What is the equation of the graphed line?

Complete equation describing how X and Y are related.

den301095 [7]

Answer:

$2$

Step-by-step explanation:

Every time the x-value increases by 1, the y-value increases by 2. Therefore, the slope of the line must be equal to $2/1=\boxed{2}$ (rise/y-values over run/x-values). In slope-intercept form $y=mx+b$ , $m$ represents the slope of the line, $b$ represents the y-intercept, and $(x,y)$ represents any point the line passes through.

Since $m$ represents the slope of the line, the value of

While the question only asks for this value, it's good to note that the equation of the function is $y=2x+7$ (find 7 by substituting any ordered pair in the table with $m=2$ ).

6 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!!!!

irakobra [83]

Answer:

D

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

Which expression is correct?"The square of the sum of a number and 5, added to 3, then squared"

brilliants [131]

Answer:

5-n squared+3 squared

Step-by-step explanation:

3 0

3 years ago

Problem 4: Solve the initial value problem

pishuonlain [190]

Separate the variables:

$y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx$

Separate the left side into partial fractions. We want coefficients a and b such that

$\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}$

$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

$\implies 1 = (a+b)y - 2a+b$

$\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13$

So we have

$\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx$

Integrating both sides yields

$\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx$

$\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C$

$\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C$

$\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C$

$\dfrac{y-2}{y+1} = e^{3x + C}$

$\dfrac{y-2}{y+1} = Ce^{3x}$

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

$\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}$

Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

7 0

2 years ago

The estimated measurements of the objects are shown below.

olga2289 [7]

The scientific notation is a method that scientists use to easily handle very large numbers or very small numbers. As an example, instead of writing down the value 0.0000000065, we write the value 6.5 x 10-9 in scientific notation. The number of places the decimal point got moved becomes the exponent of the number 10. When the movement is from left to right, the exponent is negative (for very small numbers). When it is right to left, the exponent is positive (for very large numbers).

Therefore writing estimated measurements in scientific notation:

length of a grain of salt : 0.0002 centimeters = 2 x 10-4 centimeters

width of a key ring : 0.02 centimeters = 2 x 10-2 centimeters

6 0

3 years ago