The answer would be 101
Steps:
2+8=10
10x10=100 (because of the exponent)
100+1=101
Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4
Solve the top equation for x and then substitute that into the bottom equation and solve for y:
Top equation: subtract 4 from both sides to get x = y - 4
Substitution and simplify:
y = 4(y - 4) - 10
y = 4y - 16 - 10
y = 4y - 26
-3y = -26
y = 26/3 or 8 1/3 or 8.333 (those are all the same but in different forms)
Answer:
5:40
Step-by-step explanation:
This is a problem involving the least common difference.
If you know that the red and blue trains left at the same time at 5, you know that another red train will leave at 5:08. Another blue train at 5:10.
The way to solve this will be to write out the factors of 8 and 10 and find the smallest number that they overlap.
Red:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Blue:
10, 20, 30, 40
You see that after 40 mnutes, they are both leaving the station again. After 40 minutes, at 5:40, they are both leaving.
