Find the value of x or y so that the line passing through the two points has the given slope
16. (-3, y), (-9, -2); m = 1

The required number line attached below shows a number that is greater than –3 and less than 2.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The number line indicates a number that is greater than –3 and less than 2.

Now, we have a number that represents x > -3 and x < 2. Here -3 and 2 are not included in the solution set, so there is an open circle on -3 and 2.

Thus, the solution interval for the given compound inequality is (-3, 2).

The number line is shown below.

Learn more about the number line here:

brainly.com/question/17617832

#SPJ1

Answer: 135°

Step-by-step explanation:

Since π = 180°

(3 × π)/ 4

Substitute 180° for π

= (3 × 180)/4

Simplify

= 540/4

= 135°

Answer:

D. x = 12

I hope this helps!

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The solution of the given linear system of equations is x = 2, y = 1 and z = 2.

Given that the linear system of equations is

2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3

To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:

A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]

To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:

|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12

The determinant is non-zero, hence A is invertible

A⁻¹ = 1/|A| [adj A]

where adj A is the transpose of the cofactor matrix [C] of A:

adj A = [C]T

So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:

C = [5, 2, 6; 2, -2, 2; -4, -4, -4]

Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]

To solve the system of equations, we have x = A⁻¹B as below:

x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]

To know more about linear system, visit:

https://brainly.com/question/26544018

#SPJ11

Answer:

equally likely

Step-by-step explanation:

Rainbows usually appear after it rains, but not always, there usually has to be certain specific conditions for it to happen.

Hope this helps! Have a good day! :)

Hope it helps.

If you have any query, feel free to ask.

The following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

It is given that the equation is,

y − 8 = 15 (x + 5)

y=15(x+5)+8

y=15x+75+8

y=15x+83

A linear equation has the form y = mx + b in the slope-intercept format.

Thus, the following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ1

By using addition, it can be calculated that

Trina, Juan and their father can do one boat ride.

What is addition?

Suppose there are many numbers and we need to find the sum total of all those numbers, then the operation used in this case is called addition.

This is a word problem on addition

Cost of adult admission = $7

Cost of child admission = $5

Cost of boat ride for adult  = $3

Cost of boat ride for child = $2

Total expense for adult = $(7 + 3) =$10

Total expense for child = $(5 + 2) =$7

Trina and Juan and their father have $33 to spend at the water park

Trina and Juan qualify for a child's admission

Total expense for one boat ride = $(7 + 7 + 10) = $24

Total expense for two boat rides = $(24 + 24) = $48

But they have $33 to spend

So Trina, Juan and their father can do one boat ride.

To learn more about addition, refer to the link-

https://brainly.com/question/24536701

#SPJ4

Here, x value of 8 would be located on the left tail of the normal distribution curve, 3.67 standard deviations below the mean (μ=22.3) and with a very low value in terms of percentile or probability (0.015%).

To indicate where the given x value of 8 would be on the curve, we need to plot it on a normal distribution curve with a mean (μ) of 22.3 and a standard deviation (σ) of 3.9.
First, we need to convert the given x value of 8 into a z-score by using the formula:  z = (x - μ) / σ
Plugging in the values, we get: z = (8 - 22.3) / 3.9 = -3.67
This means that the value of 8 is located 3.67 standard deviations below the mean.
Next, we need to find this point on the normal distribution curve. We can use a z-score table or a graphing calculator to find the corresponding area under the curve.
If we use a z-score table, we can look up the area to the left of -3.67, which is 0.00015. This means that only 0.015% of the data falls below this point.
To plot this on the curve, we can locate the mean (μ) and mark it as the center of the curve. Then, we can count 3.67 standard deviations to the left of the mean and mark this as the point where the value of 8 would be located.

Learn more about standard deviation here, https://brainly.com/question/475676

#SPJ11

Answer:D

Step-by-step explanation:

21.25 x 3= 63.75

21.25 x 4 = 85

21.25 x 6= 127.50

If the cost of advertising was $100,000 and the reach or circulation was 10,000,000 people, then the CPM is $10.

Cost per thousand (CPM), which is also called cost per mille, is a marketing word used to denote the price of 1,000 advertisement prints on one web page. If a publisher of a website charges $2.00 CPM, that means an advertiser must pay $2.00 for every 1,000 prints of its ad.

The CPM is calculated by dividing the cost of the advertisement by the number of people reached and then multiplying by 1000.

Given that the cost of advertising was $100,000 and the reach was 10,000,000 people, the CPM can be calculated as follows:

CPM = ($100,000 / 10,000,000) × 1000 = $10.

