Answer:
(B) 26°
Step-by-step explanation:
The angle at A made by the radius and the tangent is 90°. The angle at O is the same as arc AB, 64°. The acute angles in a right triangle are complementary, so the angle at C is the complement of 64°.
∠ACB = 90° -64°
∠ACB = 26°
Step-by-step explanation:
The GCF of 28 and 80 is 4.
<u>Distribute 4 for 28 and 80, then solve:</u>
Answer: Numbers of servings: 10 and 13, Liters of punch: 14
Step-by-step explanation:
Number of servings - 6 = Liters of punch.
Answer: 2mp
Step-by-step explanation: Let "b" represent the speed of the boat in still water
Let "c" represent the speed of the current
Let "t" represent time
Downstream(same direction) =(b+c)*t
Upstream(against current)=(b-c)*t
(b+c)*3=24
(b-c)*4=16
3b+3c=24....all sides can be divided by 3 =b+c=8
4b-4c=16.....all sides can be divided by 4 =b-c=4
Use Elimination method
b+c=8
b-c= 4 Subtracting
=====
2c=4
find c by dividing both sides by 2. c=2
if c=2, substitute to get b
b+2=8
-2=-2
======
b=6
Speed of boat in still water =6mph
rate of current=2mp
Answer:
The values of x and y are x = 6 and y = 9Step-by-step explanation:
MNOP is a parallelogram its diagonal MO and PN intersected at point A
In any parallelogram diagonals:
Bisect each other
Meet each other at their mid-point
In parallelogram MNOP
∵ MO and NP are its diagonal
∵ MO intersect NP at point A
- Point A is the mid-point pf them
∴ MO and NP bisect each other
∴ MA = AO
∴ PA = AN
∵ MA = x + 5
∵ AO = y + 2
- Equate them
∴ x + 5 = y + 2 ⇒ (1)
∵ PA = 3x
∵ AN = 2y
- Equate them
∴ 2y = 3x
- Divide both sides by 2
∴ y = 1.5x ⇒ (2)
Now we have a system of equations to solve it
Substitute y in equation (1) by equation (2)
∴ x + 5 = 1.5x + 2
- Subtract 1.5x from both sides
∴ - 0.5x + 5 = 2
- Subtract 5 from both sides
∴ - 0.5x = -3
- Divide both sides by - 0.5
∴ x = 6
- Substitute the value of x in equation (2) to find y
∵ y = 1.5(6)
∴ y = 9
The values of x and y are x = 6 and y = 9
