Expand. Your answer should be a polynomial in standard form.
(x - 2)(x - 6) =​

The highest possible price that a customer could have paid for their meal that evening exists $ 757. Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.

When determining the mean (average) of a group of values, we add up the values in the group and divide that total by the number of values in the group. As a result, the average of the set's values divided by the total number of values is equal to the set's values' sum.

Let n represent how many people were in the store that evening. Thus, a total of 56n was paid that evening by all customers. The bill for the last customer's meal was $70.00. There were (n-1) customers who had already paid a total of (56n-70) dollars before this one arrived. The average cost per customer at that time was $55 dollars.

From the above information, we get

[tex]$\frac{56 n-70}{n-1} &=55 \\[/tex]

simplifying the above equation, we get

56n - 70 = 55(n - 1)

56n - 70 = 55n - 55

n = 15

Since n = 15, it follows that there were 15 customers that evening, and the total amount paid by all customers stood therefore 56 n = 56(15) = 840 dollars.

To estimate the highest possible price that a customer could have paid for their meal that evening, we will assume that 13 of the customers paid the lowest possible price of $ 1. Then the remaining customer would have paid 840 - 13 × 1 - 70 = 757 dollars.

Therefore, the highest possible price that a customer could have paid for their meal that evening exists $ 757.

Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.

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Answer:

4x - 3y = 36

Step-by-step explanation:

⅔x-½y=6

just multiply both sides by the LCM which is 6

6×⅔x-6×½y=6×6

4x-3y=36

Answer:

The answer is run because the line is going down.

Step-by-step explanation:

There 6 quarters and 24 nickels of each coins that John Carlo has.

There are 5 cents in a nickel and 25 cents in a quarter. Let us represent the number of quarters as x so that the number of nickels that John Carlo has will be 4x.

Thus, 4x(5 cents) + x(25 cents) = 270 cents

20x cents + 25x cents = 270 cents

45x cents = 270 cents

divide through by 45

x = 270/45

x = 6

and thus there are 4(6) = 24 nickels.

Therefore, John Carlo has 6 quarters and 24 nickels each of coins.

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The solution of the given system of equations is x =1 and y = -1.

In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Given is a system of equations; 4x+2y=2 and y=-3x+2

Solving the equation by substitution, we get,

4x+2(-3x+2) = 2

4x-6x-4 = 2

-2x+4 = 2

-2x = -2

x = 1

Put x = 1 in any of the given equation,

y = -3*1+2

y = -3+2

y = -1

Hence, The solution of the given system of equations is x =1 and y = -1.

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The augmented matrix represents the following system of linear equations:

Use back substitution. It means, use the value of z given in the last equation, to find y in the second equation, and then, use these values to find x in the first equation:

The solution of the system is (x, y, z)=(7, 0, -5)

Before finding the probability of being dealt 4 Aces of cards, let's find the probability of being dealt an Ace card on each draw.

The probability of getting an specific card from a deck is given by the ratio between the amount of this specific card and the total amount of cards. We have 4 Aces in a deck, and 52 cards, therefore, the probability of getting an Ace is

Since the cards are replaced, it is the same probability of getting an Ace on each draw.

Each draw is an independent event, the probability of them happening simultaneously is given by their product. The probability of being dealt 4 Aces of cards with a replacement is

3 + √97/2 , -3 ±√97/2 are the dimensions of rectangle .

What is rectangle?

let width = x

length = x + 3

area = 22

 area of rectangle =  l * w

           22 =  x * ( x + 3 )

          22 = x² + 3x

       x² + 3x - 22 = 0

    x = -3 ± √3² - 4 .1 (-22)/2.1

   x = -3 ± √9 + 88/2

    x = -3 ±√97/2

width =  -3 ±√97/2

length =  x + 3  =  -3 +√97/2 + 3 = 3 + √97/2

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From the given option (1,10), (5,6) and (7,4) are ordered pairs that formed from combining a term in Pattern A with its corresponding term in Pattern B.

