How do you solve the problem?

Write an equation in standard form of the line passing through the points (3,3) and (-3,5)

Korvikt [17]

Answer:

The equation of line AB with points (3,3) and (-3,5) is given as

: x + 3y = 12

Step-by-step explanation:

Here, the given points are A (3, 3) and B (-3,5).

Now, slope of any line is given as :

$m = \frac{y_2 - y_1}{x_2 - x_1}$

or, $m = \frac{5-3}{-3 - 3} = \frac{2}{-6} = -\frac{1}{3}$

Hence, the slope of the line AB is (-1/3)

Now , A POINT SLOPE FORM of an equation is

(y - y0) = m (x - x0) ; (x0, y0) is any arbitrary point on line.

So, for the point (3,3) the equation of the line is

y - 3 $y-3 = -\frac{1}{3} (x-3) \implies 3y - 9 = 3 -x$

Hence, the equation of line AB with points (3,3) and (-3,5) is given as:

x + 3y = 12

8 0

2 years ago

What is the domain of the function.....<br> {TIMED PLS HURRY}

timofeeve [1]

try c im sorry if im wrong i tried

6 0

2 years ago

How are number lines and the coordinate plane related?

schepotkina [342]

a coordinate plane is a two-dimensional number line where the vertical line is called the y-axis and the horizontal is called the x-axis. And a number line is
a line on which numbers are marked at intervals, used to illustrate simple numerical operations. So how are the related........?

8 0

2 years ago

What is the reciprocal of 4 5/8

Andrei [34K]

Answer:

8/45

Step-by-step explanation:

Write 4 5/8 as an improper fraction: 45/8.

Then invert this result, obtaining:

. This is the "reciprocal" of 4 5/8.

5 0

2 years ago

Read 2 more answers

What is the variance of a portfolio invested 21 percent each in a and b and 58 percent in c?

victus00 [196]

Given the following information:

$\begin{tabular}
{|p{1.5cm}|p{1.5cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|}
\multicolumn{1}{|p{1.5cm}|}{State of economy}\multicolumn{1}{|p{2.6cm}|}{Probability of State of economy}\multicolumn{3}{|p{4.8cm}|}{Rate of Return if State Occurs}\\[1ex] 
\multicolumn{1}{|p{1.5cm}|}{}\multicolumn{1}{|p{2.6cm}|}{}\multicolumn{1}{|c|}{Stock A}&StockB&Stock C\\[2ex]
\multicolumn{1}{|p{1.5cm}|}{Boom}\multicolumn{1}{|p{2.6cm}|}{0.66}\multicolumn{1}{|p{1.27cm}|}{0.09}&0.03&0.34\\
\end{tabular}$
$\begin{tabular}
{|p{1.5cm}|p{1.5cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|}
\multicolumn{1}{|p{1.5cm}|}{Bust}\multicolumn{1}{|p{2.6cm}|}{0.34}\multicolumn{1}{|p{1.27cm}|}{0.23}&0.29&-0.14\\
\end{tabular}$

Part A:

The expected return on an equally weighted portfolio of these three stocks is given by:

$0.66[0.33 (0.09) + 0.33 (0.03) + 0.33(0.34)] \\ +0.34[0.33 (0.23) + 0.33(0.29) +0.33(-0.14)] \\ \\ =0.66(0.0297 + 0.0099 + 0.1122)+0.34(0.0759+0.0957-0.0462) \\ \\ =0.66(0.1518)+0.34(0.1254)=0.1002+0.0426=0.1428=\bold{14.28\%}$

Part B:

Value of a portfolio invested 21 percent each in A and B and 58 percent in C is given by

For boom: 0.21(0.09) + 0.21(0.03) + 0.58(0.34) = 0.0189 + 0.0063 + 0.1972 = 0.2224 or 22.24%.

For bust: = 0.21(0.23) + 0.21(0.29) + 0.58(-0.14) = 0.0483 + 0.0609 - 0.0812 = 0.028 or 2.8%

Expected return = 0.66(0.2224) + 0.34(0.028) = 0.1468 + 0.00952 = 0.1563 or 15.63%

The variance is given by

$0.66(0.2224-0.1563)^2+0.34(0.028-0.1563)^2 \\ \\ =0.66(0.0661)^2+0.34(-0.1283)^2=0.66(0.00437)+0.34(0.01646) \\ \\ =0.00288+0.0056=\bold{0.00848}$

4 0

3 years ago