Honors Analysis
Section 3.3: Solving Equations of a Single Variable
Q1.) Give the term for the intersection point of the medians of a triangle.
Q2.) What is the intersection point of the altitudes of a triangle called?
Q3.) The intersection of the angle bisectors of a triangle is the:
Q4.) The intersection point of the perpendicular bisectors of the sides of a triangle is called:
Q5.) What is the term for the square of the standard deviation?
Q6.) Write an expression for the complement of an angle measuring xº.
Q7.) Give an expression for the supplement of a yº angle.
Q8.) The complement of an angle measuring 5x degrees would be:
Q9.) If an angle measures (180 – 6x)º, what is the measure of its supplement?
Q10.)An angle and its complement are in a 1:3 ratio. What are their measures?
Solve for the unknown in the following equations. Do not round – give answers as simplified fractions as needed.
1.) 3(x – 2) – 2(2x + 3) = -282.)3.)
4.)5.)6.)
7.)8.) (be crafty!)9.)
10.) (hint: 2 answers!)11.)
Solve each literal equation for the specified variable:
12.)d = rt, for r13.), for a14.), for h
15.), for b16.), for b 17.), for y (Hint: why might factoring help?)
Write and solve an equation for each scenario:
18.)When 142 is added to a number, the result is 64 more than 3 times the number. Find the number.
19.) The sum of a number and nine is multiplied by -2 and the result is -8. Find the number.
20.) If 4 is subtracted from twice a number, the result is 10 less than the number. What is the number?
21.) On a science test, the top grade was 42 points higher than the lowest grade. The sum of the two grades
was 138. What was the lowest grade?
22.) An angle is 9º more than twice its complement. How large is the angle?
23.) Maria is exactly 10 years older than Abe. Four years ago, Maria was twice as old as Abe was then. What is Maria’s age now?
24.) The numerator of a fraction is one-half the denominator. If the numerator is increased by 2 and the
denominator is decreased by 2, the value of the fraction is 2/3. What is the numerator of the original
fraction?
25.) The supplement of an angle is four times the complement of the angle. What is the measure of the supplement?
26.) The measure of the supplement of an angle is 60 less than 3 times the measure of the complement. What is
the measure of the complement?
27.) The difference between five times the complement of an angle and twice the supplement is 40º. What is
the measure of the angle?
28.) The measure of the supplement of an angle exceeds 3 times the measure of the complement of the angle
by 10º. What is the measure of the complement?
29.)$1400 is divided between two accounts. One account pays interest, while the other pays interest. At the end of one interest period, the interest earned was $50. How much was invested in each account?
30.)After one interest period, the interest earned on a $7000 investment exceeds the interest earned on a $5000 investment by $160. The interest rate for the $7000 investment is greater than the interest rate for the $5000 investment. Find the interest rates for the two investments.
31.) The ratio of the height of a parallelogram to its base is 3:5. If the area is 135 mm2, what is the base length?
32.) A rectangular prism has a length of 3x cm, a width of cm and a height of xy cm. Its volume is 144 cm3. If the height of the prism is twice its length, what is the length of the prism?
33.)What is the length of the shortest side of whose perimeter is 64 units, if the ratio AB:BC is 4:3
and AC is 20 less than the sum of the lengths of sides AB and BC?
34.) Write an algebraic proof demonstrating that if two cylinders have the same volume and the first has a radius twice as big as the second, then the height of the second must be four times as large as the height of cylinder #1. (Reminder. For a cylinder: )
R1.) R2.)
The sum of Jim’s weight and Bob’s weight is 180 pounds. If you subtract Jim’s weight from Bob’s weight, you get half of Bob’s weight. How many pounds does Bob weigh?
Bubba is creating two fenced-in pens on his ranch. He buys an uknown length of fencing and creates two pens. He uses 1/5 of his fencing to create a perfect square pen, and the rest of the fencing is used to create a rectangular pen twice as long as it is wide (note: neither dimension of pen #2 necessarily matches the side lengths of pen #1). If the total area enclosed by the pens is 11,097 square feet, how much fencing did Bubba originally buy?