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3 years ago

What is the slope of the line that passes through the points (-2 4) and (8 -1)

Mathematics

2 answers:

Elina [12.6K]3 years ago

7 0

Answer: -2-8= -10

4+1 = 5 (the negative switches to a positive)

Your slope equals -10/5. You can look at this in a fraction for when you might use it later in point slope or slope intercept form, or you can just simplify it to -2. It might also be helpful to remember the numerator as the rise and the denominator as run, or “rise over run” if you need to graph it.

Slope = -10/5 or -2

Step-by-step explanation:

Slope, often referred to as the variable “m” can be found by solving y2-y1/x2-x1. You can do it the opposite way, though make sure the y-values are on the top.

Ahat [919]3 years ago

3 0

Answer:

-5/6

Step-by-step explanation:

-1-4=-5

8-(-2)=-6

the slope is m=-5/6

m=rise/run=y₂-y₁/x₂-x₁

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4. You read an article in your local newspaper about a discussion between the owner of a popular business and a group

Alona [7]

The business owner should be told to angle a spotlight mounted on the roof at the angle of =39°

<h3>Calculation of angle</h3>

The distance of the flagpole from the building = 55ft

The building has the height of = 45ft

The flagpole has the height of = 25ft

The angle can be calculated using the formula;

Tan θ = opposite/adjacent

Where opposite= 45ft

adjacent = 55ft

Tan θ = 45/55 = 0.82

θ = Tan–¹0.82

θ = 39°

Learn more about angles here:

brainly.com/question/25716982

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5 0

2 years ago

Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 s

Llana [10]

First, we need to work out the total number of students who were being surveyed.

We know that half of the students has two pets. The rest of the students make up the other half. So, we have 3 students + 2 students + 8 students = 13 students that make half of the sample population

That means total number of students being surveyed is 13+13=26 students

Then we work out the probability
P(One pet) = 8/26 = 4/13
P(Two pets) = 1/2
P(Three pets) = 3/26
P( Four pets) = 2/26 = 1/13

The probability distribution is shown in the table below. Let $x$ be the number of pets and $P(X=x)$ is the probability of owning the number of pets

3 0

3 years ago

Read 2 more answers

Look at the pentagonal numbers. Use finite differences to determine which function represents the pattern.

Ahat [919]

Answer:

f(x) = 1.5x - 0.5x

Step-by-step explanation:

The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.

The triangular number general formula

x (x + 1) / 2

For example,

The sequence

1, 3, 6, 10

* * *

* * * * * *

* , * *, * * *, * * * *

_____________________________

The pentagonal numbers

The sequence:

1, 5, 12, 22, 35

As shown in the picture can be divided into three triangles

Triangle 2

x (x + 1) / 2

Triangle 1 and 3 (they are triangles one unit smaller than 2)

n (n + 1) / 2

n= x-1

Replacing n

(x-1) ((x-1) + 1) / 2

(x-1) (x) / 2

(x-1) x / 2

______________

Function represents the pattern

Triangle 2 + (Triangle 1 + Triangle 3)

Triangle 1 = Triangle 3

So then,

Triangle 2 + 2* Triangle 1

x (x +1) /2 + 2* (x -1) x/2

Rearranging

0.5 x (x +1) + x(x -1)

0.5x^2 + 0.5x + x^2 -x

(0.5 x^2 + x^2) + (0.5x -x )

1.5 x^2 - 0.5 x

______

3 0

3 years ago

Read 2 more answers

Find the equation of line b described below, in slope-intercept form

Serjik [45]

Given:

Line a is perpendicular to line b .

Line a passes through the points (1,-8) and (9,-12) .

Line b passes through the point (-8, -16).

To find:

The equation of b.

Solution:

Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m_a=\dfrac{-12-(-8)}{9-1}$

$m_a=\dfrac{-12+8}{8}$

$m_a=\dfrac{-4}{8}$

$m_a=-\dfrac{1}{2}$

Product of slopes of two perpendicular lines is -1.

$m_a\times a_b=-1$

$-\dfrac{1}{2}\times a_b=-1$

$b=2$

Slope of line b is 2.

If a line passing through a point $(x_1,y_1)$ with slope m, then equation of line is

$y-y_1=m(x-x_1)$

Line b passing through (-8,-16) with slope 2. So, equation of line b is

$y-(-16)=2(x-(-8))$

$y+16=2(x+8)$

$y+16=2x+16$

Subtract 16 from both sides.

$y=2x$

Therefore, the equation of line b is $y=2x$ .

7 0

3 years ago

Which expression is equivalent to...

torisob [31]

Answer:

$x^{\frac{2}{7} } y^{-\frac{3}{5} } \\$ i.e answer A.

Step-by-step explanation:

This question involves knowing the following power/exponent rule:

$\sqrt[n]{x^m} = x^\frac{m}{n} \\\\so \sqrt[7]{x^2} = x^\frac{2}{7} \\\\and \\\\ \sqrt[5]{y^3} = y^\frac{3}{5} \\$

Next, when a power is on the bottom of a fraction, if we want to move it to the top, this makes the power become negative.

so the y-term, when moved to the top of the fraction, becomes:

$y^{-\frac{3}{5} } \\$

So the answer is: $x^{\frac{2}{7} } y^{-\frac{3}{5} } \\$

7 0

3 years ago