Tutor profile: Cassandra J.
Caia is making a storage bin for a corner of her playroom. The bin is the shape of a right triangle. One of the angle measures is 30°. What are the measures of the other two angles?
STEP 1: Here is the information that can be pulled from the problem: One of the angle measures is 30°. The storage bin is in the shape of a right triangle, so one angle has a measure of 90°. STEP 2: We know from a postulate in geometry that the sum of the measures of the angles in any triangle is 180°. STEP 3: Add the measures of the two known angles and subtract the sum from 180° to find the measure of the third angle. 30° + 90° = 120° So to find the third angle: 180° - 120° = 60° SOLUTION: The measures of the other two angles are 60° and 90°.
The sum of three consecutive even numbers is 48. What are the largest of these numbers?
STEP 1: Consecutive means one after the next. We have 3 numbers that are added together and their sum is 48. We must use variable expressions to represent each number. STEP 2: Set up the expressions as follows: Let x = first even number. Let x + 2 = second even number Let x + 4 = third even number STEP 3: Add up all expressions and set them equal to 48 and solve for x. first even number + second even number + third even number = 48 x + x + 2 + x + 4 = 48 (combine like terms) 3x + 6 = 48 (subtract 6 from both sides) 3x = 42 (divide both sides by 3) x = 14, so the first number is 14! first number: 14 second number: x + 2 or 14 + 2 = 16 third number: x + 4 or 14 + 4 = 18 Since 14, 16 and 18 are consecutive even integers and their sum is 48, this solution checks out! SOLUTION: 18 is the largest of the three numbers.
Find an equation of the line parallel to the line 3x + 6y = 5 and passing through the point (1 , 3). Write the equation in the slope intercept form.
To solve this problem, you must understand a few basics about parallel lines. STEP 1: Since all parallel lines have the same slope, we must find the slope of the line 3x + 6y = 5. Right now, the line is in standard form (Ax + By + C = 0, where A, B and C are integers). STEP 2: Put the line 3x + 6y = 5 in slope-intercept form ( y = mx + b, where m is the slope and b is the y-intercept) by solving the equation for y. 3x + 6y = 5 -3x -3x 6y = -3x + 5 (Now, divide everything by 6 to solve for y.) y = -(1/2)x + 5/6 The slope of this line, m = -(1/2), so the slope of the line we are looking for will be the same. STEP 3: Since I know that m = -(1/2), I need to find b. The line passes through the point (1,3), so x = 1 and y = 3. STEP 4: Substitute the values of y, x and m from STEP 3 into y = mx + b and find b. y = mx + b 3 = -(1/2) (1) + b 3 = -(1/2) + b (add 1/2 to both sides) + (1/2) +(1/2) 7/2 = b STEP 5: Since m = -(1/2) and b = 7/2, the answer in slope-intercept form is: y = -(1/2)x + 7/2
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