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3 years ago

14

A photograph has a length that is 4 inches longer than its width, x. Its area is given by the expression x(x + 4). If the area o

f the photograph is 96 square inches, what is the length of the photograph?

1 answer:

xxTIMURxx [149]3 years ago

6 0

Answer:

The length is 12 inches and the width is 8 inches.

Step-by-step explanation:

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In rectangle QRST, QS = x2 + 6x, and RT = 8x + 3. Find the length of QS.

valentina_108 [34]

The length of QS is 27 units.

<u>Step-by-step explanation:</u>

In the given rectangle QRST QS and RT are the diagonals. In a triangle, the opposite sides are equal and parallel. This implies that the diagonals of a rectangle are equal.

$QS=RT \ QS=x^2+6x$

$RT=8x+3$

$x^2+6x=8x+3$

$x^2+6x-8x-3=0$

$x^2-2x-3=0$

We have obtained a quadratic equation here and solving this gives the possible values of QS.This can be solved using quadratic formula

$x=(-b\pm \sqrt{(b^2-4ac))}/2a$

The quadratic equation is of the form $ax^2+bxl+c=0$

here a=1 b=-2 c=-3

$x=(-b\pm \sqrt{(b^2-4ac))}/2a$

$x=x=(2 \pm \sqrt{ (-2^2-4 \times 1 \times -3))}/(2 \times 1)$

$x=(2 \pm \sqrt{(4+12))} /2$ or

$x=(2 \pm \sqrt{16)}/2 =(2\pm 4)/2 \ \ \ \ x=(2+4)/2=3 \ \ \ \ or \ \ \ x=(2-4)/2=-1$

putting x=3 $QS=x^2+6x$

$=3^2+6 \times 3=9+18=27$

putting x=-1

$QS=(-1)^2+6 \times -1=1-6=-5$

Since a length can have only positive values QS=27 units.

5 0

3 years ago

Use the first five terms of the exponential series of ex and a calculator to approximate the value of e0.8 to the nearest hundre

crimeas [40]

The answer should be C

4 0

3 years ago

Read 2 more answers

What is:<br><br>k/3 + 17 = 12?

Anit [1.1K]

What is:
k/3 + 17 = 12?
k = -15

7 0

2 years ago

Read 2 more answers

Solve for a -1/4a-4=7/4a-3

ddd [48]

Add 1/4a to both sides
-4= 8/4a-3

Simplify
-4=2a-3

Add 3 to both sides
-1=2a

Divide both sides by 2
-1/2=a

Final answer: a=-1/2

3 0

3 years ago

rjkz [21]

Here's an answer it's number 2

5 0

3 years ago