SOLUTION: I need to pass the real test. So can someone please tell me if i got these questions wrong or right. it will really be a BIG help. Questions 1-3 Simplify the expression: 1

Algebra ->  Test -> SOLUTION: I need to pass the real test. So can someone please tell me if i got these questions wrong or right. it will really be a BIG help. Questions 1-3 Simplify the expression: 1      Log On


   

Question 490731: I need to pass the real test. So can someone please tell me if i got these questions wrong or right.
it will really be a BIG help.

Questions 1-3 Simplify the expression:
1. x2-4x+4(x2+2x-5) Answer: 5x2+12x-20
2. 5x2+4x-6(3x2-2) Answer: -13x2+4x-12
3. x2(4x-x+6) Answer: 3x2+6
Multiply the binomials:
4. (a+b)(a-b) Answer: a2-b2
Questions Multiply 5-9:
5. (4a+x)(3a-x) Answer: 12a2+7ax-x2
6. h2(5h+4) Answer: 5h3+4h2
7. (x+3)2 Answer: x2+9
8. (d-5)2 Answer: d2-25
9. (2x2)(x+4)(x-4) Answer: 2x4-16
11. To graphically solve the quadratic equation x2+3x-10=5. Answer: Use the quadratic formula, letting a=1, b=3, and c=-15.
12. If the garden box has dimensions x by x feet and an area in square feet equal to the perimeter in feet, what is the value for x that satisfies the requirements? (Hint: The box is square.) Answer: There is not enough information in the problem.
13. Given three consecutive integers with a sum of four times the second number, write an algebraic equation for this situation. Answer: 3n+3=4n
14. Factor the trinomial b2-b-6. Answer: (b+3)(b-2)
15. Factor the binomial x2-64. Answer: (x-8)(x+8)
16. Factor the binomial 9a2-16. Answer: (3a-4)(3a+4)
17. Factor the equation x2=x+20. Answer: (x+5)(x+4)
18. Solve the equation x2+5x-4=0 using the quadratic formula. Answer: x=.702 and -5.702
19.Solve the equation 3m2+6m=3 using the quadratic formula. Answer: x=2.5 and -14.5
Questions 20-21 write the value of the discriminant of each equation, decide how many different real-number roots the equation has, and determine how many points the parabola will interact with the x-axis. Do not solve the equation.
20. x2+7x+9=0 Answer: Discriminant is 13,indicating there are two real roots, with the parabola intersecting the x-axis at two points.
21. 2x2+5x+7=0 Answer: Discriminant is -31, indicating there are no real roots, with the parabola not intersecting the x-axis at all. Thanks :C
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Questions 1-3 Simplify the expression:
1. x2-4x+4(x2+2x-5) Answer: 5x2+12x-20
That can't be right. Are you supposed to multiply?
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2. 5x2+4x-6(3x2-2) Answer: -13x2+4x-12
Same as #1
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3. x2(4x-x+6) Answer: 3x2+6
Same as #1
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Multiply the binomials:
4. (a+b)(a-b) Answer: a2-b2
= a%5E2+-+b%5E2, correct.
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Questions Multiply 5-9:
5. (4a+x)(3a-x) Answer: 12a2+7ax-x2
It's -4ax and + 3ax
--> 12a%5E2+-+ax+-+x%5E2
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6. h2(5h+4) Answer: 5h3+4h2 Correct
7. (x+3)2 Answer: x2+9
%28x%2B3%29%5E2+=+x%5E2+%2B+6x+%2B+9
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8. (d-5)2 Answer: d2-25
Do it like #7
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9. (2x2)(x+4)(x-4) Answer: 2x4-16
No.
= %282x%5E2%2A%28x%5E2+-+16%29
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11. To graphically solve the quadratic equation x2+3x-10=5. Answer: Use the quadratic formula, letting a=1, b=3, and c=-15.
12. If the garden box has dimensions x by x feet and an area in square feet equal to the perimeter in feet, what is the value for x that satisfies the requirements? (Hint: The box is square.) Answer: There is not enough information in the problem.
13. Given three consecutive integers with a sum of four times the second number, write an algebraic equation for this situation. Answer: 3n+3=4n
-------------------
14. Factor the trinomial b2-b-6. Answer: (b+3)(b-2)
If you multiply your answer, you'll see the sign of b is wrong.
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15. Factor the binomial x2-64. Answer: (x-8)(x+8) Correct
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16. Factor the binomial 9a2-16. Answer: (3a-4)(3a+4) Correct
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17. Factor the equation x2=x+20. Answer: (x+5)(x+4)
Equations are solved, not factored ????
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18. Solve the equation x2+5x-4=0 using the quadratic formula. Answer: x=.702 and -5.702
Solve by factoring.
x%5E2%2B5x-4=0
(x-4)*(x-1) = 0
x = 1, 4
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19.Solve the equation 3m2+6m=3 using the quadratic formula. Answer: x=2.5 and -14.5
3m2+6m=3
m%5E2+%2B+2m+-+1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-1=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+0.414213562373095
x%5B2%5D+=+%28-%282%29-sqrt%28+8+%29%29%2F2%5C1+=+-2.41421356237309

Quadratic expression 1x%5E2%2B2x%2B-1 can be factored:
1x%5E2%2B2x%2B-1+=+%28x-0.414213562373095%29%2A%28x--2.41421356237309%29
Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-1+%29

m = x
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m+=+-1+%2B+sqrt%282%29
m+=+-1+-+sqrt%282%29
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Questions 20-21 write the value of the discriminant of each equation, decide how many different real-number roots the equation has, and determine how many points the parabola will interact with the x-axis. Do not solve the equation.
20. x2+7x+9=0 Answer: Discriminant is 13,indicating there are two real roots, with the parabola intersecting the x-axis at two points.
Correct.
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21. 2x2+5x+7=0 Answer: Discriminant is -31, indicating there are no real roots, with the parabola not intersecting the x-axis at all.
Correct.