Mathematics College

Calculate the slope of the given line using either the slope formula m = y 2 − y 1 x 2 − x 1 or by counting r i s e r u n . Simplify your answer. You can choose your method.

Answers

Answer 1

The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Replacing with the points (-8, 3) and (0,1) we get:

[tex]m=\frac{1-3}{0-_{}(-8)}=\frac{-2}{8}=-\frac{1}{4}[/tex]

Related Questions

What is the polar form of the equation? What type of polar curve is this?

Answers

The curve is given to be:

[tex]x^2+y^2+12y=0[/tex]

We can rewrite the equation in the form:

[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]

Using the Completing the Square method, we have the equation to be:

[tex]\frac{\left(x-0\right)^2}{6^2}+\frac{\left(y-\left(-6\right)\right)^2}{6^2}=1[/tex]

Therefore, the ellipse's center is (0, -6).

If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96

Answers

Answer:

2/3

Step-by-step explanation:

y = xk

6 = 72K Solve for k Divide both sides by 72

[tex]\frac{1}{12}[/tex] = k

y = xk

y = [tex]\frac{8}{1}[/tex] x [tex]\frac{1}{12}[/tex]

y = [tex]\frac{8}{12}[/tex] I can simplify by dividing the numerator and denominator by 4

y = 2/3

What is the area of this triangle?
Pls help :(

Answers

24
Remember the formula
A=1/2(B)(H)

Write this trinomial in factored form. 5a² - 30 - 14

Answers

[tex]5x^2-3x-14[/tex]

replace x with a for this exercise

we use this formula to factor

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

where a=5, b=-3 and c=-14

[tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}[/tex][tex]\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=\frac{3\pm17}{10} \end{gathered}[/tex]

we have two roots

[tex]\begin{gathered} x=\frac{3+17}{10} \\ x=2 \end{gathered}[/tex]

and

[tex]\begin{gathered} x=\frac{3-17}{10} \\ \\ x=-\frac{7}{5} \end{gathered}[/tex]

so the simplified equation is

[tex](x-2)(x+\frac{7}{5})[/tex]

now replace x for a

[tex](a-2)(a+\frac{7}{5})[/tex]

Which expression is equivalent to (m−5n−3)−3?

m−15n−9
m15n9
m−8n−6
1 over the quantity m raised to the eighth power times n raised to the sixth power end quantity

Answers

The expression (m⁻⁵n⁻³)⁻³ has an equivaent of m⁻¹⁵n⁹

How to determine the equivalent expression

From the question, the expression is represented as

(m−5n−3)−3

Rewrite the expression properly

This is done as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

This gives

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution is (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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The given expression (m⁻⁵n⁻³)⁻³ has an equivalent to the m⁻¹⁵n⁹

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is represented as (m−5n−3)−3

Rewrite the expression as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets , we have

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products, we have;

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution will be; (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Read more about equivalent expression at;

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Patrick is buying a new car. He can choose the body style, color and engine type. If there are 54 ways he can select a car, with there body styles and two engine choices , his many colors are available

Answers

Given:

Total Number of ways = 54

Number of body styles = 3

Number of engine choices = 2

Let's find the number of colors available.

To find the number of colors available, we have:

Number of ways = Number of body styles x Number of engine choices x Number of colors

54 = 3 x 2 x c

Where c represent the available number of colors.

Let's find c.

54 = 3 x 2 x c

54 = 6c

Divide both sides by 6:

[tex]\begin{gathered} \frac{54}{6}=\frac{6c}{6} \\ \\ 9=c \\ \\ c=9 \end{gathered}[/tex]

Therefore, there are 9 colors available to select from.

ANSWER:

what is the line that passes through points(-6,-10)(-2,-10)

Answers

The line passes through the points, (-6,-10) and (-2,-10)

We know equation of the line passing through points (x',y') and (x'',y'') is given by:

[tex]y-y^{\prime}=\frac{y^{\prime}^{\prime^{}}-y^{\prime}}{x^{\prime}^{\prime}-x^{\prime}}(x-x^{\prime})[/tex]

So the equation of the line is:

[tex]\begin{gathered} y-(-10)=\frac{-10-(-10)}{-2-(-6)_{}}(x-(-6)) \\ \Rightarrow y+10=0 \\ \Rightarrow y=-10 \end{gathered}[/tex]

The equation of the line is y=-10

The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =

For part c) and e), Is the assumption of normal necessary? NoYes

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The distribution is: x¯ ~ N(22, 1.45).

b) The distribution is: ∑x ~ N(902, 59.55).

c) P( ¯x > 19.8214) = 0.9332 = 93.32%.

d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.

e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.

f) Q1 for the x¯distribution = 21 points a game.

g) P( ∑x > 829.0774) = 0.8888 = 88.88%.

Assumption of normality is not necessary, as the sample sizes are greater than 30.

Normal Probability Distribution

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of [tex]\n\mu[/tex] and the standard deviation is of [tex]\sigma\sqrt{n}[/tex].Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.

For a single game, the mean and the standard deviation of the number of points scored are given as follows:

[tex]\mu = 22, \sigma = 9.3[/tex]

For the average of 41 games, the standard error is:

[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]

Hence the distribution is: x¯ ~ N(22, 1.45).

For the sum of the 41 games, the mean and the standard error are given as follows:

41 x 22 = 902.[tex]s = 9.3\sqrt{41} = 59.55[/tex].

Hence the distribution is: ∑x ~ N(902, 59.55).

In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem: