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°.
Answer:
x-3 ,
Step-by-step explanation:
Answer:
<h2>1</h2>
Step-by-step explanation:
Median of a dataset is the value at the centre of the dataset after rearrangement.
Given the data {8,x , 4,1}, the median of the set will be two values(x and 4). Since we have two values as the median, we will take their average.
Median of the first data set = x+4/2 ...(1)
For the second dataset {9,y , 5,2}, the median will be y+5/2
Since we are told that the medians of both datasets are equal, we will equate the value of the medians of both datasets as given below;
x+4/2 = y+5/2
cross multiplying;
2(x+4) = 2(y+5)
Dividing both sides by 2 will give;
x+4 = y+5
From the resulting equation;
y-x = 4-5
y-x = -1
(y-x)² = (-1)² = 1
Answer:
x = 26
Step-by-step explanation:
m<RTS = 4x - 14 (given)
Based on the inscribed angle theorem, the measure of the inscribed angle in a semicircle = right angle (90°)
Therefore,
4x - 14 = 90
4x - 14 + 14 = 90 + 14 (addition property of equality)
4x = 104
4x/4 = 104/4
x = 26
Answer:
k=8192
Step-by-step explanation:
The number of teams,t remaining after each round, r, can be expressed as:
- 8 Teams will advance to the quarterfinals.
First, we determine the round,r at which there will be 8 teams left.
Using this value of r