A rectangle has length 3x^2 + 2x - 1 and width 5x - 7. What is the Perimeter?(Do not include spaces in your answer. Use ^ for exponents. For example the length would be typed 3x^2+2x-1.)
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, the length is 3x^2 + 2x - 1 and the width is 5x - 7. Substituting these values into the formula, we have:
P = 2(3x^2 + 2x - 1 + 5x - 7)
Simplifying the expression inside the parentheses:
P = 2(3x^2 + 7x - 8)
Expanding and combining like terms:
P = 2(3x^2) + 2(7x) + 2(-8)
P = 6x^2 + 14x - 16
Therefore, the perimeter of the rectangle is 6x^2 + 14x - 16.
A rectangle has length 3x^2 + 2x - 1 and width 5x - 7. What is the Area?(Do not include spaces in your answer. Use ^ for exponents. For example the length would be typed 3x^2+2x-1.)
The area of a rectangle is given by the formula A = length * width. In this case, the length is 3x^2 + 2x - 1 and the width is 5x - 7. Substituting these values into the formula, we have:
A = (3x^2 + 2x - 1)(5x - 7)
Multiplying the binomials using the distributive property, we get:
A = 15x^3 - 21x^2 + 10x^2 - 14x - 5x + 7
Combining like terms, we have:
A = 15x^3 - 11x^2 - 19x + 7
Therefore, the area of the rectangle is 15x^3 - 11x^2 - 19x + 7.