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1. Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the

Sveta_85 [38]

Answer:

#1) y = -4x + 1; #2) parallel; #3) y = -1/2x + 5/2; #4) y = 2x + 4; #5) Never

Step-by-step explanation:

#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1). First we simplify our equation using the distributive property:

y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6

Lines that are parallel have the same slope; this means we want a line through (1, -3) with a slope of -4. Using point-slope form,

$y-y_1=m(x-x_1)\\\\y--3=-4(x-1)\\\\y+3=-4(x)-4(-1)\\\\y+3=-4x+4\\\\y+3-3=-4x+4-3\\\\y=-4x+1$

#2) We must first write our second equation in slope-intercept form by isolating the y term:

2x+y=7

Subtract 2x from each side"

2x+y-2x = 7-2x

y = -2x+7

This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2. To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2. Using point-slope form,

$y-0=\frac{-1}{2}(x-5)\\\\y=\frac{-1}{2}(x)+\frac{-1}{2}(-5)\\\\y=\frac{-1}{2}x+\frac{5}{2}$

#4) The slope of Main Street on the diagram, found by using rise/run, is 2. This means the bike path will also have a slope of 2 in order to be parallel. The park entrance is at (0, 4). This makes the equation y = 2x+4.

#5) Two lines with the same slope are always parallel. They are never perpendicular.

3 0

3 years ago

Read 2 more answers

The town of Lantana needs $14,000 for a new playground Lantana elementary school raised 5358, Lantana Middle School raised $2,83

slavikrds [6]

Answer: The answer is actually 1,676. But you can estimate it to 2,000. so the town of Lantana would have about 2,000 dollasrs left to raise to reach there goal.

Step-by-step explanation:

You would first make sure you add all the number like 5,358+2,834+4,132. And once you get you answer you subtract 14,000 from the number you got!

I really hope that helps.

8 0

2 years ago

Read 2 more answers

You randomly choose one of the tiles. Without replacing the first tile. What is the event of the compound event? Write your answ

Luden [163]

Answer:

87777777777777777777777777

Step-by-step explanation:

7 0

4 years ago

Never been good at similar figures.. xP

Otrada [13]

1 is false, 2 is true, 3 is false, 4 is false

5 0

3 years ago

Rosa climbs a 16-meter tower to ride a straight water slide. After landing in the slash pool, she walks 9 meters back to the bas

erastova [34]

Answer:

The length of slide is 18.36 meters

Step-by-step explanation:

The given scenario forms a right-angled triangle where

The height of tower id perpendicular, the distance between slash pool and base of tower is base and the length of slide will be hypotenuse.

Height of tower = h = 16 meters

Distance between slash pool and base of tower = b = 9 meters

Length of slide = s = ?

As it is a right angled triangle, we can use Pythagoras theorem to find the length of slide

Pythagoras theorem states that:

$(Hypotenuse)^2 = (Base)^2+(Perpendicular)^2\\s^2 = b^2+h^2\\s^2 = (9)^2+(16)^2\\s^2 = 81+256\\s^2 = 337\\s^2 = 18.36\ meters$

Hence,

The length of slide is 18.36 meters

4 0

3 years ago