See the picture attached to better understand the problem
we know that
A quadrilateral is called Cyclic quadrilateral <span>if its all vertices lie on the circle.
</span><span>The opposite angles of a Cyclic - quadrilateral are supplementary
</span>so
∠A+∠C=180°
and
∠
B
+∠D=180°
therefore
the answer is<span>
C) The sum measure of ∠B and ∠D equals 180°</span>
Problem: A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? How much does each person cost? Show this using y = mx + b form.
Solution:
Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.
Then, when there are 30 people on the bus (x = 30), the cost was $180 (y = 180). This means the point (x, y) = (30, 180).
Also, when there were 50 people on the bus, the cost was $220. So that is the point (50, 220).
You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.
The slope of the line joining two points is the rise divided by the run. That means
m = (y2 - y1) / (x2 - x1)
So we put in the values of (30, 180) and (50, 220):
m = (220 - 180) / (50 - 30)
m = 40 / 20
m = 2.
The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:
y = 2x + b.
This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:
220 = 2(50) + b
220 = 100 + b
b + 100 = 220
b = 120.
Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:
y = 2x + 120.
For the other questions, I can look at the equation I got. The y-intercept (b value) is $120. That means that we are adding $120 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.
Here's an example: if you had just 10 people on the bus, you'd pay $120 for the empty bus and $2 for each person. That's $20 for the people and $120 for the bus. That total is $140. Let's see if (10, 140) works in the equation we got:
y = 2x + 120
140 ?=? 2(10) + 120
140 ?=? 20 + 120
yes. 140 = 140. It does work.
Now you try it with your question.
Answer:
1.92%
Step-by-step explanation:
The probability for first case, picking a queen out of deck, will be:
as there will be 4 queens in a deck, one of each suit.
For the second pick, the probability of picking a diamond card, will be:
here the total will remain 52 as he has replaced the first card and not kept it aside and there will be 13 cards in diamond suit (including the three face cards).
Thus the net probability for both cases will be:
Thus total probability for the combined two cases will be 1.92%
<u>Answer</u>
3
<u>Explanation</u>
The two lines in the diagram are secants meeting outside the circle.
The products of a secant and the extension of the chord of one line is equal to the products of a secant and the extension of the chord of the other line.
∴ 4 × 9 = x × 12
36 = 12x
x = 36/12
= 3
