Answer:
In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).
Step-by-step explanation:
There is really no need to use any quadratics or roots.
( Consider the same problem on the plain number line first. )
How do you find the number between 2 and 5 which is twice as far from 2 as from 5?
You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get
4=2+23(5−2)
It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then
R=P+23(Q−P)
so in your case we get
R=(0,−1)+23(3,3)=(2,1)
Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)
Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get
s=a+b=2b+b=3b
⇔b=13s⇒a=23s
Answer:
Option B is correct, i.e. The amount of water originally in Wilson's can was 2.5 gallons.
Step-by-step explanation:
Given is the graph of Amount of water (in gallons) v/s Time (in seconds).
It is a linear graph whose general equation is given as follows:-
y=mx+b.
Where y = Amount of water, x = Time, m = slope, b = y-intercept (when time is zero).
Finding slope of line, m = (2.3 - 2.5)/(1 - 0) = -0.2 gallons per second.
Finding y-intercept of line, b = 2.5 gallons (at t=0).
Hence, option B is correct, i.e. The amount of water originally in Wilson's can was 2.5 gallons.
Answer:
(6,5)
Step-by-step explanation:
The equation is in point slope form: 
'm' is the slope.
(x1, y1) is the point used to create the equation.
The number 6 replaces the x1 spot.
The number 5 replaces the y1 spot.
So a point that lies on the line should be (6,5).
1) Zoe's town
April = 5 7/8 inches
May = 2 1/8 inches less than in April
5 7/8 ⇒ ((5*8)+7)/8 = 47/8
2 1/8 ⇒ ((2*8)+1)/8 = 17/8
47/8 - 17/8 = 30/8 ⇒ 3 6/8 ⇒ 3 3/4 inches rainfall in May.
April rainfall : 5 7/8 inches
May rainfall : 3 3/4 inches
Greatest Prime number less than 50 is 47. So, 47 students plus 3 teachers. There is a total of 50 people going on the trip.
1,354 ounces of paint ÷ 6 ounces per jar = 225.66 jars or 226 jars
