Please carefully check for any typos.
I’ll use ^ for exponents. So x^2 means x2.
1. Perform the indicated operation and simplify.
w-5/w-7 –w+1/w+7 +w-35/w2-49
my answer is 39/w+7
9
w+7
2.
2
sqrt of -1/8
My answer is 3sqrt-1/2
I’m guessing this is the cube root of -1/8, not what you wrote…
The answer is just -1/2
3.
Find the vertex, the line of symmetry, and the maximum or minimum value of
Of f(x). graph the function.
F(x)=1/4(x+7)2+4
My answer is vertex is -14,0 the line of symmetry is x=-14, the max/min value of
F(x) is 4. The value , f(-7)=4 minimum the
Graph would be upward on the left side.
Vert: (-7, 4)
Symm: x = -7
Minimum is 4
U shape, shifted left and up
4. Subtract. Simplify by collecting like radical terms if possible
9sqrt of 50-8sqrt of 2
My answer is 37sqrt of 2
5.
Solve.
4x2-12x2+5=0
My answer is x=sqrt2/2,srqt2/2,sqrt10/2,sqrt-10/2
Assuming the first power is 4…
√𝟐 √𝟏𝟎 √𝟐 √𝟏𝟎
,
,−
,−
𝟐 𝟐
𝟐
𝟐
6. Add. Simplify if possible.
7y/y2-81+y/y-9
My answer is y(y+16)/(y-9)(y+9)
Sure, but you can simplify:
y^2 + 16y
y^2 - 81
7. Find a polynomial for the perimeter and for the area
a+8
a
perim = 4a + 16
Area = a^2 + 8a
8. Multiply and simplify by factoring. Assume that all the expressions under
Radicals represent nonnegative numbers.
3
sqrt y7 3sqrt 16y8
My answer is 2y5 3sqrt of 2
𝟑
Do you mean: 𝟐𝒚𝟓 √𝟐
It’s a cube root, not square root.
9. Multiply (-4t)2(3t6)2
My answer is 114t14
It’s: 144t^14
10. If a pro basketball player has a vertical leap of about 30 inches, what is his hang time? Use the
Hang-time function V=48T2 Didn’t answer.
Doesn’t it say to round to the tenth? That’s very important!
0.8
11. Solve: Sqrt 7x+46=x+4 My answer 63
Isn’t the (7x+46) all under the root?
It’s 5
12. Evaluate the polynomial for x=2
3x2-4x+4 my answer is 8
13. Solve. X2+6x-4=0 my answer is x= 3+ sqrt13,-3-sqrt 13
Close, it’s:
-3+√13, -3-√13
14. Simplify by removing factors of 1.
8q2+8q/72q2+64q my answer is 9+1/9q+8
Close again, it’s:
q+1
9q+8
15. Factor: r2+8r+16= my answer is (r+4)2
16. Solve: (x+8)(x-10)(x+6)>0 my answer is -8<x<-6 or x> 10
17. Divide and simplify. K4/k12 my answer is 1/k8
18. Identify the degree of each term of the polynomial and the degree of the polynomial.
-3x3+4x2+4x+9
The degree of the first term 3
The degree of the second term 2
The degree of the third term 1
The degree of the fourth term. 0
The degree of the polynomial . 3
19. Multiply: (c+g)(c2-cg+g2) my answer is c3+g
It’s:
c^3 + g^3
20. Rewrite the following expression with positive exponents
(3xy)-3/8 Did not answer
1/ (3xy)^3/8
21. Multiply and simplify: 4b2/5b2-20b+20*5b-10/2b my answer is 2b3/b-2
Just:
2b
b-2
22. Multiply: (9x+9)(9x2+2x+6) my answer 81x3+99x2+72x+54
23. Find and following. Assume that variables can represent any real number.
Sqrt (a+4)2 Did not answer
|a+4|
24. Factor completely: 64r2+25-80r my answer is (8r-5)2
25. (2sqrt of 2-4sqrt of 7)(4sqrt of 2+8sqrt of 7) Did not answer
-208
26. Solve t2+6t-27=0 My answer is t=-9,3
27. Add. (2x2-7xy+y2)+(-6x2-8xy-y2)+(x2+xy-5y2). my answer is -32-14xy-5y2
Close, it’s:
-3x^2 – 14xy – 5y^2
28. Express using a positive exponent z-9. my answer is 1/z9
29. For the following equation, state the value of the discriminant and then describe the
Nature of the solution -12x2+6x+9=0 my answer is 1+sqrt of 13/4, 1-sqrt of -13/4
You didn’t solve the right question here:
D = 468
Two real
30. Find the variation constant and an equation of variation where y varies directly as x and y=54
When x=9. The variation constant is K= The equation of variation is y= Did not answer
K=6
y = 6x
31. Factor completely:
6x7-12x6+24x5
Complete factorization is : My answer is 6x5(x2-2x+4)
32. Subtract. Simplify, if possible
3-y/y-7 – 9y-7/7-y MY answer is 4(2y-1)/y-7
You can simplify it:
8y-4
y-7
33. Find the greatest common factor for the group terms
-66a4,11a5 My answer is -11a4.
No minus:
11a^4
34. Simplify by taking roots of the numerator and the denominator. Assume that all
Expressions under radicals represent positive numbers.
