parallelagram abcd has the angle measures shown

Answer: A = 15 units²

Step-by-step explanation:

The figure has 1 pair of parallel sides and is therefore a trapezium.

The area (A) of a trapezium is calculated as

A =  h (b₁ + b₂ )

where h is the perpendicular height between bases and b₁, b₂ are bases

here h = 3, b₁ = 3 , b₂ = 7 , then

A =  × 3 × (3 + 7) = 1.5 × 10 = 15 units²

In the word problems given above, the results are:

1) Let's call the number we're looking for "x". According to the problem, "three times a number" is the same as 60 minus 21, which is 39. So we can write the equation:

3x + 21 = 60

Subtract 21 from both sides:

3x = 39

Divide by 3:

x = 13

Therefore, the number we're looking for is 13.

2)

Let's call the number we're looking for "x" again. According to the problem, "three times the difference between a number and three" is the same as "four times the number". So we can write the equation:

3(x - 3) = 4x

Simplify:

3x - 9 = 4x

Subtract 3x from both sides:

-9 = x

Therefore, the number we're looking for is -9.

3)

Let's call the first of the three consecutive integers "x". The next two would be x+1 and x+2. According to the problem, their sum is 48, so we can write the equation: x + (x+1) + (x+2) = 48

Simplify:

3x + 3 = 48

Subtract 3 from both sides:

3x = 45

Divide by 3:

x = 15

So the three consecutive integers are 15, 16, and 17. To answer the second part of the question, we can substitute these values into the given expression:

3m - z(1st) = 3(16) - 15(15) = 48 - 225 = -177


4)
Let's call the smallest of the three consecutive odd integers "x". The next two would be x+2 and x+4. According to the problem, twice the smallest is seven more than the largest, so we can write the equation:

2x = (x+4) + 7

Simplify:

2x = x + 11

Subtract x from both sides:

x = 11

So the three consecutive odd integers are 11, 13, and 15. The middle number is 13.


5)
Let's call the width of the rectangle "w". According to the problem, the length is 3 cm more than the width, so the length is w + 3. The perimeter is the sum of all four sides, which is:

P = 2w + 2(w + 3) = 4w + 6

We know that the perimeter is 22 cm, so we can write the equation:

4w + 6 = 22

Subtract 6 from both sides:

4w = 16

Divide by 4:

w = 4

So the width is 4 cm, and the length is 7 cm (since it's 3 cm more than the width). To find the area, we use the formula:

A = (L)(W) = (7)(4) = 28 square cm


6)

Let's denote the length of side a as x. Then we know that side b is 3 times the length of side a, or 3x, and side c is 1 more than twice the length of side a, or 2x+1.

Since the perimeter of the triangle is 43 inches, we can write the equation:

a + b + c = 43

Substituting in our expressions for b and c, we get:

x + 3x + 2x + 1 = 43

Simplifying the left-hand side, we get:

6x + 1 = 43

Subtracting 1 from both sides, we get:

6x = 42

Dividing both sides by 6, we get:

x = 7

thus:

a = 7

b= 3x = 21; na d

c = 2x + 1 = 14+1

c = 15

Thus the sum of sides a and b =
21 + 7
= 28

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The value of x in the proportion 1650 = x(156.25) is 10.56

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Given the proportion:

1650 = x(156.25)

We are required to solve for x. To find x, divide both sides of the equation by 156.25:

1650 / 156.25 = x(156.25) / 156.25

x =  1650 / 156.25

x = 10.56

The value of x is 10.56

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After all the spending costs, Tino's weekly salary is approximately $60.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Let's call Tino's weekly salary "x".

Each week, Tino sets aside half of his salary for rent, so:

0.5x = rent

He also sets aside half of his salary for credit card payments, so

0.5x = credit card payments

And he sets aside a quarter of his salary for groceries and utilities, so:

0.25x = groceries and utilities

And he has approximately $15 left for entertainment, so:

x - 0.5x - 0.5x - 0.25x = 15

We can simplify this equation by combining the terms on the left side:

x - 1.25x = 15

And then solving for x:

-0.25x = 15

x = 60

Therefore, Tino's weekly salary is approximately $60.

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The volume of the solid is -5.54 cubic units.

The region is bounded by the parabola x = 1 + (y-2)^2 and the line x = 2. To use the method of cylindrical shells, we imagine rotating this region around the x-axis, which gives us a solid shape.

