Question

simplify (2x^5y^2)(3x^ - 1y).
5x^4y^3
6x^4y^3
6x^5y^2
6x^2y
question 11(multiple choice worth 1 points)
(06.02 mc)
the three sides of a triangular fence have lengths 4x + 5, y - 7, and 3x - 2. what is the total perimeter?
7x + y + 10 feet
7x + y - 4 feet
7x + y feet
4x + y - 4 feet
question 12(multiple choice worth 1 points)
(06.04 mc)
the length of a rectangle is represented by the function l(x)=2x. the width of that same rectangle is represented by the function w(x)=8x^2 - 4x + 1. which of the following shows the area of the rectangle in terms of x?
(l + w)(x)=8x^2 - 2x + 1
(l + w)(x)=8x^2 - 6x + 1
(l·w)(x)=16x^3 - 4x + 1
(l·w)(x)=16x^3 - 8x^2+2x

Explanation:

Question 1: Simplify \((2x^{5}y^{2})(3x^{3}y)\)

Step1: Multiply coefficients

\(2\times3 = 6\)

Step2: Apply exponent - rule for \(x\) terms

\(x^{5}\times x^{3}=x^{5 + 3}=x^{8}\) (using \(a^{m}\times a^{n}=a^{m + n}\))

Step3: Apply exponent - rule for \(y\) terms

\(y^{2}\times y=y^{2+1}=y^{3}\) (using \(a^{m}\times a^{n}=a^{m + n}\))

Step4: Combine results

\(6\times x^{8}\times y^{3}=6x^{8}y^{3}\)

Question 11: The three sides of a triangular fence have lengths \(4x + 5\), \(y-7\), and \(3x - 2\). What is the total perimeter?

Step1: Write perimeter formula

Perimeter \(P=(4x + 5)+(y - 7)+(3x - 2)\)

Step2: Combine like - terms of \(x\)

\(4x+3x=7x\)

Step3: Combine constant terms

\(5-7 - 2=5-(7 + 2)=5 - 9=-4\)

Step4: Combine results

\(P = 7x+y-4\)

Question 12: The length of a rectangle is represented by the function \(L(x)=2x\). The width of that same rectangle is represented by the function \(W(x)=8x^{2}-4x + 1\). Which of the following shows the area of the rectangle in terms of \(x\)?

Step1: Write area formula

Area \(A = L(x)\times W(x)\)

Step2: Substitute functions

\(A=(2x)(8x^{2}-4x + 1)\)

Step3: Distribute \(2x\)

\(A=2x\times8x^{2}-2x\times4x+2x\times1\)

Step4: Simplify each term

\(2x\times8x^{2}=16x^{3}\), \(2x\times4x = 8x^{2}\), \(2x\times1=2x\)

Step5: Combine results

\(A = 16x^{3}-8x^{2}+2x\)

Answer:

B. \(6x^{8}y^{3}\)