In this diagram, the area of the large square is equal to the combined areas of the tilted square and the four right triangles.
(the picture)
When written as an equation, this relationship can be simplified algebraically, as shown in these 4 steps.

Step 1: (a + b) (a + b) = c2+ 2ab

Step 2: a2 + 2ab + b2 = c2 + 2ab

Step 3: a2 + 2ab ─ 2ab + b2 = c2 + 2ab ─ 2ab

Step 4:


What equation fits in the box in Step 4 to complete the proof

(part B)
Builders use the equation from Part A to determine the number, height, and depth of stairs necessary to extend from the first floor to the second floor of a building.

Given that the ceiling is 12 feet high, stairs are 8 inches high and the stairwell is 16 feet long, describe in detail how a builder could use the equation to determine the number, height, and depth of the stairs.​

Step-by-step explanation:

mean: (3 + 2 + 7 + 7 + 3 + 8 + 5 + 7 + 2 +8)/10 = 5.2

median: 2, 2, 3, 3, 5, 7, 7, 7, 8, 8 hence median is (5 + 7) / 2 = 6

mode: 7

Topic: mean median mode

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Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

\(\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}\)

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

\(\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}\)

Another identity is:

\(\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}\)

Therefore:

\(\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\)

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

\(\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\)

Another identity:

\(\displaystyle \large{\sin^2x+\cos^2x=1}\)

Therefore:

\(\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}\)

Hence proved, this is proof by using identity helping to find the specific identity.

Step-by-step explanation:

Since bx can be defined for all real numbers r, the domain of an exponential function is all real numbers. The range of bx is all real numbers greater than 0. ... If b > 1, then f is an increasing function. I.e. f(x) increases in value as x increases.

The net income for Griffin's Goat Farm, Inc., was \(\$184,340\).

The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:

\(OCF = EBIT + Depreciation - Taxes + \triangle Working Capital\)

where EBIT is earnings before interest and taxes.

Calculate EBIT by subtracting interest expense from operating income:

EBIT = Operating Income - Interest Expense

We do not have the information for operating income, but we can use the fact that interest expense was. \(\$165,000\) to calculate EBIT.

EBIT = Interest Expense / (1 - Tax Rate)

= \(\$165,000 / (1 - 0)\)

= \(\$165,000\)

Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by \(\$69,000\), which means that working capital increased by  \(\$69,000\).

Therefore:

\(\triangle Working Capital = \$69,000\)

Now, we can calculate OCF:

OCF = EBIT + Depreciation - Taxes + Δ Working Capital

=\(\$165,000 + 0 - 0 +\ $69,000\)

=\(\$234,000\)

Therefore, the firm’s 2018 operating cash flow (OCF) was \(\$234,000\) .

To calculate the net income for Griffin's Goat Farm, we can use the following formula:

Net Income = EBIT - Interest Expense - Taxes

where EBIT is earnings before interest and taxes. We can calculate EBIT as:

EBIT = Sales - Costs - Depreciation

= \(\$686,000 - \$332,000 - \$65,000\)

=\(\$289,000\)

Next, we need to calculate taxes. We are given a tax rate of 24%, so:

Taxes = Tax Rate x (EBIT - Depreciation)

= \(0.24 \times (\$289,000 - \$65,000)= \$56,160\)

Now, we can calculate net income:

Net Income = EBIT - Interest Expense - Taxes

= \(\$289,000 - \$48,500 - \$56,160= \$184,340\)

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Considering that each input is related to only one output, the correct option regarding whether the relation is a function is:

A. yes.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are no repeated inputs, hence the relation is a function and option A is correct.

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Answer:

Line

Step-by-step explanation:

Extends in two directions

The geometric term modeled by a bridge support beam is "cylinder."

Given data:

A bridge support beam often takes the form of a cylindrical shape to provide structural integrity and distribute the weight of the bridge and its load evenly. Cylinders have circular cross-sections.

A bridge support beam is often modeled as a "cylindrical" structure in geometry. Cylinders are three-dimensional geometric shapes characterized by their curved lateral surface and two circular bases of the same size and shape. When designing bridge support systems, engineers often opt for cylindrical beams due to their inherent strength and ability to distribute weight efficiently.

