Answer:
A, 40.16
Step-by-step explanation:
cosθ = adjacent (BC) / hypotenuse (AB)
cos 17° = BC / 42
BC = 40.16
In constructing the equation, you need to know the following:
1. What don't we know? How many minutes you must talk to have the same cost for both calling plans. So, let x be the number of minutes.
2. What do we know? Plan 1 charges $17.50 per month plus $0.17 per minute used and Plan 2 charges $32 per month plus $0.07 per minute used.
So the equation must look like this: 17.50 + .17x = 32 + 0.07x
Solving the equation:
1. Multiply both sides by 100
(100) 17.5 + .17x = 32 + 0.07x (100)
1750 + 17x = 3200 + 7x
2. Subtract 1750 from both sides
1750 + 17x - 1750 = 3200 + 7x - 1750
17x = 7x +1450
3. Subtract 7x from both sudes
17x - 7x = 7x + 1450 - 7x
10x = 1450
4. Divide both sides by 100
10x / 10 = 1450/10
x= 145 minutes
145 minutes is the number of minutes you must talk to have the same cost for both calling plans.
First, make a dotted line through the figure, so that you have a rectangle and a triangle. Rectangle area is base times height. 15 times 6 is 90. Triangle formula fro area is base times height divided by 2. Subtract 6 from 24, because that is the height of the triangle. 18x15 is 270. 270 equals 360.
Answer:
20 units³
Step-by-step explanation:
Since<em> all dimensions are being reduced by 1/3</em>, that means that the total volume will decrease by <em>1/3 * 1/3 * 1/3 = 1/27</em> the size of its original.
That means that the new volume is 1/27 * 540 = 20 units³
Answer:
f(x) = (3x -12)/(x² -7x +12)
Step-by-step explanation:
The equation for a rational function can be written from the clues offered by the horizontal and vertical asymptotes, the y-intercept, and any "holes" in the function graph. Here, those clues are ...
- horizontal asymptote: y = 0
- vertical asymptote: x = 3
- hole: (x, y) = (4, 3)
- y-intercept: (0, -1)
__
The horizontal asymptote at y=0 tells you the denominator is of higher degree than the numerator. The vertical asymptote at x=3 tells you (x-3) is a factor of the denominator. The hole at x=4 tells you there is a factor of (x-4) in both numerator and denominator.
At this point, the function is tentatively ...
Evaluating this at the y-intercept, x=0, gives ...
f(0) = -1 = a/(0 -3) = -a/3
a = 3 . . . . . multiply by -3
Then our rational function, consistent with all of the features of the graph, is ...
