Mr. Imani wants to purchase paper and notebooks for his classroom. At Dollar Discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. This is modeled by 1.25p + 2.50n. Evaluate for p = 10 and n=30 to find how much it will cost Mr. Imani to purchase 10 packs of paper and 30 notebooks. (1 point)
Responses
$62.50
$62.50
$450.00
$450.00
$87.50
$87.50
$43.75
To find out how much it will cost Mr. Imani to purchase 10 packs of paper and 30 notebooks, we substitute p = 10 and n = 30 into the expression 1.25p + 2.50n.
1.25*10 + 2.50*30
= 12.50 + 75
= 87.50
Therefore, it will cost Mr. Imani $87.50 to purchase 10 packs of paper and 30 notebooks.
The formula for finding the volume of a square prism is s2h, where s is the length of each side of the square base and h is the height of the prism. Evaluate to find the volume given values of s = 4 and h = 6.(1 point)
Responses
144 cubic centimeters
144 cubic centimeters
576 cubic centimeters
576 cubic centimeters
96 cubic centimeters
96 cubic centimeters
48 cubic centimeters
To find the volume, we substitute s = 4 and h = 6 into the formula s^2h.
4^2 * 6
= 16 * 6
= 96
Therefore, the volume of the square prism is 96 cubic centimeters.
Each month Ms. Tanaka is paid a base salary of $2,500 in addition to $100 for each television that she sells. This is modeled by 2,500 + 100t, where t represents the number of televisions. Evaluate for t = 12 to find how much Ms. Tanaka will earn for selling 12 televisions this month.(1 point)
Responses
$2,612
$2,612
$3,700
$3,700
$2,600
$2,600
$31,200
To find out how much Ms. Tanaka will earn for selling 12 televisions this month, we substitute t = 12 into the expression 2,500 + 100t.
2,500 + 100 * 12
= 2,500 + 1,200
= 3,700
Therefore, Ms. Tanaka will earn $3,700 for selling 12 televisions this month.
obert is preparing a poster-board presentation. He wants to make a decorative pattern with 10 squares to fill part of the poster. The area of the poster board is 720 square inches. To find how much space Robert will have left for his presentation if he uses squares with 7-inch sides, evaluate 720 − 10s2 when s = 7.(1 point)
Responses
580 square inches
580 square inches
230 square inches
230 square inches
34,790 square inches
34,790 square inches
9,940 square inches
To find out how much space Robert will have left for his presentation, we substitute s = 7 into the expression 720 - 10s^2.
720 - 10 * 7^2
= 720 - 10 * 49
= 720 - 490
= 230
Therefore, Robert will have 230 square inches left for his presentation.
Mr. Rodriguez has a vegetable garden that borders his house. He wants to put a fence around it. It costs $7 per yard for the materials. Evaluate 7(l + 2w), where l is the length and w is the width of his garden, to find the cost for a garden that has a length of 5 yards and a width of 2 yards.(1 point)
Responses
$16
$16
$39
$39
$98
$98
$63
To find the cost for a garden with a length of 5 yards and a width of 2 yards, we substitute l = 5 and w = 2 into the expression 7(l + 2w).
7(5 + 2*2)
= 7(5 + 4)
= 7(9)
= 63
Therefore, the cost for the garden with a length of 5 yards and a width of 2 yards would be $63.
Simplify 8a − 2a
To simplify the expression 8a - 2a, we combine the like terms:
8a - 2a = 6a
Therefore, the simplified expression is 6a.
Simplify 4x + 8x using the properties of operations.(1 point)
Responses
12x2
12 x squared
4x + 8
4 x plus 8
4 + 8x
4 plus 8 x
12x
To simplify the expression 4x + 8x, we can combine the like terms by adding their coefficients:
4x + 8x = (4 + 8)x = 12x
Therefore, the simplified expression is 12x.
