Answer:
Step-by-step explanation:
Given: quadrilateral ABCD inscribed in a circle
To Prove:
1. ∠A and ∠C are supplementary.
2. ∠B and ∠D are supplementary.
Construction : Join AC and BD.
Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,
∠1=∠2-----(1)
∠3=∠4-----(2)
∠5=∠6-------(3)
∠7=∠8------(4)
Also, sum of angles of quadrilateral is 360°.
⇒∠A+∠B+∠C+∠D=360°
→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4
→→→2∠1+2∠4+2∠6+2∠8=360°
→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,
→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)
As, ∠A+∠B+∠C+∠D=360°
∠A+∠C+180°=360°
∠A+∠C=360°-180°------Using A
∠A+∠C=180°
Hence proved.
credit: someone else
Answer:
1.5 cm/s
Step-by-step explanation:
The unit rate is the same as the slope.
To find the slope, we use the slope formula:

Using our points, we have
m = (9-0)/(6-0) = 9/6 = 3/2 = 1.5 cm/s
Answer:
but its right
Step-by-step explanation:
Answer:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): 
Alternative hypothesis (H1): 
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no
Step-by-step explanation:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): 
Alternative hypothesis (H1): 
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no
F(x) = 2x² - 8x - 10.
This is a parabola open upward (since a>0) with an axis of symmetry = -b/2a:
a) axis of symmetry: x = -(-8)/(2*2) = 8/4 = 2. Then x = 2, which is the x component of the vertex
b) for x = 2, f(x) = f(2) = - 18 (component of y of the vertex)
c) VERTEX(2, - 18)
d) DISCRIMINENT: b² - 4.a.c = 64 - 4*2*(-10) = 144