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1 year ago

Find the rate of change for the situation. You run 14 miles in two hours and 28 miles in four hours.

Mathematics

1 answer:

krek1111 [17]1 year ago

4 0

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

$\begin{array}{ccll} \stackrel{x}{miles}&\stackrel{y}{hours}\\ \cline{1-2} 14&2\\ 28&4 \end{array}\qquad \qquad \begin{array}{llll} (\stackrel{x_1}{14}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{28}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{28}-\underset{x_1}{14}}}\implies \cfrac{2}{14}\implies \cfrac{1}{7} \end{array}$

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Help me with this problem!

kipiarov [429]

Answer:

y = -(2/3)x + 3

Step-by-step explanation:

The slope of the equation that was given is - 2/3

The slope in a slope intercept equation is the number in front of the x when the value of the number in front of the y = 1 and x and y are on opposite sides of the equal sign. Let's translate that.

The original equation is y = -(2/3)x + 5/3

y and x have to be on opposite sides of the equal sign [They are]
The slope is the number in front of the x. That's (-2/3). That makes A incorrect.

Now you need to use the given point

The point is (-3 , 5) Put this into the equation that you have so far

y = (-2/3)x + b

y = 5

x = -3

5 = (-2/3)(-3/1) + b Substitute in the givens

5 = (-2 * -3)/3 + b Multiply -2 * - 3 = 6

5 = 6/3 + b Divide the 6 by 3

5 = 2 + b Divide

5 - 2 = b Subtract 2 from both sides

3 = b Switch sides

b = 3

Answer y = (-2/3)x + 3 or C

8 0

2 years ago

Compare Look at these equations. Do you think they are all linear equations? Can they

Georgia [21]

Answer:

Yes they can all be written in y = mx + b. You just have to move the terms around.

Step-by-step explanation:

y = 2x -3, this is already in slope-intercept form

Now, y - 2 = x + 2: We can add 2 on both sides to cancel out the one on the left side:

y - 2 = x + 2

y - 2 + 2 = x + + 2

y = x + 4 <-- This is in y = mx + b form

Now the last one, 3x = 9 + 3y

We can first divide all terms by 3,

3x = 9 + 3y

/3 /3 /3

x = 3 + y: Then we can subtract 3 from both sides:

x - 3 = 3 + y - 3

x - 3 = y

These are all linear equations because none of the x's have bigger powers than 1. x^2 is a quadratic equation and x^3 is cubic equation.

6 0

2 years ago

What is the solution to 4+ 2x=4

Ivenika [448]

Answer:

Step-by-step explanation:

7 0

3 years ago

Can someone explain to me this derivative : y=3x√x

dimaraw [331]

Answer:

(9/2)√x.

Step-by-step explanation:

Convert the radical to an exponent.

x√x = x^1 * x^1/2

= x^(1 + 1/2)

= x^3/2

So the derivative of 3x^3/2 is found as follows:

y' = 3 * 3/2x^(3/2 - 1)

= (9/2)x^1/2

= (9/2)√x.

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3 years ago

119. Beatrice decides to deposit $100 per month at the end of every month in a bank with an annual interest rate of 5.5% compoun

sveta [45]

Answer:

Beatrice will accumulate $1230.72 at the end of the year.

Step-by-step explanation:

We can write:

$(1+\frac{0.055}{12})=z$

$100=C$ for deposits

The first month would have only the deposit reflected in her balance, then, expanding some steps of the calculation would yield:

$S_{1}=C\\S_{2}=Cz + C\\S_{3}=Cz^{2}+Cz + C\\S_{n}=Cz^{n-1} +...+Cz+C$

A geometric series is given by:

$1+x+...+x^{m}=\frac{x^{m+1}-1}{x-1}$

Translating our series to the short form:

$S_{n}=C(\frac{z^{n}-1}{z-1} )$

plugin in the values for the 12 month gives:

$S_{12}=100(\frac{(1+\frac{0.055}{12})^{12} -1}{\frac{0.055}{12}})=1230.7169$

3 0

3 years ago