1. A. What is the formula for the Pythagorean Theorem? (1 point)

B. Find the missing leg of the triangle using the Pythagorean Theorem. Remember that drawings may not be to scale (Round to the nearest tenth).
Show your work. (4 points)
20 ft
18 ft
x

Answer:

Step-by-step explanation:

Like terms are terms that have the same letter or letters. They can be collected together by adding or subtracting. 9y, 3y and 2y are like terms because they contain the letter y and only the letter y.

4y + 3y + 2y = 9y

The final balance in the bank register is $1020.49 on October 13th.The Excel sheet for the given transaction is shown below. In the given scenario, the transactions that have been made by the customer are recorded in the bank register. The register contains information about all the transactions made by the customer, whether it is a purchase, deposit, or a fee.

The bank register helps the customer to keep track of the balance in their bank account and to reconcile the balance with the bank statement. It is important to enter the transactions in the bank register as soon as they are made to avoid any errors and to keep the balance up-to-date. Excel sheet: Explanation of the transactions: -

The account is opened with $300 on October 1st. - A pretzel is purchased from "Doughy Pretzel" with check 100 for $3.18 on October 1st. - Gas is bought with the debit card for $34.35 on October 5th. - "River Rider's Extreme" is bought with the debit card for $265.17 on October 6th. - There is an overdraft fee of $38 on October 7th. - $755.49 is deposited on October 13th. Therefore, the final balance in the bank register is $1020.49 on October 13th.

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The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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Answer:

(C) Multiply first equation by -2 and second equation by 3, solution (1, 1)

Step-by-step explanation:

Simultaneous equations are set of equations which possess a common solution. The equations can be solved by eliminating one of the unknowns by multiplying each of the equations in a way that a common coefficient is obtained in the unknown to be eliminated.

Given the simultaneous equations:

3x - 5y = -2

2x + y = 3

First step:

Multiply first equation by -2 and multiply second equation by 3,

-6x + 10y = 4

6x + 3y = 9

Second step:

Add the two equations together,

13y = 13

Divide both sides by 13

y = 1

Third step:

Put y = 1 in the first equation

3x - 5(1) = -2

3x - 5 = -2

3x = 5 - 2

3x = 3

Divide both sides by 3:

x = 1

solution (x,y) = (1,1)

Option C

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Answer:

85.33 or 85.3

Step-by-step explanation:

both versions of the answer should be correct. the second one is just the first one without an extra 3.

im not totally sure if you also need the graph version and/or if that was what you were referring to.

i rlly hope this helps.

if you need answers for graphing i recommend using desmos. its pretty helpful for getting answers really fast.

hope this helps!!! :) <3 (pls rate and like bc every time i answer a question no one ever does it :,) )

1200 kg / 12 quintal

= 100 kg per quintal

so 1 quital = 100 kg

The teacher can include up to 8 questions of each type (multiple-choice and short-answer) in Order for the test to take students less than 45 minutes to complete.

A teacher is making a history test composed of the same number of multiple-choice questions as short-answer questions. She estimates it will take students an average of 2 minutes to complete each multiple-choice question and an average of 3.5 minutes to complete each short-answer question.

Write an inequality to determine how many questions, n, the teacher can include if the test must take students less than 45 minutes to complete.The test has the same number of multiple-choice and short-answer questions, so let n be the number of each type of question.

The time taken to complete multiple-choice questions is 2n, while the time taken to complete short-answer questions is 3.5n.Using the inequality of time, if the test must take students less than 45 minutes to complete, then;2n+3.5n<45.Distribute the number of questions (n)2n+3.5n=5.5n5.5n<45

Divide both sides of the inequality by 5.5n<45/5.5n<8.18...n≤8

Therefore, the teacher can include up to 8 questions of each type (multiple-choice and short-answer) in order for the test to take students less than 45 minutes to complete.

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The teacher is creating a test with an equal number of multiple-choice and short-answer questions. The time equation for the test can be written as 2n + 3.5n < 45, where n represents the number of questions. This inequality can be solved to find the maximum number of questions the teacher can include.

The subject of this question is an inequality that involves the total time taken by students to complete the test. In this case, the teacher is creating a test that has an equal number of multiple-choice and short-answer questions. Each multiple-choice question takes an average of 2 minutes, while each short-answer question takes an average of 3.5 minutes. The total time for the test should be less than 45 minutes.

Since the same number of multiple-choice (2n minutes) and short-answer questions (3.5n minutes) are present, the inequality will be:

2n + 3.5n < 45

This is the inequality representing how many questions, n, the teacher can include if the test must take students less than 45 minutes to complete. By solving this inequality, the teacher can determine the maximum number of questions that can be included in the test.

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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The amount of sandwich they eat altogether is 2/3

A fraction can be defined as the part of a whole number, a whole number, a whole element.

The different types of fractions are listed as;

From the information given, we have that;

Angie ate 1 / 3 of the sandwich

Kim ate another 1 / 3 of the sandwich

To determine the total amount, we have;

1/3 + 1/3

add the values

1 + 1/3

add the values, we get;

2/3

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The complete question:

Angie and Kim are sharing a large sub sandwich. Angie ate 1 / 3 of the sandwich, and Kim ate another 1 / 3 of the sandwich. Please work out in detail.

Applying the system of equations given, we can conclude that: a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

To solve the system of equations, let's substitute the value of x from the first equation into the second equation:

x = 4y

8 + 2y = 4y

Simplifying the equation, we get:

8 = 2y

Dividing both sides by 2:

4 = y

Now, substitute the value of y back into the first equation to find x:

x = 4y

x = 4(4)

x = 16

Therefore, Nikhil has been employed by the company for 16 years, and Mae has been employed for 4 years.

The correct answer is option a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

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The domain of the function f(x) = {√(x + 2)} is x ≥ -2, where {} denotes the fractional part.

To find the domain of the function, we need to consider the values of x for which the expression inside the square root is defined. In this case, the expression x + 2 must be non-negative (since we cannot take the square root of a negative number). So we set x + 2 ≥ 0 and solve for x.

x + 2 ≥ 0

x ≥ -2

Therefore, the domain of the function is x ≥ -2. This means that the function is defined for all real numbers greater than or equal to -2.

In the second paragraph, we explain that the domain of the function f(x) = {√(x + 2)} is x ≥ -2. The function involves taking the square root of (x + 2) and then considering the fractional part of the result.

The expression inside the square root must be non-negative, which means x + 2 ≥ 0. Solving this inequality, we find x ≥ -2. Thus, any real number greater than or equal to -2 is included in the domain of the function.

For example, if we choose x = -2, the expression inside the square root becomes 0, and taking the square root of 0 gives us 0. The fractional part of 0 is also 0. As we move to x > -2, the square root expression becomes positive, resulting in non-zero fractional parts.

So, the function is defined and has a non-zero fractional part for all real numbers greater than -2. However, for x < -2, the expression inside the square root becomes negative, which is not defined in the real number system. Therefore, the domain of the function is x ≥ -2.

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