Answer:
19. C
20. D
21. B
22. A
Step-by-step explanation:
If an angle is subtended from an arc and it goes to the opposite end of the circle, the angle is HALF of the measure of the arc. If it goes to the center, it is SAME measure as arc.
19.
Arc BC is DOUBLE of Angle BAC, so
78 * 2 = 156
Answer is C
20.
Arc BEC is DOUBLE of Angle BAC, so
114 * 2 = 228
Answer is D
21.
Angle ABC is HALF of Arc AC, so
Angle ABC = 110/2 = 55
Answer is B
22.
Angle ABC is HALF of Arc AC, so
Angle ABC = 218/2 = 109
Answer is A
Answer:
They are currently ranked 5.
The reason so many objects orbit the Sun in nearly the same plane (called the ecliptic) and in the same direction is that they all formed from this same disk.
While the planets were forming, there was not much peace in our solar system. Clumps of matter of all sizes often collided, and either stuck together or side-swiped each other, knocking off pieces and sending each other spinning. Sometimes the gravity of big objects would capture smaller ones in orbit. This could be one way the planets acquired their moons.
Answer:
The solutions of the equation |2 x-3|=17
are x=10
and x=-7
Step-by-step explanation:
Given equations is |2 x-3|=17.
It is required to find out the values of x satisfying the given equation.
To find it out, use the fact that the solution of this type of equation is 2x-3=17.
Or 2x-3=-17 and simplify the equations using simple mathematical operations.
Step 1 of 2
Solve the equation 2x-3=17,
Add 3 on both sides of the equation 2x-3=17,
2x-3+3=17+3
2x=20
Divide by 2 on both sides of the equation 2x=20,
Step 2 of 2
Solve the equation 2x-3=-17,
Add 3 on both sides of the equation 2x-3=-17,
Divide by 2 on both sides of the equation 2x=-14,
If the amount of monkeys is m, lions is a, and lizards is b, then a+b+m=151, 17+a=m (since there are 17 more monkeys than lions), and 30+a=b. Substituting those values in (17+a=m and 30+a=b), we have 30+17+a+a+a=151=47+3a. Subtracting 47 from both sides, we get 104=3a. Next, we can divide both sides by 3 to get 104/3=a (the number of lions), 104/3+17=the number of monkeys, and 104/3+30=the number of lizards. Somehow we end up with a fraction (not a whole number), so there are 2/3rds of monkeys floating around using this logic.
