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3 years ago

Find the next three numbers in the pattern 2, 3, 5, 8, ? ? ?

Mathematics

2 answers:

VMariaS [17]3 years ago

8 0

Answer:

13, 21, 34

Step-by-step explanation:

Fibonnaci's Sequence

2+1 = 3

3+2 = 5

5+3 = 8

8+5 = 13

13+8 = 21

21+13 = 34

kompoz [17]3 years ago

7 0

9,11,14

the pattern is add one then add two then add three

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hello! 20 points for this one answered correctly and explained! question: which pair of numbers with sum 8 has the largest produ

Andre45 [30]

4&4 b/c 4+4=8 & 4x4=16

8 0

3 years ago

A boat travels 30 miles up the river in the same amount of time it takes to travel 38 miles down the same river. If the current

Ksenya-84 [330]

X miles per hour - speed of the boat in still water
(x - 2) - speed up the river
(x + 2) - speed down the river

$\frac{30}{x - 2}$ = $\frac{38}{x + 2}$
30 * (x + 2) = 38 * (x - 2)
30x + 60 = 38x - 76
- 8x = - 136
x = 17 miles per hour - the speed of the boat in still water.

5 0

3 years ago

(9.70 x 10^6) + (8.3 x 10^5)=

nexus9112 [7]

Answer:

1.053 *10 ^7

Hope this helps, you can look it up on google by the way ^^

5 0

3 years ago

Read 2 more answers

A vehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles. At this rate, how many miles can the vehicle travel per gallon

Vesna [10]

We know that
1 1/8 gallons----------> (1*8+1)/8-------> 9/8 gallons
13 1/2 miles----------> (13*2+1)/2-------> 27/2 miles

if 9/8 gallons-------------------> 27/2 miles
1 gallons----------------------> X
X=(27/2)/(9/8)---------> 216/18--------> 12 miles

the answer is 12 miles

6 0

3 years ago

Read 2 more answers

Consider the three points ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 ) . Let ¯ x be the average x-coordinate of these points, and let ¯ y

loris [4]

Answer:

$m=\dfrac{3}{2}$

Step-by-step explanation:

Given points are: ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 )

The average of x-coordinate will be:

$\overline{x} = \dfrac{x_1+x_2+x_3}{\text{number of points}}$

1) Finding $(\overline{x},\overline{y})$

Average of the x coordinates:

$\overline{x} = \dfrac{1+2+3}{3}$

$\overline{x} = 2$

Average of the y coordinates:

similarly for y

$\overline{y} = \dfrac{3+3+6}{3}$

$\overline{y} = 4$

2) Finding the line through $(\overline{x},\overline{y})$ with slope m.

Given a point and a slope, the equation of a line can be found using:

$(y-y_1)=m(x-x_1)$

in our case this will be

$(y-\overline{y})=m(x-\overline{x})$

$(y-4)=m(x-2)$

$y=mx-2m+4$

this is our equation of the line!

3) Find the squared vertical distances between this line and the three points.

So what we up till now is a line, and three points. We need to find how much further away (only in the y direction) each point is from the line.

Distance from point (1,3)

We know that when x=1, y=3 for the point. But we need to find what does y equal when x=1 for the line?

we'll go back to our equation of the line and use x=1.

$y=m(1)-2m+4$

$y=-m+4$

now we know the two points at x=1: (1,3) and (1,-m+4)

to find the vertical distance we'll subtract the y-coordinates of each point.

$d_1=3-(-m+4)$

$d_1=m-1$

finally, as asked, we'll square the distance

$(d_1)^2=(m-1)^2$

Distance from point (2,3)

we'll do the same as above here:

$y=m(2)-2m+4$

$y=4$

vertical distance between the two points: (2,3) and (2,4)

$d_2=3-4$

$d_2=-1$

squaring:

$(d_2)^2=1$

Distance from point (3,6)

$y=m(3)-2m+4$

$y=m+4$

vertical distance between the two points: (3,6) and (3,m+4)

$d_3=6-(m+4)$

$d_3=2-m$

squaring:

$(d_3)^2=(2-m)^2$

3) Add up all the squared distances, we'll call this value R.

$R=(d_1)^2+(d_2)^2+(d_3)^2$

$R=(m-1)^2+4+(2-m)^2$

4) Find the value of m that makes R minimum.

Looking at the equation above, we can tell that R is a function of m:

$R(m)=(m-1)^2+4+(2-m)^2$

you can simplify this if you want to. What we're most concerned with is to find the minimum value of R at some value of m. To do that we'll need to derivate R with respect to m. (this is similar to finding the stationary point of a curve)

$\dfrac{d}{dm}\left(R(m)\right)=\dfrac{d}{dm}\left((m-1)^2+4+(2-m)^2\right)$