If you cut the largest possible circular tabletop from a square whose sides measure two feet each, how much wood is wasted?Use 3.14 for .
Answer(s): D
Step 1: Find the area of the square.2 feet × 2 feet = 4 square feetStep 2: Find the area of the circle, using the formula A = r2. (The radius equals half the diameter; the diameter of this circle is 2 feet the same length as one side of the square.) 3.14 × r2 = 3.14 × 12 = 3.14 square feet Step 3: Subtract 3.14 square feet from 4 square feet to find the wood that is wasted, 0.86 square feet.
Solve for x:3x + 2 = -13
Step 1: Subtract 2 from each side of the equation in order to eliminate -2 from the left side. (You are undoing the addition.)3x + 2 - 2 = -13 - 23x = -15Step 2: Now divide each side by 3 to find x. (You are undoing the multiplication.) 3x/3 = -15/3x = -5
An artist sold 4 of his paintings. These represented 0.05 of all the artwork he had done.How many paintings had he made at that point?
Answer(s): B
Let p stand for the total number of paintings the artist has made. The 4 paintings he sold are equal to 0.05 of all his paintings. This can be expressed as an equation:0.05p = 4To solve for p, divide both sides by 0.05. This undoes the multiplication of 0.05 and p and gives you the value of p so that you know the total number of paintings the artist has painted.
One of the equal angles of an isosceles triangle is 40 degrees.What is the angle opposite the unequal side?
Answer(s): C
In an isosceles triangle, two of the sides are equal. This means that the angles opposite them are equal, too. If one is 40 degrees, then so is the other. To find the angle opposite the unequal side, begin by adding the equal angles.40 + 40 = 80 degreesTo find the third angle, subtract this amount from 180 (the number of degrees in any triangle) 180 - 80 = 100 degrees (third angle).
If you divide 24x3 + 16x2 - 8x by 8x, how many x's will be there in the quotient?
An easy way to do this example is to break it into three examples, dividing each by 8x. Divide the numbers first and then the letters. However, to divide the exponents of x, just find the difference between them. (Thus, x3 ÷ x = x(3-1) = x2)24x3/8x + 16x2/8x - 8x/8x = 3x2 + 2x - 1Since the question asks only how many x's there are in the quotient (not how many x2's), the answer is 2.
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