Answer:
19
Step-by-step explanation:
The triangle inequality tells you the possible values of x are ...
24 -10 < x < 24 +10
14 < x < 34
There are 19 integer values of x in this range.
Answer:
c
Step-by-step explanation:
Here's how this works:
Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:
![[sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?](https://tex.z-dn.net/?f=%5Bsin%28x%29cos%28x%29%5D%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D%2B%5Bsin%28x%29cos%28x%29%5D%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%20%3D%3F)
In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:
Put everything over the common denominator now:
Since 
, we will make that substitution:
We could separate that fraction into 2:
×
and 
Therefore, the simplification is
sec(x)csc(x)
Answer:
D: 12
Step-by-step explanation:
The range is the difference between the largest value in the date minus the smallest value in the data.
In this set of numbers given, the largest value is 12 and the smallest value is 0
so: 12-0 = 12
The range of this data is 12
Answer:
57°
Step-by-step explanation:
We can see that LOM is MON + LON so we can set up an equation to find the value of x then substitute that back into MON to find the value of that angle.
→ In equations its important to keep both sides equal and do operations to both sides and not one because then if you do an operation to only one side then you have changed the equation so it's important to do operations on both sides and that's an important rule to bare in mind.
2x + 33 + 3x + 20 = 113
→ Simplify
5x + 53 = 113
→ Minus 53 from both sides to isolate 5x
5x = 60
→ Divide both sides by 5 to isolate x
x = 12
But we are not finished, we have only found the value of x not the value of MON as we were asked so we have to substitute x back into the expression to find the value of MON
2x + 33
→ Substitute x = 12 back into the expression
2 × 12 + 33
→ Simplify
24 + 33 = 57
The value of MON is 57°
Answer:
B
Step-by-step explanation:
