3 years ago

What is the slope of the line of best fit?

Mathematics

1 answer:

Ierofanga [76]3 years ago

7 0

Step-by-step explanation:

The line passes through the origin and point (30,3)

so, slope of the graph( miles per minute)= 3/30 = 1/10 miles per minute

Or, slope of the graph miles per hour

$= \frac{3}{ \frac{30}{60} } = \frac{3 \times 60}{30} = 6$

option B

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David wants to fill his backyard swimming pool. His garden hose delivers 40 gallons in 5 minutes. How many gallons of water will

svetlana [45]

Answer:

Part a) $160\ gallons$

Part b) $480\ gallons$

Step-by-step explanation:

Part a) How many gallons of water will be in the pool after 20 minutes?

we know that

Using proportion

$\frac{40}{5}\frac{gallons}{minutes}=\frac{x}{20}\frac{gallons}{minutes} \\ \\x=40*20/5\\ \\x=160\ gallons$

Part b) How many gallons of water will be in the pool after 1 hour

we know that

1 hour = 60 minutes

Using proportion

$\frac{40}{5}\frac{gallons}{minutes}=\frac{x}{60}\frac{gallons}{minutes} \\ \\x=40*60/5\\ \\x=480\ gallons$

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3 years ago

If the acceleration of an object is given by dv/dt = −2v, Find the position function s(t) if v(0) = 7 and s(0) = 0.

kirill [66]

Answer:

Step-by-step explanation:

Given that acceleration of an object is

$\frac{dv}{dt} =-2v\\\frac{dv}{v} =-2dt\\ln v = -2t+C\\$

is the solution to the differential equation

Since v(0) =7

we get ln 7 = C

Hence $lnv = -2t+ln 7\\v=7e^{-2t}$

since velocity is rate of change of distance s we have

$v=\frac{ds}{dt} =7e^{-2t}\\s= [tex]s(t) =\frac{-7}{2} (e^{-2t})+C)[$

substitute t=0 and s=0

$C=7/2$

So solution for distance is

$s(t) =\frac{-7}{2} (e^{-2t}-1)$

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3 years ago

Solve each equation for the given variable a-2b=-10 for b

Ymorist [56]

A-2b=-10
add 2b on both sides
a=2b-10
add 10 to both sides
a+10=2b
divide both sides by 2
a/2+10/2=a/2+5=b
b=5+a/2

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frutty [35]

Answer:

Step-by-step explanation:

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A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree.

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10^2 -4^2 = x^2
100 -16 = x^2
84= x^2
Find the square root of 84 which is approximately 9.2
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