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To assign the name seconds in a decade to the number of seconds between midnight January 1, 2010, and midnight January 1, 2020, we can follow these steps:

Find the number of days between January 1, 2010, and January 1, 2020. First, let's find the number of leap years and non-leap years in this span of a decade. 2012 and 2016 are leap years because they are divisible by 4 but not by 100. 2010, 2011, 2013, 2014, 2015, 2017, 2018, 2019, and 2020 are non-leap years because they are not divisible by 4.

Convert the number of days to seconds.1 day = 24 hours × 60 minutes × 60 seconds = 86,400 secondsNumber of seconds in a decade = 86,400 seconds/day × 4,017 days = 34,958,400 seconds.Therefore, we can assign the name seconds_in_a_decade to the number of seconds between midnight January 1, 2010, and midnight January 1, 2020, which is 34,958,400 seconds.

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To calculate the number of seconds between January 1, 2010 and January 1, 2020, we need to consider the number of seconds in each year, taking into account both leap years and non-leap years. There are 8 non-leap years and 2 leap years, resulting in a total of 315,532,800 seconds in the decade.

To calculate the number of seconds between January 1, 2010, and January 1, 2020, we need to determine the number of seconds in each year and add them up.

A non-leap year has 365 days, which is 365 * 24 * 60 * 60 = 31,536,000 seconds. A leap year has 366 days, which is 366 * 24 * 60 * 60 = 31,622,400 seconds.

There are two leap years within the span of a decade (2012 and 2016), so we will have 8 non-leap years and 2 leap years. The total number of seconds for the non-leap years is 8 * 31,536,000 = 252,288,000 seconds. The total number of seconds for the leap years is 2 * 31,622,400 = 63,244,800 seconds. Adding these two values together gives us the total number of seconds in a decade: 252,288,000 + 63,244,800 = 315,532,800 seconds.

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Answer:

Step-by-step explanation:

Answer:

The numbers are 109, 110, 111, 112 and 113.

Step-by-step explanation:

have a good day and may i have brainleast plz

The number of unit cubes it would take to completely fill the prism with no gaps between unit cubes is 72

From the question, we are to determine how many unit cubes it would take to completely fill the prism with no gaps between unit cubes.

To do this, we will calculate the volume of rectangular prism

Assuming each cube is 1 cubic unit

Then,

From the top view,

The length of the rectangular prism = 9 units

The width of the rectangular prism = 2 units

From the Right-side view,

The height of the rectangular prism = 4 units

Thus,

The volume of the rectangular prism = 9 × 2 × 4

Volume of the rectangular prism = 72 cubic units

Now,

Number of cubes required to fill the rectangular prism = Volume of the prism / Volume of the cubes

Number of cubes required to fill the rectangular prims = 72 / 1

Number of cubes required to fill the rectangular prims = 72

Hence, the number of unit cubes it would take is 72

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x^3 ‐ 7x^2

Explanation:

x^2(x-7) = x^3 ‐ 7x^2

Answer:

hope this answer helps you dear...take care and may u have a great day ahead!

The old price at which dora bought 20 liters of petrol is $0.30 per liter.

Given, dora bought 20 liters of petrol at old price.

The cost of petrol rises by 2 cents later.

Then she bought 10 liters at the new price.

Altogether the petrol costs = $9.20

old price for 1 liter = ?

let the old price for 1 liter of petrol be x.

Based on the conditions , we formulate:

20x+10(x+2)=920

20x+10x+20=920

30x+20=920

30x=920-20

30x=900

x=900/30

x=30

x=$0.30

hence the old price of the petrol is $0.30 per liter.

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Answer:

1.25

Step-by-step explanation:

125/100 = 1.25

Answer:

it's 1.25

Step-by-step explanation:

125 ÷100 = 1.25

Answer: 9z + 2

Step-by-step explanation: you have to add and subtract everything in the equation.

Answer:

shessshhhhh

gang gang

Step-by-step explanation:

digga g

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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Answer:

The answer is obviously A. y<5/3x-3.

Step-by-step explanation:

You point the y-intercept at -3, then go up 5/3rds. After that, you draw a dashed line because the less than symbol isn't open. Then you shade below the line.

The variance of the length of the critical path is 5.76.

Option A is the correct answer.