3
sqrt of 64x14/y3 Did not answer
I’m assuming it’s a cube root, not a square root…
𝟒𝒙𝟒
𝟑
√𝒙𝟐
𝒚
35. Rewrite with a rational exponent : 7sqrt of 19 My answer is 7sqrt of 19
Is this the 7th root of 19? If so:
19 ^ 1/7
That’s 19 to the 1/7 power.
36. Add: (3a4-2a3+4a2+14a-8)+(a5+7a3+5a2-4a+4)+(-6a4+a2-6a-6)
My answer is -3a4+5a3+10a2+4a-10+a5
I’d reorder it:
a5-3a4+5a3+10a2+4a-10
37. Rationalize the denominator. Assume that all expressions under radicals represent
Positive numbers. Sqrt of a –sqrt of b/sqrt of a + sqrt of b Did not answer
𝑎 + 𝑏 − 2√𝑎𝑏
𝑎−𝑏
38. Factor completely: 4w2-121 Did not answer
(2w-11)(2w+11)
39. Simplify by removing factors of 1. S2-49/(s+7)2 My answer is 50s-49/s
s-7
s+7
40. Find the x=intercept for the graph of the equation y=x2-2x-3
The x- intercepts are
Did not answer
(-1, 0), (3, 0)
41. Solve: 8/v=9/v -1/2 my answer is v=2
42. Television sets. What does it mean to refer to a 20-in TV set or a 25-in TV set?
Such units refer to the diagonal of the screen. A 35-in TV set also has a width of 28 inches.
What is its heights? What is the heights of a 35-in TV ? ___ inches.
DID not answer.
21
43. Find all numbers for which the rational expression is undefined.
T3-3t/t2-9 My answer is t(t2-3)/(t-3)(t+3)
You didn’t answer the given question… the answer is:
-3, 3
44. Solve: r2-5r-50=0 My answer is r= -5,10
45. Multiply: (b+1/3)(b+1/2) My answer is (2b+1)(3B+1)/6
You need to multiply out. It’s:
b^2 + 5/6 b + 1/6
46. Use the FOIL method to find the product.
(5x6-6)(x8-6) My answer is 5x14+6x8-30x6-36
Close, it’s:
5x14+6x8-30x6+36
47. a) Solve 5x2=15 Find the x-intercepts of f(x)=5x2-15
My answer is a) what is the solution x=sqrt of 3, -sqrt of 3
x-intercepts are (0,-15).
Sol: √3, -√3
Inter: (√3, 0), (-√3, 0)
48. Write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation in standard form, ax2+bx+c=0
Solution: 10. Only solution.
x^2 – 20x + 100
49. Simplify by factoring. Assuming that all expressions under radicals represent
nonnegative numbers. Sqrt of 20a2b My answer is 2a sqrt of 5b.
50. In a right triangle, find the length of the side not given. B=1,c= sqrt of 26
MY answer is sqrt of 26a/a.
Answer is: 5
51. Find the vertex, the line of symmetry, the maximum or minimum value of the
Quadratic function, and graph the function.
F(x)=-2x2+2x+7
The x-coordinate of the vertex is: MY answer is ½
The y- coordinate of the vertex is: My answer is -15/2, no, just 15/2
The equation of the line of symmetry is : My answer is x=15/2, no it’s 1/2
The maximum/minimum of f(x) is My answer is 15/2
The value, f(1/2)=15/2 is My answer is Maximum and the graph would be upside
Down to the right. Yes, it’s upside down U shape, shifted up and right.
52. Divide and simplify: 5w-40/4 / w-8/14w My answer is 35w/2
53. Factor the trinomial: a3-4a2-32a. My answer is a(a+4)(a-8)
54. Multiply and simplify. Assume variables represent nonzero real numbers
X13*x0 My answer is x13
55. Factor : 42-13s+s2 My answer is (s-6)(s-7)
56. Solve for x: 4x(x-5)-5x(x-4)= -1 My answer is 1,21/4
Answers are:
-1, 1
57. If the side of a square are lengthened by 5 cm, the area becomes 196 cm2.
Find the length of a side of the original square.
The length of a side of the original square is 9 cm.
58. Convert to decimal notation. 8.87x107 Did not answer
88700000
59. Use the quadratic formula to solve the equation: x2-3x= -6
My answer is x=3+I sqrt of 15/2,3-I sqrt of 15/2
I can’t tell if you mean this:
3 + 𝑖√15 3 − 𝑖√15
,
2
2
60. Subtract the polynomials: (-11b2+4b+3)-(6b2+3)
My answer is -17b2+4b
61. Divide: (30b3+3b2+36b+23)/(6b+3)
My answer is 5b2-2b+7+2/6b+3
62. Use rational exponents to simplify: 4sqrt of x8
My answer is x2
Isn’t this the 4th root of x^8? Don’t you only need to fill in the exponent, so just 2?
63. Find the following: 18sqrt for(-4)18 My answer is -4
No, it’s 4, no minus sign.
64. Factor completely: 112r2+392rd+343d2 My answer is 7(4r+7d)2
65. Use rational exponents to write x1/3*y1/7*z1/6 as a single radical expression
Did not answer
nd
42 root of (x^14 y^6 z^7)
66. Jack usually mows his lawn in 7 hours. Marilyn can mow the same yard in 5 yard.
How much time would it take for them to mow the lawn together?
They could mow the lawn in___hours if they worked together.
2 11/12
(that’s 2 and 11/12)