The shell has thickness Δx and height y, and is located at a distance x from the y-axis. To find the volume of the solid, we'll add up the volumes of all the cylindrical shells.

The volume of a cylindrical shell is given by the formula V = 2πrhΔx, where r is the radius of the shell and h is its height. In this case, the radius of the shell is x - 2 (the distance from the y-axis to the edge of the region), and the height is y. So we have:

V = 2π(x - 2)yΔx

To find the total volume of the solid, we integrate this expression over the range of x values that corresponds to the region we're interested in. The region is bounded by x = 1 + (y-2)^2 and x = 2, so we integrate with respect to x from x = 1 + (y-2)^2 to x = 2:

V = ∫[1+(y-2)²]^2 2π(x - 2)y dx

To evaluate this integral, we can use the substitution u = y - 2, which gives us:

V = ∫1^0 2π(u^2 + 3) (1 + u)^2 du

This integral can be evaluated using the power rule and the substitution v = 1 + u:

V = 2π/5 [(1 + u)^5 - (1 + u)^3] from 1 to 0

V = 2π/5 [1 - 32/5]

V = 2π/5 ( -22/5)

V = - 8.8π/5

So the volume of the solid is approximately -5.54 cubic units. Note that the negative sign means that the solid is oriented in the opposite direction from what we might expect - in other words, it has a hole in it.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The identity to be used here is [ (a - b)² = a² - 2ab + b² ]

First, try to get the given expression in form of terms on the RHS of the above identity

[tex]\qquad \sf  \dashrightarrow \: 4y {}^{2} - 6yz + 9 {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 {}^{2})( {y}^{2}) - 2(3)(y)(z) + (3 {}^{2} ) {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (3z) {}^{2} [/tex]

[ it's in form of a² - ab + b² now, add and deduct ab here ]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (9z) {}^{2} - (2y)(3z) + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - 2(2y)(3z) + (3z) {}^{2} + (2y)(3z)[/tex]

[ Apply the identity ]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + 6yz[/tex]

[ That's probably the answer, it can't be simplified more ]

To factorize the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex], we can use the quadratic formula.

We have the quadratic expression [tex]\sf\:ax^2 + bx + c \\[/tex], where $$\sf\:a = 4$$, $$\sf\:b = -6y $$, and $$\sf\:c = 9z^2 $$.

The quadratic formula states that for any quadratic equation of the form [tex]\sf\:ax^2 + bx + c = 0 \\[/tex], the solutions for $$\sf\:x $$ can be found using the formula:

[tex]\sf\:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]

Applying this formula to our quadratic expression, we get:

[tex]\begin{align}\sf\:x &= \frac{-(-6y) \pm \sqrt{(-6y)^2 - 4(4)(9z^2)}}{2(4)} \\ &= \frac{6y \pm \sqrt{36y^2 - 144z^2}}{8} \\ &= \frac{6y \pm \sqrt{36(y^2 - 4z^2)}}{8} \\ &= \frac{6y \pm 6\sqrt{y^2 - 4z^2}}{8} \\ &= \frac{3}{4}y \pm \frac{3}{4}\sqrt{y^2 - 4z^2}\end{align} \\[/tex]

Thus, the factored form of the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex] is [tex]\sf\:(\frac{3}{4}y + \frac{3}{4}\sqrt{y^2 - 4z^2})(\frac{3}{4}y - \frac{3}{4}\sqrt{y^2 - 4z^2}) \\[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

✨[tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

The inequality that determines the maximum number of people that can go to the park is given as follows:

5.75 + 29.75x ≤ 210.

The costs associated with going to the park are given as follows:

Hence the total cost for x people going to the park is given by the following equation:

C(x) = 5.75 + 29.75x.

They can spend at most $210, hence the inequality that determines the maximum number of people that can go to the park is given as follows:

C(x) ≤ 210

5.75 + 29.75x ≤ 210.

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The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.

Given expression y² - 13y + ?

Comparing with the general equation

a = 1

b = -13

For perfect square trinomial

b² = 4ac

(-13)² = 4 * 1 * c

169 = 4c

c = 169/4

So the expression becomes,

y² - 13y + 169/4 = (y - 13/2)²

Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.

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Answer:

= 10.

