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Thepotemich [5.8K]
4 years ago
5

Which ordered pair could you remove from the relation {(–2, –1), (–1, 1), (–1, 0), (0, 1), (1, 0)} so that it becomes a function

?
Mathematics
2 answers:
JulijaS [17]4 years ago
7 0
Either -1,1 or -1, 0......  -1 cannot be 1 and 0 at the same time.
aliina [53]4 years ago
7 0

Answer:

the relation {(–2, –1), (–1, 1), (0, 1), (1, 0)}  is a function

the relation {(–2, –1), (–1, 0), (0, 1), (1, 0)} is a function

Step-by-step explanation:

the relation {(–2, –1), (–1, 1), (–1, 0), (0, 1), (1, 0)}

A relation is a function , when each input has only one output

First number in the relation is the input x

second number is the output y

The given relation is not a function because input -1 has to output 1  and 0

(–1, 1), (–1, 0)

To make this relation as a function , we need to remove (-1,1) or (-1,0)

the relation {(–2, –1), (–1, 1), (0, 1), (1, 0)}  is a function

the relation {(–2, –1), (–1, 0), (0, 1), (1, 0)} is a function

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"write an equation of the perpendicular bisector or the segment with endpoints Q(-2,0) and R(6,12). what does y equal? ​
anygoal [31]

Answer:

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

Step-by-step explanation:

Given points are:

Q(-2,0)\ and\ R(6,12)Q(−2,0) and R(6,12)

First of all, we have to find the slope of the given line

So,

m = \frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1

Here

(x1,y1) = (-2,0)

(x2,y2) = (6,12)

Let m1 be the slope of QR:

Then

\begin{gathered}m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}\end{gathered}m1=6+212−0=812=23

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of two perpendicular lines is -1

\begin{gathered}m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}\end{gathered}m1.m2=−123.m2=−1m2=−1∗32m2=−32

The bisector will pass through the mid-point of QR

\begin{gathered}M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)\end{gathered}M=(2x1+x2,2y1+y2)M=(2−2+6,20+12)M=(24,212)M=(2,6)

Slope-intercept form of equation is:

y = m_2x+by=m2x+b

Putting the value of slope

y = -\frac{2}{3}x+by=−32x+b

Putting (2,6) in the equation

\begin{gathered}6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}\end{gathered}6=−32(2)+b6=−34+bb=6+34b=318+4b=322

So,

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

Hence,

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

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Answer:

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