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2 years ago

Write an equation perpendicular to x-4y=20 that passes through the point 2,-5

Mathematics

1 answer:

marshall27 [118]2 years ago

3 0

Answer:

4x +y = 3

Step-by-step explanation:

Perpendicular lines have slopes that are the negative reciprocals of one another. When the equation of the line is written in standard form like this, the equation of the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Doing this much would give you ...

4x +y = (constant)

Note that we have chosen to make the equation read 4x+y, not -4x-y. The reason is that "standard form" requires the leading coefficient to be positive.

Now, you just need to make sure the constant is appropriate for the point you want the line to go through. So, it needs to be ...

4(2) +(-5) = constant = 3

The line of interest has equation ...

4x + y = 3

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Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 8 and 22 minutes, inclusive. Let X =

salantis [7]

Answer:

$P(X>14)= 1-P(X$

And replacing we got:

$P(X>14)= 1- \frac{14-8}{22-8}= 0.5714$

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

Step-by-step explanation:

We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:

$X \sim Unif (a= 8, b=22)$

And for this case we want to find the following probability:

$P(X>14)$

We can find this probability using the complement rule and the cumulative distribution function given by:

$P(X$

Using this formula we got:

$P(X>14)= 1-P(X$

And replacing we got:

$P(X>14)= 1- \frac{14-8}{22-8}= 0.5714$

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

6 0

2 years ago

Express 3.222......in p/q form

beks73 [17]

Answer:

3.22222...... = $\frac{29}{9}$

Step-by-step explanation:

In this question we have to convert the number given in recurrent decimals into fraction.

Recurrent decimal number is 3.22222.......

Let x = 3.2222......... -------(1)

Multiply this expression by 10.

10x = 32.2222........... -------(2)

Now subtract the expression (1) from (2),

10x = 32.22222.....

9x = 29

x = $\frac{29}{9}$

Therefore, recurrent decimal number can be written as $\frac{29}{9}$ which is in the form of $\frac{p}{q}$ .

6 0

2 years ago

Solve for x in the equation x squared minus 12 x + 36 = 90. x = 6 plus-or-minus 3 StartRoot 10 EndRoot x = 6 plus-or-minus 2 Sta

goldenfox [79]

Answer: x = 6 plus-or-minus 3 StartRoot 10

Step-by-step explanation:

The given quadratic equation is expressed as

x² - 12x + 36 = 90

Rearranging the equation so that it takes the the standard form of

ax² + bx + c, it becomes

x² - 12x + 36 - 90 = 0

x² - 12x - 54 = 0

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 1

b = - 12

c = - 54

Therefore,

x = [- - 12 ± √(- 12² - 4 × 1 × - 54)]/2 × 1

x = [12 ± √(144 + 216)]/2

x = [12 ± √360]/2

x = (12 ± 6√10)/2

x = 6 + 3√10

3 0

2 years ago

Read 2 more answers

Lindsay and menonhave 1,240 stickers.menon has 4 times as many stickers as Lindsay.menon decides to have 6 stickers on each page

Lemur [1.5K]

a) Menon has 992 stickers. We can find this by writing an algebraic expression for the number of stickers, with x being the number that Lindsay has. This gives us:

x + 4x = 1240

5x = 1240

x = 248

Now we multiply 248 by 4 to get 992.

b) There are 2 stickers left over. First we have to divide 992 by 6, which gives us 165 as a whole number, but then a remainder of 2. That means that there are two stickers left.

c) Menon needs 4 more stickers, as 6 - 2 = 4, and there are 6 stickers per page.

I hope this helps! Let me know if you have any questions :)

5 0

2 years ago

a package shaped like a cube has an edge that is 28 cm long. How much space is available to pack inside your box?

Tema [17]

Answer: 21,952 cm³

Explanation:

Volume = 28 x 28 x 28 = 29 152 cm³

7 0

2 years ago