1. D
2. A
3. A
Hope it helps!
Answer:
D. angle 7 and angle 5.
Step-by-step explanation:
It is actually option 'D.' This is because angle 7 and angle 5 are vertical angles; vertical angles are always congruent.
Answer:
Step-by-step explanation:
It is convenient to let technology help out. Some graphing calculators will accommodate a model of your choice. Others are restricted to particular models, of which yours may not be one.
A spreadsheet solver may also offer the ability to optimize two variables at once. For that, you would write a function that gives the sum of the squares of the differences between your data points and those predicted by the model. You would ask the solver to minimize that sum.
If you want to do this "the old-fashioned way," you would write the same "sum of squares" function and differentiate it with respect to m and b. Solve the simultaneous equations that make those derivatives zero. (My solver finds multiple solutions, so the neighborhood needs to be restricted in some way. For example m > 0, b > 0, or sum of squares < 1.)
Rearrange the equation as
cos(x) - √(1 - 3 cos²x) = 0
cos(x) = √(1 - 3 cos²x)
Note that both sides have to be positive, since the square root function is non-negative. If we end up with any solutions that make cos(x) < 0, we must throw them out.
Take the square of both sides.
(cos(x))² = (√(1 - 3 cos²(x))²
cos²(x) = 1 - 3 cos²(x)
4 cos²(x) = 1
cos²(x) = 1/4
cos(x) = ± √(1/4)
cos(x) = ± 1/2
We throw out the negative case and we're left with
cos(x) = 1/2
This has general solution
x = arccos(1/2) + 360° n or x = -arccos(1/2) + 360° n
(where n is any integer)
x = 60° + 360° n or x = -60° + 360° n
Now just pick out the solutions that fall in the interval 0° ≤ x < 360°.
• From the first solution set, we have x = 60° when n = 0.
• From the second set, we have x = 300° when n = 1.
So the answer is D.
Answer:
Slope=0.10
Interpretation: For every minute Olivia is in the cafe she is getting charged 10 cents
Step-by-step explanation:
The slope is a constant followed by a variable (a,x,b,z,etc...) So the only constant with a variable after it was the 10.
