Answer:
lines a and b are parallel. The slopes are -1/3
None of the lines are perpendicular to each other.
Step-by-step explanation:
To figure out if any of the lines are parallel or perpendicular to each other, you have to find the slopes of each line. To find the slope look at the graph find the rise over run for all of the lines:
line a: This line goes down one every time it goes over 3, which can be represented by -1/3
line b: This lines goes down one every time it goes over 3, which can also be written as -1/3
line c: This line goes up 5 every time it goes over 2, which makes the slope 5/2
When two lines are parallel, they have the same slope. Line a and line b have the same slope, so they are parallel.
When two lines are perpendicular, their slopes are negative reciprocals of each other. Since none of the slopes are a negative reciprocal of another slope, we have no perpendicular lines.
Hope this helps :)
Answer:
5 x^2 y^ (-3) z = ?
Step-by-step explanation:
We know the volume of a rectangular prism is given by
V = l*w*h
V = 2x^2 * y^-2 * ?
We are given the volume
V =10x^4 y^-5 z
Set the two equal
10x^4 y^-5 z = 2x^2 * y^-2 * ?
Divide each side by 2x^2 y^-2
10x^4 y^-5 z /2x^2 y^-2 = 2x^2 * y^-2 * ?/2x^2 * y^-2
10x^4 y^-5 z/ 2x^2 y^-2 = ?
Simplifying
10/2 * x^4/x^2 y^-5/ y^-2 z = ?
We know that a^b/ a^c = a^(b-c)
5 x^ (4-2) y^(-5 - -2) z = ?
5 x^2 y^ (-5 +2) z = ?
5 x^2 y^ (-3) z = ?
1) Road Trip: Let’s say two friends are meeting at a playground. Mary is already at the park but her friend Bob needs to get there taking the shortest path possible. Bob has two way he can go - he can follow the roads getting to the park - first heading south 3 miles, then heading west four miles. The total distance covered following the roads will be 7 miles. The other way he can get there is by cutting through some open fields and walk directly to the park. If we apply Pythagoras's theorem to calculate the distance you will get:
(3)<span>2 </span>+ (4)2 =
9 + 16 = C2
√25 = C
5 Miles. = C
Walking through the field will be 2 miles shorter than walking along the roads. .
2) Painting on a Wall: Painters use ladders to paint on high buildings and often use the help of Pythagoras' theorem to complete their work. The painter needs to determine how tall a ladder needs to be in order to safely place the base away from the wall so it won't tip over. In this case the ladder itself will be the hypotenuse. Take for example a painter who has to paint a wall which is about 3 m high. The painter has to put the base of the ladder 2 m away from the wall to ensure it won't tip. What will be the length of the ladder required by the painter to complete his work? You can calculate it using Pythagoras' theorem:
(5)<span>2 </span>+ (2)2 =
25 + 4 = C2
√100 = C
5.3 m. = C
Thus, the painter will need a ladder about 5 meters high.
3) Buying a Suitcase: Mr. Harry wants to purchase a suitcase. The shopkeeper tells Mr. Harry that he has a 30 inch of suitcase available at present and the height of the suitcase is 18 inches. Calculate the actual length of the suitcase for Mr. Harry using Pythagoras' theorem. It is calculated this way:
(18)<span>2 </span>+ (b)2 = (30)2
324 + b2 = 900
B2 = 900 – 324
b= √576
= 24 inches
