Answer:
65% as a fraction would be 13/20
Step-by-step explanation:
Answer:
7.2/3 ± (isqrt2)/3
8.2±i
9.-0.4±0.2
10.1/3±1/3sqrt19
Step-by-step explanation:
7. a =3, b=-4, c=2
plugging in to the quadratic formula
(2 ± isqrt2)/3
8.a=1,b=-4.c=5
plugging in to the quadratic formula
2±i
9.a=5,b=4,c=2
plugging in to the quadratic formula
-0.4±0.2
10.a=-3,b=2,c=6
plugging in to the quadratic formula
1/3±1/3sqrt19
-5x + y = 5 . . . . . (1)
-4x + 2y = 2 . . . . (2)
(1) x 2 => -10x + 2y = 10 . . . (3)
(2) - (1) => 6x = -10 => x = -8/6 = -4/3
From (1), -5(-4/3) + y = 5 => y = 5 - 20/3 = -5/3
Therefore, x = -4/3; y = -5/3
Let L be the low copper alloy and H be the high copper alloy.
We need 0.15L + 0.60H = 0.42 and L + H = 100
L=100 - H
Substituting this into the second equation for L, we get:
0.15(100-H) + 0.60H = 0.42(H+L)
15 - 0.15H + 0.60H = 0.42(H+100-H)
15 + 0.45H = 0.42(100)
0.45H = 42 - 15 = 27
H = 27/.45 = 60 lbs
Back substitution, L = 40 lbs.
The answer is B.
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The triangles on the two ends are congruent. So, to find the prism area, it is enough to take the area of one of the triangles and multiply it by the prism depth, which is 20 units.
Use the Pythagorean theorem to find the height of the triangle. 5^2 - 3^2 = 4^2, so the height is 4. Multiply half times height times base: 1/2 x 4 x 3 = 6. Multiply that by the depth, 20. 6x20=120. The answer is in cubic units, or units^3