Which of the following cannot be determined?

How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?

Arturiano [62]

Answer:

$y = \frac{2}{3} x + 2$

Step-by-step explanation:

Start by finding the slope of the given line.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope of given line

$= \frac{5 - ( - 1)}{ - 2 - 2}$

$= \frac{5 + 1}{ - 4}$

$= \frac{6}{ - 4}$

$= - \frac{3}{2}$

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

$- \frac{3}{2} m = - 1$

$m = - 1 \div ( - \frac{3}{2} )$

$m = - 1 \times ( - \frac{2}{3} )$

$m = \frac{2}{3}$

$y = \frac{2}{3}x + c$ , where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

$\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}$

Midpoint of given line

$= ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )$

$=( \frac{0}{2} , \frac{4}{2} )$

= (0, 2)

$y = \frac{2}{3} x + c$

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is $y = \frac{2}{3} x + 2$ .

7 0

2 years ago

Everything else right but just can’t figure that fraction out.

krok68 [10]

Answer: 1/5

Step-by-step explanation: Since there are 5 blue/green marbles in the bag of 20 it would be 5/20 or 1/5.

6 0

2 years ago

g In 2013, the Pew Research Foundation reported that 43% of U.S. adults report that they live with one or more chronic condition

SOVA2 [1]

Answer:

We are 95% confident that the true proportion of U.S. adults who live with one or more chronic conditions is between 39.7% and 46.33%

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 43\% = 0.43$

The standard error is $SE = 0.017$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = (100-95)\%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * SE$

=> $E = 1.96 * 0.017$

=> $E = 0.03332$

Generally 95% confidence interval is mathematically represented as

$\r p -E < p < \r p +E$

=> $0.43 -0.03332 < p < 0.43 + 0.03332$

=> $0.39668 < p < 0.46332$

Converting to percentage

$(0.39668 * 100)< p < (0.46332*100)$

$39.7\% < p < 46.33 \%$

7 0

3 years ago

The sum of two numbers is 30 and their difference is 6

Studentka2010 [4]

I'm going to assume that you are trying to find the two numbers. Based on the information in the problem, we can create the following equations (where $a$ and $b$ are the two numbers):

$a + b = 30$

$a - b = 6$

We have a systems of equations. In this case, it would be easier to use elimination by adding vertically. This produces the result:

$2a = 36$

$a = 18$

To find $b$ , substitute the value for $a$ into one of the earlier equations:

$18 + b = 30$

$b = 12$

The two numbers are 12 and 18.

4 0

2 years ago

Two sides of a triangle are equal in length and double the length of the shortest side. The perimeter of the triangle is 36 inch

Lostsunrise [7]

To solve this, you can set up an equation. Make the length of the shortest side x, so the 2 sides double the length will equal 2x. Since they all equal the perimeter of 36, do x + 2x + 2x =36. These values all represent the sides(2 longer, one short). Combine like terms to get 5x=36 then divide by 5 to find the value of x. x=7.2in meaning the shorter side is 7.2 inches while the longer sides are both 14.4 inches each since they are double in size.

3 0

3 years ago