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)

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)

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.