Write the numbers in the domain with commas between them (for example, {1, 2, 3}

Find the value of k so that the graph of 13y + kx = 4 and the line containing the points (5, -8) and (2, 4) are parallel.

guajiro [1.7K]

the graph of 13y + kx = 4 and the line containing the points (5, -8) and (2, 4) are parallel.

We find the slope of parallel line using two given points

(5, -8) and (2, 4)

Slope formula is

$slope = \frac{y_2-y_1}{x_2-x_1}$

$slope = \frac{4-(-8)}{2-5}$

$slope = \frac{12)}{-3}=-4$

so slope = -4

Slope of any two parallel lines are always equal

Lets find the slope of the equation 13y + kx = 4

Subtract kx on both sides

13 y = -kx + 4

Divide both sides by 13

$y= \frac{-kx}{13} + \frac{4}{13}$

Now slope = -k/13

We know slope of parallel lines are same

So the slope of 13y + kx = 4 is also -4

Hence we equation the slope and find out k

$\frac{-k}{13}=-4$

Multiply by 13 on both sides and divide by -1

k = 52

the value of k = 52

4 0

3 years ago

Read 2 more answers

The class average on a math test was an 82 with a standard deviation of 5. If the

Alex787 [66]

Answer:

Option 3 and 4.

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation$

Given that mean (μ) = 82, standard deviation (σ) = 5

1) For x = 74:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{74-82}{5} =-1.6$

Option 1 is incorrect

2) For x < 87

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{87-82}{5} =1$

From the normal distribution table, P(x < 87) = P(z < 1) = 0.8413 = 84.13%

Option 2 is incorrect

3) For x = 95:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{95-82}{5} =2.6$

Option 3 is correct

4) For x < 77

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{77-82}{5} =-1$

From the normal distribution table, P(x < 77) = P(z < -1) = 0.16 = 16%

Option 4 is correct

5) For x > 92

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{92-82}{5} =2$

From the normal distribution table, P(x > 92) = P(z > 2) = 1 - P(z < -2) = 1 - 0.9772 = 0.0228 = 2.28%

Option 5 is incorrect

8 0

3 years ago

Find the minimum product of two numbers whose difference is 17. <br> what are the numbers?

Marysya12 [62]

A number is an arithmetic value that is used to represent a quantity and calculate it. The two numbers will be 17 and 0, so the product of the two is minimal.

<h3>What are Numbers?</h3>

A number is an arithmetic value that is used to represent a quantity and calculate it. Numericals are written symbols that represent numbers, such as "3."

Given the difference between the two numbers is 17. Let the first number be zero, then the second number will be 17. Thus, the product of the two numbers will be 0, which is the minimum.

If the first number is further increased such as 1, then the other number will be 18, and the product of the two will be 18, which is greater than zero.

Hence, the two numbers will be 17 and 0, so the product of the two is minimal.

Learn more about Numbers:

brainly.com/question/17429689

#SPJ1

7 0

2 years ago

Negative 99610=1700 minus 55g

Stella [2.4K]

-99610=1700-55g
-1700 -1700
-101310=-55g
---------- ------
-55 -55

1842=g

4 0

3 years ago

You have 108 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the River

Licemer1 [7]

Answer:

The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.

Step-by-step explanation:

Given that,

The length of fencing of the rectangular plot is = 108 ft.

Let the longer side of the rectangular plot be x which is also the side along the river side and the width of the rectangular plot be y.

Since the fence along the river does not need.

So the total perimeter of the rectangle is =2(x+y) -x

=2x+2y-y

=x+2y

So,

x+2y =108

⇒x=108 -2y

Then the area of the rectangle plot is A = xy

A=xy

⇒A= (108-2y)y

⇒ A = 108y-2y²

A = 108y-2y²

Differentiating with respect to x

A'= 108 -4y

Again differentiating with respect to x

A''= -4

For maximum or minimum, A'=0

108 -4y=0

⇒4y=108

$\Rightarrow y=\frac{108}{4}$

⇒y=27.

$A''|_{y=27}=-4$

Since at y= 27, A''<0

So, at y=27 ft , the area of the rectangular plot maximum.

Then x= (108-2.27)

=54 ft.

The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.

3 0

3 years ago