Step-by-step explanation:

=

[tex]50 \times \frac{2}{10} \\ = 5 \times 2 \\ = 10.[/tex]

The answer becomes for the given expression is: 10.

Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in mathematics refers to the continual addition of sets of the same size. One of the fundamental mathematical processes is multiplication. The result of multiplying two or more integers together is known as the product. The first number used in a multiplication operation between two numbers is referred to as the multiplicand.

Given that,

= 50 × (2/10)

= 50 × (1/5)

= 10

Thus, for the given expression the answer becomes: 10

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The derivative of the composite function f(x) = (3 · x · cos x + √x) / [5 · x² · (sin x + 1)] is equal to f'(x) = [[3 · cos x - 3 · x · sin x + (1 / 2√x)] · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · [5 · x · (sin x + 1) + 5 · x² · cos x]] / [5 · x² · (sin x + 1)]².

In this problem we must determine the derivative of the composite function f(x) = (3 · x · cos x + √x) / [5 · x² · (sin x + 1)]. This can be done by using the following derivative rules:

Derivative of the addition of two functions

d [f(x) + g(x)] / dx = df(x) / dx + dg(x) / dx

Derivative of the product of two functions

d [f(x) · g(x)] / dx = [df(x) / dx] · g(x) + f(x) · [dg(x) / dx]

Derivative of the division of two functions

d[f(x) / g(x)] / dx = [[df(x) / dx] · g(x) - f(x) · [dg(x) / dx]] / [g(x)]²

Derivative of a function and a constant

d [c · f(x)] / dx = c · df(x) / dx

Derivative of a power function

d [xⁿ] / dx = n · xⁿ⁻¹

Derivative of cosine

d [cos x] / dx = - sin x

Derivative of sine

d [sin x] / dx = cos x

Now we proceed to determine the derivative of the function by derivative rules:

f'(x) = [d [3 · x · cos x + √x] / dx · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · d [5 · x² · (sin x + 1)] / dx] / [5 · x² · (sin x + 1)]²

f'(x) = [[3 · cos x - 3 · x · sin x + (1 / 2√x)] · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · [5 · x · (sin x + 1) + 5 · x² · cos x]] / [5 · x² · (sin x + 1)]²

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Answer:

The difference in height is 8cm

Step-by-step explanation:

Volume of a cylinder=hπr²

When the bottle is full 5652:

5652=hπr²

5652=h*3.14*7.5²

5652=h*176.625

5652/176.625=h

Height=32cm

When the bottle is full by 4239:

4239=hπr²

4239=h*3.14*7.5²

4239=h*176.625

4239/176.625=h

Height=24cm

Difference in height:

32-24=8

The difference in height is 8cm

In this question you're given that a coin is flipped 12 times. Now I'll make some assumption here. The first assumption is that the coin is fair. That means the probability of getting ahead in a trial in the toss is the same as probability of getting a deal in the toss and that would be half And second. The all the 12 flips or tosses are independent of each other. And thirdly that the probability of getting ahead, it's the same in each toss and you can see that in each talks there's only two outcomes ahead or not ahead which is a so this is considered a success and this is a failure. It just happened to be the probability of the success and the probability of failure is the same at heart. So this actually follows a binomial distribution model. But in the event that you have not learned by normal distribution we can just go by simple probability multiplication rule. So in probability and it's times or is plus. But the assumption of independent trials and the coin is fair is still the same whether you're using binomial distribution or just simple probability multiplication rule, no Probability of obtaining 12 heads in a row when flipping a coin would be the first pulse, you get a hit. And the second course you also get ahead. And the third toss you get ahead. So on so forth. Up to the last toss, which is the 12th toss, you also get a hit. So it's hit for every toss. So what this means is that probability of first courses ahead is half so that's half now. N and in probability means multiple execution. So just times and second hand is second thoughts is also ahead. So there's a half and so N. S. A. Terms enter is ahead, so that's another half, so so on, so forth. All the way to the last end here. Mr toms And the 12 is also a hit. So this times, how so what we have here is half to the power of 12 since half is multiplying itself 12 times. And so the answer is 1/4 oh 96 Or 0.0002, 44 six, decimal places. Now, if you are using binomial distribution to solve this problem, you will be after this part here. You will be letting X be the number of heads. Oh 12 courses. Right, So X follows the binomial distribution Number of trials is 12, 12 horses. And probability of success in this case is probability of getting ahead in a in a toss is half, so probability of X equals two. R. Where r is the number of heads in 12 courses will be 12, choose our half to the power of our and one minus half is also half To the power of 12 minus are so probability of obtaining 12 heads in a role. So we will be looking at probability of X equals 2, 12. So just suck 12 into the arm. So is this and you will get the same answer of 0.000244

