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3 years ago

Which is a real world example of two planes intersecting?

1 answer:

7 0

One example is the idea of two parts of a book that open up. Each flat part is a plane and the two planes intersect along the spine of the book.

Another example would be a wall intersecting with the floor. Both are flat surfaces.

A third example would be a laptop's screen as one plane and the keyboard as the other plane. They intersect at the hinge of the laptop.

For each example, the surface has a finite amount of area and it doesn't extend forever in all four directions. Theoretically, a plane is where the flat surface extends in all four directions infinitely. Though of course, real life has limitations but the idea is still applicable in a way.

Note how for each example, the two planes intersect to form a line. Also, each plane must be flat without bending or curving in any way.

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Need help with the question, I already have the degree and leading coefficient but not the constant term for this polynomial. f(

melisa1 [442]

Degree: 7
term: -3x^7
coefficient: -3

3 0

4 years ago

Is the relation {(1, 3), (-4, 0), (3, 1), (0,4), (2, 3)} a function? Why or why not?

gavmur [86]

Answer:

Yes.

The relation is a function because every element in the domain (the x's) is mapped to one element in the range (the y's).

Step-by-step explanation:

For a relation that is a set of points all you have to look for while igorning any duplicate points is that all of the x's are different. If there are any 2 (or more) x's that are the same, then it is not a function.

So there are no duplicate points.

For example the set {(1,5),(2,5)(1,5)} is really just {(1,5),(2,5)}.

Anyways the x's in the points are (in order from left to right):

-4

All of these are different, I did not list a value for x that was same anywhere in that list. So it is a function.

The relation is a function because there is no x that gets mapped to more than one y.

6 0

3 years ago

Insect Weights Consider a dataset giving the adult weight of species of insects. Most species of insects weigh less than 5 grams

Ann [662]

Answer:

Step-by-step explanation:

71 grams would definitely be an outlier on the high side, whereas "most" species would weigh much less. Thus, the graph of this distribution of weights would be skewed towards the lower side, that is, to the left.

8 0

4 years ago

1. a line with a slope of 1/3 passes through the point (3, 6) . which point also lies on this line?

valentina_108 [34]

1) Substituting into point-slope form, the equation of the line is y-6=⅓(x-3), which rearranges to:

y-6 = ⅓x - 1
y = ⅓x + 5

So, we can now substitute in the coordinates of each of the options to see which point lies on the line.

3 = ⅓(6) + 5 -> 3 = 7, which is false.
6 = ⅓(7) + 5 -> 6 = 22/3, which is false.
-3 = ⅓(-3) + 5 -> -3 = 4, which is false.
3 = ⅓(-6) + 5 -> 3 = 3, which is true.

So, the answer is (4) (-6, 3)

2) Substituting into point-slope form, the equation of the line is y - 5 = ¾(x-2), which rearranges to:

y - 5 = 0.75x - 1.5
y = 0.75x + 3.5

So, we can now substitute in the coordinates of each of the options to see which point lies on the line.

8 = 0.75(6)+3.5 -> 8 = 8, which is true.
9 = 0.75(5) + 3.5 -> 9 = 7.25, which is false.
1 = 0.75(-1) + 3.5 -> 1 = 2.75, which is false.
2 = 0.75(6) + 3.5 -> 2 = 8, which is false.

So, the answer is (1) (6, 8).

3 0

2 years ago

The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to

Morgarella [4.7K]

Answer:

9 mph

Step-by-step explanation:

Let he speed of the boat on the lake is x.

<u>Considering the speed of the current it will take him:</u>

22.5/(x + 6) + 22.5/(x - 6) = 9
2.5 / (x + 6) + 2.5 / (x - 6) = 1
2.5(x - 6 + x + 6) = (x + 6)(x - 6)
2.5*2x = x² - 36
x² - 5x - 36 = 0
x = (5 ± √(5² + 4*36))/2 = (5 ± 13) / 2
x = (5 + 13)/2 = 9 mph (negative root is discarded as the speed should be positive)

7 0

2 years ago