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jenyasd209 [6]
4 years ago
12

Write an equation of the line that passes through the given points: (9/2,1), (-7/2,7) please show step by step how to do this. T

he answer should be: y=-3/4x+35/8.
Mathematics
1 answer:
Viktor [21]4 years ago
6 0

Explanation:

The easiest way to do this is to make use of the 2-point form of the equation for a line. For points (x₁, y₁) and (x₂, y₂), the equation is ...

  y=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1

Filling in your given points, the equation becomes ...

  y=\dfrac{7-1}{\frac{-7}{2}-\frac{9}{2}}(x-\frac{9}{2})+1

After you fill in the values, it is a matter of simplifying the resulting equation.

y=\dfrac{6}{\frac{-16}{2}}(x-\frac{9}{2})+1=\dfrac{-12}{16}(x-\frac{9}{2})+1=-\dfrac{3}{4}x+\left(\dfrac{-3}{4}\cdot\dfrac{-9}{2}\right)+1\\\\y=-\dfrac{3}{4}x+\dfrac{27+8}{8}\\\\y=-\dfrac{3}{4}x+\dfrac{35}{8}

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VMariaS [17]

The inequality boils down to

|<em>y</em>| > <em>y</em>

By definition of absolute value, we have

• |<em>y</em>| = <em>y</em> if <em>y</em> ≥ 0

• |<em>y</em>| = -<em>y</em> if <em>y</em> < 0

So if <em>y</em> ≥ 0, we have

<em>y</em> > <em>y</em>

but this is a contradiction.

On the other hand, if <em>y</em> < 0, we have

-<em>y</em> > <em>y</em>   ==>   2<em>y</em> < 0   ==>   <em>y</em> < 0

and no contradiction.

Now replace <em>y</em> with (<em>x</em> + 1)/(<em>x</em> - 1) + 1. Then you're left with solving

(<em>x</em> + 1)/(<em>x</em> - 1) + 1 < 0

(<em>x</em> + 1 + <em>x</em> - 1)/(<em>x</em> - 1) < 0

2<em>x</em>/(<em>x</em> - 1) < 0

The left side is negative if either 2<em>x</em> > 0 and <em>x</em> - 1 < 0, or 2<em>x</em> < 0 and <em>x</em> - 1 > 0. The first case reduces to <em>x</em> > 0 and <em>x</em> < 1, or 0 < <em>x</em> < 1. In the second case, we get <em>x</em> < 0 and <em>x</em> > 1, but <em>x</em> cannot satisfy both conditions, so we throw this case out.

7 0
3 years ago
After stepping into a room with unusual lighting, Reagan's pupil has a radius of 1 millimeter. What is the pupil's area?
Alexeev081 [22]
Answer: The formula is PI * RADUIS²
So, multiplying the radius by itself is 1, and then multiplying 1 by PI is the same as 3.14 .



8 0
2 years ago
The sum of the coordinates of the vertex of the parabola at y = x2 + 3 is _____.
Novosadov [1.4K]

Answer: The sum is 3.

Step-by-step explanation:

If we have a parabola, y = a*x^2 + b*x + c

We want to find the point (x, y) that corresponds to the vertex of that parabola.

The vertex of the parabola is at x value:

x = -b/2a

in this case

a = 1, b = 0, c = 3

then our vertex is at:

x = -0/2*1 = 0

Now we evaluate y(x) in this value and get:

y(0) = a*0^2 + 3 = 3

Then the vertex is at the point (0, 3)

the sum of the coordinates of the vertex is:

S = 0 + 3 = 3

7 0
3 years ago
Suppose that x=6 and y=8. If y is inversely related to x, what is y when x=3?
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3 years ago
A school bus has 25 seats, with 5 rows of 5 seats. 10 students from 2nd grade and 5 students from 1st grade travel on the bus. H
andre [41]

Answer:

(Answer in attachment, explanation below)

Step-by-step explanation:

The answer is B. 5P5 x 20P15.

This is because to make the second grade students to sit in the first row we have 5 seats and 5 students so we will permute the 5 students to those 5 seats. So 5P5.

Now we are left with 20 seats and 15 first grade students so we can simply permute those 15 students into those 20 seats. So 20P15.

Finally using the counting rule principle we will multiply both of these so 5P5 x 20P15.

No. of students from first grade = 15

No. of students from second grade = 5

There are 5 rows of seats

Each row contains 5 seats

Total seats = 25

No. of ways for second-grade students occupy the first row(i.e first 5 seats) =  

Remaining seats = 20

No. of students from first grade = 15

So, No. of ways for first-grade students occupy remaining seats =  

So,  No. of ways for the students can be seated if all of the second-grade students occupy the first row =  

So, Option B is true

Hence No. of ways for the students can be seated if all of the second-grade students occupy the first row is

7 0
3 years ago
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