Answer:
m = -2
Step-by-step explanation:
24 = -6(m + 1) + 18 (Given)
24 = -6(m) + -6(1) + 18 (Distributive Property of Equality)
24 = -6m - 6 + 18 (Simplify)
24 = -6m + 12 (Simplify)
24 - 12 = -6m + 12 - 12 (Subtraction Property of Equality)
12 = -6m (Simplify)
(Division Property of Equality)
-2 = m (Simplify)
m = -2 (Distributive Property of Equality)
Answer:
2 / 5
Step-by-step explanation:
Fractions are written in the form part/whole, in this case, the part is 18 and the whole is 45 so the fraction would be 18 / 45 which simplifies to 2 / 5.
Answer:
The dimensions of the rectangle = 60ft by 107ft
Where 60 ft = Width of the playing field
107ft = Length of the playing field
Step-by-step explanation:
A playing field is Rectangular is shape, hence,
The formula for Perimeter of a rectangle = 2(L + W)
P = 334 ft
L = 47 + W
W = W
Hence we input these values in the formula and we have:
334 = 2(47 + W + W)
334 = 2(47 + 2W)
334 = 94 + 4W
334 - 94 = 4W
240 = 4W
W = 240/4
W = 60
There fore, the width of this playing field = 60 ft
The length of this rectangle is calculated as:
47 + W
47 + 60
= 107 ft
The length of this playing field = 107ft
Therefore the dimensions of the rectangle = 60ft by 107ft
Answer:
0.64, 65%, 2/3, 7/10.
Step-by-step explanation:
2/3=0.667
65%=0.65
7/10=0.7
From least to greatest:
0.64, 65%, 2/3, 7/10
Answer:
- 33 1/3 liters of 30%
- 16 2/3 liters of 45%
Step-by-step explanation:
Let x represent the liters of 45% solution needed. Then the amount of HCl in the mix is ...
0.45x +0.30(50 -x) = 0.35(50)
0.15x = 0.05(50) . . . . . simplify, subtract 0.30(50)
x = (0.05/0.15)(50) = 50/3 = 16 2/3 . . . liters of 45% HCl
33 1/3 liters of 30% and 16 2/3 liters of 45% HCl are needed.
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<em>Comment on the solution</em>
You may notice that the general solution to a mixture problem of this sort is that the fraction of the mix that is the highest contributor is ...
(mix % - low %) / (high % - low %) = (.35 -.30) / (.45 -.30) = .05/.15 = 1/3
