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nexus9112 [7]
3 years ago
14

Which unit of measurement is part of the metirc system

Mathematics
1 answer:
Goryan [66]3 years ago
7 0
Millimeter centimeter meter kilometer
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Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}
Deffense [45]

Start with a line segment connecting two points, A and B. \dfrac{DA}{BA}=3 means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with \dfrac{DB}{BA}=2, or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, \dfrac{AB}{CB}=\dfrac12, so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let d be the length of AB. Then the length of CD in terms of d is 4d. We have the coordinates of C and D, and the distance between them is \sqrt{(4-0)^2+(0-4)^2}=4\sqrt2. So

4d=4\sqrt2\implies d=\sqrt2

The slope of the line through C and D is

\dfrac{0-4}{4-0}=-1

and so the equation of the line through these points is

y-4=-(x-0)\implies x+y=4

So the coordinates of A are (x,y)=(x,4-x). The distance between C and A is d=\sqrt2, so we have

\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1

Since A falls to the right of C (in the x,y plane, not just in the sketch), we know to take the positive value x=1. Then the y coordinate is y=4-1=3.

All this to say that A is the point (1, 3), so

2x+y=2+3=5

5 0
3 years ago
What transformation of the parent function f(x) is made to get 4f(x+2)
LenKa [72]

Answer: A vertical stretch of 4 and a translation of -2 units in the x-direction.

Step-by-step explanation:

       Changes of the parent function can be written, in this case as <em>a</em>f(x)(x - <em>k</em>) where <em>a</em> is the stretch factor and <em>k</em> is the movement left or right on the x-axis.

       In this case, a = 4 and k = 2. Since the k is negative, the function will be moved -2 units on the x-axis.

<em>Learn more about </em><em>transformations of a parent function</em><em> here:</em>

<em>brainly.com/question/13822715</em>

7 0
1 year ago
The top of the Boulder Dam has an angle of elevation of 1.2 radians from a point on the Colorado River. Measuring the angle of e
Nana76 [90]

Answer:

382.925 feets

Step-by-step explanation:

The solution diagram is attached below :

Converting radian measurement to degree :

radian angle * 180/π = degree angle

1.2 * 180/π = 68.755°

0.9 * 180/π = 51.566°

Height of dam is h:

Using trigonometry :

Tan θ = opposite / Adjacent

Tan 68.755° = h / x

h = x Tan 68.755° - - - (1)

Tan 51.566° = h / (155+x)

h = (155+x) tan 51.566° - - - (2)

Equate (1) and (2)

x Tan 68.755 = (155+x) Tan 51.566

x Tan 68.755 = 155tan 51.566 + x tan 51.566

x Tan 68.755 = 195.32311 + x Tan 51.566

x Tan 68.755 - x Tan 51.566 = 195.32311

x(tan 68.755 - tan 51.566) = 195.32311

x * 1.3120110 = 195.32311

1.3120110x = 195.32311

x = 195.32311 / 1.3120110

x = 148.87307

Using :

h = x Tan 68.755

h = 148.87307 * tan(68.755)

h = 382.92539

h = 382.925 feets

5 0
2 years ago
Need help with 10 and 11 can’t figure it out
Artyom0805 [142]
Wish I could help on so sorry
5 0
3 years ago
Easy answer!!!! Will give brainliest
pochemuha

Answer:

A and B

Step-by-step explanation:

6 0
3 years ago
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