Question 1. Midpoint
Answer: M(-2,4)
Explanation:
1) The coordinates of the midpoint, M (x,y) between two points (x₁,y₁) and (x₂, y₂) are:
x = (x₁ + x₂) / 2 and y = (y₁ + y₂) / 2
2) Replacing the coordinates of the given points P (-4, 1) and Q (0,7) you get:
x = (- 4 + 0) / 2 = - 2, and
y = (1 + 7) / 2 = 4
So, the answer is M (-2,4)
Question 2: The distance between the two midpoints is:
Answer: 7.21
Explanation:
1) Use the formula of distance, which is an application of Pythagora's theorem:
d² = (x₂ - x₁)² + (y₂ - y₁)²
2) Substitute values:
d² = (0 - (-4))² + (7 - 1)² = 4² + 6² = 16 + 36 = 52 ⇒ d = √52 ≈ 7.21
Answer:
Step-by-step explanation:
Short answer: C
Remark
Since b is all by itself in equation 2, Substitute it into equation 1.
2a + 3b = 5
b = a - 5 Put this result in equation 1. Be sure and use brackets.
2a + 3(a - 5) = 5 Remove the brackets.
2a + 3a - 15 = 5 Notice the -5 inside the brackets becomes - 15
Combine like terms on the left.
5a - 15 = 5 Add 15 to both sides
5a = 5 + 15
5a = 20 Divide by 5
a = 20/5
a = 4
So far, c is the only possible answer.
b = a - 5
b = 4 - 5
b = - 1
Answer:
$55.80
Step-by-step explanation:
First, find how much Janet saved by finding 1/5 of 15.50:
15.50/5
= 3.1
Find how much Rob saved by multiplying 3.1 by 12:
3.1(12)
= 37.2
Then, find the total saved amount by adding them all together:
15.50 + 3.1 + 37.2
= 55.8
So, they saved $55.80 in total
D= distance
t= time
s= speed
FORMULA
Distance= speed * time
STEP 1:
Find total distance
Jim's D + John's D= 3 miles
STEP 2:
Distance= (Jim's speed * time) + (John's speed * time)
D= 4t + 5t
3 miles= 9t
divide both sides by 9
3/9= t
reduce by 3
1/3 hour= t
STEP 3:
1 hour= 60 minutes
=1/3 * 60
=(60/3)
= 20 minutes
ANSWER: They will travel 20 minutes before they meet.
Hope this helps! If it does, please mark me brainliest! :)
