Guess and check to find the missing numbers at this data set. The mean of the data set is 105. The mode is 108. (100, 102, ?, 108)

Answer:

x = -6 and x=3

Step-by-step explanation:

We have been given the equation to solve

[tex](x-2)(x+9)=4x[/tex]

Let us simplify the left hand side of the equation using FOIL (first outer in last).

[tex]x^2+9x-2x-18=4x\\\\x^2+7x-18=4x\\\\x^2+3x-18=0[/tex]

Now, let us find the factors using AC method.

Middle term 3x can be written as 6x - 3x

[tex]x^2+3x-18=0\\\\x^2+6x-3x-18=0\\\\x(x+6)-3(x+6)=0\\\\(x+6)(x-3)=0\\\\x=-6,3[/tex]

Now, let us check the solution by plugging values in the original equation

For x= -6

[tex](-6-2)(-6+9)=4(-6)\\\\(-8)(3)=-24\\\\-24=-24\Rightarrow\text{ True}[/tex]

Thus, x=-6 is a solution.

For x= 3

[tex](3-2)(3+9)=4(3)\\\\(1)(12)=12\\\\12=12\Rightarrow\text{ True}[/tex]

Thus, x=3 is a solution.

Therefore, the solutions are x = -6 and x=3

y-intercept is -6 (0,-6) and the x-intercept is -3 (-3,0)

Answer: a.) 22.5 lb and b.) 67.5 lb

Step-by-step explanation:

a.Weight of 1/5 square foot sample of wood = 1/2 lb

Multiplying 5 on both sides we get ,

weight of 1 square foot sample of wood=1/2×5=5/2 lb

Now, 1 square yard = 9 square feet

Thus weight of sample of wood in 1 square yard = 9 ×weight of 1 square foot sample of wood=9×5/2=45/2=22.5 lb

b. Weight of three square yards of wood=3 times weight of wood in 1 square yard

=3×22.5=67.5 lb

Each square foot of wood weighs 2.5 lbs, so one square yard (or 9 square feet) weighs 22.5 lbs. Josh would therefore need 67.5 lbs of wood to construct his birdhouses.

This question requires a basic understanding of ratio and proportion. The information given is that Josh's sample of wood, which covers an area of 1/5 square foot, weighs 1/2 lb. However, wood is sold by the hardware store in square yards, and we know that 1 square yard equals 9 square feet.

In other words, each single square foot of wood weighs 2.5 lbs (1/2 lb divided by 1/5). So, the weight of 1 square yard of wood (9 square feet), would be 2.5 lbs per square foot times 9, or 22.5 lbs.

If Josh needs three square yards of wood for his birdhouses, he would therefore need 3 times 22.5 lbs, or 67.5 lbs.

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Remark

Start with the product

Let the unknown number = x

The unknown number x is multiplied by 6

At this point you get 6x

====================================

Now you add 15

6x + 15 = 9

Solve

6x + 15 = 9      Subtract 15 from both sides.

6x = 9 - 15       Collect the terms on the right.

6x = - 6            Divide by 6

x = - 6/ 6

x = - 1

answer:  [tex]x = \frac{5}{8}[/tex]

work:

[tex]\frac{4}{5} (2x + 5) - 4 = 1[/tex]  | distribute [tex]\frac{4}{5}[/tex] into the parentheses

[tex]1\frac{3}{5}x + 4 - 4 = 1[/tex]  | cancel out the + 4 and -4 because they equal to 0

[tex]1\frac{3}{5}x = 1[/tex]  | divide by [tex]\frac{3}{5}[/tex]

[tex]x = \frac{5}{8}[/tex]  | final answer

hope this helps! correct me if anything is wrong ❤ from peachimin

The number is 63 which is divided by -7 and the quotient is increased by 12, the result is 3.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division, thus, can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We have been given that when a number is divided by -7 and the quotient is increased by 12 and the result is 3.

Let the number be x;

x ÷ -7

By hit and trial method, if we consider a number which is a multiplier of 7 and 3.

then it would be 63, now apply this number to the given condition.

63÷ -7 =  -9

Also, the quotient is increased by 12, the result is 3.

