The area of a rectangle can be expressed by 2x ^ 2 - 7x - 4 if the rectangle has an area of 45 find the positive value for x

The positive value of x for the rectangle is 7 units.

A rectangle is a quadrilateral (has four angles and four sides) in which opposite sides are equal to each other.

Given that the area of a rectangle has an expression 2x² - 7x - 4 and has an area of 45. hence:

2x² - 7x - 4 = 45

2x² - 7x - 49 = 0

x = -3.5 and x = 7

Therefore the positive value of x for the rectangle is 7 units.

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x = 7

Step-by-step explanation:

Equating the expression for area to the given area

2x² - 7x - 4 = 45 ( subtract 45 from both sides )

2x² - 7x - 49 = 0 ← in standard form

To factor consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 49 = - 98 and sum = - 7

The factors are - 14 and + 7

Use these factors to split the middle term

2x² - 14x + 7x - 49 = 0 ( factor the first/second and third/fourth terms )

2x(x - 7) + 7(x - 7) = 0 ← factor out (x - 7)

(x - 7)(2x + 7) = 0

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = -

Thus the positive value for x is x = 7

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

the answer is 62.8 cubic units