Answer:
6.13
Step-by-step explanation:
Using Sine Law we know that
![\dfrac{a}{SinA}=\dfrac{b}{SinB}=\dfrac{c}{SinC}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%7D%7BSinA%7D%3D%5Cdfrac%7Bb%7D%7BSinB%7D%3D%5Cdfrac%7Bc%7D%7BSinC%7D)
Using your figure let's assign sides and angles:
A=? B = 60° C = 70°
a = 5 b = ? c = x
If we put that into our formula:
![\dfrac{5}{Sin?}=\dfrac{?}{Sin60}=\dfrac{x}{Sin70}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7BSin%3F%7D%3D%5Cdfrac%7B%3F%7D%7BSin60%7D%3D%5Cdfrac%7Bx%7D%7BSin70%7D)
Notice that we have too many unknowns. We need to complete at least one ratio to do this, so how do we do this?
Notice we have 2 angles given, so we solve for the third angle. The sum of all angles in any triangle is always 180°
∠A + ∠B + ∠C= 180°
∠A + 60° + 70° = 180°
∠A + 130° = 180°
∠A = 180° - 130°
∠A = 50°
Now we can use this to solve for x.
![\dfrac{5}{Sin50}=\dfrac{x}{Sin70}\\\\\dfrac{(5)(Sin70)}{Sin50} = x\\\\\dfrac{4.6985}{0.7660}=x\\\\6.1338 =x](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7BSin50%7D%3D%5Cdfrac%7Bx%7D%7BSin70%7D%5C%5C%5C%5C%5Cdfrac%7B%285%29%28Sin70%29%7D%7BSin50%7D%20%3D%20x%5C%5C%5C%5C%5Cdfrac%7B4.6985%7D%7B0.7660%7D%3Dx%5C%5C%5C%5C6.1338%20%3Dx)
So the closest answer would be 6.13
Answer:
x=38.5
Step-by-step explanation:
![\sqrt{23^{2}- 18^{2}} =\sqrt{205}](https://tex.z-dn.net/?f=%5Csqrt%7B23%5E%7B2%7D-%2018%5E%7B2%7D%7D%20%20%20%3D%5Csqrt%7B205%7D)
cos(x)=![\frac{18^{2} +23^{2} -205}{2(18)(23)}](https://tex.z-dn.net/?f=%5Cfrac%7B18%5E%7B2%7D%20%2B23%5E%7B2%7D%20-205%7D%7B2%2818%29%2823%29%7D)
x=38.5(correct to the nearest tenth)
Answer:
10.75
Step-by-step explanation:
To get the average, we always SUM UP all the numbers and divide by the number of numbers.
We do this for "change" row since we want average of "change".
Let's add up all the changes:
11 + 12 + 10 + 10 + 11 + 10 + 11 = 75
How many numbers are there?
There are 7 numbers
Now, the average:
Average = Sum/Number of Numbers
Average = ![\frac{75}{7}=10.75](https://tex.z-dn.net/?f=%5Cfrac%7B75%7D%7B7%7D%3D10.75)
The average = 10.75
Answer:
D
Step-by-step explanation:
I tried the last one and it did not work so maybe D