Answer:
-5
Step-by-step explanation:
Parallel lines have the same slope.
To compare the slopes of two different lines, you have to get
both equations into the form of
y = 'm' x + (a number) .
In that form, the 'm' is the slope of the line.
Notice that it's the number next to the 'x' .
The equation given in the question is y = 3 - 2 x .
Right away, they've done something to confuse you.
You always expect the 'x' term to be right after the 'equals' sign,
but here, they put it at the end. The slope of this line is the -2 .
Go through the choices, one at a time.
Look for another one with a slope of -2 .
Remember, rearrange the equation to read ' y = everything else ',
and then the slope is the number next to the 'x'.
Choice #4: y = 4x - 2 . The slope is 4 . That's not it.
Choice #3: y = 3 - 4x . The slope is -4 . That's not it.
Choice #2). 2x + 4y = 1
Subtract 2x from each side: 4y = 1 - 2x
Divide each side by 4 : y = 1/4 - 1/2 x .
The slope is -1/2. That's not it.
Choice #1). 4x + 2y = 5
Subtract 4x from each side: 2y = 5 - 4x
Divide each side by 2 : y = 5/2 - 2 x .
The slope is -2 .
This one is it.
This one is parallel to y = 3 - 2x ,
because they have the same slope.
Answer:
Step-by-step explanation:
Given that,
Base = 42
Perpendicular height = 31
We need to find the value of 
. It can be calculated using trigonometry as follows :
Put all the values,
So, the value of .
Answer:
There are 12 male teachers.
Step-by-step explanation:
Ratio of male teachers to female teachers in a school is 1 to 5.
For every 1 male teacher, there is one female teacher.
There are 60 female teachers.
Divide 60 by 5 = 12.
12 times 1 = 12
There are 12 male teachers.
We determine line m as follows:
*First, by theorem we have the following:
Here m1 & m2 are the slopes of two perpendicular lines. For all lines that are perpendicular that is true, so we calculate the slope of line m using the slope of the function given [Which has a slope of 7/4]:
So, the slope of line m is -4/7. Now, using this slope and the point (-1, 4) we replace in the following expression:
Here x1, y1 & m1 are the x-component of the point, the y-component of the point, and the slope of the line respectively, so we replace and solve for y:
And that last function of y is the line m.
