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Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be
written using function notation?
42-

A function f is said to be one-to-one, or injective, if it has the property that for any two different inputs, it produces two different outputs.

More formally, a function f: X -> Y is one-to-one (or injective) if for every x1, x2 in X, if x1 ≠ x2 then f(x1) ≠ f(x2).

This means that no two different elements of the domain X map to the same element of the codomain Y. If you were to draw a horizontal line through any point on the graph of a one-to-one function in the Cartesian plane, that line would intersect the graph at most one time. This is known as the "horizontal line test" for one-to-one functions.

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Answer:

Step-by-step explanation:

34. I haven't seen Tom since his wedding day.

36. Mary hasn't spoken French in years.

37. I haven't had a good night's sleep in ten weeks.

38. He hasn't paid taxes since 1970.

40. The windows haven't been cleaned for 3 months.

41. It's been years since I took photographs.

The perfect tense is a grammatical construction used to express actions that are completed or have happened before the present moment. It indicates that an action was performed and finished in the past but has relevance or impact on the present.

There are three main forms of the perfect tense: present perfect, past perfect, and future perfect.

1. Present Perfect Tense: This tense is used to describe an action or event that started in the past and has a connection to the present. It emphasizes the result or completion of the action.

2. Past Perfect Tense: This tense is used to describe an action or event that occurred before another action or a specific point in the past. It expresses an action completed before a specified time in the past.

3. Future Perfect Tense: This tense is used to describe an action that will be completed before a specified time or point in the future.

Each form of the perfect tense can be used with different time references to indicate the relationship between the completed action and the present or other points in time.

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Based on the given data, the relationship appears to be exponential.

To determine if the relationship between the given values is linear, exponential, or neither, we can examine the pattern in the data.

If the relationship is linear, we would expect the values of y to increase or decrease at a constant rate as the values of x increase. In other words, there would be a constant slope between the points.

If the relationship is exponential, we would expect the values of y to change by a constant factor as the values of x increase. In this case, the relationship would exhibit exponential growth or decay.

Looking at the given values of x and y, we can observe the following differences between consecutive x-values: 7, 9, 9, 9. These differences are not constant, indicating that the relationship is not linear.

To determine if the relationship is exponential, we can examine the ratios between consecutive y-values: 5/10 = 0.5, 10/20 = 0.5, 20/40 = 0.5. These ratios are constant, suggesting that the relationship may be exponential with a common ratio of 0.5.

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The remaining balance on a CD with a $2,200 initial investment and a 2.95% interest rate after three years would be roughly $2,393.10.

The compound interest formula is as follows:

Balance = Principal * (Rate/100 + Rate * 1)Time

Where

Principal (P) is equal to $2,200.

Rate (R) = 2.95% = 2.95/100 = 0.0295 in decimal form.

Time (T) = 3 years.

The following formula is substituted for the values:

Balance =[tex]$2,200 * (1 + 0.0295)^3.[/tex]

Exponent calculation:

Balance = [tex]$2,200 * (1,0295)^3[/tex]

Calculating the result:

Balance ≈ $2,200 * 1.089135

Balance ≈ $2,393.10

So, the remaining balance on a CD with a $2,200 initial investment and a 2.95% interest rate after three years would be roughly $2,393.10.

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The rental car is getting approximately 37.56 miles per gallon.

To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:

1 km/l ≈ 2.82475 mpg

Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:

13.3 km/l x 2.82475 mpg ≈ 37.56 mpg

So, your rental car is getting approximately 37.56 miles per gallon.

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Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.

We have,

The number of different homework sets Mrs. Brown could assign can be calculated using the combination formula.

In this case, she wants to choose 8 problems out of 11 available problems. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where n is the total number of items to choose from and r is the number of items to be chosen.

Using this formula:

C(11, 8) = 11! / (8! x (11 - 8)!)

C(11, 8) = 11! / (8! x 3!)

Simplifying the factorial expressions:

C(11, 8) = (11 x 10 x 9 x 8!) / (8! x 3 x 2 x 1)

The factorial terms cancel out:

C(11, 8) = (11 x 10 x 9) / (3 x 2 x 1)

C(11, 8) = 165

Therefore,

Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.

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To express the value 6 × 10^(-10), you can use scientific notation or decimal notation. Here are some valid expressions that equal 6 × 10^(-10):

0.0000000006

6E-10

6 × 10^(-10)

These expressions represent the same value, which is 6 multiplied by 10 raised to the power of -10.

Decimal is a number system used in everyday arithmetic and mathematics. It is also known as the base-10 system because it uses ten digits (0-9) to represent numbers. Each digit's position in a decimal number represents a power of 10.

