The answer: The 3 (three) consecutive odd integers are: -3, -1, 1.
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Explanation:
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To represent 3 (three consecutive odd integers):
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Let "x" be the first odd integer.
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Let "(x+2)" be next consecutive odd integer.
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Let "(x+4") be the third odd integer.
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The sum of these three consecutive odd integers:
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x + (x + 2) + (x + 4) = x + x + 2 + x + 4 = 3x + 6 ;
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Six ("6") times the sum of these 3 (three) consecutive odd integers =
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6*(3x+6) = 6(3x + 6) = -18 (as given in the problem).
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Given: 6(3x + 6) = -18 ; We can divide EACH SIDE of the equation by "6", to cancel the "6" on the left-hand side into a "1";
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{6(3x + 6) } / 6 = -18 / 6 ; to get:
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3x + 6 = -3 ; Now, we can subtract "6" from EACH SIDE of the equation:
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3x + 6 - 6 = -3 - 6 ; to get:
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3x = -9 ; Now, we can divide EACH SIDE of the equation by "3"; to isolate "x" on one side of the question; and solve for "x" ;
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3x / 3 = -9 / 3 ; x = - 3 ;
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Remember, from above:
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Let "x" be the first odd integer. We know that "x = -3".
Is this an odd integer? Yes!
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Let "(x+2)" be next consecutive odd integer. So (x+2) = (-3+2) = -1.
Is this an odd integer? Yes! Is this "{-1}" the next consecutive odd integer with respect to "{-3}"? Yes!
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Let "(x+4") be the third odd integer. So (x+4) = (-3+4) = 1.
Is this an odd integer? Yes! Is this "{1"} the next consecutive odd integer with respect to "{-1}"? Yes!
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So, our 3 (three) consecutive odd integers are: -3, -1, 1.
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To check our work: Is 6 times the sum of our 3 consecutive odd integers, equal to "(-18)" ?
The sum of our 3 consecutive odd integers = -3 + (-1) + 1 = -3 - 1 + 1 = -3.
6 * -3 = ? -18? Yes!
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Answer: Z'(-7;8)
suppose the coordinates of Z' is Z'(x,y)
we have:
=> Z'(-7;8)
Step-by-step explanation:
Answer:
33.333
Step-by-step explanation:
A rate is a special ratio in which the two terms are in different units. A rate is a little bit different than the ratio, it is a special ratio. For this case, the rate would have units of miles per minutes. We calculate as follows:
rate = 36 miles / 45 min = 0.8 miles per min
distance traveled = 0.8 miles per min ( 60 min ) = 48 miles
Linda should use ...
15 gallons of 80% juice
5 gallons of 60% juice
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Let g represent the number of gallons of 80% juice needed. Then (20-g) is the number of gallons of 60% juice Linda will use. The amount of juice in the mixture can be written as
0.80g +0.60(20 -g) = 0.75×20
0.20g = 20(0.75 -0.60) = 20×0.15
g = 20×0.15/0.20 = 15
The amount of 80% juice needed is 15 gallons, so 5 gallons of 60% juice are needed.
