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3 years ago

Find the distance between the points (-2, 4) and (4, -6). 0 212 2/(10) O2V(34)

Mathematics

1 answer:

Fittoniya [83]3 years ago

5 0

Answer:

2 $\sqrt{34}$

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (4, - 6)

d = $\sqrt{(4+2)^2+(-6-4)^2}$

= $\sqrt{6^2+(-10)^2}$

= $\sqrt{36+100}$

= $\sqrt{136}$ = $\sqrt{4(34)}$ = $\sqrt{4}$ × $\sqrt{34}$ = 2 $\sqrt{34}$

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Mika can eat 21 hot dogs in 66 minutes. She wants to know how many minutes it would take her to eat 35 hot dogs if she can keep

Ierofanga [76]

Answer:

110 minutes

Step-by-step explanation:

66÷21=3.14

35×3.14=110

6 0

3 years ago

seven people arrive to dinner, but the circular table only seats six. if two seatings such that one is a rotation of the other a

Alenkinab [10]

6 different people chosen from 7 can sit around the circular table in 840 ways.

Given that there are 7 people who have arrived for dinner.

But the circular table only seats 6.

Hence 1 person can be left out.

This can be done in 7 ways, which is a simple case of permutation.

A permutation is a combination of objects arranged in a particular sequence. The elements of sets are arranged in this case in a linear or sequential sequence.

Now 6 people will have to sit on the circular table.

Now from the properties of combination we know that , if n people sit around a circular table, then they can sit in n! ways.

Therefore 6 people can sit around a circular table in 6! ways.

6! = 120

Therefore total number of ways = 120 × 7 = 840

Hence 6 different people chosen from 7 can sit around the circular table in 840 ways.

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5 0

1 year ago

Alonso multiplied the fractions 312and (−414) and got a product of −1218. Describe the mistake that Alonso made. What is the cor

weqwewe [10]

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8 0

3 years ago

a volley ball player servers the ball. The ball follows a path given by the equation y=-0.01x^2+0.5x+3 where x and y are measure

dolphi86 [110]

Answer:

(a)

Distance from player should be 13.82 feet or 36.2 feet

(b)

The ball will go over the net

Step-by-step explanation:

we are given

The ball follows a path given by the equation

$y=-0.01x^2+0.5x+3$

where

x and y are measured in feet and the origin is on the court directly below where the player hits the ball

(a)

net height is 8 ft

so, we can set y=8

and then we can solve for x

$8=-0.01x^2+0.5x+3$

$8\cdot \:100=-0.01x^2\cdot \:100+0.5x\cdot \:100+3\cdot \:100$

$800=-x^2+50x+300$

$-x^2+50x-500=0$

$x^2-50x+500=0$

we can use quadratic formula

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-500\right)}}{2\left(-1\right)}$

$x=5\left(5-\sqrt{5}\right),\:x=5\left(5+\sqrt{5}\right)$

$x=13.82,x=36.2$

So, distance from player should be 13.82 feet or 36.2 feet

(b)

we can plug x=30 and check whether y=8 ft

$y=-0.01(30)^2+0.5(30)+3$

$y=9ft$

we know that

height of net is 8 ft

so, the ball will go over the net

5 0

3 years ago

1. Kyle and John are twins who decided to plan an imaginary trip that started with cliff jumping. There were two different spots

Vikki [24]

Answer:

a) Δx = -35ft

b) Δx = -25ft

c) Kyle traveled 10ft more than John

Step-by-step explanation:

We define a coordinate reference system() in which y = 0 corresponds to the water surface.

a) The initial position of Kyle in our coordinate reference system is:

$x_{o} = 20 ft$

and his final position is:

$x_{f} = -15 ft$

Therefore, he traveled

Δx = $x_{f} - x_{o} = -15 - 20 = -35 ft$

b) The initial position of John in our coordinate reference system is:

$x_{o} = 15 ft$

and his final position is:

$x_{f} = -10 ft$

Therefore, he traveled

Δx = $x_{f} - x_{o} = -10 - 15 = -25 ft$

c) Then, Kyle traveled 10ft more than John

6 0

3 years ago