Simplify 9g−7h−6g + 2h . (1 point)
Responses
3g + 5h
3 g plus 5 h
2gh − 4gh
2 g h minus 4 g h
3g − 5h
3 g minus 5 h
−2gh
To simplify the expression 9g - 7h - 6g + 2h, we can combine like terms:
9g - 6g - 7h + 2h = (9g - 6g) + (-7h + 2h) = 3g - 5h.
Therefore, the simplified expression is 3g - 5h.
Simplify 2a − 4b +7 + 8a + 6b − 2.(1 point)
Responses
12ab + 5
12 a b plus 5
10a − 2b +5
10 a minus 2 b plus 5
10a + 2b +5
10 a plus 2 b plus 5
−2ab + 14ab + 5
To simplify the expression 2a - 4b + 7 + 8a + 6b - 2, we can combine like terms:
(2a + 8a) + (-4b + 6b) + (7 - 2) = 10a + 2b + 5.
Therefore, the simplified expression is 10a + 2b + 5.
Simplify 37x + 27x using properties of operations.(1 point)
Responses
514x
Start Fraction 5 over 14 End Fraction x
57x
Start Fraction 5 over 7 End Fraction x
514x2
Start Fraction 5 over 14 End Fraction x squared
57x2
To simplify the expression 37x + 27x, we can combine the like terms by adding their coefficients:
37x + 27x = (37 + 27)x = 64x
Therefore, the simplified expression is 64x.
Simplify 37x + 27x using properties of operations.(1 point)
Responses
Start Fraction 5 over 14 End Fraction x
Start Fraction 5 over 7 End Fraction x
Start Fraction 5 over 14 End Fraction x squared
To simplify the expression 37x + 27x, we can combine the like terms by adding their coefficients:
37x + 27x = 64x
Therefore, the simplified expression is 64x.
Simplify 3/7x + 2/7x using properties of operations.(1 point)
Responses
514x
Start Fraction 5 over 14 End Fraction x
57x
Start Fraction 5 over 7 End Fraction x
514x2
Start Fraction 5 over 14 End Fraction x squared
57x2
To simplify the expression (3/7)x + (2/7)x, we can combine the like terms by adding their coefficients:
(3/7)x + (2/7)x = (3 + 2)/(7)x = 5/7x.
Therefore, the simplified expression is (5/7)x.
Simplify 6/7c − 5/9d − 1/2 c + 13d.(1 point)
Responses
514c + 29d
Start Fraction 5 over 14 End Fraction c plus Start Fraction 2 over 9 End Fraction d
59c + 412d = 59c +13d
Start Fraction 5 over 9 End Fraction c plus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c plus Start Fraction 1 over 3 End Fraction d
59c − 412d = 59c −13d
Start Fraction 5 over 9 End Fraction c minus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c minus Start Fraction 1 over 3 End Fraction d
514c − 29d
To simplify the expression 6/7c - 5/9d - 1/2c + 13d, we can combine like terms:
(6/7c - 1/2c) + (-5/9d + 13d) = (12/14c - 7/14c) + (-10/9d + 117/9d) = 5/14c + 107/9d.
Therefore, the simplified expression is 5/14c + 107/9d.
Simplify 6/7c − 5/9d − 1/2 c + 1/3d.(1 point)
Responses
514c + 29d
Start Fraction 5 over 14 End Fraction c plus Start Fraction 2 over 9 End Fraction d
59c + 412d = 59c +13d
Start Fraction 5 over 9 End Fraction c plus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c plus Start Fraction 1 over 3 End Fraction d
59c − 412d = 59c −13d
Start Fraction 5 over 9 End Fraction c minus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c minus Start Fraction 1 over 3 End Fraction d
514c − 29d
To simplify the expression 6/7c - 5/9d - 1/2c + 1/3d, we can combine like terms:
(6/7c - 1/2c) + (-5/9d + 1/3d) = (12/14c - 7/14c) + (-10/9d + 3/9d) = 5/14c - 7/14c - 7/9d.
Now, we can simplify the expression further:
(5/14c - 7/14c) - 7/9d = -2/14c - 7/9d = -1/7c - 7/9d.
Therefore, the simplified expression is -1/7c - 7/9d.