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Algebra II Review Questions, Thank You!?
this are the only one that i got trouble doing out of /72
10.) Solve 2x2 + 6x = 5 by using the quadratic formula.
a. -6+-√76/4
b. 6+-√76/4
c.-6+-√-4/12
d. -6+-√-4/4
14.) Which statement below is true about the system of equations?
y=x^2+6
y=-2x^2+3x+6
a. (0,6) is the only solution to the system
b. The systems has two solutions, one being (-2,10)
c. The system has two solutions, one is (1, 7)
d. The system has no solution
17.) With a tail wind, a plane traveled 800 mi in 5 hours. With a head wind, the plane traveled the same distance in 8 hours. Which system of equations could be used to solve this problem?
a. (s + w)5 = 800 and (s - w)8 = 800
b. (s - w)5 = 800 and (s + w )8 = 800
c. 5s + 8w = 800 and 5s - 8w = 800
d. none of the above
21.) Select the best equation for the following word problem. The sum of three consecutive even integers is 42.
a. x + x + 1 + x + 2 = 42
b. x + x + 1 + x + 3 = 42
c. x + x + 2 + x + 4 = 42
d. x + 2 + x + 4 + x + 6 = 42
The admission for a school play is $4.00 for students and $2.00 for adults. On Saturday 200 people attended with ticket sales totaling $500. Which system of equations would be used to solve this problem?
a. a-s=200
2a-4s=500
b. a+s=200
2.00+4.00=500
c. a=s-900
2a+4s=500
d. a+s=200
2a+4s=500
26.) The conjugate of the complex number 4 - 5i is
a. 4 + 5i
b. 5i - 4
c. 5i + 4
d. -4 + 5i
28.) If a quadratic equation has 2 unique rational roots, how many times will its graph intersect the x-axis?
a. Zero times
b. One time
c. Two times
d. Three times
37.) If y varies directly as x and y = 10 when x = 2, what is y when x = 3?
a. y = 9
b. y = 11
c. y = 15
d. y = 16
39.) The system
-8x+10y=20
y=4/5x+2
consists of:
a. One solution, since the lines intersect
b. No solution, because the lines are parallel
c. Infinite solutions, because the lines are the same
d. No solution, because the lines are in different planes
44.) The name of an algebraic property and an example are given. Which one is incorrect?
a. Associative Property of Multiplication 5(3*2) = (5*2)3
b. Commutative Property of Addition 4+3 = 3+4
c. Identity Property of Multiplication 4*1 = 4
d. Transitive Property of Equality, if a = b and b = c, then a = c
Thank You!
3 Answers
- Leo DLv 61 decade agoFavorite Answer
Hello -•ღ. Jεииí.ღ •-!Ƹ̵̡Ӝ̵̨̄Ʒ!
What have you tried and parts exactly are you having trouble with? If you have trouble with parts of maths, you might need a better explanation or you might have more trouble further along.
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10. The quadratic formula is simply that for the equation:
y(x) = ax² + bx + c,
You can solve for x using:
x = (−b ± √(b² + 4a(y − c)))/(2a)
The quation can be divide into the discriminent part within the square root, b² + 4a(y − c) and the mean value −0.5b/a And y(x) will usually be zero but it can be nonzero too.
Your example is: 2x² + 6x = 5,
So a = 2, b = 6, c = 0 and y(x) = 5
Plug that into the equation:
x = (−6 ± √(36 + 8·5))/4 // Add the part in the root.
x = (−6 ± √76)/4 // Simplify the radical, 76 = 19·4
x = (−6 ± 2√19)/4 // Divide by four.
Answer: x = −1.5 ± 0.5√19
This is the same as choice a which is (−6 ± √76)/4
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14. Solving for a quadratic system of equations is the same as solving for a linear system of equations, just set the two equal.
y = x² + 6
y = −2x² + 3x + 6
Set the two y's together.
y = y // Substitute.
x² + 6 = −2x² + 3x + 6
Then solve, 6 and 6 on opposite sides of the equal sign cancel each other out.
x² = −2x² + 3x // Add 2x² − 3x to both sides, cancelling the right side out.
3x² + 3x = 0 // You can factor (x + 1) from both sides.
(x + 1)3x = 0
Remember that in order for a quadratic to be true, either one or both of the multiplicands has to be zero.
((x + 1) = 0) OR (3x = 0)
So x = {−1, 0}
Now that you know x, solve for y by substituting.
y(x) = {−1, 0}² + 6 // Square.
y(x) = {1, 0} + 6 // Add
y(x) = {7, 6}
To check, substitute it into the other equation as well:
y(x) = −2{−1, 0}² + 3{−1, 0} + 6
y(x) = {−2, 0} + {−3, 0} + 6
y(x) = {−1, 6}
Since y ≠ y for x = −1, it can't be that. The correct answer is choice a, (x, y(x)) = (0, 6).
Answer: Q.E.D: (x, y(x)) = (0, 6)
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17. I'm not really sure of. I don't see anything that you need to solve for. So I'm going with (d), but it's really more like nothing to solve.
Edit:
Let t = the tailwind, h = the headwind.
t = 800 / 5 mph = 160 mph
t - h = 800 / 8 mph = 100 mph
160 mph - h = 100 mph
h = 60 mph
Best I could come up with o.o Maybe you'd get credit for that.
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21) The sum of two consecutive integers means the sum of an integer, followed by another integer. 10, 11, 12 are three consecutive integer. In other words, if x is the smallest integer, (x + 1) would be the second smallest, and they follow like that.
They omit the parentheses in this problem, but I'm sure with that explanation you'll still pick the right one =)
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Next question)
The equation I'd use follows:
Let s = the number of students (unit: people) ∴ a(s) = (200 people − s) = the number of adults (unit: people).
$4.00s + $2.00a(s) = $500 people.
The closest answer to this equation is (d), a + s = 200, 2a + 4s = 500.
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26) The conjugate of a complex number, a + bi, is any number z′ which equals a − bi, try to find the conjugate of 4 − 5i that way =)
In this problem, a = c and b = d (but b is normalised), so I'm sure that they want you to answer in a + bi form, which is stupid since it's the same thing.
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28) The roots of the equation are where the graph of it intercepts the x-axis. Use this information =)
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37) Not enough information. Define "varies directly".
Apparently, "varies direction" means "is directly proportional to"
x:y :: 2:10, so x:y :: 1:5
You can think of : as a fraction bar, and :: as an equal sign, but they identify an "analogy" a special kind of equation.
Since x:y :: 1:5, then if x = 3, y = 15 (so c).
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39) I can't tell, is the second equation equal to 0.8x + 2, or 0.8/x + 2? Because technically, it should be the first one. The second one would be written 4/(5x).
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44) Try to spot the one that doesn't belong = P
a) Shows two things going on. The parenthesis shifted and 3 and 2 changed places.
b) Shows one thing going on. 4 and 3 switched places.
c) Shows one thing going on. 4 multiplied by 1 is 4.
d) Shows one thing going on, since a = b and b = c, you can cut out the middle man and say that a = c.
I hope that this all helped! If you need further explanations please email me! =)
Source(s): Me!