The solution of x in the rhombus is 3

From the question, we have the following parameters that can be used in our computation:

The rhombus

Also, we have

LN = 14

AN = x + 4

Using the above as a guide, we have the following equation:

LN = 2 * AN

substitute the known values in the above equation, so, we have the following representation

2 * (x + 4) = 14

Evaluate the expression

x + 4 = 7

Subtract 4 from both sides

so, we have the following representation

x = 3

Hence, the solution is 3

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Answer:

Alex spends more time 2/5 of 100 is 40%

A valid inference about the data of Video Games Play Time among students is A). 50% of students spend 2- or 3 hours playing video games.

An inference is an evidence-based conclusion.

Inferences are reached when the necessary facts are available, and the researcher has done some calculations and reasoning using the facts.

Video Games Play Time

Hours Played     Number of Students

0                                        2

1                                         4

2                                        6

3                                        8

4                                        5

5 or more hours               3

Total number of students 28

Number of students = 14 (6 + 8)

14/28 - 50%

50% = 50%

Number of students = 8 (5 + 3)

8/28 = 28.6%

28.6% > 10%

Number of students = 10 (4 + 6)

10/28 = 35.7%

35.7% > 10%

Number of students = 13 (8 + 5)

13/28 = 46.3%

46.3% ≠ 50%

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Video Games Play Time

Hours Played     Number of Students

0                                        2

1                                         4

2                                        6

3                                        8

4                                        5

5 or more hours               3

Total number of students 28

A). 50% of students spend 2- or 3 hours playing video games.

B). Less than 10% of the students spend 4 or more hours playing video games.

C). Less than 10% of the students spend 1- or 2 hours playing video games.

D). More than 50% of the students spend 3- or 4 hours playing video games.

The probability of selecting a Democrat and then an Independent is  (6/16) * (6/15) = 3/40. The probability of selecting two Republicans with replacement is (4/16) * (4/16) = 1/16.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. It is the ratio of the number of favorable outcomes to the total number of possible outcomes in a given situation. Probability is used in many fields, such as mathematics, statistics, science, engineering, economics, and social sciences, to model and analyze uncertain situations and make predictions about the future based on available data.

(a) selecting a Democrat and then an Independent without replacement.

The probability of selecting a Democrat on the first draw is 6/16, and the probability of selecting an Independent on the second draw, without replacement, is 6/15. So the probability of selecting a Democrat and then an Independent is:

(6/16) * (6/15) = 3/40

(b) selecting two Republicans with replacement.

The probability of selecting a Republican on the first draw is 4/16, and with replacement, the probability of selecting another Republican on the second draw is also 4/16. So the probability of selecting two Republicans with replacement is:

(4/16) * (4/16) = 1/16

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Let's consider what the question asks for:

   --> the length of 'y'

To solve:

 --> we need to use trigonometry

     --> let's determine which function to use based on the image given

           below

         --> (look at image attached)

Let's use angle with measure of 53:

 --> the side with length of 'y' is adjacent to it

       [tex]cos(53)=\dfrac{y}{10} \\\\y=10*cos(53)=6.02[/tex]

Thus the length of that particular side is about:

 --> 6.0

Answer: 6.0

Answer:

9.968

Step-by-step explanation:

[tex]c^2=a^2+b^2 -2ab*cos(C)[/tex]

and more generally, a side squared of a triangle is equal to the other two sides squared then added, minus double the product of the other two sides and the cosine of the opposite angle, generally denoted as the capital letter of the side. (c is the side, C is the opposite angle)

in this case the other two sides are 7 and 10, so we can say that a=7, b=10 if  it helps understand this a bit more, but "a" and "b" really just represent the other two sides.

the opposite angle is: [tex]\frac{5\pi}{13}[/tex] and the unknown is "a", but we can just express it as "c" for the sake of simplicity. Now plugging in all the known values we get the following equation:

[tex]c^2=7^2+10^2-2(7)(10)cos(\frac{5\pi}{13})\\\\c^2=49+100-140cos(\frac{5\pi}{13})\\\\c^2=149-140cos(\frac{5\pi}{13})[/tex]

Now from here we can just use a calculator to approximate the cosine, but make sure it's in radian mode! otherwise your answer may be incorrect as degrees are different than radians.

