The floors and walls of gerald's attic form an equilateral triangle what is the approximate height h of the attic?

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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Answer:

Step-by-step explanation:

In numerical order:

      \(1\frac{2}{3},1\frac{3}{4}\)

Since there are only 2 scores the median(middle score)  will be the same as the mean:

     \((1\frac{2}{3}+ 1\frac{3}{4}) \div 2=(\frac{20}{12}+ \frac{21}{12}) \div 2=\frac{41}{12} \times \frac{1}{2} =\frac{41}{24}=1\frac{17}{24}\)

Answer: The answer to your question is to not ask clearly you just answered your own question like yoooooooooooooooooooo.

Step-by-step explanation:

The value of x in the triangle is 20

From the triangle, we have the following equivalent ratios:

5x+ 10 : 121 = 10 : 11

Express as fraction

5x  + 10/121 = 10/11

Multiply both sides by 121

5x + 10 = 110

Subtract 10 from both sides

5x  = 100

Divide both sides by 5

x = 20

Hence, the value of x in the triangle is 20

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The given sequence converges.

The limit of the given sequence is :  1/4.

The given sequence is an = tan(5n)/(3 + 20n).
To determine if the sequence converges or diverges, we can use the limit comparison test.
We know that lim n→∞ tan(5n) = dne, since the tangent function oscillates between -∞ and +∞ as n gets larger.
Thus, we need to find another sequence bn that is always positive and converges/diverges.

Let's try bn = 1/(20n).
Then, we have lim n→∞ (tan(5n)/(3 + 20n)) / (1/(20n))
= lim n→∞ (tan(5n) * 20n) / (3 + 20n)
= lim n→∞ (tan(5n) / 5n) * (5 * 20n) / (3 + 20n)
= 5 lim n→∞ (tan(5n) / 5n) * (20n / (3 + 20n))

Now, we know that lim n→∞ (tan(5n) / 5n) = 1, by the squeeze theorem.

And we also have lim n→∞ (20n / (3 + 20n)) = 20/20 = 1, by dividing both numerator and denominator by n.

Therefore, the limit comparison test yields:
lim n→∞ (tan(5n)/(3 + 20n)) / (1/(20n)) = 5

Since the limit comparison test shows that the given sequence is similar to a convergent sequence, we can conclude that the given sequence converges.

To find the limit, we can use L'Hopital's rule to evaluate the limit of the numerator and denominator separately as n approaches infinity:
lim n→∞ tan(5n)/(3 + 20n) = lim n→∞ (5sec^2(5n))/(20) = lim n→∞ (1/4)sec^2(5n) = 1/4.

Therefore, the limit of the given sequence is 1/4.

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B. Similar spreads different centers.

sec²x

........Hope I helped!..................

Answer:

118

Step-by-step explanation:

you should have learned this in 1st grade

Answer: 14 boxes

Step-by-step explanation:

Divide 110 by 8 and you get 13.75. You will then round up to the nearest hole number to make sure that almost all the boxes have 8 muffins in each.

Answer:

it should be C I guess.

Im sorry if it is wrong

-8 is the solution of inequality 4(1.2z+1.25)<19.4

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality 4(1.2z+1.25)<19.4

4.8z+5<19.4

4.8z<19.4-5

4.8z<14.4

z<3

-8 is the solution of 4(1.2z+1.25)<19.4

2(1.1z+2.5)≥−3.8

2.2z+5≥−3.8

2.2z≥−8.8

z≥-4

-8 is not the solution of 2(1.1z+2.5)≥−3.8

Hence, -8 is the solution of inequality 4(1.2z+1.25)<19.4

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Answer:

x = 2

Step-by-step explanation:

Given

5x - 4 = - 3x + 12 ( add 3x to both sides )

8x - 4 = 12 ( add 4 to both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Answer:

5.4

Step-by-step explanation:

The scale of the 2 shapes is 1:1.8. so if the smaller shape's side is 3, insert 3 into the ratio. Now, multiply 3*1.8, and you get your answer of 5.4

Answer: 100 to 200 mm

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Therefore, the percent of the agency fee that Ms. Gonzalez received is:x = 42025/48750 × 100% = 86.15% (rounded to the nearest tenth of a percent).Answer: Ms. Gonzalez received 86.2% of the agency fee.

Given information: Ms. Gonzalez worked for a real estate agency, Remax. She sold a house for $975000. The agency fee for the sale was 5% of the sale price. Mrs. Hamilton received $6725 of the agency fee as her commission. The question is:

What percent of the agency fee did Ms. Gonzalez receive?

Here is the solution:

Let's calculate the agency fee on the sale price of $975000.Agency fee = 5% of sale price = (5/100) × 975000 = $48750.

Now, Ms. Hamilton received $6725 from the agency fee. So, the remaining amount of the agency fee went to Ms. Gonzalez. Let the amount received by Ms. Gonzalez be x.

So, Ms. Gonzalez received the remaining amount of the agency fee as her commission, i.e., $48750 - $6725 = $42025.

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74100

170000

36000

I believe this is right!

Answer:

120° will be found on in the second quadrant of the unit circle. Specifically, the reference angle will be 60°. This is because the angle measurement starts from the positive x axis, and rotates 120° counter-clockwise. The angle formed at this point between the line and the x-axis (negative direction) is 60°.

The special right triangle formed will have a hypotenuse of 1, and a reference angle of 60°.

