10/12 ft or 5/6 ft). Hence, the total volume of water...
Jonathan: Let a=the number of kilograms of the first alloy Let b=the number of kilograms of the second allow From the statement of the problem, we can write two equations: 1) Since we know that the total number of kilograms in the combined mixture...
Danielle I concur with Jason's answer. My original response was for a line perpendicular to the y-axis.
Kenge: In Vivian's solution, note that 8 1/3% was rounded to the nearest thousandths (0.083) prior to solving the problem, which resulted in an answer of 548. If we choose not to round, we get a slightly different result, as follows: 8 1/3% can...
Theresa: This is a quadratic equation that can be solved by first putting it into the form at2+bt+c=0, and then using the quadratic formula to solve for t. Since both the left and right side of the given equation are divisible by 5, we could simplify by multiplying...
Herbert Let n=the number of nickels and q=the number of quarters. From the problem statement, we know two things: The total number of coins is 57; This means that n+q=57 The total value of the coins is $8.85; Since each nickel is worth .05 and...
Hannah When comparing two fractions, the best thing to do is to get both fractions to have the same denominator (or a "common denominator") and then compare numerators. For the two fractions 4/5 and 5/6, the least common denominator is 30. The...
Ma: Let's break the word problem down. Let a=number of adults and c=number of children We know two things: 1. The total number of people in attendance equals 84 or a+c=84 2. The total take is $432, comprised of adults each paying...
Chris: When multiplying two numbers, the number of decimal places in the product is equal to the sum of the decimal places in the two numbers being multiplied. So, for example 5.28*3.17 which equals 16.7376 contains 2 places in the first number and 2 places in...
Paige: The first step is to determine the slope of the equation we're trying to solve for. Since two parallel lines have the same slope, we need to compute the slope (m) of the equation 3x+2y=5. This can be obtained by converting the equation into slope-intercept...
Theresa: Per your formula, B=(705w)/h2, where w=weight in pounds and h=height in inches. From the info provided, we know that B=25 and h=74 inches (6ft * 12 inches per foot + 2 inches). Substituting these values in the formula, we get: 25=(705w)/(74*74) ...
Jesus Assuming the expression is 4x4-8x2-192: First, since all three terms are divisible by 4, factor out the 4 to get: 4(x4-2x2-48) Next, factor the (x4-2x2-48) portion, by searching for two factors of the form (x2+a)(x2+b), which when multiplied...
See Vivian's and Ryan's answers
Cristina Assuming the starting equation is (8/9)*x+9=11 or (8x)/9+9=11: First isolate the x term by subtracting 9 from both sides: (8x)/9 + 9 - 9 = 11 - 9 (8x)/9 = ...
Crista: The first thing you should do is eliminate the parentheses by distributing the factor outside, as follows: 3*6x+3*3-2x+6=0 18x + 9 -2x+6=0 Next, collect like terms and simplify: 18x-2x+9+6=0 16x+15=0 Now,...
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