In a decimal number, the digits to the left of the decimal point represent whole numbers, while the digits to the right of the decimal point represent fractions or parts of a whole. For example, in the decimal number 123.45, the digit "1" represents 100, the digit "2" represents 10, the digit "3" represents 1, the digit "4" represents 0.1, and the digit "5" represents 0.01.

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Length of gz = 12 units

Length of ot = 14.4 units

Given,

Triangle EGD with centroid at Z .

Now,

As we know that centroid divides the line segment in the ratio 2:1 .

Firstly calculate the length of gz,

gu = 18 unit

gz:zu = 2:1

gz = 2/3  * 18

gz = 12 units .

Secondly calculate the length of ot,

zt = 4.8 units

oz:zt = 2:1

oz = 4.8 * 2

oz = 9.6 units

ot = 9.6+ 4.8

ot = 14.4 units

Hence with the centroid length of ot and gz can be found out .

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The index forms are of different bases and thus cannot be multiplied and their exponents added.

To determine Deigo's mistake, we need to know index forms and their rules.

Index forms are defined as mathematical forms that are used in representing numbers or variables that are too large or too small in more convenient forms.

They are also called scientific notation or standard forms.

The rules of index forms are;

From the information given, we have;

6⁴ × 8³ = 48⁴⁷

They are not of like bases and thus cannot be multiplied

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b)50

since its a Equilateral triangle, then the two base angels have the same measure

abd since both triangles are symmetric, they have the same measurements

so 180-80 = 2x

x = 50⁰

Answer:

approximately 4.2667%

Step-by-step explanation:

To calculate the percentage above the website's estimate that Jerrold set his asking price, we can use the following formula:

Percentage above = ((Asking price - Website estimate) / Website estimate) * 100

Percentage above = (($750,000 - $715,000) / $715,000) * 100

Percentage above ≈ 4.895

Therefore, Jerrold set his asking price approximately 4.895% above the website's estimate.

To calculate the percentage below his asking price that Jerrold sold for, we can use the following formula:

Percentage below = ((Selling price - Asking price) / Asking price) * 100

Percentage below = (($718,000 - $750,000) / $750,000) * 100

Percentage below ≈ -4.2667

Therefore, Jerrold sold his house approximately 4.2667% below his asking price.

The product of the expression 7 x 63 is 441.

We have,

To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:

7 x 63 = 7 x (60 + 3)

Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:

7 x (60 + 3) = 7 x 60 + 7 x 3

Simplifying further:

7 x 60 + 7 x 3 = 420 + 21

Therefore,

The product of 7 x 63 is 441.

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No, the trapezoids are not similar because their corresponding angles do not have the same measures.

The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.

Let's examine the angles of the trapezoids:

In trapezoid ABCD:

Angle A = 137 degrees

Angle B = 90 degrees

Angle C = 90 degrees

Angle D = 43 degrees

In trapezoid EFGH:

Angle E = 136 degrees

Angle F = 90 degrees

Angle G = 90 degrees

Angle H = 44 degrees

By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.

However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.

Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.

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Given statement solution is :- The quartile value above which 75% of the data lies is 31.625.

To find the value above which 75% of the data lies, you can determine the third quartile (Q3) of the data set. In this case, the upper quartile (Q3) is given as 30.5.

Since the data is represented on a number line with tick marks every one-half unit, we can divide the range between Q3 and the maximum value (32) into four equal parts. Each part represents 25% of the data.

To find the value that corresponds to 75% of the data lying above, we need to determine the value that is three-fourths of the way between Q3 and the maximum value.

First, calculate the range between Q3 and the maximum value: 32 - 30.5 = 1.5.

Next, divide the range by four to find the size of one-fourth of the range: 1.5 / 4 = 0.375.

Now, multiply the size of one-fourth of the range by three to find the size of three-fourths of the range: 0.375 * 3 = 1.125.

Finally, add the size of three-fourths of the range to Q3 to find the value above which 75% of the data lies: 30.5 + 1.125 = 31.625.

Therefore, the quartile value above which 75% of the data lies is 31.625.

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The possible degrees of a function from it's graph are found with the sum of the multiplicities of each root of the function.

On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.

On the graph, these are the values of x for which the graph of the function crosses or touches the x-axis.

The multiplicity of each root is given as follows:

Hence the degree is found with the sum of the multiplicities of the zeros of the function.

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The output value of f(-1) include the following: -13.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains.

Since the value of x is -1, the output value of this piecewise-defined function can be calculated by using the first function as follows;

f(x) = 3x - 10

f(-1) = 3(-1) - 10

f(-1) = -3 - 10

f(-1) = -13

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The phrase "only under the assumption that at least one set X exists" means that a certain statement or conclusion holds true or can be deduced only if there is a set X that exists.

