5. (m^2-m-3)+(m-4)
A. m^2+m-1
B. m^2+2m-7
C. m^2-7
D. m^2-1
6. (4x^2-2x-1)-(-3x^3+2)
A. -3x^3+4x^2-2x+1
B. -3x^3+4x^2-2x-3
C. 3x^3+4x^2-2x+1
D. 3x^3+4x^2-2x-3
9. 100^12/100^8
A. 100^12/8
B. 100^96
C. 100^4***
D. 100^20
16. (1.1*10^-5)(3*10^-2)
A. 4.1*10^-7
B. 4.1*10^10
C. 3.3*10^-7
D. 3.3*10^10
19. 3k^2(-2k^2-4k+7)
A. -6k^3-k+10k
B. -6k^4-12k^3+21k^2
C. k^4-k^3+10k^2
D. 6k^4--12k^3+10k^2
20. (2k+3)(k-1)
A. 2k^2+k-3
B. 2k^2+k+2
C. 2k^2-k-3
D. 2k^2-k+2
21. (-y+4)(2y-1)
A. 2y^2+7y+3
B. 2y^2+5y-4
C. -2y^2+9y-4
D. -2y^+6y+3
Thank you to who ever helps!!! I have a harder time with these!!!
5C
6D
9 correct
16C
19B
20A
21C
Review your methods and try them till you get these answers.
5. B. m^2+2m-7
6. A. -3x^3+4x^2-2x+1
9. C. 100^4
16. A. 4.1*10^-7
19. B. -6k^4-12k^3+21k^2
20. A. 2k^2+k-3
21. B. 2y^2+5y-4
5. To simplify the expression (m^2-m-3)+(m-4), we can combine like terms.
The like terms are the terms with the same variables and same exponents.
In this case, we have m^2 and m, which are like terms, and -m-3 and -4, which are also like terms.
Combining m^2 and m gives us m^2 + m, and combining -m-3 and -4 gives us -m-7.
Putting it all together, we have (m^2-m-3)+(m-4) = m^2 + m - m - 3 - 4 = m^2 - 7.
Therefore, the answer is C. m^2 - 7.
6. To simplify the expression (4x^2-2x-1)-(-3x^3+2), we can remove the second set of parentheses by distributing the negative sign to each term inside.
Distributing the negative sign gives us (4x^2 - 2x - 1) + (3x^3 - 2).
Now we can combine like terms. We have 4x^2 and 3x^3 as like terms, and -2x and -1 and -2 as like terms.
Combining 4x^2 and 3x^3 gives us 3x^3 + 4x^2, and combining -2x, -1, and -2 gives us -2x - 3.
Putting it all together, we have (4x^2-2x-1)-(-3x^3+2) = 3x^3 + 4x^2 - 2x - 3.
Therefore, the answer is B. 3x^3 + 4x^2 - 2x - 3.
9. To simplify the expression 100^12/100^8, we can use the properties of exponents.
When dividing two numbers with the same base, we can subtract the exponents.
In this case, the base is 100, and we have 12 as the exponent in the numerator and 8 as the exponent in the denominator.
12 - 8 = 4, so the expression simplifies to 100^4.
Therefore, the answer is C. 100^4.
16. To simplify the expression (1.1*10^-5)(3*10^-2), we can multiply the coefficients and add the exponents of the powers of 10.
1.1 * 3 = 3.3, and 10^-5 * 10^-2 = 10^(-5+(-2)) = 10^-7.
Putting it all together, we have (1.1*10^-5)(3*10^-2) = 3.3*10^-7.
Therefore, the answer is C. 3.3*10^-7.
19. To simplify the expression 3k^2(-2k^2-4k+7), we can distribute the 3k^2 to each term inside the parentheses.
Distributing gives us -6k^4 - 12k^3 + 21k^2.
Therefore, the answer is B. -6k^4 - 12k^3 + 21k^2.
20. To simplify the expression (2k+3)(k-1), we can use the distributive property.
Distributing gives us 2k^2 + 2k - k - 3.
Combining like terms, we have 2k^2 + k - 3.
Therefore, the answer is A. 2k^2 + k - 3.
21. To simplify the expression (-y+4)(2y-1), we can again use the distributive property.
Distributing gives us -2y^2 + y + 8y - 4.
Combining like terms, we have -2y^2 + 9y - 4.
Therefore, the answer is C. -2y^2 + 9y - 4.
To simplify the expressions and find the correct options, we'll go through each problem step by step:
5. (m^2-m-3)+(m-4)
Start by simplifying the parentheses: m^2 - m - 3 + m - 4
Combine like terms: m^2 - m + m - 3 - 4
Combine like terms again: m^2 - 7
Therefore, the correct option is C. m^2 - 7.
6. (4x^2-2x-1)-(-3x^3+2)
To simplify, distribute the negative sign within the parentheses: 4x^2 - 2x - 1 + 3x^3 - 2
Combine like terms: 3x^3 + 4x^2 - 2x - 1 - 2
Simplify further: 3x^3 + 4x^2 - 2x - 3
Therefore, the correct option is B. -3x^3 + 4x^2 - 2x - 3.
9. 100^12/100^8
When dividing powers with the same base, subtract the exponents: 100^(12-8)
Simplify the exponent: 100^4
Therefore, the correct option is C. 100^4.
16. (1.1 * 10^-5)(3 * 10^-2)
To multiply numbers written in scientific notation, multiply the coefficients and add the exponents: (1.1 * 3) * (10^(-5 + -2))
Simplify the multiplication and add the exponents: 3.3 * 10^-7
Therefore, the correct option is C. 3.3 * 10^-7.
19. 3k^2(-2k^2 - 4k + 7)
Multiply each term in the parentheses by 3k^2: -6k^4 - 12k^3 + 21k^2
Therefore, the correct option is B. -6k^4 - 12k^3 + 21k^2.
20. (2k + 3)(k - 1)
Use the FOIL method (First, Outer, Inner, Last) to multiply: 2k * k + 2k * (-1) + 3 * k + 3 * (-1)
Simplify: 2k^2 - 2k + 3k - 3
Combine like terms: 2k^2 + k - 3
Therefore, the correct option is A. 2k^2 + k - 3.
21. (-y + 4)(2y - 1)
Use the FOIL method: -y * 2y - y * (-1) + 4 * 2y - 4 * (-1)
Simplify: -2y^2 + y + 8y + 4
Combine like terms: -2y^2 + 9y + 4
Therefore, the correct option is C. -2y^2 + 9y + 4.
I hope these explanations help! Let me know if you have any further questions.