So, the CPM is $10.

To know more about Cost per thousand, here

https://brainly.com/question/6448600

#SPJ4

Answer:

There is nothing here.

Step-by-step explanation:

By the way I hope you have a nice day!!! :)

(1)Elena should purchase a rainproof tarp that is at least 140 ft² in size. Option E (2)it would take 140 ft³ of water to fill the tent completely. Option A.

(1) To determine the size of the rainproof tarp Elena should purchase, we need to calculate the total surface area of the tent.

The tent has 4 sides, and each side has the same dimensions. Given that the height of the tent is 8.75 ft and the length and breadth are both 4 ft, the surface area of each side can be calculated as:

Side area = Length × Height = 4 ft × 8.75 ft = 35 ft²

Since there are 4 sides, the total surface area of the tent is:

Total tent surface area = Side area × 4 = 35 ft² × 4 = 140 ft²

Therefore, Elena should purchase a rainproof tarp that is at least 140 ft² in size.

The correct option would be e) X-Large: 144 ft², as it is the only size that is equal to or greater than the required size.

(2) If the tent fills up completely with water, we can calculate the volume of water it would hold using the formula:

Volume = Length × Breadth × Height

Given that the length and breadth of the tent are both 4 ft and the height is 8.75 ft, we can substitute these values into the formula:

Volume = 4 ft × 4 ft × 8.75 ft = 140 ft³

Therefore, it would take 140 ft³ of water to fill the tent completely.

Hence, the correct answer is 140 ft³. So Option E is correct  for 1. and Option A is correct for 2

For more question on tent visit:

https://brainly.com/question/29280067

#SPJ11

Answer:

100

Step-by-step explanation:

if its the same then its 100

The equation that represents the length of the completed tunnel based on the number of days is y = 45x + 140.

Option A is the correct answer.

We have,

From the table,

We take two ordered pairs:

(15, 815) and (20, 1040)

Now,

The equation can be written as y = mx + c.

And,

m = (1040 - 815) / (20 - 15)

m = 225/5

m = 45

And,

(15, 815) = (x, y)

815 = 15 x 45 + c

c = 815 - 675

c = 140

Now,

y = mx + c

y = 45x + 140

Thus,

The equation that represents the length of the completed tunnel based on the number of days is y = 45x + 140.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ1

Answer:

20 mins

Step-by-step explanation:

2003 17 2005 20

Answer:

\(-3x^2+6xy+4\)

Step-by-step explanation:

\((3x^2+2xy+7)-(6x^2-4xy+3)=\\\\3x^2-6x^2+2xy+4xy+7-3=\\\\-3x^2+6xy+4\)

Hope this helps!

Answer:

3x2-6xy

Step-by-step explanation:

I think i dont know

Answer:

see below

Step-by-step explanation:

Each person payed a specific amount, so you would divide the rental cost by the amount of people and get $38.75 per person

Evaluate the expression is -10.

You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. As 6 + 6 = 12, the variable x in the preceding example is equal to 6. We can replace our variables with their values if we know what they are, then evaluate the expression after doing so.

The division can be done as follows when assessing the phrase 8 4:

−8 ÷ −4 = 2

The expression is thus reduced to:

2 - 12

12 is subtracted from 2 to yield:

-10

Thus, -10 is the correct response.

To know more Evaluate the Expression about

https://brainly.com/question/21469837

#SPJ1

Answer:

a. The slope of EK is \(\frac{1}{2}\)

b. The equation of line EK is y = \(\frac{1}{2}\) x -  \(\frac{3}{2}\)

Step-by-step explanation:

The form of the equation of a line is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

∵ BECK is a rhombus

∵ The diagonal is the line that joins two opposite vertices

∵ B and C are opposite vertices in the rhombus

∵ E and K are opposite vertices in the rhombus

∴ BC and EK are the diagonals of the rhombus BECK

∵ The diagonals of the rhombus are ⊥ and bisect each other

∴ EK is ⊥ bisector to BC

→ Let us find the slope and the mid-point of BC

∵ B = (3, 5) and C = (7, -3)

∴ x1 = 3 and y1 = 5

∴ x2 = 7 and y2 = -3

→ Substitute them in the rule of the slope above to find it

∵ m = \(\frac{-3-5}{7-3}\) = \(\frac{-8}{4}\) = -2

∴ m = -2

∴ The slope of BC = -2

→ To find the slope of EK reciprocal the slope of BC and change its sign

∴ m⊥ = \(\frac{1}{2}\)

