Answer:
The equation of the line we want to write is 4y = -x + 22
Step-by-step explanation:
Here, we want to write the equation of a line
.
The standard equation of a straight line is given as:
y = mx + c
where m is the slope and c represents the y-intercept
Now, let’s look at the line y = 4x + 16
The slope of this line is 4
Now, the equation of the line we want to write is perpendicular to this line
When two lines are perpendicular, the product of their slopes = -1
Hence;
m * 4 = -1
m = -1/4
So the slope of the line we want to write is -1/4
Now, using the point-slope form for the new equation;
y-y1/x-x1 = m
From the point given (x1,y1) = (10,3)
Thus;
y-3/x-10 = -1/4
4(y-3) = -1(x - 10)
4y - 12 = -x + 10
4y = - x + 10 + 12
4y = -x + 22
Answer:
6.5
Step-by-step explanation:
DeltaMath
Answer:
see below
Step-by-step explanation:
To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.
The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.
D (2,2)
You could also see this on a graph, see image.
E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.
E is (-1,1)
Then we are able to calculate the slope of DE and BC.
To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.
Slope of DE:
(2-1)/(2--1)
= 1/3
Slope of BC:
(0--2)/(3--3)
=2/6
=1/3
The slopes of BC and DE are equal, so the segments are parallel.
(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)
Answer:
y = 21
x = 74
Step-by-step explanation:
-x + 4y = 10
x - 3y = 11
Let the first eqn be eqn 1 and the second be eqn 2
ie
- x + 4y = 10 --------eqn 1
x - 3y = 11 ----------eqn 2
From eqn 1, make x the subject of the formula
Carrying x over the equal to in order to change the sign from - to +
4y - 10 = x
Substitute the value of x in eqn 2
4y - 10 - 3y = 11
Collecting like terms
4y - 3y = 11 + 10
y = 21
The value of y is 21
Then, substitute the value of y into eqn 1
-x + 4y = 10
-x + 4(21) = 10
-x + 84 = 10
84 -10 = x
In order to get rid of the - sign
x = 74
Therefore,
x = 74
y = 21
