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10 November, 22:08

Instructions: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.

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  1. 10 November, 22:13
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    The correct answers are:

    5x²+70x+245 ≥ 1050; and

    Yes.

    Explanation:

    Let x be the width of the tablet. Since the width of the TV is 7 inches more than the tablet, the width of the TV would be x+7.

    The length of the TV is 5 times the width; this makes the length 5 (x+7) = 5x+35.

    The area of the TV would be given by

    (x+7) (5x+35).

    Since Andrew wants the area to be at least 1050, we set the expression greater than or equal to 1050:

    (x+7) (5x+35) ≥ 1050

    Multiplying this, we have:

    x*5x+x*35+7*5x+7*35 ≥ 1050

    5x²+35x+35x+245 ≥ 1050

    Combining like terms,

    5x²+70x+245 ≥ 1050

    To see if 8 is a reasonable width for the tablet, we substitute 8 for x:

    5 (8²) + 70 (8) + 245 ≥ 1050

    5 (64) + 560+245 ≥ 1050

    320+560+245 ≥ 1050

    1125 ≥ 1050

    Since this inequality is true, 8 is a reasonable width.
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