We know that the adjacent line, the line opposite the 30° angle, will be 1/2 the hypotenuse, or -1/2. Negative because it goes in the negative x direction.

The opposite end, or vertical side, will be √3/2.

sin(120) = opposite/hypotenuse = √3/2 ÷ 1 = √3/2

cos (120) = adjacent/hypotenuse = (-1/2) / 1 = -1/2

tan (120) = opposite / adjacent = (√3/2) / (-1/2) = -√3

Step-by-step explanation:

Hope this helps...

1. height(in.)

2. arm span (in.)

3. (30,27)

Answer:

p=5.50b

Step-by-step explanation:

Answer:

p = 5.50b

Step-by-step explanation:

When you find the relationship between p and b, you see that b has to be multiplied by 5.50 in order to match the given p values. Therefore, the 2nd choice is the correct answer.

Answer:

w = 34°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

2w + 1 + 2w + 43 = 180 , that is

4w + 44 = 180 ( subtract 44 from both sides )

4w = 136 ( divide both sides by 4 )

w = 34

Answer: W = 34°

Step-by-step explanation:

Use the angle sum theorem!

2w + 2w + 1 + 43 = 180

4w + 44 = 180

4w = 136

w = 34

Answer:

your perimeter will be 40cm

The 4 sides of a square are the same length. Find the length of a side by taking the square root of the area.

Side = sqrt(100) = 10 cm

Perimeter = side length x 4

Perimeter = 10 x 4 = 40 cm

Answer:

The line parallel to this equation would be y=3x+25

Step-by-step explanation:

A parallel line has the same slope but a different y-intercept (so just ignore the "-1" in the equation )  Our goal is to find the y-intercept ("b")

We will start with  

y=3x+b, plug in (-9,-2) for the x and y

-2=3(-9)+b

-2=-27+b,    add 27 to both sides

-2+27=-27+27+b    (the 27's on the right side cancel side)

b=25

our new equation is y=3x+25

Answer:

y=2x+1

Step-by-step explanation:

The median of the following set of numbers  (18, 26, 29, 18, 44) is 26. The correct option to this question is option A

To find median of the following sequence (18, 26, 29, 18, 44) we will arrange them in ascending order

                            18 , 18 , 26 , 29 , 44   . . . . . .  . . . .(1)

Since the number of terms is odd we will apply the formula

                     Median  = \(\frac{(n+1)}{2} th\) term . . . . . . .(2)

       Here n = number of terms

As per question the n = 5

Therefore putting in equation 2 we get

                      Median = \(\frac{(5+1)}{2} th\) term

                      Median = \(\frac{6}{2} th \\\)  term

                      Median = 3 term

Hence the third term from the sequence ( shown in 1 ) we get the median that is 26

Hence the median of the following set of numbers (18, 26, 29, 18, 44) is 26 .

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The median is:

26

Explanation:

First, we will arrange the numbers from least to greatest.

18, 26, 29, 18, 44

Rearrange

18, 18, 26, 29, 44.

Now, the median is the number in the middle, which is 26.

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Answer:

The new slope is 1 and the line is shifted flatter.

Step-by-step explanation:

Line A slope is 4.

Line B slope is 1.

The y-intercept rose up 3

As far as slope, it became flatter because the line only rises 1 'square' for every 1 'square' it travels to the right. It was rising 4 'squares' for every 1 to the right.  

Answer:

99.7%

Step-by-step explanation:

Note that 92 and 128 are 3 standard deviations from the mean

The emperical rule or the  68–95–99.7 rule states that 68% of outcomes are wihtin 1 standard deviation from the mean

95% of outcomes are within 2 standard deviations from the mean

99.7% of outcomes are within 3 standard devations from the mean

This is 3 standard deviations so the answer is 99.7

The radius of the circle O is R = 2.82 centimeters.

If we have a circle of radius R, and we dilate it by a scale factor k, the new radius is:

k*R

And we know that the area of a circle of radius R is:

A = pi*R²

Where pi = 3.14

If the radius of circle O is R, we know that O' is a dilation of scale factor 3, then the new radius is 3R

And we know tha tthe area of O' is:

A' = 225 cm² = 3.14*(3R)²

Now we can solve that to get the value of R.

3R=  √( (225 cm²)/3.14)

3R = 8.46 cm

R = 8.46cm/3

R = 2.82cm

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Option b. The oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be $372,000.

The yearly straight-line devaluation cost for the machine would be $186,000 ($930,000/5). In any case, since no deterioration was perceived in 2020, the collected devaluation toward the start of 2021 would be $0 rather than $186,000. In this manner, the complete devaluation cost for 2021 would be the yearly deterioration of $186,000 in addition to the get up to speed devaluation for 2020 of $186,000, for a sum of $372,000. This make up for lost time devaluation is important to address the blunder made in the earlier year and guarantee that the resource is appropriately recorded on the asset report. Accordingly, the right response is $372,000.

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The complete question is:

On January 1, 2020, Oriole Corp. acquired a machine at a cost of $930000. It is to be depreciated on the straight-line method over a 5-year period with no residual value. Because of a bookkeeping error, no depreciation was recognized in Oriole's 2020 financial statements. The oversight was discovered during the preparation of Oriole's 2021 financial statements. Depreciation expense on this machine for 2021 should be

$232500.

$372000.

$186000.

$0.