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a_sh-v [17]
3 years ago
8

What is the greatest common factor of the polynomial expression 2x^3 - 4x^2 + 6x?

Mathematics
1 answer:
iren2701 [21]3 years ago
5 0

Step-by-step explanation:

2 {x}^{3}  - 4 {x}^{2}  + 6x \\  = 2x( {x}^{2}  - 2x + 3) \\  \because \: 2x \: is \: common \: from \: all \: terms \\  \therefore \: greatest \: common \: factor = 2x

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Expand the polynomial<br> (x^(2)+xy-y^(2))(x+y)
xxTIMURxx [149]

Answer:

It's already expanded.

6 0
3 years ago
Can you please explain this?​
Leni [432]

Answer:

The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.

Step-by-step explanation:

Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. s_{1} = -s_{2}^{-1})

Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:

(3,5)-(1,1) and (0, 2)-(5, 12)

To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate.  That will give us a valid Δx and Δy to get the slope.

In the first pair, 3 > 1, so we'll subtract the second point from the first:

s = \Delta y / \Delta x\\s = \frac{5 - 1}{3 - 1}\\s = 4/2\\s = 2

So the first pair of vectors describe a line with a slope of 2.  Let's look at the other pair:

s = \Delta y / \Delta x\\s = (12 - 2) / (5 - 0)\\s = 10 / 5\\s = 2

That also gives us a slope of 2, meaning that the two lines are parallel.

This same process will need to be done for the other three questions.  We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image.  For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.

6 0
3 years ago
A shipping company uses an inclined conveyor belt to load or unload packages. The dock is 15 feet above ground. The base of the
alexgriva [62]
Hey there! :D

Think of this like a triangle. The dock is 15 feet above ground. It is the side of the triangle. The line connecting the bottom of the dock to the base of the conveyor belt is 40 feet. This is like the base. 

The conveyor belt itself is at a diagonal, and should be the hypotenuse. 

Use the Pythagorean theorem. 

a^2+b^2=c^2

15^2+40^2= c^2 

225+1,600= c^2

Add the values together. 

1,825= c^2

Find the square root of 1,825. 

c= 42.7 (rounded to the nearest tenth) 

The conveyor belt is 42.7 feet long.

I hope this helps!
~kaikers


7 0
3 years ago
Multiple choice. Use the Law of Sines to find the missing angle of the triangle. Find m angle C to the nearest tenth if c = 111
nalin [4]

Answer:

Both A and B are possible.

Step-by-step explanation:

It's both!

This is a might tricky. First you have to find the altitude. You have to determine if this is a real triangle.

Sin(22) = opposite / hypotenuse. The hypotenuse = 111. The angle is 22

opposite = hypotenuse * sin(22)

opposite = 111 * sin(22)

opposite = 41.58  and this is the altitude.

What have you learned?

Since 42 is larger than 41.58 you have 2 solutions to the triangle. One of the angles is acute, and the other one is obtuse. They are supplementary angles.

Sin(C) / c = Sin(A) / a

Sin(C) = c * Sin(22) / 42

Sin(C) = 111*sin(22)/ 42

Sin(C) = .99003

Sin(C) = 81.9

So that's your first answer. The second answer comes from Finding the supplement to this angle

supplement + 81.9 = 180

supplement = 180 - 81.9

supplement = 98.1

7 0
3 years ago
Simplify the following expression. 6.72 + 0.088
lana [24]
6.808 is the correct answer
Hope this helped you
4 0
3 years ago
Read 2 more answers
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