In the given question,

Pattern A follows the rule "add 2" and Pattern B follows the rule subtract 2

Pattern A: 1, 3, 5, 7, 9

Pattern B: 10, 8, 6, 4, 2

We have to find which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B.

From the given question,

Pattern A:  1, 3, 5, 7, 9

Pattern B:  10, 8, 6, 4, 2

As given in the pattern A all numbers are 2 number up from the previous one and in pattern B each number is 2 number down from the previous one.

We have to combine a term in Pattern A with its corresponding term in Pattern B.

We have to combine with corresponding terms that means we combine one term from pattern A and one from pattern B.

Now the term after combining are

1, 10, 3, 8, 5, 6, 7, 4, 9, 2

So the combination of terms that can be formed are

(1, 10), (10,3), (3, 8), (8,5), (5, 6), (6,7), (7, 4), (4,9), (9,2)

Hence, from the given option (1,10), (5,6) and (7,4) are ordered pairs that formed from combining a term in Pattern A with its corresponding term in Pattern B.

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The 100th term of the arithmetic sequence is 203.

Let the first term of the arithmetic sequence be a and the common difference be d.

The general term of the sequence is given by

[tex]T_{n} = a + (n-1)d[/tex]

It is given that the 6th term is 15, we have :
[tex]T_{6} = a +5d[/tex]  

a + 5d = 15......equation(1)

It is given that the 9th term is three times the 2nd term, we have :

[tex]T_{9} = 3*T_{2} \\a + 8d = 3(a +d)\\a + 8d = 3a +3d\\a -3a = 3d -8d = -5d\\-2a = -5d\\2a = 5d\\a = \frac{5d}{2}[/tex]

Putting this value in equation(1)

[tex]\frac{5d}{2} + 5d = 15 \\\\5d + 10d = 30\\15d= 30\\d = \frac{30}{15} = 2[/tex]

a = 5*2/2 = 5

Hence, the first term is 5 and the common difference is 2.

Now, evaluating the 100th term of the sequence, we have :

[tex]T_{n} = a +(n-1)d\\T_{100} = a +99d\\T_{100} = 5 +99*2 = 5 +198 = 203[/tex]

Hence, the 100th term of the arithmetic sequence is 203.

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Answer:

5

Step-by-step explanation:

y=x+5 cuz it works out for everything

The graph of the function:

Can be obtained by using the parent function:

Whose graph is shown below:

We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:

And the graph is:

Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:

The graph is shifted 4 units to the right as shown:

Answer: 9.7 seconds

Step-by-step explanation:

[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]

The total number of cards in a deck of cards is: 52

The total number of club cards is: 13

The total number of cards that less than 5 is: 8.

The probability of selecting a club card is,

The probability of selecting a card that is less than five is,

The total number of club card that is less than 5 is 3.

The probability of selecting a club card and a card that is less than 5 is,

The probability of selecting a card that is a club or less than 5 is,

Thus, the probability of selecting a club card or card that is less than 5 is 9/26.

Answer:

The total deposit is $721.31.

Step-by-step explanation:

Given the expression:

Let's solve the expression using distributive property.

To use distributive property, distribute the term ouside the parentheses to the terms in the parentheses.

Apply distributive property:

Distribute 4 to the values inside the parentheses:

ANSWER:

68

The expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.

So, the expression to represent the total cost will be:

The expression that gives the total cost.

Let, the number of miles are 'n' and the total cost be 'C'.

Now,

Therefore, the expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.

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Alicia has at most $196 this means that her amount of money is less or equal than $196, we can express this as an inequality, like this:

Where x represents the cost associated with the hat and the gloves and y is the money that left after the purchase of these articles

Explanation

The unit rate os obtained as shown as follows:

Answer is A. The unit rate is equal to $17.

Answer:

1. find the 2 points and determine their coordinates.

2. determine the difference in the rise or y-coordinates.

3. determine the difference in the run or x-coordinates.

