What is the surface area and volume of a cube that has side lengths of 9.5 cm?
A cube is a shape that has 6 square sides, all of equal area. The surface area can be found by finding the area of one side and multiplying by 6. The area of one side of this cube is length x width (L x W): 9.5cm x 9.5cm = 90.25 sq. cm Multiply this by 6 (as there are 6 sides on the cube) to find the total surface area: 90.25cm x 6 = 541.5 sq. cm The unit for area is "squared" - in this case sq. cm The volume of a cube can be found by finding the area of the base and multiplying that by the height: V = area of base x height We can represent the area of the base as L x W, so V = L x W x H The length, width and height of the cube are all the same, in this case 9.5 cm. Find volume by multiplying: V = 9.5 cm x 9.5 cm x 9.5 cm = 857.375 cu. cm The unit for volume is "cubic" - in this case cu. cm
Sam is one year older than Bill. In 5 years their combined ages will be 149. How old is Bill now?
Let "s" stand for Sam and "b" stand for Bill. Bill's age in terms of "s" is "s + 1", since he is one year older than Sam. In 5 years Sam will be his current age plus 5: s + 5 in 5 years Bill will be his current age plus 5: (s + 1) + 5 = S + 6 Sam's age in 5 years, plus Bill's age in 5 years is equal to 149: (s + 5) + (s +6) = 149 Solve for s by combining the variables and combining the integers: 2s + 11 = 149 Subtract 11 from both sides of the equation: 2s = 138 Divide both sides of the equation by 2: s = 69 Sam's current age is 80. Bill's current age is one year older than Sam's: 69 + 1 = 70
Find the equation of a line that contains the point (5, 2) and is perpendicular to the line 2y - 8 = 6x
First put 2y - 8 = 14x into slope-intercept form (y = mx + b, where m is the slope, b is the y-intercept) to find the slope of the given line. Add 8 to both sides of the equation: 2y = 6x + 8 Divide both sides of the equation by 2, to isolate the y: y = 3x + 4 This line has a slope of 3. Since the line we are asked to find an equation for is perpendicular to this line, it has a slope that is the opposite reciprocal of 3. We can start to write the equation of this new line as: y = -1/3x + b Now we need to find the y-intercept of this new line. Plug in the given point contained on this line (5, 2) for x and y: 2 = 3(5) + b Solve for b: 2 = 15 + b Subtract 15 from both sides of the equation: -13 = b Now we can write the equation for the line requested because we have slope, -3 and b, -13 y = -3x -13