Which polynomial does the model represent?
–x³ + 2x² – 3x + 2
• x² + x – 2
• –x² – x + 2
• –x² + x – 2
The polynomial represented by the model is –x³ + 2x² – 3x + 2.
4x^2 + 4 - 5x + x - 2x^2 + 8
Combining like terms, we have:
2x^2 - 4x + 12
So the simplified expression is 2x^2 - 4x + 12.
3x^2 + 5x - 7x + 3 - 5x^2 + 2
Combining like terms, we have:
-2x^2 - 2x + 5
So the simplified expression is -2x^2 - 2x + 5.
what are the coefficients in the polynomial 5x^2 + 2x - 4
The coefficients in the polynomial 5x^2 + 2x - 4 are:
- 5 is the coefficient of the term x^2.
- 2 is the coefficient of the term x.
- (-4) = 4 is the constant term or coefficient.
(m^2 - m - 4) + (m-5)
First simplify each set of parentheses, and then combine like terms by adding:
(m^2 - m - 4) + (m-5)
= m^2 - m - 4 + m - 5 (distribute the addition)
= m^2 - m + m - 4 - 5 (group like terms)
= m^2 - 9
So the simplified expression is m^2 - 9.
(7x^2 - x - 2) - (6x^3 + 3)
First distribute the negative sign to every term inside the parentheses:
(7x^2 - x - 2) - (6x^3 + 3)
= 7x^2 - x - 2 - 6x^3 - 3 (distribute the negative)
= -6x^3 + 7x^2 - x - 5
So the simplified expression is -6x^3 + 7x^2 - x - 5.
Suppose you earned 6t + 2 dollars on Mondaya and 9t - 6 on Tuesday. What were your total earnings? Simplify your answer.
To find the total earnings, we need to add the earnings from Monday and Tuesday:
Total earnings = (6t + 2) + (9t - 6)
= 6t + 9t + 2 - 6 (group like terms)
= 15t - 4
So the simplified expression for the total earnings is 15t - 4 dollars.
f^2 x f^4
When we multiply variables with the same base, we add their exponents. Therefore,
f^2 x f^4 = f^(2+4) = f^6.
So the simplified expression is f^6.
144^14 / 144^2
When we divide two exponents with the same base, we subtract their exponents. Therefore,
144^14 / 144^2 = 144^(14-2) = 144^12.
So the simplified expression is 144^12.
Which of the following expressions is true?
4^3 x 4^5 < 4^12
5^2 x 5^3 > 5^5
3^2 x 3^4 = 3^2
5^2 x 5^4 = 5^8
The first expression is true. When we multiply two exponents with the same base, we add their exponents. Therefore,
4^3 x 4^5 = 4^(3+5) = 4^8
And, 4^12 > 4^8.
So 4^3 x 4^5 < 4^12 is true.
The second expression is false. When we multiply two exponents with the same base, we add their exponents. Therefore,
5^2 x 5^3 = 5^(2+3) = 5^5
And 5^2 x 5^3 = 5^5, so 5^2 x 5^3 = 5^5 is true.
The third expression is also true. When we multiply two exponents with the same base, we add their exponents. Therefore,
3^2 x 3^4 = 3^(2+4) = 3^6
So 3^2 x 3^4 = 3^6 is true.
The fourth expression is also true. When we multiply two exponents with the same base, we add their exponents. Therefore,
5^2 x 5^4 = 5^(2+4) = 5^6
So 5^2 x 5^4 = 5^8 is false.
Therefore, the only true expression is 4^3 x 4^5 < 4^12.
Which of the following expressions is true?
2^4 x 2^3 = 2^12
3^3 x 3^6 > 3^8
4^2 x 4^2 > 4^4
5^5 x 5^2 = 5^10
The first expression is false. When we multiply two exponents with the same base, we add their exponents. Therefore,
2^4 x 2^3 = 2^(4+3) = 2^7
So 2^4 x 2^3 = 2^7 is false.