-9 + 12 = 3

Hence, the number is 63.

Learn more about division here:

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If the problem did not give you the percentile it would be confusing. You would not know if they wanted money or just a number!!! So it is pretty important.

Step-by-step explanation:

Well we won't give you the table, but it's pretty easy. It's a fixed rate so you know he charges the same thing every time. 36 / 3 = 12

So if he mows the lawn and gets paid $12 each time, you can multiply everthing in your x input to get your y output. So for x = 8 your y output would be y = 96 because 12 * 8 = 96

Multiply normally, ignoring the decimal points.

Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.

So, 16.04 (5.25)=84.21

Answer:

Step one- You first get the decimals -example-( 3.2 x 2.4 )

Step two- You then put the biggest decimal at the top and smallest at the bottom -example-( 3.2

                            x 2.4 )

You can take away the decimal points for now if it helps.

Step three- You multiply the first number, in this case, the first number is 4. Then multiply the 4 by the top numbers ( Only multiply the 4 an the 2 then multiply the 4 and the 3.)

Then you do the same to the 2 at the bottom.

After you finish multiplying that, then you add the numbers leftover.

Finally you count how many numbers are behind the decimal. In this case, there are 2 numbers behind the decimal, so you would put the decimal 2 numbers behind.

You will begin to see how it works.

EXAMPLE OF ME DOING THE PROBLEM.

3x - 5y = 6

-3x         -3x

      -5y = -3x + 6

       [tex]\frac{-5y}{-5} = \frac{-3x}{-5} + \frac{6}{-5}[/tex]

          [tex]y = \frac{3}{5}x - \frac{6}{5}[/tex]  ⇒  m = [tex]\frac{3}{5}[/tex]

perpendicular slope (m⊥) = [tex]-\frac{5}{3}[/tex]

Point-Slope equation:

m = [tex]-\frac{5}{3}[/tex]    (x₁ , y₁)= (-8, 0)

y - y₁ = m(x - x₁)

y - 0 = [tex]-\frac{5}{3}[/tex](x - (-8))

    y = [tex]-\frac{5}{3}[/tex](x + 8)

    y = [tex]-\frac{5}{3}x - \frac{40}{3}[/tex]

You can use the sin function to solve this.

Think of a triangle with the conveyor being the longest side (hypotenuse). The height (the vertical side) is H=17m. The angle of elevation is a=36.2. We are looking for length of the hypotenuse, L.

The sin is the ratio of height to hypotenuse: sin(36.2) = H/L = 17/L

Now solve for L:

L = 17/sin(36.2) = 17m/0.59 = 28.78m

The conveyor needs to be approx. 28.8m long to get close to the max. efficient angle.

Solving a system of linear equations involves finding the point where the two equations intersect when plotted on a graph. This can be done using a graphing calculator by first entering the equations into the calculator, then finding the point of intersection, which represents the solution.

To start solving the given system of linear equations: 2.1x+4.2y=14.7 and −5.7x−1.9y=−11.4, you first need to enter them into your graphing calculator. The intersection point of the two lines represented by these two equations will be your solution. If you don't see a clear intersection point, use the Intersection tool in your graphing calculator, which will provide the respective x and y coordinates of the intersection. This represents the solution to your set of equations.

For instance, if you have a calculator where you can plot both equations on the same graph, find the intersection point, the result is the solution of the system. If the graphing calculator finds an intersection at (x,y), that means x is the solution for the variable x and y is the solution for the variable y. This process is analogous to figuring out where the two lines would cross if you graphed them on a sheet of paper.

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To solve a system of linear equations using a graphing calculator, you first need to rewrite the equations in slope-intercept form: y = mx + b. Then input these equations into the graphing calculator. The intersection of the two graphs is the solution.

To solve the given system of linear equations—[tex]2.1x+4.2y=14.7[/tex]and [tex]-5.7x-1.9y=-11.4[/tex]—using a graphing calculator, you first have to rewrite the equations in slope-intercept form (y = mx + b), where 'm' represents the slope and 'b' represents the y-intercept.

