Question
A parallelogram's area is given by the expression 4x2 + 2x + 6. The height of the parallelogram is 2x2.
Which expression represents the base of the parallelogram?
2 + x +
2 +
2 +
2 + x +
Which expression represents the base of the parallelogram?
2 + x +
2 +
2 +
2 + x +
Answers
Answered by
GPT-4o mini
To find the expression representing the base of the parallelogram, we can use the formula for the area of a parallelogram, which is:
\[
\text{Area} = \text{base} \times \text{height}
\]
Given that the area is \( 4x^2 + 2x + 6 \) and the height is \( 2x^2 \), we can set up the equation:
\[
4x^2 + 2x + 6 = \text{base} \times 2x^2
\]
To find the base, we can divide both sides by the height (\( 2x^2 \)):
\[
\text{base} = \frac{4x^2 + 2x + 6}{2x^2}
\]
Now, we can simplify the right-hand side:
\[
\text{base} = \frac{4x^2}{2x^2} + \frac{2x}{2x^2} + \frac{6}{2x^2}
\]
\[
\text{base} = 2 + \frac{1}{x} + \frac{3}{x^2}
\]
So the expression that represents the base of the parallelogram is
\[
2 + \frac{1}{x} + \frac{3}{x^2}
\]
However, from the options you've given, it seems they are incomplete or not set up for this type of answer.
If you need to use options filled with "2 + x + ...", you may need to reevaluate how to express the base. If the options provided are strictly as you've listed, none of them can accurately represent the base derived from the calculation above.
If possible, please provide clearer multiple choice options!
\[
\text{Area} = \text{base} \times \text{height}
\]
Given that the area is \( 4x^2 + 2x + 6 \) and the height is \( 2x^2 \), we can set up the equation:
\[
4x^2 + 2x + 6 = \text{base} \times 2x^2
\]
To find the base, we can divide both sides by the height (\( 2x^2 \)):
\[
\text{base} = \frac{4x^2 + 2x + 6}{2x^2}
\]
Now, we can simplify the right-hand side:
\[
\text{base} = \frac{4x^2}{2x^2} + \frac{2x}{2x^2} + \frac{6}{2x^2}
\]
\[
\text{base} = 2 + \frac{1}{x} + \frac{3}{x^2}
\]
So the expression that represents the base of the parallelogram is
\[
2 + \frac{1}{x} + \frac{3}{x^2}
\]
However, from the options you've given, it seems they are incomplete or not set up for this type of answer.
If you need to use options filled with "2 + x + ...", you may need to reevaluate how to express the base. If the options provided are strictly as you've listed, none of them can accurately represent the base derived from the calculation above.
If possible, please provide clearer multiple choice options!