<h3>
Answer: perpendicular slope is -2/3</h3>
=================================================
Work Shown:
Solve the given equation for y
2y = 3x - 10
y = (3x-10)/2 ..... divide both sides by 2
y = (3x)/2 - 10/2
y = (3/2)x - 5
The equation is in y = mx+b form with m = 3/2 as the slope.
The perpendicular slope is -2/3 because we flip the fraction and the sign from positive to negative.
Note how multiplying the original slope 3/2 and the perpendicular slope -2/3 leads to -1
(3/2)*(-2/3) = -1
This is true for any pair of perpendicular lines, assuming neither line is vertical.
The closest distance up the tree where the wire reaches is 17.93 foot.
<u>Explanation:</u>
Given-
Length of the wire, L = 12 foot
angle, Ф= 48°
Distance upto which the wire reaches the tree, x = ?
We know,
cos Ф = base/ hypotenuse
cos 48° = 12/ x
0.669 = 12/x
x = 17.93 foot
Therefore, the closest distance up the tree where the wire reaches is 17.93 foot.
Answer: 24 min
Step-by-step explanation:
2 hrs / 5 carts = 120 min / 5 carts
120 / 5 = 24 min / 1 cart
A.
If we take 7 paintings to be hung in 7 spaces side by side, the first space can have any one of the 7 paintings, the second space can have any one of the remaining 6 paintings (as 1 is already hung), the third space can have any one of the remaining 5 paintings (as 2 already hung)...It goes on like this.
So we have 
ways to arrange all the paintings from left to write. <em>(in factorial notation it is 7!=5040)</em>
B.
We use combinations rather than permutations because order doesn't matter. If we name the paintings A,B,C,D,E,F, and G, groups of 3 paintings of ABC or ACB are the same. So we evaluate 
using the combination formula,
We have,
C.
This is similar to part A in some ways. Any 3 pictures can be arranged in 
different ways. 
. So, 6 different ways.
ANSWER:
A) 5040 ways
B) 35 different groups
C) 6 ways
