Tutor profile: Aaron S.
Write a two-column proof. Given: Line segment AB is congruent to line segment DB and Point C is the midpoint of line segment AD. Prove: Triangle ABC is congruent to triangle DBC.
Statement 1: Line segment AB is congruent to line segment DB. Reason 1: Given. Statement 2: Point C is the midpoint of line segment AD. Reason 2: Given. Statement 3: Line segment AC is congruent to line segment DC. Reason 3: Definition of midpoint (If a point is a midpoint of a line, the it divides that segment into two congruent parts.). Statement 4: Line segment BC is congruent to line segment BC. Reason 4: Reflexive Property of Congruence (A line segment is congruent to itself.) Statement 5: Triangle ABC is congruent to Triangle DBC. Reason 5: Side-Side-Side Postulate (If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.)
Double-Stuffed Oreos are $2.99 for a 15 oz package. Family size packages are $3.99 for 19.1 oz. Local-Mart's version of Oreos, Tuxes, are $2.00 for a 15.35 oz package. Which one is the best buy per ounce?
To compare the three types of cookies, it is helpful to find the unit rate for each one. This is found by calculating the price per ounce of the package. All unit rates compare two quantities, but the second quantity must be 1 (which is the denominator). To find the unit rate for the Double-Stuffed Oreos, you can make a fraction of $2.99/15 oz. Next, divide 2.99 by 15 to get 0.199. This means the unit rate for Double-Stuffed Oreos is $0.199/1 oz. To find the unit rate for the family size packages, you can make a fraction of $3.99/19.1 oz. Next, divide 3.99 by 19.1 to get 0.209. This means the unit rate for the Family size package is $0.209/1 oz. Lastly, to find the unit rate for the Tuxes package, you can make a fraction of $2.00/15.35 oz. Next, divide 2.00 by 15.35 to get 0.130. This means the unit rate for Tuxes is $0.13/1 oz. Therefore, the best buy per ounce is the Tuxes package because it has the lowest (cheapest) unit rate per 1 ounce.
Two swimmers swim in opposite directions in the San Francisco Bay. The speed of the first swimmer is 2mph faster than the second. After 3 hours, they are 12 miles apart. Find both of their speeds.
Let the speed of the second swimmer be represented by x and the speed of the first swimmer be represented by x + 2. Distance traveled can be calculated by multiplying the rate (speed) by time. The distance traveled in 3 hours was 12 miles, so the equation 12 = 3(x) + 3(x+2) can be created. Next, distribute the 3 to the (x+2) to equal 3x + 6. Then, combine like terms on the right side of the equation to get the new equation 12 = 6x +6. Next, solve for x by subtracting 6 from both sides of the equation to get 6 = 6x. Then, divide both sides of the equation by 6 to isolate x; your final equation is 1 = x. This means the speed of the second swimmer (represented by x) is 1 mph and the first swimmer's speed (represented by x + 2) would be 3 mph.
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