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Korolek [52]
3 years ago
15

The dimensions of a rectangle are x+3 and x+4. The area of the rectangle is 72. Set up an equation that models this rectangle an

d solve in order to determine the value of x.
Mathematics
1 answer:
vodomira [7]3 years ago
3 0

Answer: x = 5

Step-by-step explanation:

The area of a rectangle is the length times the width. Since the dimensions are given as functions of x, youre going to have to use FOIL to combine them, then set that answer equal to the given value of 72.

l*w = (x+3)*(x+4) = x^2 + 7x +12 = 72

Subtract 72 on both sides. There is a reason why we'll do this instead of subtracting 12. The quadratic formula will help us to solve for x.

x^2 + 7x - 60 = 0

Apply the quadratic formula

\frac{-7 (+/-)\sqrt{7^2-(4)*(1)*(-60} }{2*1} =\frac{-7(+/-)17}{2}

We cant have a negative x value because that would result in negative dimensions and a negative area, which is impossible in this context. So you want to add the 17 instead of subtracting it.

x = 5 and x = -12

An alternate way is just factoring the trinomial to:

(x+12)(x-5) = 0

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Answer:

1. Given

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Step-by-step explanation:

Statement 1:

The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.

Statement 2:

BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence, BT = TD

Statement 3:

Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.

Statement 4:

A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, BC ||AD is because of the definition of a parallelogram.

Statement 5:

Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal.

Statement 6:

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Statement 7:

As the two triangles are congruent, then their corresponding parts are also equal.

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5 0
3 years ago
One half of your CDs are scratched. One fifth will not play properly. You have 40 CDs. How many will not work play properly
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I hope this helps!
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