To do this, isolate 'y' in both equations. For the first equation, you would do the following:

Repeat the same process with the other equation and you will have two equations with 'y' isolated. Input these two equations into your graphing calculator. Where the graphs intersect represents the solution to the system of equations, that is, the values of x and y that satisfy both equations.

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16 just divide 64 by 4

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

Factors of 28: 1, 2, 4, 7, 14, 28

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

The greatest common factor of 42, 28, and 70 is 14.

[tex]\boxed{=14}[/tex]

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

The answer is y = 6 which is option B.

Solution for y:

4y + 13 = 37

= 4y = 37 - 13

= 4y = 24

= y = 24/4

= y = 6

Solution

1. The algebraic expression =  -0.5n - 3.8, where n is the number of minutes.

2. Here the variable "n" represents the number of minutes.

Thank you.

For this case we have the following data:

In this way, the depth of the diver for a certain number of minutes is given by:

[tex]3.8 + 0.5x[/tex], where x represents the number of minutes

Answer:

Question 1: [tex]3.8 + 0.5x\\[/tex]

Question 2: x represents the number of minutes

20 plus 10 equals 30.

The equation of a line formula is y=mx+b.

y = 1/4x - 2

m= 1/4

b= -2

Answer"

y=4x+-2

Step-by-step explanation:

It is 128.1 pounds.....

Answer:

There is 127.91lbs in that many kilograms.

Step-by-step explanation:

In order to find this, you need to know the unit rate. There is 2.2lbs in every kilogram. Therefore, we can multiply the number of kilograms that we have by 2.2 to get the correct answer.

58.14*2.2 = 127.91

We know that Company B will be less expensive at first, but Company A will become a better option as the miles rack up. Eventually, Company A will be less expensive. There will be a point where the price will be the same for each company.  

150 + .20x = Company A

70 + .40x = Company B

If we set these two equations equal to each other, we find out when the price will be the same.

150 + .20x = 70 + .40x

If we solve for x, we find out how many miles must be driven in a day to make the rental cost the same. After that, Company A will be a better deal.

At 350 miles, the rental costs for company A and company B become the same. This result is found by setting the two cost functions equal to each other and solving for the number of miles.

To find when the rental costs from both companies are the same, you need to set the expenses equal to each other and solve for miles (m). The cost for company A can be represented as 130 + 0.30m (130 dollars for the daily rental and 0.30 dollars per mile) and the cost for company B is represented as 60 + 0.50m (60 dollars for the daily rental and 0.50 dollars per mile).

Upon setting the costs equal to each other: 130 + 0.30m = 60 + 0.50m, and simplifying, you'll get 0.20m = 70. Therefore, by dividing by 0.20, m = 350.

So, at 350 miles, the rental costs for both companies A and B are the same, with each charging the same amount for the truck rental.

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The cost function for renting a limo for the prom is Cost(c) = 200 + 25c, where c is the number of passengers. The domain is {4, 6, 8, 10}, representing the possible number of passengers (4 to 10). A table of values for this domain shows the total costs at 300, 350, 400, and 450 respectively for groups of 4, 6, 8, and 10 passengers.

To calculate the cost of renting a limo for the prom including the cost of refreshments based on the number of passengers, we can define a function Cost(c) where c represents the number of passengers. The function can be written as:

Cost(c) = 200 + 25c

The domain of this function is the set of all possible numbers of passengers, which ranges from 4 to 10 (counting in groups of two, since each friend brings a date). Therefore, the domain is {4, 6, 8, 10}.

Next, we'll create a table of values with this domain to calculate the costs associated with each potential number of passengers:

(4, 300)

(6, 350)

(8, 400)

(10, 450)

Each ordered pair represents (number of passengers, total cost).

Your answer would be: A) 0

Letters' B, C, and D are all greater than or equal -3 when they substitute "X".

Hope this helps you :)

Greetings, the answer is 11.

Steps:

9+6=15

-4·15

-60

The correct answer is -60

Answer:

9.5

Step-by-step explanation:

the 1st 10 prime numbers are ..wait let me look at my notes from 8th grade..oh found them here they are

2,3,5,7,11,13,17,19,23 and 29

hoped this helped:)