Can someone help me please

Calculate the slope of a line with a run of 3 and a rise of 9.

Mrrafil [7]

Answer:

<u>Slope = 3</u>

Step-by-step explanation:

Slope is calculated as the "Rise/Run" of a straight line. The Rise is the change in the value of y, or the amount y changes per change in x. Run is the change in the x value. A line with a run of 3 and a rise of 9 is calculated as:

Rise/Run = 9/3 or 3

This means that the value of y will increase by 3 for every increase of 1 in the value of 3.

Slope in "m" in the slope-intercept form of a straight line equation: y = mx + b

The line y = 3x + 2 tells us the it has a slope of 3 and intercepts the y axis at x = 2.

Example points (y = 3x + 2)

(0,2)

(1,5)

(4,14)

Note that y changes by 12 when x changes by 4. Rise/Run = 12/4 or 3.

4 0

2 years ago

I just need #2 <br><br> thanks for giving your time to help me

SVEN [57.7K]

2.
1099.99x 0.58 =637.9942
1099.99-637.9942= 461.9958
461.9958x 0.065=30.029727
461.9958-30.029727=431.967073

The answer round is 431.96

3.
42.95x1/5= 8.59
42.95-8.59 = 34.56
34.56 x 0.07=2.4192
34.56-2.4192= 32.1408
Round it is 32.14

4.
1250x0.85= 1062.5
1250-1062.5 =187.5

7 0

3 years ago

The product of two consecutive even numbers is 12 more than the square of the smaller number.

vivado [14]

Answer:

6 and 8

Step-by-step explanation:

Let's start off by thinking at what the question is asking us.

The product (multiplication) of two even numbers (x)(x+2) is which means =,

12 more (12) than the square of the smaller number (x).

So put that all together and you get (x)(x+2)=12+x^2=

Distribute the x, (x)(x+2)=

x^2+2x=x^2+12 Subtract x^2 from both sides.

2x=12

Divide both sides by 2 and you get x=6

So the two numbers are 6,8

6(8)=12+6^2

48=48

6 0

3 years ago

Determine the exact formula for the following discrete models:

marshall27 [118]

I'm partial to solving with generating functions. Let

$T(x)=\displaystyle\sum_{n\ge0}t_nx^n$

Multiply both sides of the recurrence by $x^{n+2}$ and sum over all $n\ge0$ .

$\displaystyle\sum_{n\ge0}2t_{n+2}x^{n+2}=\sum_{n\ge0}3t_{n+1}x^{n+2}+\sum_{n\ge0}2t_nx^{n+2}$

Shift the indices and factor out powers of $x$ as needed so that each series starts at the same index and power of $x$ .

$\displaystyle2\sum_{n\ge2}2t_nx^n=3x\sum_{n\ge1}t_nx^n+2x^2\sum_{n\ge0}t_nx^n$

Now we can write each series in terms of the generating function $T(x)$ . Pull out the first few terms so that each series starts at the same index $n=0$ .

$2(T(x)-t_0-t_1x)=3x(T(x)-t_0)+2x^2T(x)$

Solve for $T(x)$ :

$T(x)=\dfrac{2-3x}{2-3x-2x^2}=\dfrac{2-3x}{(2+x)(1-2x)}$

Splitting into partial fractions gives

$T(x)=\dfrac85\dfrac1{2+x}+\dfrac15\dfrac1{1-2x}$

which we can write as geometric series,

$T(x)=\displaystyle\frac8{10}\sum_{n\ge0}\left(-\frac x2\right)^n+\frac15\sum_{n\ge0}(2x)^n$

$T(x)=\displaystyle\sum_{n\ge0}\left(\frac45\left(-\frac12\right)^n+\frac{2^n}5\right)x^n$

which tells us

$\boxed{t_n=\dfrac45\left(-\dfrac12\right)^n+\dfrac{2^n}5}$

# # #

Just to illustrate another method you could consider, you can write the second recurrence in matrix form as

$49y_{n+2}=-16y_n\implies y_{n+2}=-\dfrac{16}{49}y_n\implies\begin{bmatrix}y_{n+2}\\y_{n+1}\end{bmatrix}=\begin{bmatrix}0&-\frac{16}{49}\\1&0\end{bmatrix}\begin{bmatrix}y_{n+1}\\y_n\end{bmatrix}$

By substitution, you can show that

$\begin{bmatrix}y_{n+2}\\y_{n+1}\end{bmatrix}=\begin{bmatrix}0&-\frac{16}{49}\\1&0\end{bmatrix}^{n+1}\begin{bmatrix}y_1\\y_0\end{bmatrix}$

or

$\begin{bmatrix}y_n\\y_{n-1}\end{bmatrix}=\begin{bmatrix}0&-\frac{16}{49}\\1&0\end{bmatrix}^{n-1}\begin{bmatrix}y_1\\y_0\end{bmatrix}$

Then solving the recurrence is a matter of diagonalizing the coefficient matrix, raising to the power of $n-1$ , then multiplying by the column vector containing the initial values. The solution itself would be the entry in the first row of the resulting matrix.

5 0

3 years ago

if you take a train to san francisco some location it will take 9 hours and 27 minutes if you take a plane it will take 1 hour a

AnnyKZ [126]

You would save 7 hours and 31 minutes if you take a plane

3 0

3 years ago