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Kobotan [32]
3 years ago
6

Solve for each unknown variable, #67

Mathematics
1 answer:
mel-nik [20]3 years ago
3 0
3x +10= 2x + 34

x = 24

82°
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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
Find the equation of quadratic function determined from the graph below?
Aleksandr [31]

Step-by-step explanation:

The x-intercepts are x = -1 and x = 5, so:

y = k (x + 1) (x − 5)

The vertex is (2, -3), so:

-3 = k (2 + 1) (2 − 5)

-3 = -9k

k = 1/3

y = 1/3 (x + 1) (x − 5)

Simplifying:

y = 1/3 (x² − 4x − 5)

y = 1/3 x² − 4/3 x − 5/3

3 0
3 years ago
Hi please help I’m rlly behind in school!!!
Butoxors [25]

Answer:

17 pounds

Step-by-step explanation:

Median:

Weights of the dogs are:

3 , 8 , 10 , 11 , 14 , 17 , 22 , 24, 25 , 35 , 40

Number of data = 11

So, median will the middle term which is the 6the term.

Median = 17

4 0
2 years ago
What is 300 times 2,,,,,....................
xxTIMURxx [149]
It is 600............
3 0
3 years ago
Read 2 more answers
2x^4–5x^3+x^2+3x+2=?<br><br> X=5
DanielleElmas [232]

Answer:

2x^4–5x^3+x^2+3x+2=

2 \times 5^4–5 \times 5^3+5^2+3 \times 5+2

= 2 × 625 – 5 × 125 + 25 + 3 × 5 + 2

=1250 – 625 + 25 + 15 +2

= 1292 – 625

= 667

3 0
2 years ago
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