We'll assume this is an arbitrary triangle ABC.
A) No, the sines of two different angles can be whatever they want
B) sin(B)=cos(90-B)
Yes, that's always true. The "co" in cosine means "complementary" as in the complementary angle, which adds to 90. So the sine of an angle is the cosine of the complementary angle.
C) No, the correct identity is sin(180-B)=sin B. Supplementary angles share the same sine.
D) Just like A, different triangle angles often have different cosines.
Answer: Choice B
In order to solve this problem, use sign conventions. Since deposit indicates cash inflow, that would take the positive sign. On the other hand, withdrawals take negative sign. We add these integers to the original balance. he solution is as follows:
$100 + $25 + $50 + $15 + (⁻$40) =<em> $150</em>
Mom drove for 11 hours.
Dad drove for 3 hours.
<u>Step-by-step explanation</u>:
- Total distance = 895 miles
- Mom drove a speed of 65 mph
- Dad drove a speed of 60 mph
Let 'x' be the number of hours drove by mom.
Let 'y' be the number of hours drove by dad.
x + y = 14 ---------------(1)
65x + 60y = 895 ---------(2)
Multiply eq(1) by 60 and subtract eq(2) from (1),
60x + 60y = 840
-(<u>65x + 60y = 895</u>)
<u> -5x = -55 </u>
x = 55/5
x = 11
∴ Mom drove for 11 hours.
Substitute x=11 in eq(1)
11+y = 14
y = 3
∴ Dad drove for 3 hours.