4. place the rise over the run and divide to find slope

A solution to a system of linear equations in two variables is an ordered pair that makes BOTH equations true.

When is the system of equations is said to be consistent?

If there is at least one combination of values for the unknowns that satisfies each equation in the system—that is, makes each equation hold true as an identity—then a system of equations, whether linear or nonlinear, is said to be consistent.

When is the system of equations is said to be non-consistent?

If there isn't a set of values for the unknowns that solves every equation, then the system of equations is said to be inconsistent.

Ex: Consider a system of linear equations:

x+3y=6                    

x=-3y+6                       …..(1)

2x+8y= -12                  …..(2)

Substitute equation (1) in (2)

2(-3y+6)+8y=-12

-6y+12+8y=-12

           2y=-24

            y=-12              ….(3)

Substitute equation (3) in (1)

x+3(-12)=6

x-36=6

x=42

Here, the order pair (x,y)=(42,-12) is the solution of the given linear equations and satisfy equations (1) and (2)

> 42+3(-12) = 42-36             .....From (1)

                  = 6 = RHS

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EXPLANATION

The sum of 79 and 34 is

Answer: 113

EXPLANATION

Let's see the facts:

%Earns= 13% commission/week

Last week sold = $7,500

In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:

$Earns = 0.13 (decimal form)*$7,500

Earns = $975

Last week, he made $975 in commission.

If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year

The ordered pair that is a solution for the inequality 2x + 3y < 12 and

3x - 2y ≥ 18 is

The solution is sought by substituting to each of the pair to the equation and comparing the answers

for  D. (4,-9)

2 * 4 + 3 * -9 < 12

-19 < 12   correct

3x - 2y ≥ 18

3 * 4 - 2 * -9 ≥ 18

30  ≥ 18 correct

This proves that option D is the correct option

trying for A. (5,0)

2 * 5 + 3 * 5 < 12

25 < 12   incorrect

3x - 2y ≥ 18

3 * 5 - 2 * 0 ≥ 18

15  ≥ 18 incorrect

trying for B. (3,-1)

2 * 3 + 3 * -1 < 12

3 < 12   correct

3x - 2y ≥ 18

3 * 3 - 2 * -1 ≥ 18

11  ≥ 18 incorrect

When any part is incorrect the pair is not a solution

trying for C. (-1,3)

2 * -1 + 3 * 3 < 12

7 < 12   correct

3x - 2y ≥ 18

3 * -1 - 2 * 3 ≥ 18

-9  ≥ 18 incorrect

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Answer:

so you need to divide this and turn it into a coefficient for the answer

Step-by-step explanation:

The value of x is 0.94 or 3.34 with the functions given.

The function is given as:

f = (x, 4 x - 17)

g = (x, (2 x + 8) / 5)

We get that:

g⁻¹ (x) = (2 x + 8) / 5

f o f (x)

= f (f (x))

= (4x [ 4x - 17] - 17)

= 16 x² - 68 x - 17

ATQ:

16 x² - 68 x - 17 = (2 x + 8) / 5

80 x² - 340 x - 85 = 2 x + 8

80 x² - 342 x - 93 = 0

Solving the equation:

D = b² - 4 ac

D = (-342)² - 4 (80) (-93)

D = 36681

x = (342 ± √36681) / 2(80)

x = (342 ± 191.52) / 160

x = 0.94 or x = 3.34

Therefore, the value of x is 0.94 or 3.34 with the functions given.

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Given:

The inequality is,

Required:

To choose the correct value for the given inequality.

Explanation:

Consider the given inequality,

Consider the first option, 6

Put x=6 in to the given inequality, we get

Clearly the statement is false.

Now consider the next option, 4

Put x=4 in to the given inequality, we get

Clearly the statement is false.

Now consider the next option, 0

Put x=0 in to the given inequality, we get

Clearly the statement is false.

Final Answer:

There is no values in the given options .

Answer:

49

Step-by-step explanation:

10 to 23 is 13, and 23 to 36 is 13. so you just add 13 to 36 to get 49