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2 years ago

Which of the following tables does not represent a function?

Mathematics

1 answer:

uranmaximum [27]2 years ago

3 0

Answer:

It's the 3rd option

Step-by-step explanation:

A function cannot have one value of 5 associated to more than one value on y

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A triangle has vertices at (1,10), (-5,2), and (7,2). What is its orthocenter. Show your work.

kondor19780726 [428]

Answer:

Question: What is the orthocenter of a triangle with the vertices (-1,2) (5,2) and (2,1)?

The coordinates of point A are (-1,2), point B are (5,2), and point C are (2,1).

The orthocent is the intersection of the three altitudes. An altitude goes from a vertex and is perpendicular to the line containing the opposite side.

In the coordinate plane the equations of the altitudes can be found and then a system of equations can be solved.

Altitude 1. From point C perpendicular to the line containing side AB.

Slope of line AB is 0 (horizontal line), a vertical line is perpendicular to a horizontal line. Thus, the equation of altitude 1 is x=2 .

Altitude 2. From point B perpendicular to the line containing side AC.

Slope of line AC is −13 , the slope of a line perpendicular to line AC is 3. The equation of altitude 2 is y=3x−13

Altitude 3. From point A perpendicular to the line containing side BC.

Slope of line BC is 13 , the slope of a line perpendicular to line BC is −3 . The equation of altitude 3 is y=−3x−1

The orthocenter is the point where all three altitudes intersect.

x=2

y=3x−13

y=−3x−1

Use substitution to solve the first two equations y=3(2)−13=−7

The orthocenter is the point (2,−7)

we did not need the third equation, but we can use it as a check, plug the coordinates into the third equation:

−7=−3(2)−1

−7=−6−1

−7=−7 it works.

3 0

3 years ago

Write the equation of a line that has a slope of -7 and a y intercept of 9. ( Hint: Use the formula y = mx + b )

iogann1982 [59]

The y intercept is 9 and the unit rate is -7

So we plug these numbers in
y= -7x (the unit rate)+ 9 (y intercept)

y= -7x+9

8 0

3 years ago

Read 2 more answers

What is the ratio fraction form of 25:9

kipiarov [429]

Answer:

25/9

Step-by-step explanation:

Fraction is 25/9 and it's simplified.

Hope my answer has helped you if not i'm sorry.

6 0

3 years ago

Solve the inequality n/-3 + 8 > 6.

yan [13]

-(n/3)+8>6
-n+24>18
-n>-6
n<6

8 0

3 years ago

Find the mean of each distribution.

Vanyuwa [196]

Answer:

a) 23 °C

b) 5.81 m² (2 dp)

Step-by-step explanation:

This set of data is presented as a <u>Dot Plot</u>.

The frequency (how often a data value occurs) is represented by the number of dots above each data value.

For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.

To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.

$\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}$

This set of data is presented as a <u>stem and leaf diagram</u>, where the units and tenths are split. The units column is the 'stem' and the tenths become the 'leaf'.

Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8

To find the mean, sum the data values, then divide by the total frequency.

To find the total frequency, simply count the number of values in the leaf part of the diagram.

Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4

Total frequency = 11

$\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}$

4 0

2 years ago

Read 2 more answers