Answer:
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
Step-by-step explanation:
Given:
Let
A(x₁ , y₁) = (1 , 4) and
B( x₂ , y₂ ) = (-1 , 2)
To Find:
θ = ?
Solution:
Slope of a line when two points are given is given bt

Substituting the values we get

Also Slope of line when angle ' θ ' is given as

Substituting Slope = 1 we get


We Know That for angle 45°,
tan 45 = 1
Therefore

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
So first convert to improper fractions
7 and 7/8=7+7/8=56/8+7/8=63/8
3 and 1/4=3+1/4=12/4+1/4=13/4
so nowe we have
63/8+13/4
convert bottom number to same
which is 8
13/4 times 2/2=26/8
now we have
63/8-26/8=37/8=4 and 5/8
answer is 4 and 5/8
answer
10
step-by-step explanation
the equation given is sin(x) = cos(y) with x = 2k + 3 and y = 6k + 7
substitute in 2k+ 3 for x in sin(x) and substitute in 6k + 7 for y in cos(y)
sin(x) = cos(y)
sin(2k + 3) = cos(6k + 7)
we know that sin(x) = cos(90 -x)
sin(2k + 3)
= cos(90 - (2k + 3) )
= cos(90 - 2k - 3)
= cos(87 - 2k)
substitute this into the equation sin(2k + 3) = cos(6k + 7)
sin(2k + 3) = cos(6k + 7)
cos(87 - 2k) = cos(6k + 7)
87 - 2k = 6k +7
80 = 8k
k = 10
1. False
2. True
3. False
4. False??