∴ The slope of EK = \(\frac{1}{2}\)

a. The slope of EK is \(\frac{1}{2}\)

→ Substitute the value of the slope in the form of the equation above

∵ y = \(\frac{1}{2}\) x + b

→ To find b substitute x and y in the equation by the coordinates

   of a point on the line

∵ The mid-point of BC is the mid-point of EK

∵ The mid-point of BC = (\(\frac{3+7}{2},\frac{5+-3}{2}\)) = (\(\frac{10}{2},\frac{2}{2}\)) = (5, 1)

∴ The mid-point of EK = (5, 1)

→ Substitute x by 5 and y by 2 in the equation

∵ 1 =  \(\frac{1}{2}\)(5) + b

∴ 1 =  \(\frac{5}{2}\) + b

→ Subtract  \(\frac{5}{2}\) from both sides

∴  \(-\frac{3}{2}\) = b

→ Substitute the value of b in the equation

∵ y = \(\frac{1}{2}\) x + \(-\frac{3}{2}\)

∴ y = \(\frac{1}{2}\) x -  \(\frac{3}{2}\)

b. The equation of line EK is y = \(\frac{1}{2}\) x -  \(\frac{3}{2}\)

The volume in a pyramid is given by the next formula:

Where:

Ab is the area of the base

h is the heigh of the pyramid.

The area of the base is:

where l is length and w is the width

l=49cm

w=36cm

Then, the volume of the figue is:

The expected number of times that both coins have come up tails will be 0.5 or 50%.

The probability of both coins coming up tails on a single flip is 1/4, since each coin has a 1/2 probability of coming up tails and the events are independent. If we flip the coins n times, the number of times both coins come up tails is a binomial random variable with parameters n and 1/4.

The expected value of a binomial random variable is given by np, where p is the probability of success on a single trial. In this case, we have p = 1/4, so the expected number of times that both coins come up tails in n flips is n(1/4). Therefore, if we flip the coins twice simultaneously, the expected number of times that both coins come up tails is (2)*(1/4) = 0.5.

To learn more about coins, click here:

https://brainly.com/question/29869268

#SPJ11

Answer:

gradient = - \(\frac{3}{2}\)

Step-by-step explanation:

Parallel lines have equal slopes/ gradients

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

4y + 6x = 8 ( subtract 6x from both sides )

4y = - 6x + 8 ( divide terms by 4 )

y = - \(\frac{6}{4}\) x + \(\frac{8}{4}\)

y = - \(\frac{3}{2}\) x + 2 ← in slope- intercept form

with slope / gradient = - \(\frac{3}{2}\)

The gradient of a parallel line is then m = - \(\frac{3}{2}\)

Answer:

$3.42

Step-by-step explanation:

the cost = 11.4 × 0.30 = $ 3.42

Answer:

8 times

Step-by-step explanation:

because you do the number of times the event occurs in the sample space divided by the number of outcomes in the sample space.

The cardinality of the set a and relation r such that r =  {(a, b) | a divides b} is equal to 14.

Set is defined as,

{1,2,3,4,5,6}

The relation r defined on set a as 'r = {(a, b) | a divides b}. means that for each pair (a, b) in r, the element a divides the element b.

To find the cardinality of r,

Count the number of ordered pairs (a, b) that satisfy the condition of a dividing b.

Let us go through each element in set a and determine the values of b for which a divides b.

For a = 1, any element b ∈ a will satisfy the condition .

Since 1 divides any number. So, there are 6 pairs with 1 as the first element,

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6).

For a = 2, the elements b that satisfy 2 divides b are 2, 4, and 6. So, there are 3 pairs with 2 as the first element,

(2, 2), (2, 4), (2, 6).

For a = 3, the elements b that satisfy 3 divides b are 3 and 6. So, there are 2 pairs with 3 as the first element,

(3, 3), (3, 6).

For a = 4, the elements b that satisfy 4 divides b are 4. So, there is 1 pair with 4 as the first element,

(4, 4).

For a = 5, the elements b that satisfy 5 divides b are 5. So, there is 1 pair with 5 as the first element,

(5, 5).

For a = 6, the element b that satisfies 6 divides b is 6. So, there is 1 pair with 6 as the first element,

(6, 6).

Adding up the counts for each value of a, we get,

6 + 3 + 2 + 1 + 1 + 1 = 14

Therefore, the cardinality of the relation r is 14.

Learn more about cardinality here

brainly.com/question/30482462

#SPJ4

Answer:

Ste1p-by-step explanation:

1330