In other words, the validity or applicability of the statement is conditional upon the existence of at least one set X.

This phrase indicates that the argument or reasoning being presented depends on the existence of a specific set or group. Without the existence of such a set, the statement or conclusion being made may not hold true or may not be applicable.

It's important to note that without further context, the meaning and implications of this phrase may vary depending on the specific subject or context in which it is used.

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A) Two equations are,

S = 18 + 4t

L = 30 + 3t

Where, "t" represents the number of weeks that have passed.

B)  It will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.

C) when the amount of rocks in their collection is equal, Samuel and Lewis will have 66 rocks each.

Part A:

For a system of equations to represent the number of rocks in each person's collection.

Let "S" be the number of rocks in Samuel's collection and "L" be the number of rocks in Lewis's collection.

Hence, We can represent the situation as follows:

Equation 1:

S = 18 + 4t

Equation 2:

L = 30 + 3t

Where, "t" represents the number of weeks that have passed.

Part B:

To find out how many weeks it will take for Samuel and Lewis to have the same number of rocks in their collections, we need to set Equation 1 equal to Equation 2 and solve for "t".

This gives us the following:

S = L

18 + 4t = 30 + 3t

1t = 12

t = 12 weeks

Hence, It will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.

Part C:

For number of rocks Samuel and Lewis will have when the amount of rocks in their collection is equal, we can substitute the value of "t" that we found in Part B into either Equation 1 or Equation 2.

Hence, substituting "t = 12" into Equation 1 gives,

S = 18 + 4(12)

S = 18 + 48

S = 66 rocks

Therefore, when the amount of rocks in their collection is equal, Samuel and Lewis will have 66 rocks each.

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Point A will have coordinates (-2, -3), which overlaps with the coordinates of Point B (3, -1).

To determine the new coordinates of Point A after the translation, we can start with the coordinates of Point B and apply the inverse translation.

Given that Point B has the coordinates (3, -1), we know that Point A after translation will have the same coordinates. We need to determine the inverse translation that will bring Point B back to its original position, and then apply that inverse translation to Point B.

The inverse translation of moving 2 units up and 5 units to the right is moving 2 units down and 5 units to the left. Therefore, we need to subtract 2 from the y-coordinate and subtract 5 from the x-coordinate of Point B.

Applying this inverse translation to Point B (3, -1), we have:

New x-coordinate of Point A = 3 - 5 = -2

New y-coordinate of Point A = -1 - 2 = -3

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Based on the given clues, the mystery number is 12.

Let's analyze the clues given to find the mystery number:

It is a 2-digit number: This means the number is greater than or equal to 10 and less than 100.

It is a factor of 48: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

It is a multiple of 6: The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, and so on.

The sum of the digits is 3: From the clues, we know that the mystery number is a 2-digit number, so let's consider the possible numbers where the sum of the digits is 3:

12 (1 + 2 = 3)

21 (2 + 1 = 3)

Now let's check which of these numbers satisfy the first three clues:

12: This number is a factor of 48 (48 ÷ 12 = 4) and it is a multiple of 6 (12 ÷ 6 = 2). The sum of the digits is 3. Therefore, 12 satisfies all the clues.

21: This number is not a factor of 48 (48 ÷ 21 ≈ 2.29), so it doesn't satisfy the second clue.

Based on the given clues, the mystery number is 12.

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Answer:

50% ate uncle joe and 50% ate robert so, uncle joe make 14 cookies

Answer:

1. Michael ate 50% of the cookies, so the remaining cookies are 50% of the total. Let's denote the total number of cookies as T. So, after Michael ate his share, 0.5 x T cookies remained.

2. Robert then ate 50% of what was left, leaving only 50% of the cookies that were left after Michael ate. So, after Robert ate his share, 0.5 x 0.5 x T = 0.25 x T cookies remained.

3. We know that 14 cookies remained after Robert ate his share.

So, we can set up the equation 0.25 x T = 14 and solve for T:

T = 14/0.25 = 56

So, Uncle Joe made 56 chocolate chip cookies.

Step-by-step explanation:

Hope it helps!!!

A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:

a. Revenue Function:

Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.

