Answer:
Refer the digram & explanation.
Step-by-step explanation:
<u>GIVEN :-</u>
- Tangents PQ & PR drawn to a circle with center O from an external point P.
<u>TO PROVE :-</u>
<u>CONSTRUCTION :-</u>
<u>FACTS TO KNOW BEFORE SOLVING :-</u>
- (Angle at which tangents are inclined to each other from the external point) + (Angle the tangents subtend at the center of the circle) = 180°.
<u>PROCEDURE :-</u>
∠QPR + ∠QOR = 180°
⇒ ∠QOR = 180° - ∠QPR
In ΔQOR , OQ = OR (∵ Radii of the circle are equal)
⇒ ΔQOR is an isosceles triangle (∵ OQ = OR i.e. two sides of the triangle are equal.)
⇒ ∠OQR = ∠ORQ (∵ In an isosceles triangle , the base angles are equal)
So,
∠QOR + ∠OQR + ∠ORQ = 180°
⇒ ∠QOR + 2∠OQR = 180° (∵ ∠OQR = ∠ORQ)
⇒ 180° - ∠QPR = 180° - 2∠OQR (∵ ∠QPR + ∠QOR = 180°)
⇒ -∠QPR = -2∠OQR (∵ Cancelling 180° from both the sides.)
⇒ ∠QPR = 2∠OQR (Proved)
Step-by-step explanation:
looking at the diagram, AC is the hypotenuse, AD is the adjacent and CD is the opposite (based on the position of the angle).
Since you are looking for CD, you would use Sine (SOHCAHTOA). Sine would be opposite over hypotenuse and following the same procedure, you will the cross multiply to get your answer
We are going to denote the number of additional minutes with
, and the total cost of the call with
.
From PONCO, we know that they charge $1.25 for the first minute, and $0.30 for each additional minute; knowing that our additional minute is
and our total cost of the call is
, we can set up an equation to relate the values:
we are going to call this equation (1)
From CowBell, we know that they charge 1.40 for the first minute, and $0.25 for each additional minute. so just like before we can set up an equation to relate the values:
We are going to call this equation (2)
Since the total cost
of equations (1) and (2) is the same, we can equate them to find
:
We can conclude that after 3 additional minutes the cost of the calls will be the same; therefore, the correct answer is
B.
Answer:
Step-by-step explanation:
Given that from a well shuffled set of playing cards (52 in number) a card is drawn and without replacing it, next card is drawn.
A - the first card is 4
B - second card is ace
We have to find probability for
P(A) = no of 4s in the deck/total cards =
After this first drawn if 4 is drawn, we have remaining 51 cards with 4 aces in it
P(B) = no of Aces in 51 cards/51 =
Hence
(Here we see that A and B are independent once we adjust the number of cards. Also for both we multiply the probabilities)
The slope of AB and the slope of DC based on the information about the coordinate will be -2 and -2 respectively.
<h3>How to illustrate the information?</h3>
From the information given, we are told to use the slope formula along with the coordinates of points A, B, C, and D to find the slope.
The slope of AB based on the information will be:
= (-1 -3)/(-1 --3)
= -4/2
= 2
The slope of DC will be:
= 2-6/(1 --1)
= -4/2
= -2
Therefore, the slope of AB and the slope of DC based on the information about the coordinate will be -2 and -2 respectively.
Learn more about coordinate on:
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