Question

1

Select all the correct locations on the tables.

Andrew wants to purchase a new television with a screen length that is five times its width. The width of the television screen is 7 inches more than the width of his tablet. Andrew also wants the area of the new television screen to be at least 1,050 square inches.

If x is the width of Andrew's tablet, determine which inequality could represent this situation. Then, determine if 8 inches is a reasonable width for his tablet.

Answer 1

Answer:

Part 1) The inequality that represent this situation is $5(x+7)^{2} \geq1,050$  or  $5x^{2}+70x+245 \geq1,050$

Part 2) Yes, 8 inches is a reasonable width for his tablet

Step-by-step explanation:

Part 1)

Let

L -----> the length of the screen television

W ----> the width of the screen television

x ---->  the width of Andrew's tablet

we know that

$L=5W$ ------> equation A

$W=x+7$ ----> equation B

The area of the television is

$A=LW$ -----> equation C

Substitute equation A and equation B in equation C

$A=5(x+7)(x+7)$

$A=5(x+7)^{2}$

$5(x+7)^{2} \geq1,050$

$5(x^{2}+14x+49) \geq1,050$

$5x^{2}+70x+245 \geq1,050$ ------> inequality that represent this situation

Part 2) Determine if 8 inches is a reasonable width for his tablet

For x=8 in

Substitute in the inequality

$5(8+7)^{2} \geq1,050$

$5(15)^{2} \geq1,050$

$1,125 \geq1,050$ -----> is true

therefore

Yes, 8 inches is a reasonable width for his tablet