Answer:
The coordinates of point S are (5, 9) will make line PQ // line RS ⇒ A
Step-by-step explanation:
<em>Parallel lines have the same slopes</em>
The slope of a line = Δy/Δx, where
Let us first find the slope of the line PQ.
∵ P = (-2, -2) and Q = (0, 7)
∴ Δx = 0 - (-2) = 0 + 2 = 2
∴ Δy = 7 - (-2) = 7 + 2 = 9
∴ The slope of PQ = 9/2
∵ Line PQ // line RS
∴ The slope of line PQ = the slope of line RS
∴ The slope of line RS =9/2
∵ Point R = (3, 0) and point S = (x, y)
∵ The slope of line RS = 9/2
∵ The slope = Δy/Δx
∴ Δy/Δx = 9/2
→ That means Δy = 9 and Δx = 2
∵ Δy = y - 0
∵ Δy = 9
∴ 9 = y
∵ Δx = x - 3
∵ Δx = 2
∴ 2 = x - 3
→ Add 3 to both sides
∴ 2 + 3 = x - 3 + 3
∴ 5 = x
∴ The coordinates of point S are (5, 9) will make line PQ // line RS
Answer:
372 in ^2
Step-by-step explanation:
Wrapping a present is surface area
SA = 2( lw+wh+hl)
= 2 ( 12*3 + 12*10 + 3*10)
= 2 ( 36+120+30)
= 2 (186)
= 372 in ^2
Answer:
(a) 1, 2, 3, 6, 8
Step-by-step explanation:
Given
Required
The sequence of hours worked each day
<em>See attachment for options</em>
From the question, we understand that:
This means that, the middle number is 3 (when sorted)
So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively
Next, is to determine the mean of (a) and (d)
The mean of a data is calculated as:
So, we have:
(a)
(d)
Option (a) is true, because it has:
Answer:
area is
Step-by-step explanation:
1 3/5 - 5/6 = 23/
30
≅ 0.7666667
Answer:
Question 1: 71 and 72
Question 2: Child 1: 60 lbs, Child 2: 15 lbs
Step-by-step explanation:
Question 1:
Consecutive numbers are 2 numbers right next to each other.
You know the numbers will have to be double digits number.
71 and 72 are consecutive numbers. The sum of them is 143.
71+72=143
Question 2:
For this problem, we can use system of equations to find the mass of the 2 children. Let's say x is the first child and y is the second child.
Equation 1
x+y=75
This equation comes from the combined mass of the 2 children.
Equation 2
x=4y
This equation comes from the first child being 4 times the mass of the second child.
Since we know the value of x, we can use substitution to find y.
4y+y=75
5y=75
y=15
Now that we know the second child is 15 lbs, we can plug this into any of the 2 equations to find the mass of the first child.
x=4(15)
x=60