Answer:
1. ∠LOQ = 80°
2. ∠LRQ = 40°
3. ∠LBQ = 40°
Step-by-step explanation:
- The measure of a central angle (angle that goes to the center of the circle) is EQUAL to the ARC from which it is intercepted.
- The measure of the angle that is on opposite side, on the circumference, of the circle is HALF of the ARC from which it is intercepted.
It is given that ARC QL has a measure of 80.
- Central angle from ARC QL (with same measure) are angle LOQ only.
- Opposite angles (half of measure of ARC QL) from ARC QL (on opposite side on circumference) are angles LRQ and LBQ.
<u>1.</u>
m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.
∠LOQ = 80°
<u>2.</u>
m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.
∠LRQ = 
∠LRQ = 40°
<u>3.</u>
m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.
∠LBQ =
∠LBQ = 40°
Answer:
The inverse of f(x) is 
(x) = ± 
+ 
Step-by-step explanation:
To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where
- h =
∵ f(x) = 3x² - 3x - 2
→ Compare it with the 1st form above to find a and b
∴ a = 3 and b = -3
→ Use the rule of h to find it
∵ h = 
= 
=
∴ h =
→ Substitute x by the value of h in f to find k
∵ k = 3( )² - 3( ) - 2
∴ k = 
→ Substitute the values of a, h, and k in the vertex form above
∵ f(x) = 3(x - )² +
∴ f(x) = 3(x - )² - 
Now let us find the inverse of f(x)
∵ f(x) = y
∴ y = 3(x - )² -
→ Switch x and y
∵ x = 3(y - )² -
→ Add to both sides
∴ x + = 3(y - )²
→ Divide both sides by 3
∵ 
= (y - )²
→ Take √ for both sides
∴ ± = y -
→ Add to both sides
∴ ± + = y
→ Replace y by (x)
∴ (x) = ± +
∴ The inverse of f(x) is (x) = ± +
Because one is negative and one is positive
Answer:
1/16
Step-by-step explanation:
There is a 50% chance of it being a boy or a girl also known as 1/2
So the first baby has a 1/2 chance, same for the second, and third, Which means that there is a 1/2, then another 1/2 and another 1/2. So you would have to multiply them all, 1/2*1/2*1/2 = 1/8. For the girl, again, it is 1/2 chance of being a girl, while the other 1/2 is a boy. So 1/8*1/2 is 1/16. So the probability so the women having 3 boys then a girl, is 1/16.
Hope this helps
