Answer:
(2, 1 )
Step-by-step explanation:
Given the 2 equations
y = 6x - 11 → (1)
- 2x - 3y = - 7 → (2)
Substitute y = 6x - 11 into (2)
- 2x - 3(6x - 11) = - 7 ← distribute and simplify left side
- 2x - 18x + 33 = - 7
- 20x + 33 = - 7 ( subtract 33 from both sides )
- 20x = - 40 ( divide both sides by - 20 )
x = 2
Substitute x = 2 into (1) for corresponding value of y
y = 6(2) - 11 = 12 - 11 = 1
Solution is (2, 1 )
Answer: To find the critical value, follow these steps.
Compute alpha (α): α = 1 - (confidence level / 100)
Find the critical probability (p*): p* = 1 - α/2.
To express the critical value as a z-score, find the z-score having a cumulative probability equal to the critical probability (p*).
Step-by-step explanation:
<h3>
Answer: Approximately 13 square units (choice B)</h3>
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Explanation:
The given reflex angle is 215 degrees. A reflex angle is anything over 180 degrees, but less than 360. Subtract 215 from 360 to get the measure of angle AOB
angle AOB = 360 - 215 = 145
angle AOB = 145 degrees
We'll use this later.
Now find the area of the full circle. Use the formula A = pi*r^2. The radius is r = sqrt(10) which can be found through the distance formula or the pythagorean theorem. You want to find the length of either OA or OB to get the radius.
The area of the circle is
A = pi*r^2
A = pi*(sqrt(10))^2
A = 10pi
This is the exact area of the full circle, but we want just a fractional portion of it. Specifically we want the pie slice that is formed by angle AOB
area of sector AOB = [ (angle AOB)/360 ] * (area of full circle)
area of sector AOB = (145/360)*10pi
area of sector AOB = 145pi/36
area of sector AOB = 145*3.14/36
area of sector AOB = 12.647 approximately
area of sector AOB = 13 square units approximately, after rounding to the nearest whole number
Answer:
x=8
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