[tex]c^2=149-140(0.3546)\\\\c^2=149-49.64468\\\\c^2=99.355315814\\\\c=\sqrt{99.355315814}\\\\c=9.96771367035\\\\c\approx 9.968[/tex]

So the side is approximately 9.968 units in length.

Answer:

51°

Step-by-step explanation:

180°-129°=51°

I hope it helps you

The provided statement indicates that Jim and Terrence each possess eight model automobiles, whereas Terrence owns six, making an 8:6 ratio. Jim is the owner of the 48 model card, then.

If b is really not equal to 0, then an arrangement of the numbers a and b expressed as a/b is a ratio. An equation known as a percent establishes two ratios with the identical value. You might, for instance, write the ration as described in the following: 1: 3 in the case of 1 male and 3 girls.

You are aware that Jim and Terrence own an 8:6 ratio in terms of the total number of model automobiles they own.

Accordingly, you can answer the task as follows: Let's say Jim owns x model automobiles.

8/6 = x/36

x = 36*8/6

x = 288/6

x = 48

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Answer:

Step-by-step explanation:

To find the probability of the sum of two randomly selected numbers from a set being greater than 12, we need to first find the total number of possible combinations of two numbers and then count the number of combinations that result in a sum greater than 12.

The set contains four numbers, so there are 4 choose 2 possible combinations of two numbers, which is equal to (4! / (2! * (4 - 2)!)), or 6 combinations. These combinations are:

(0,6), (0,12), (0,15), (6,12), (6,15), (12,15)

Next, we'll count the number of combinations that result in a sum greater than 12. These combinations are:

(6,15), (12,15)

There are 2 combinations that result in a sum greater than 12.

Finally, to find the probability, we'll divide the number of favorable outcomes (combinations with a sum greater than 12) by the total number of outcomes (all possible combinations of two numbers), and express the result as a fraction:

probability = 2 / 6

Reducing the fraction, we get:

probability = 1 / 3

So, the probability that the sum of two randomly selected numbers from the set is greater than 12 is 1/3.

That's how you find the probability of the sum of two randomly selected numbers from a set being greater than a certain value. By counting the number of favorable outcomes and dividing by the total number of possible outcomes, you can find the probability of a certain event.

Answer:

Step-by-step explanation:

The number of Dr. Pepper cans are 39.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Julia bought a total of 52 cans of Dr. Pepper and Sprite.

There were three times as many cans of Dr. Pepper as Sprite.

Let number of sprite cans be x.

Then, the number of Dr. Pepper cans will be 3x.

Now, x+3x=52

4x=52

x=13

So, 3x=39

Therefore, the number of Dr. Pepper cans are 39.

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Answer: the correct choice is b

Step-by-step explanation:

Answer:  Choice C)  [tex]7i\sqrt{2}[/tex]

Work Shown:

[tex]\sqrt{-98} = \sqrt{-1*49*2}\\\\\sqrt{-98} = \sqrt{-1}*\sqrt{49}*\sqrt{2}\\\\\sqrt{-98} = i*7*\sqrt{2}\\\\\sqrt{-98} = 7i\sqrt{2}\\\\[/tex]

The level of confidence Evelyn used is 92%. Therefore, option B is the correct answer.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

Given that, one sample z interval for proportions and gets a margin of error of 0.0758.

If her sample proportion was 0.75 and her sample size was 100.

We know that, p±z×√p(1-p)/n

Where, P is sample proportion, n is the sample size and z is the standardized normal distribution

Here, 0.75±0.0758×√0.75(1-0.75)/100

= 0.75±0.0758×√0.1875/100

= 0.92

=92%

Therefore, option B is the correct answer.

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Answer:

Step-by-step explanation:

When we use the distance formula for two points ( x, y ) and ( x', y¹ ) Then formula is (distance)² = (x - x¹)² + (y - y¹)² This is quite similar to the formula used in a right angle triangle

Its 10/29 so its answers this