Answer:
x = -8
Step-by-step explanation:
I will show each step algebraically. If you need further explanation, feel free to ask questions :)
Rewrite
Subtract 7
Multiply by reciprocal (2/1)
I hope this helps!
Answer:
5x+8
Step-by-step explanation:
Answer:
∠A ≈ 66°
∠B ≈ 24°
AC ≈ 1.2
Step-by-step explanation:
SOH CAH TOA and the Pythagorean theorem are useful tools for solving right triangles. The first tells you ...
Sin = Opposite/Hypotenuse
For ∠A, that means ...
sin(A) = BC/AB = 2.7/2.95
The inverse sine function (sin⁻¹ or arcsin) is used to find the angle from its sine value, so ...
A = arcsin(2.7/2.95) ≈ 66°
Likewise, the ratio for angle B involves the adjacent side:
Cos = Adjacent/Hypotenuse
cos(B) = BC/AB = 2.7/2.95
B = arccos(2.7/2.95) ≈ 24°
Of course, angles A and B are complementary, so once you know angle A, you know that angle B is ...
∠B = 90° -∠A = 90° -66° = 24°
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The Pythagorean theorem can be used to find the unknown side. It tells you ...
AB² = AC² + BC²
2.95² = AC² + 2.7²
AC = √(2.95² -2.7²) ≈ 1.2
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These calculations are shown in the attachment using a TI-84 graphing calculator set to degrees mode. Any scientific or graphing calculator will do.
Answer:
He would gain by choosing air travel if, and only if, he values his time at more than $5 per hour.
Step-by-step explanation:
The problem states that:
A bus ticket from Washington to St. Louis costs $100, while it takes 32 hours to arrive.
A plane ticket from Washington to St. Louis costs $250, while it takes 2 hours to arrive.
Other things constant, Andrew would gain by choosing air travel if, and only if, he values his time at more than
If Andrew choses to go by plane, he saves 32-2 = 30 hours at the expense of $250-$100 = $150.
So, dividing the extra cost by the number of hours saved:
He would gain by choosing air travel if, and only if, he values his time at more than $5 per hour.