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:
Yvette cleared 10 large driveways
Step-by-step explanation:
small driveway = x
big driveway = y
x+y = 25
15x + 25y = 475
y = 25-x
15x + 25(25-x) = 475
-10x + 625 = 475
10x = 150
x= 15
15 + y = 25
y =10
10 large driveways, 1 5 small driveways
Answer:
y=-1/4x
Step-by-step explanation:
METHOD 1: The basic slope-intercept equation is <em>y=ax+b</em>. To achieve the slope with two points, this is the equation:

All you have to do is insert points (-4, 1) and (4, -1) into their corresponding locations.

With this equation, you will be able to find the slope. Then you can simply graph it to connect the two dots.
METHOD 2: Simply connect the two dots with a straight line (use a ruler or something with a straight edge.) Then count how many spaces up/down and left/right. If the line goes from top to bottom from left to right, it is a negative slope (hence, the -1/4.)
Answer:
(a) The net change of the function is 12.
(b) The average rate of change of the function 4.
Step-by-step explanation:
The average rate of change of function
over the interval
is given by this expression:
average rate of change = 
It is a measure of how much the function changed per unit, on average, over that interval.
Given:

(a) To find the net change of the function, first we calculate the values of
and 

The net change is simply the difference

(b) The average rate of change takes the net change and divides it by the change in the
value.
