Annie Gil Viloria

Annie Gil Viloria

Answered question

2022-08-29

Identify which of the following equations are quadratic and which are NOT. If the equation is quadratic write FACT, if NOT, write BLUFF

1. 3m+8=15

2. x^2-5x+10=0

3. 12-4x =0

4. 2t^2-7t=12

5. 6-2x+3x^2=0

6. 25-r^2=4r-5r^2+10

7. 3x(x-2)=-7

8. 2h(h-6)=2h+3

9. (x+2)^2=0

10. (w-8)(w+5)=14+w^2

Answer & Explanation

karton

karton

Expert2023-05-25Added 613 answers

1. 3m+8=15
This equation is not quadratic because it is a linear equation in terms of m. It can be simplified to solve for m:
3m=158
3m=7
m=73
Therefore, the equation is BLUFF (not quadratic).
2. x25x+10=0
This equation is quadratic because it contains a quadratic term (x2). It is in the standard form of a quadratic equation (ax2+bx+c=0), with a=1, b=5, and c=10. Therefore, the equation is FACT (quadratic).
3. 124x=0
This equation is linear because it is a linear equation in terms of x. It can be simplified to solve for x:
4x=12
x=124
x=3
Therefore, the equation is BLUFF (not quadratic).
4. 2t27t=12
This equation is quadratic because it contains a quadratic term (t2). It is in the standard form of a quadratic equation, with a=2, b=7, and c=12. Therefore, the equation is FACT (quadratic).
5. 62x+3x2=0
This equation is quadratic because it contains a quadratic term (3x2). It is in the standard form of a quadratic equation, with a=3, b=2, and c=6. Therefore, the equation is FACT (quadratic).
6. 25r2=4r5r2+10
This equation is quadratic because it contains a quadratic term (r2). It can be simplified and rearranged to get all terms on one side:
4r+4r2r225+10=0
3r24r15=0
Therefore, the equation is FACT (quadratic).
7. 3x(x2)=7
This equation is quadratic because it contains a quadratic term (x2) when the expression is expanded. Expanding the equation gives:
3x26x=7
Therefore, the equation is FACT (quadratic).
8. 2h(h6)=2h+3
This equation is quadratic because it contains a quadratic term (h2) when the expression is expanded. Expanding the equation gives:
2h212h=2h+3
Therefore, the equation is FACT (quadratic).
9. (x+2)2=0
This equation is quadratic because it contains a quadratic term (x2) when the expression is expanded. Expanding the equation gives:
x2+4x+4=0
Therefore, the equation is FACT (quadratic).
10. (w8)(w+5)=14+w2
This equation is not quadratic because when expanded, the quadratic terms cancel out:
w23w40=14+w2
3w40=14
3w=54
w=543
w=18
Therefore, the equation is BLUFF (not quadratic).

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