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marissa [1.9K]
3 years ago
5

#19 The distance between the points (4, 1) and (9, 1) is

Mathematics
1 answer:
kirill115 [55]3 years ago
4 0

Hello!

Given the two points, (x_{1}, y_{1}) and (x_{2}, y_{2}), and to find the distance between these two points is found by using the formula:

d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}

(x_{1}, y_{1}) is assigned to one the points, in this case, is (4, 1).

(x_{2}, y_{2}) is assigned to other point, which is (9, 1).

Then, plug in these values into the formula and solve.

d = \sqrt{(9-4)^{2}-(1-1)^{2}}

d = \sqrt{5^{2}-0^{2}}

d = \sqrt{25}

d = 5

Therefore, the distance between the two points is 5.

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2x + 2y = 6<br> 3x − 2y = 29
Mazyrski [523]

Answer:

x = 7

y = -4

Step-by-step explanation:

5x = 35

x=7

14 + 2y = 6

2y = -8

y = -4

7 0
3 years ago
A tennis tournament has 2n contestants. We want to pair them up for the first round of singles matches. Show that the number of
ddd [48]

There are

\dbinom{2n}2 = \dfrac{(2n)!}{2! (2n-2)!}

ways of pairing up any 2 members from the pool of 2n contestants. Note that

(2n)! = 1\times2\times3\times4\times\cdots\times(2n-2)\times(2n-1)\times(2n) = (2n-2)! \times(2n-1) \times(2n)

so that

\dbinom{2n}2 = \dfrac{(2n)\times(2n-1)\times(2n-2)!}{2! (2n-2)!} = \boxed{n(2n-1)}

4 0
1 year ago
Chang made $156 for 13 hours of work at the same rate, how many hours would he have to work to make $108?
sdas [7]

Answer:

  9 hours

Step-by-step explanation:

"At the same rate" means time and wages are proportional.

  time/wages = t/$108 = (13 h)/$156

  t = 108(13 h)/156 . . . . . . . . . . . . . . . units of dollars cancel

  t = 9 h

Chang would have to work 9 hours to make $108.

8 0
2 years ago
PLEASE HELP DUE TODAY
AleksAgata [21]

9514 1404 393

Answer:

  16 square units

Step-by-step explanation:

When you plot the points, you see they define a trapezoid with bases of lengths 2 and 6, and a height of 4. The area formula is ...

  A = (1/2)(b1 +b2)h

  A = (1/2)(2 +6)(4) = 16

The area of the trapezoid is 16 square units.

4 0
2 years ago
Please math help and please show work!
Galina-37 [17]
Since they are similar triangles, they are just enlarged versions of each other. This means that the left-most angle of triangle XYZ is also 35°.

Angles in a triangle add up to 180°, so we can find the missing angle by subtracting the two known angles from 180.

180 - 70 - 35 = 75
The right-most angle of triangle XYZ would be 75°.

Hope this helps!
6 0
2 years ago
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