The revenue function can be formulated as:

Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)

In equation form:

Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

b. Constraints:

The constraints for the availability of ingredients can be formulated as follows:

Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280

Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300

Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80

Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250

Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190

Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

c. Solve the system of linear inequalities using E x c e l Solver:

To solve the system of linear inequalities using E x c e l Solver, follow these steps:

1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:

| | A | B |

|-----|-----------|-----------------|

| 1 | Cakes | Selling Price |

| 2 | Cake 1 | $9 |

| 3 | Cake 2 | $12 |

| 4 | Cake 3 | $4 |

| 5 | Cake 4 | $5 |

| 6 | Cake 5 | $8 |

| | | |

| | | Formula |

| 9 | Milk | 280 |

| 10 | Sugar | 300 |

| 11 | Eggs | 80 |

| 12 | Flour | 250 |

| 13 | Cream | 190 |

2. In cell B16, enter the formula for the revenue:

=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11

3. In cell B18, enter the formula for the milk constraint:

=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6

4. In cell B19, enter the formula for the sugar constraint:

=7×B2 + 4×B3 + 5×B4

5. In cell B20, enter the formula for the egg constraint:

=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6

6. In cell B21, enter the formula for the flour constraint:

=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6

7. In cell B22, enter the formula for the cream constraint:

=4×B2 + 5×B4 + B5 + 3×B6

8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:

=B2

9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:

=B3

=B4

=B5

=B6

10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.

11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).

12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).

13. Click on the "Add" button in the "Subject to the Constraints" section.

14. In the Constraint window, select the range B18:B22 for the constraint cells.

15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.

16. Set the Solver options as desired, and click on the "Solve" button.

E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.

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Susan uses 500 milliliters of solution b to obtain a resulting mixture with 102 milliliters of pure alcohol.

Let's set up the equation based on the given information.

Let x represent the amount of solution b in milliliters.

Since Susan uses 100 milliliters less of solution a than solution b, the amount of solution a is (x - 100) milliliters.

We know that solution a has a concentration of 13% alcohol, which means that for every 100 milliliters, it contains 13 milliliters of alcohol.

Similarly, solution b has a concentration of 10% alcohol, which means that for every 100 milliliters, it contains 10 milliliters of alcohol.

Given that the resulting mixture has 102 milliliters of pure alcohol, we can set up the equation:

0.13(x - 100) + 0.1x = 102

Simplifying the equation, we have:

0.13x - 13 + 0.1x = 102

0.23x - 13 = 102

0.23x = 115

x = 115 / 0.23

x = 500

Therefore, Susan uses 500 milliliters of solution b to obtain a resulting mixture with 102 milliliters of pure alcohol.

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Answer:295

Step-by-step explanati: 59 5 .

Converting the temperature from Celsius to Fahrenheit:

Subtract the given temperature by 32 and divide it by 1.8°C.

°C = (F - 32) / 1.8°C,   or use the equation °F= 1.8 °C+32

(°F-32) / 1.8°C

a) The given temperature is 60°F

substitute the given values in the above equation:

(60 - 32) / 1.8

28 / 1.8

= 15.5555 approx 16°C

60°F = 16°C

b) The given temperature is 10°F

°C = (F - 32) / 1.8°C

substitute the given values in the above equation:

(10 -32) / 1.8

-22 / 1.8

-12.222 approx -12°C

10°F = -12°C

correct question:

What is the temperature in °C, if the temperature is

a) 60F

b) 10F

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It will take John approximately 2.69 hours to paint the room alone.

Let's denote the individual rates of John, Rick, and Molli as J, R, and M, respectively. We are given the following information:

John, Rick, and Molli can paint the room together in 5 hours.

Molli alone can paint the room in 14 hours.

Rick alone can paint the room in 10 hours.

To find the equation comparing the group rate to the sum of the individual rates, we can use the concept of work done. The amount of work required to paint the room is the same, regardless of who is doing the work.

The equation can be expressed as:

1/5 = 1/J + 1/R + 1/M

Now, let's substitute the given information into the equation. We know that:

M = 14 (since Molli can paint the room alone in 14 hours)

R = 10 (since Rick can paint the room alone in 10 hours)

Substituting these values, the equation becomes:

1/5 = 1/J + 1/10 + 1/14

To solve for J, we can find the least common denominator (LCD) of 10 and 14, which is 70:

14J + 7J + 5J = 70

26J = 70

J = 70/26

J ≈ 2.69

Therefore, it will take John approximately 2.69 hours to paint the room alone.

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The numbers are 1 and 8.

We have,

Let's assume the lesser number as "x" and the greater number as "8x".

According to the given information, when the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number:

8x - x = 5x + 2

Simplifying the expression:

7x = 5x + 2

Subtracting 5x from both sides:

2x = 2

Dividing both sides by 2:

x = 1

So, the lesser number is 1 and the greater number is 8 times that, which is 8.

Therefore,

The numbers are 1 and 8.

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