Download Week 3.2 ——————- Review Questions: - Lines

Week 3.2
——————Review Questions:
- Lines
- Circles
——————–
1. Find the center, radius and x,y-intercepts for the circle given by the equation 4x2 + 16x + 4y2 −
32y = 20.
2. Find the equation of the line which is perpendicular to the line 4x + 2y − 3 = 0 and passes through
the origin.
———————
New Material
- Systems of Linear Equations
- Systems of Nonlinear Equations
———————
3. Solve
(
y = 2x
y=x
4. Find where y = 2x + 1 and y = − 12 x + 3 intersect.
5. Given circle A which has the equation x2 + y2 = 4 and circle B which has the equation (x − 2)2 +
(y − 3)2 = 52 , do A and B intersect each other? If so where?
6a. Solve
(
x2 + y2 = 42
(x − 2)2 + (y − 2)2 = 22
6b. Solve (This problem was changed to make it more doable)
(
x2 + y = 6
(x)2 + (y)2 = 22
7. Your friend is looking forward to the superbowl. He claims that the Falcons will score precisely
34 points and the Patriots will score 31 points. He also forsees that the Falcons will score 4
touchdowns and 2 field goals and that the Patriots will score 4 touchdowns and only 1 field goal.
Unfortunately for you, you don’t remember how the scoring works, but you still remember how to
solve a systems of equations. How much is a touchdown worth (including the extra point) and how
much is a fieldgoal worth?
8. You are outside, with a frisbee. You invited your friends, but unfortunately they are all busy. So
you decide to play a game of throw and catch, where you throw the frisbee and run after it to catch
it. Assume that the horizontal speed of the frisbee is 10 ms and that after you throw the frisbee, you
need 2 seconds before you can run. Now, assume that you can run 12 ms . How far do you need to
run, and how long will it take you?
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9. Find two positive numbers such that the product of the two numbers is 136 and the sum of the
two numbers is 25.
10. You’re going to make Poutine. So you go to the grocery store to buy cheese curds and potatoes.
You buy 1 bag of 5lbs potatoes and 3 bags of 16oz cheese curds which came out to be 14. Your
friend who came along with you also bought potatoes and cheese curds. Her total came out to be 13
for 2 bags of 5lbs potatoes and 1 bag of 16oz cheese curds. How much does each bag of cheese
curds cost? How much does each bag of potatoes cost?
11. Solve
(
x2 + 2xy = 6
2x2 − xy = 2
12. Solve
(
7
5
4 x + 2 y = 24
9
7
−5
16 x − 4 y = 2
13. This piece of paper has an area of 93.5in2 and a perimeter of 39in. What are the dimensions?
14. What values of x satisfy 2x + 5 ≤ 8
15. What values of x satisfy |2x + 5| ≤ 8.
16. What values of x satisfy |2x + 5| ≥ 8.
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