A point (-0.8, 0.6) will be a point on the unit circle in the second quadrant. Since it is a unit circle, its radius is 1, and we have
sin(α) = y = 0.6
cos(α) = x = -0.8
tan(α) = y/x = 0.6/-0.8 = -0.75
The angle is α = arccos(-0.8) ≈ 143.13°
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For the unit circle, the trig values are always the coordinates or their ratio as shown above, regardless of quadrant.
Answer:
1. C
2. D
Step-by-step explanation:
1.
Pattern A is adding by 2's (1 -> 3, 4 -> 6, 7 -> 9 and so on).
Pattern B is multiplying by 2's (2 -> 4, 3 -> 6, 4 -> 8 and so on).
2.
If 0.25 gallons of paint = 24 ft^2, then 1 gallon will equal?
Set up an equation:
Variable x = area of ft^2 for 1 gallon of paint
0.25/24 = 1/x
Cross multiply
0.25 × x = 24 × 1
0.25x = 24
To make calculations easier, you can convert the decimal into a fraction: 0.25 = 1/4
1/4x = 24
Multiply both sides by 4
1x = 96
x = 96 ft^2
Check your work:
0.25/24 = 1/96
0.25 × 96 = 24 × 1
24 = 24
Correct
Answer:
For this scenario, I used the elimination method. Organize the equations, so it's easier to subtract from each other. My x-variable will represent the number of hot dogs and my y-variable will represent the number of sodas.
3x+2y=213
x + y =87
We need to make sure one of the monomials are alike in each equation, so we can eliminate a variable. Distribute 3 to each number/variable in the second equation.
3x+2y=213
3(x+y=87) --> 3x+3y=261
Now we can eliminate x.
3x+2y=213
- 3x+3y=261
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-y=-48
Divide -1 to both sides to get y=48. So, you sold 48 cans of soda. Now, we can find the number of hot dogs by substituting 48 into the second equation to get x+48=87. Subtract 48 to both sides to result with x=39. So, you sold 39 hot dogs.
Answer:
I hope this helps. This is what a number line looks like and how you do it.
