Answer:
a = 4
b = 2√3
Step-by-step explanation:
Here, we want to get the missing side lengths
We start by looking at the values that we are given
from the question, a faces the right-angle and is called the hypotenuse; it is also the longest side
b faces the angle given and is also called the opposite
Lastly, the side marked 2 is the adjacent side
Now, the triangle given is called a 30-60-90 triangle
In a 30-60-90 triangle, the ratio of the sides are given as
1: √3:2
Thus, we have 1 as the adjacent
The opposite would be √3 * 2 = 2 √3 = b
Lastly , a = 2 * 2 = 4
9514 1404 393
Answer:
- C. (-∞, -2)∪(-2, 1)∪(1, ∞)
- A. The first 12 are $2 ea; $1 ea after
Step-by-step explanation:
1. The denominator in the first part of the function definition factors as ...
x² +x -2 = (x -1)(x +2)
This has zeros at x = -2 and x = 1, which will be values of x excluded from the domain. (These zeros are in the domain x < 2, which is applicable to this part of the function definition.)
The second part of the function definition is defined for all x ≥ 2, so the only exclusions are x = -2 and x = 1. The domain of the piecewise function is ...
(-∞, -2)∪(-2, 1)∪(1, ∞)
__
2. It is helpful to take a look at the graph to see what the axis labels are. The x-axis is labeled "number of cupcakes", so "12" on that axis means "12 cupcakes". The y-axis is labeled "total cost", which we are to presume is in dollars. That means the slope of the graph is Δy/Δx = "dollars per cupcake", the cost of one cupcake.
We observe that the slope of the graph decreases at x=12. This means the cost of a cupcake goes down after 12 are purchased. The appropriate description is ...
The first 12 cupcakes cost $2 each, and all cupcakes after that cost $1 each.
(The other choices have either increasing slope at the breakpoint, or a different breakpoint, or both, so cannot be right.)
9514 1404 393
Answer:
13 cm, 39 cm, 39 cm
Step-by-step explanation:
If x is the short side, then the other two sides are 3x and 3x. The perimeter is the sum of side lengths:
x +3x +3x = 91
x = 91/7 = 13
3x = 3(13) = 39
The length of the short side is 13 cm; the other two sides are 39 cm.
This is simply a word problem that needs to be brought into the form of an equation and then solved. Since there is only one unknown variable in the form of "x" and one equation, so it is possible to find the value of "x".
Let us assume the unknown number to be = x
Then
(3x/5) + (x/4) = 34
(12x + 5x)/20 = 34
17x/20 = 34
17x = 34 * 20
17x = 680
x = 680/17
= 40
So the unknown number in the question is 40. I hope the procedure is clear to you and in future it will not be a problem for you to solve such questions.