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3 years ago

What is the slope of a line perpendicular to the line whose equation is x-y=6x. Fully reduce your answer.

Mathematics

2 answers:

Over [174]3 years ago

5 0

Answer

1/5

Step-by-step explanation:

The slope of a perpendicular line is the negative reciprocal. Since y=-5x(m=-5), the slope is -(-1/5) which is 1/5

Wittaler [7]3 years ago

3 0

<h3>Answer:</h3>

$\boxed{\boxed{\pink{\bf \leadsto Hence \ the \ Slope \ the \ line \ is \ \dfrac{1}{5} . }}}$

<h3>Step-by-step explanation:</h3>

A linear equation is given to us and we need to find the slope of the line perpendicular to it . Given linear equation to us is ,

$\bf\implies x - y = 6x$

Let's convert this into Slope intercept form to find the slope of the line . The slope intercept form is y = mx + c , where m is the slope of the line.

$\bf\implies x - y = 6x \\\\\bf\implies x - y -6x = 0 \\\\\bf\implies- y - 5x = 0 \\\\\bf\implies y = -5x \\\\\bf\implies \boxed{\red{\bf y = -5x + 0 }}$

Hencs on comparing to the standard form of Slope intercept form of the line , we get to know that the slope of the line is -5.

The equation of a perpendicular line to y = -5x

must have a slope that is the negative reciprocal of the original slope. Hence ,

$\bf\implies m_{perpendicular}= - \dfrac{1}{m}\\\\\bf\implies m_{perpendicular}= -\dfrac{1}{-5}\\\\\bf\implies \boxed{\red{\bf Slope_{perpendicular}= \dfrac{1}{5} }}$

<h3>★ Hence the slope of the line is⅕.</h3>

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Is (x-3) a factor of f(x) = x^2 - 32?

Leokris [45]

Answer:

$No$

Explanation:

Here, we want to use the factor theorem to check if the given linear expression is a factor of the binomial

Now, according to the factor theorem, a factor of a polynomial would leave no remainder when divided by it

Mathematically, it means when we substitute the factor value into the polynomial, it is expected that the remainder is zero is the substituted is a factor of the polynomial

We set x-2 to zero:

$\begin{gathered} \text{ x-2 = 0} \\ x\text{ = 2} \end{gathered}$

Now, we substitute 2 into the polynomial as follows:

$f(2)\text{ = }2^2-32\text{ = 4-32 = -28}$

There is a remainder of -28 and thus, the linear factor is not a factor of the binomial

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1 year ago

State of the given functions are inverses. Part 3. NO LINKS!!!!

Effectus [21]

Answer:

h(x)=-x-1

let y =-x-1

interchanging role of x & y

x=-y-1

y=-x-1

h-¹(x)=-x-1

again

f(x)=(2-3x)/2

let

y=(2-3x)/2

interchanging role of x & y

x=(2-3y)/2

2x-2=-3y

y=(2-2x)/3

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Given function are not inverse of each other.

10.

f(x)=-x+3

let y=-x+3

interchanging role of x & y

x=-y+3

y=3-x

f-¹(x)=-x+3

equal to g(x)=-x+3

Given function are inverse of each other.

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2 years ago

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Rachel is a lunchroom supervisor at West School. The children eat lunch at 15 long tables. When all tables are used, 240 childre

Diano4ka-milaya [45]

240÷15=16 seats at each table

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3 years ago

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A data set with a mean of 34 and a standard deviation of 2.5 is normally distributed

tresset_1 [31]

Answer:

a) $z= \frac{34-34}{2.5}= 0$

$z= \frac{39-34}{2.5}= 2$

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

b) $P(X$

$z= \frac{31.5-34}{2.5}= -1$

So one deviation below the mean we have: (100-68)/2 = 16%

c) $z= \frac{29-34}{2.5}= -2$

$z= \frac{36.5-34}{2.5}= 1$

For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%

Step-by-step explanation:

For this case we have a random variable with the following parameters:

$X \sim N(\mu = 34, \sigma=2.5)$

From the empirical rule we know that within one deviation from the mean we have 68% of the values, within two deviations we have 95% and within 3 deviations we have 99.7% of the data.

We want to find the following probability:

$P(34 < X$

We can find the number of deviation from the mean with the z score formula:

$z= \frac{X -\mu}{\sigma}$

And replacing we got

$z= \frac{34-34}{2.5}= 0$

$z= \frac{39-34}{2.5}= 2$

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

For the second case:

$P(X$

$z= \frac{31.5-34}{2.5}= -1$

So one deviation below the mean we have: (100-68)/2 = 16%

For the third case:

$P(29 < X$

And replacing we got:

$z= \frac{29-34}{2.5}= -2$

$z= \frac{36.5-34}{2.5}= 1$

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2 years ago

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Sergio039 [100]

The ratio of Isabella’s money to Shane’s money is 3:11

Isabella has $33.

We can make a proportion to solve for how much money Shane has.
A proportion is two ratios that are set equal to each other.

Let’s call Shane’s money ‘S’

We get this proportion: 3/11 = 33/x

If we cross multiply we get:
(33) * (11) = (3) * (x)

Simplifying it, we get:
363 = (3) * (x)

Divide both sides by 3, we get:
x = 121

However, the question asks how much money they have together.

Isabella + Shane = Total
33 + 121 = $154

They have $154 together.

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