What is one sixth plus one fourth?

Given GHI G (4,-3), H (-4,2), and I (2,4), find the perpendicular bisector of HI in standard form.

Olin [163]

Answer:

$3x+y=0$

Step-by-step explanation:

step 1

Find the slope of segment HI

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

H (-4,2), and I (2,4)

substitute the given points

$m=\frac{4-2}{2+4}$

$m=\frac{2}{6}$

simplify

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

step 2

Find the slope of the perpendicular line to segment HI

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=\frac{1}{3}$

so

$m_2=-3$

step 3

Find the midpoint segment HI

we know that

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

H (-4,2), and I (2,4)

substitute

$M(\frac{-4+2}{2},\frac{2+4}{2})$

$M(-1,3)$

step 4

we know that

The perpendicular bisector of HI is a line perpendicular to HI that passes though the midpoint of HI

Find the equation of the perpendicular bisector of HI in point slope form

$y-y1=m(x-x1)$

we have

$m=-3$

$M(-1,3)$

substitute

$y-3=-3(x+1)$

step 5

Convert to slope intercept form

$y=mx+b$

Isolate the variable y

$y-3=-3x-3$

$y=-3x-3+3$

$y=-3x$

step 6

Convert to standard form

$Ax+By=C$

where

A is a positive integer

B and C are integers

$y=-3x$

Adds 3x both sides

$3x+y=0$

see the attached figure to better understand the problem

3 0

4 years ago

1.

svetoff [14.1K]

The following statements are true;

The expression 23h represents the total charge for Elegance Home Painting.

If José hires the painters for 10 hours, then Elegance Home Painting will be cheaper.

If José hires the painters for 20 hours, then Krystal Klean Painting will be cheaper.

Step-by-step explanation:

Given,

Amount charged by Krystal Klean painting to come out = $175.00

Per 30 minutes charges = $7

1 hour charges would be $14.

Let,

h be the number of hours.

Total cost for Krystal Klean = 14h + 175

Amount charged by Elegance per hour = $23

Total cost = 23h

The expression 23h represents the total charge for Elegance Home Painting.

As Jose will choose from both painters, therefore, he will only hire one.

For 10 hours;

h = 10

Krystal Klean;

Total charges = 175 + 14(10)

Total charges = 175 + 140 = $315

Elegance Home;

Total charges = 23(10) = $230

If José hires the painters for 10 hours, then Elegance Home Painting will be cheaper.

For 20 hours;

h = 20

Krytal Klean,

Total charges = 175 + 14(20) = $455

Elegance Home = 23(20) = $460

If José hires the painters for 20 hours, then Krystal Klean Painting will be cheaper.

6 0

3 years ago

Help please! <br><br> Which graph below shows the rule output = 5 times input

skelet666 [1.2K]

The first graph does. This is because of the rate of growth most likely being 5x.

8 0

3 years ago

Read 2 more answers

Can two box plots have the same range and iqr and yet represent completely diff data.. explain

Mila [183]

Yes it is possible. Consider the following scenarios

Scenario A:
Min = 5
Q1 = 10
Median = 12
Q3 = 18
Max = 22

The IQR is equal to the difference of Q3 and Q1
IQR = Q3-Q1 = 18-10 = 8
The range is the difference of the min and max
Range = Max - Min = 22 - 5 = 17

So in summary for scenario A, we have
IQR = 8
Range = 17

----------------------------------------------------------

Now consider another scenario, call it scenario B, where

Min = 100
Q1 = 102
Median = 105
Q3 = 110
Max = 117

I claim that the IQR and Range for scenario B is going to be the same as in Scenario A. Let's find out

IQR = Q3 - Q1 = 110 - 102 = 8
Range = Max - Min = 117 - 100 = 17

So
IQR = 8
Range = 17
which is identical to scenario A.

-------------------------------------------------------------------------------

Scenario B has completely different data than scenario A, yet the IQR and Range are equal to scenario A's counterparts. This shows that it is possible to have 2 completely sets of data yet have the same IQR and range.

The wrap up here, and the answer to the question, is "yes it is possible" with the explanation given above.

4 0

3 years ago

945 round nearest ten

Pavlova-9 [17]

945 rounded to the nearest ten is 950

7 0

3 years ago

Read 2 more answers