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pedrojsq271
21.07.2019 •
Mathematics
20 ! 2 questions
segment ab falls on line 2x − 4y = 8. segment cd falls on line 4x + 2y = 8. what is true about segments ab and cd?
they are perpendicular because they have the same slope of −2.
they are perpendicular because they have slopes that are opposite reciprocals of −2 and one half.
they are coincident lines because they have the same slope and the same y-intercept.
they are coincident lines because they have the same slope and a different y-intercept.
annie is creating a stencil for her artwork using a coordinate plane. the beginning of the left edge of the stencil falls at (1, −1). she wants to align an important detail on the left edge of her stencil at (3, 0). she knows this is 1: 3 of the way to where she wants the end of the stencil. where is the end of the stencil located?
(1.5, −0.75)
(2.5, −0.25)
(6, 2)
(9, 3)
Solved
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Ответ:
Part 1) They are perpendicular because they have slopes that are opposite reciprocals of −2 and one half.
Part 2) The coordinates of the end of the stencil are (9,3)
Step-by-step explanation:
Part 1)
step 1
Find the slope of segment AB
we have
Segment AB falls on line
> isolate the variable y
Divide by 4 both sides
so
The slope of segment AB is m=1/2
step 2
Find the slope of segment CD
we have
Segment CD falls on line
> isolate the variable y
Divide by 2 both sides
so
The slope of segment CD is m=-2
step 3
Compare the slopes
mAB=1/2
mCD=-2
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal each other (the product is equal to -1)
(1/2) and -2 are opposite reciprocal
therefore
Segment AB and segment CD are perpendicular
Part 2)
Let
A(1,-1) and B(3,0)
Find the x-distance between point A and B
dx=(3-1)=2 units
we know that
The point (3,0) s 1:3 of the way to where she wants the end of the stencil
Multiply by 3 the x-distance between point A and B
3(2)=6 units
The x-coordinate of the end of the stencil will be 6 units plus the x-coordinate point (3,0)
x-coordinate=6+3=9
Find the y-distance between point A and B
dy=(0+1)=1 units
we know that
The point (3,0) s 1:3 of the way to where she wants the end of the stencil
Multiply by 3 the y-distance between point A and B
3(1)=3 units
The y-coordinate of the end of the stencil will be 3 units plus the y-coordinate point (3,0)
y-coordinate=3+0=3
therefore
The coordinates of the end of the stencil are (9,3)
Ответ:
25
Step-by-step explanation:
a² + 7a + 7
a = 2
Plug in the value of 2 for every occurance of a.
(2)² + 7(2) + 7
First, solve the exponent.
4 + 7(2) + 7
Now, multiply.
4 + 14 + 7.
Add.
25
This is your answer.
Hope this helps!