Write and solve an equation.

9. In one baseball season, Peter hit twice the difference of home runs Alice hit and 6. Altogether, they hit 18 home runs. How many home runs did each player hit that season?

10. The perimeter of a pallalelogram is 72 meters. The width of the pallalelogram is 4 meters less than its lengh. Find the length and the width of the pallalelogram.

The table is shown in figure.

Here,

Function is given as;

f (x) = x - 5

We have to complete the table.

What is Function?

A relation between a set of inputs having one output each, is called Function.

Now,

Function is given as;

f (x) = x - 5

Hence, after putting all the given values of x, we get;

Put x = -1,

Then, f (x) = -1 - 5 = - 6

Put x = 0

Then, f (x) = 0 - 5 = -5

Put x = 1

Then, f (x) = 1 - 5 = -4

Put x = 2

Then, f (x) = 2 - 5 = -3

Put x = 4

Then, f (x) = 4 - 5 = -1

Therefore, All values of f (x) are;

⇒ -6, -5, -4, -3, -1

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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.

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]

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 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:

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 :)

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

16 just divide 64 by 4

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

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

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

Greetings, the answer is 11.

Steps:

9+6=15

-4·15

-60

The correct answer is -60

20 plus 10 equals 30.

yes it would be rational

Since repeated decimals are rational in nature, hence, 6.565656... is rational

Rational numbers are numbers that can be written as the ratio of two integers. For example:

All repeating decimals are also classified as rational numbers. For example:

The given decimal value 6.565656... is a repeating decimal. The three dots after the decimal values shows that the number is a repeating decimal.

Since repeated decimals are rational in nature, hence, 6.565656... is rational

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You must find the unit cost in dollars per gallon for each purchase by dividing the cost by the number of gallons.

Graven: $55.20 for 15 gallons

$55.20/(15 gal) = $3.68/gal

Project: $72.80 for 20 gallons

$72.80/(20 gal) = $3.64/gal

Answer: Project paid less per gallon.

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.

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.

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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).

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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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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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.

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

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

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:

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