Solve the simultaneous equations 3x+y=172 x+y=12
1 answer:
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Answer:
(x, y) = (80, -68)
Step-by-step explanation:
Subtract the second equation from the first.
(3x +y) -(x +y) = (172) -(12)
2x = 160 . . . . . . . . . simplify
x = 80 . . . . . . . . . divide by 2
y = 12 -x = 12 -80 = -68 . . . . . find y from the second equation
The solution is (x, y) = (80, -68).
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Answer:
1.5 seconds
Step-by-step explanation:
Since f(x) represents the distance from the ground to the rock (in feet), we just need to find the values of x for which f(x) = 340. Substituting f(x) = 340 into f(x) = -16x² - 4x + 382 gives us:
340 = -16x² - 4x + 382
0 = -16x² - 4x + 42 (Subtract 340 from both sides)
16x² + 4x - 42 = 0 (Multiply entire equation by -1, "flip" equation)
8x² + 2x - 21 = 0 (Divide entire equation by 2)
(4x + 7)(2x - 3) = 0 (Factor LHS)
4x + 7 = 0 or 2x - 3 = 0 (Zero Product Property)
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or
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Answer:
The first one
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan30° = =
=
Multiply both sides by 8
8 × tan30° = b, that is
b = 8tan30°