We have,

To calculate the variance of the length of the critical path in the Critical Path Method (CPM) with three-time estimates (PERT), we can use the formula:

Variance = (Standard Deviation)²

Given that the standard deviation is 2.4, we can substitute it into the formula:

Variance = (2.4)² = 5.76

Therefore,

The variance of the length of the critical path is 5.76.

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The value of Steve's portfolio before the announcement was $52.15.

Let's denote the original value of Steve's portfolio before the announcement as "P".

The drop in the stock price is given as 6.75%, which means the stock price decreased by 6.75% from the original value.

To calculate the original value (P), we can use the following equation:

P - 6.75% of P = $48.62

P - (6.75/100) x P = $48.62

P - 0.0675P = $48.62

0.9325P = $48.62

P = $48.62 / 0.9325

P ≈ $52.15

Therefore, the value of Steve's portfolio before the announcement was $52.15.

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Answer:

=9

Step-by-step explanation:

3x9=27

27/3=9

If you are considering accepting the large contract, there are several things you should consider. Capacity and Cash flow are two points to think about in the short run:

1. Capacity: Can your small bakery handle the increased demand for muffins? You will need to consider whether you have enough equipment, staff, and space to produce 3000 to 4000 muffins a day. If you don't have the capacity, you may need to invest in more equipment, hire more staff, or even move to a larger space. All of these factors will increase your costs and may impact your profitability.

2. Cash flow: While the bank may lend you the money to buy the ingredients, you will need to consider your cash flow. You will need to purchase more ingredients, pay for additional labor, and cover other expenses associated with the increased production. This will require a significant investment, and you will need to ensure that you have enough cash on hand to cover your expenses until you receive payment for the large contract. You may need to renegotiate payment terms with the customer or explore other financing options to ensure that you have the necessary cash flow to meet your obligations.

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Answer:

700 seats

Step-by-step explanation:

- If 630 tickets filled 90% of the seats, \(x\) tickets filled 100% of the seats

multiply 630 by 630 tickets = 90/100

- Set up a proportion

630 tickets/90 = \(x\) tickets/100

\(x\) = 700 tickets = 700 seats

The value of the profitability index of the project is 2.381.

We know that the growth rate is 4% and the cash flow is $3.7 million, so we can calculate the present value of all future cash flows as follows;

PV of all subsequent cash flows = 3.7 million * (1 + 0.04) / (0.11 - 0.04) = $68.1333 million

Total PV = PV of first-year cash flow + PV of all subsequent cash flows = $3.3154 million + $68.1333 million = $71.4487 million

Finally, we can calculate the profitability index as;

Profitability index = PV of future cash flows / Initial investment = $71.4487 million / $30 million = 2.381

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Answer:

-21

Step-by-step explanation:

Answer:

i know its already been answered but yes, it is -21

Step-by-step explanation:

hope it helps, can anyone look at my most recent question? i'll appreciate it

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer: 6 candies

Step-by-step explanation:

So if the teacher buys 12 packs of 8 candies she will have 96 candies in total giving each of the 30 students 3 candies. That leaves her with 6 candies to enjoy by herself.

Answer:

5 and 12 inches

Step-by-step explanation:

Let the shorter leg be x.

13²=x²+(x+7)²

169=x²+x²+14x+49

169=2x²+14x+49

120=2x²+14x

120=2x(x+7)

60=x(x+7)

60=x²+7x

x=5

shorter length=5, longer length=12

Answer:

5/36 is your answer.

Step-by-step explanation:

If the red die shows a "2", then the blue die must take on the values from the set {2,3, 4, 5, 6} in order for the sum of both dice to be larger than 4.

1+2=3

2+3 = 5

2+4 = 6

2+5 = 7

2+6 = 8

There are 6*6 = 36 total ways to roll two dice and exactly 5 ways to get the conditions stated above. The probability of getting a sum greater than 2 is 5/36

The probability that the sum of the two dice is greater than 2 will be 35/36. Then the correct option is B.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

Cindy throws one red and one blue regular (six-sided) fair dice. The total number of events will be

Total events = 6 x 6 = 36

The probability that the sum of the two dice is greater than 2 will be given as

P = 1 - 1 / 36

P = 35 / 36

The probability that the sum of the two dice is greater than 2 will be 35/36. Then the correct option is B.

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