The second expression is true. When we multiply two exponents with the same base, we add their exponents. Therefore,
3^3 x 3^6 = 3^(3+6) = 3^9
And 3^3 x 3^6 > 3^8.
Therefore, 3^3 x 3^6 > 3^8 is true.
The third expression is false. When we multiply two exponents with the same base, we add their exponents. Therefore,
4^2 x 4^2 = 4^(2+2) = 4^4
So 4^2 x 4^2 = 4^4 is true.
The fourth expression is also true. When we multiply two exponents with the same base, we add their exponents. Therefore,
5^5 x 5^2 = 5^(5+2) = 5^7
So 5^5 x 5^2 = 5^10 is false.
Therefore, the expressions that are true are 3^3 x 3^6 > 3^8 and 4^2 x 4^2 > 4^4.
(1.8 x 10^1) (7 x 10^5) in scientific notation.
When we multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. Therefore,
(1.8 x 10^1) (7 x 10^5) = (1.8 x 7) x 10^(1+5) = 12.6 x 10^6.
To express this in scientific notation, we need to move the decimal point one place to the left, and add 1 to the exponent:
12.6 x 10^6 = 1.26 x 10^(6+1)
So (1.8 x 10^1) (7 x 10^5) in scientific notation is 1.26 x 10^7.
(1.1 x 10^-5) (3 x 10^-2) in scientific notation
When we multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. Therefore,
(1.1 x 10^-5) (3 x 10^-2) = 3.3 x 10^(-5-2) = 3.3 x 10^-7.
So (1.1 x 10^-5) (3 x 10^-2) in scientific notation is 3.3 x 10^-7.
simplify the expression
6t^3 x 6t^3
When we multiply two variables with the same base, we add their exponents. Therefore,
6t^3 x 6t^3 = 6x6 x t^3xt^3 = 36t^(3+3) = 36t^6.
So the simplified expression is 36t^6.
3x^2 + 6 - 2x + 5x - 4x^2 + 9
Combining like terms, we have:
(3x^2 - 4x^2) + (-2x + 5x) + (6 + 9)
= -x^2 + 3x + 15
So the simplified expression is -x^2 + 3x + 15.
simplify 3x^2 + 5x - 7x + 3 - 5x^2 + 2
Combining like terms, we have:
3x^2 - 5x^2 + 5x - 7x + 3 + 2
= -2x^2 - 2x + 5
So the simplified expression is -2x^2 - 2x + 5.
what are the coefficients in the polynomial 7x^2 - 4x + 6
The coefficients in the polynomial 7x^2 - 4x + 6 are:
- 7 is the coefficient of the term x^2.
- (-4) = -4 is the coefficient of the term x.
- 6 is the constant term or coefficient.
So the coefficients are -7, -4, and 6.
(m^2 - m + 3) + (m - 1
First simplify each set of parentheses, and then combine like terms by adding:
(m^2 - m + 3) + (m - 1)
= m^2 - m + 3 + m - 1 (distribute the addition)
= m^2 + 2 (combine like terms)
So the simplified expression is m^2 + 2.
(5x^2 + x - 3) - (-2x^3 + 4)
First distribute the negative sign to every term inside the parentheses:
(5x^2 + x - 3) - (-2x^3 + 4)
= 5x^2 + x - 3 + 2x^3 - 4 (distribute the negative)
= 2x^3 + 5x^2 + x - 7
So the simplified expression is 2x^3 + 5x^2 + x - 7.
suppose you earned 6t + 2 dollars on monday and 9t - 6 dollars on tuesday what were your total earnings? simplify your answer
To find the total earnings, we need to add the earnings from Monday and Tuesday:
Total earnings = (6t + 2) + (9t - 6)
= 6t + 9t + 2 - 6 (group like terms)
= 15t - 4
So the simplified expression for the total earnings is 15t - 4 dollars.