Given
∠ABC is an inscribed angle
Find out the m∠BDA and m∠BCA .
To proof
First find the value of the central angle ( intercepted arc measure BA)
∠BOA = 360° - 250°
= 110 °
Thus the intercepted arc AB is of measure 110°
FORMULA

thus putting the value in the above equation
we get

∠BDA = 55°
Now find out ∠BCA
In the quadilateral AOBC
As shown in the diagram AC & BD are tangent
thus
∠CAO = 90°
∠CBO = 90°
As we know the sum of a quadilateral is 360°.
thus
∠AOB + ∠CAO + ∠CBO +∠ BCA = 360°
Put the value as mentioned above
110° +90° + 90° +∠BCA = 360°
∠BCA = 360° - 290°
∠BCA = 70°
Hence proved
Answer:
Option A. 3.5x + 15 ≥ 55
Step-by-step explanation:
Points Rosh received for becoming a member = 15
Points Rosh received for visiting the moving theater = 3.5
Total points needed for a free movie ticket = 55
For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.
Total points = Points received on becoming a member + Points received on x visits
So,
Total Points = 15 + 3.5x
These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:
3.5x + 15 ≥ 55
So, option A gives the correct answer
Answer:
Step-by-step explanation:
The density of an object can be found by taking its mass and dividing by its volume.
Hence if density is D , Mass is M and Volume is V

a)
M = 500 gms
V = 40 cubic cm

b)
M = 125 gms
V = 1.4 cubic cm


D =89.28 gm per cc
Answer:
The length of side st is 15.
Step-by-step explanation:
A tangent is a straigth line that touches a circle externally at a point on the circumference. Considering one of its properties that tangents from the same point to a fixed point outside a circle are equal.
Then,
/rn/ = /rp/
/tm/ = /tn/
/sm/ = /sp/
But, /rp/ = 7, /rt/ = 17 and /sm/ = 5.
Then,
/rt/ = /rn/ + /tn/
17 = 7 + /tn/ (∵ /rp/ = /rn/ = 7)
⇒ /tn/ = 10
Since /nt/ = 10, then /tm/ = 10 (/tm/ = /nt/)
So that,
/st/ = /sm/ + /tm/
= 5 +10
/st/ = 15
The length of side st is 15.
Answer:
StartRoot 53 EndRoot units
XY = √53
Step-by-step explanation:
Choose which is point 1 and point 2 so you don't confuse the coordinates.
Point 1 (–4, 0) x₁ = –4 y₁ = 0
Point 2 (3, 2) x₂ = 3 y₂ = 2
Use the formula for the distance between two points.




Therefore the line of segment XY is √53.