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bearhunter [10]
3 years ago
12

Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the poi

nts used to determine the slope and how the equation was determined.

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
6 0

Answer:

y=\frac{5}{7}x+\frac{135}{7}

Step-by-step explanation:

You only need two points on a line to find the equation for that line.

We are going to use 2 points that cross that line or at least come close to. You don't have to use the green points... just any point on the line will work.  You might have to approximate a little.

I see ~(67.5,67.5) and ~(64,65).

Now once you have your points, we need to find the slope.

You may use \frac{y_2-y_1}{x_2-x_1} where (x_1,y_1) \text{ and } (x_2,y_2) are points on the line.

Or you can line up the points vertically and subtract then put 2nd difference over 1st difference.

Like this:

(  64  ,   65  )

-( 67.5, 67.5 )

--------------------

-3.5        -2.5

So the slope is -2.5/-3.5=2.5/3.5=25/35=5/7.

Now use point-slope form to find the equation:

y-y_1=m(x-x_1) where m is the slope and (x_1,y_1) is a point on the line.

y-65=\frac{5}{7}(x-64)

Distribute:

y-65=\frac{5}{7}x-\frac{5}{7}\cdot 64

Simplify:

y-65=\frac{5}{7}x-\frac{320}{7}

Add 65 on both sides:

y=\frac{5}{7}x-\frac{320}{7}+65

Simplify:

y=\frac{5}{7}x+\frac{135}{7}

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Find the sum. ???? 2 0<br> −2 3<br> ???? + ????1 5<br> 0 1<br> ????
julia-pushkina [17]

Answer:

\left[\begin{array}{cc}2&0\\-2&3\end{array}\right]+\left[\begin{array}{cc}1&5\\0&1\end{array}\right]=\left[\begin{array}{cc}3&5\\-2&4\end{array}\right]

Step-by-step explanation:

If you have two matrices:

A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\and\\B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]

The sum of the matrices is:

A+B=\left[\begin{array}{cc}a+e&b+f\\c+g&d+h\end{array}\right]

In this case we have:

A=\left[\begin{array}{cc}2&0\\-2&3\end{array}\right]\\\\\\B=\left[\begin{array}{cc}1&5\\0&1\end{array}\right]

The <u>sum</u> is:

A+B=\left[\begin{array}{cc}2+1&0+5\\-2+0&3+1\end{array}\right]\\\\\\A+B=\left[\begin{array}{cc}3&5\\-2&4\end{array}\right]

The answer is:

\left[\begin{array}{cc}2&0\\-2&3\end{array}\right]+\left[\begin{array}{cc}1&5\\0&1\end{array}\right]=\left[\begin{array}{cc}3&5\\-2&4\end{array}\right]

4 0
4 years ago
The volume of the cone is 50π ft³. The height is 6 ft. What is the radius of the​ cone?
laila [671]

Answer:

r = 5 feet

Step-by-step explanation:

see attached for reference

recall that volume of a circular cone is given by

V = (1/3) πr²h, where

V = volume = given as 50π ft³

r = radius (we are asked to find this)

h = height of cone = given as 6 feet

Substituting the above known values into the equation:

V = (1/3) πr²h

50π = (1/3) π (r²)(6)

50π = π (r²)(2)  (divide both sides by 2)

25π = π r²   (divide both sides by π)

25 = r²

r = ±√25

r = ±5   (since radius cannot be negative, we select the positive value

r = 5 feet

3 0
4 years ago
Solve these problems for me please! ASAP show all work!<br><br> 7.24 ÷ 7=?<br> 11.4 ÷ 19?
GalinKa [24]
7.24/7=1.04
7.00/7= 1  0.24/7= .04   1+0.04=1.04

11.4/19= 0.6
https://www.calculatorsoup.com/calculators/math/longdivisiondecimals.php?dvsor=19&dvdnd=11.4&decimal...

Kinda hard to show work for second one so posted a link.
7 0
3 years ago
Frank wants to buy an entertainment system that costs $500, including taxes. To pay for the entertainment system, he will use a
AleksandrR [38]

The percent increase from the original cost of the entertainment system to the cost of the entertainment system using the payment plan is 12%.

<u>Step-by-step explanation</u>:

  • The original cost of entertainment system = $500
  • The cost using payment plan= $125+ ($72.50\times 6)
  • cost by payment plan ⇒ 125+ 435 = $560

Percentage increase = (higher value - lower value/ lower value) \times 100

⇒ ((560-500)/500) \times 100

⇒ (60/500) \times 100

⇒ 0.12 \times 100

⇒ 12%

3 0
3 years ago
The ages of three brothers are consecutive integers with a sum of 96. how old are the brothers?
Troyanec [42]

consecutive integers have a difference of 1 between them

let the brothers have ages n , n + 1 and n + 2 thus

n + n + 1 + n + 2 = 96

3n + 3 = 96

subtract 3 from both sides of the equation

3n = 96 - 3 = 93

divide both sides by 3

n = \frac{93}{3} = 31

The ages are 31 , 32 and 33



8 0
3 years ago
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