Answer:
Step-by-step explanation:
Let a represent the charges made hourly by Mechanic 1 and b represent that of Mechanic 2;
a + b = 165, a = 165 - b
10a + 5b = 1200
substitute the value of a in the second equation;
10(165 - b) + 5b = 1200
1650 - 10b +5b = 1200
1650 - 5b = 1200
-5b = 1200 - 1650
-5b = -450
b = 450/5
b = $90/hr
If mechanic 2 charged $90/hr,
a + 90 = 165
a = 165 - 90
a = $75/hr being the hourly rate charged by mechanic 1.
Answer:
A. 1/2.
Step-by-step explanation:
The ratio of the sides of a 30-60-90 triangle is 2:1:√3 where 2 is the hypotenuse. 1 is the shortest leg and √3 is the longest leg.
In the diagram we see that the longest leg is opposite the 60 degree angle.
So the longest leg is 3.5√x and the shortest leg ( from applying the ratios) = 3.5√x / √3.
and the hypotenuse is 2 * 3.5√x / √3 (using the ratios again).
So sin 30 = shortest leg / hypotenuse = 3.5√x / √3 / 2 * 3.5√x / √3
= 1/2.
Answer: 22 minutes
Step-by-step explanation: 500-170 means that he drained 330 gallons of water so 330 divided by 15 gallons a minute so you get 22 so it takes 22 minutes to have 170 gallons left in the pool
Answer:
-13t - 5z
Step-by-step explanation:
-6t + 2z - 7z - 7t
= -13t - 5z
Where p is the distance the focus is above the vertex, the equation of a parabola with vertex (h, k) can be written as
... y = 1/(4p)·(x -h)² +k
The vertex is halfway between the focus and directrix. The focus of your parabola is on the y-axis at y=6, and the directrix of your parabola is at y=-6, so the vertex of your parabola is on the y-axis at y=0. That is, the vertex is
... (h, k) = (0, 0).
The distance p from the focus at y=6 to the vertex at y=0 is 6 units, so
... p = 6.
Filling these values into the equation gives
... y = 1/(4·6)·(x -0)² +0
... y = (1/24)x²
