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Using trigonometry formulas, the value of tan(x-y) = -16/63

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

Given

cot y = 4/3

1/tan y = 4/3

Cross multiply

tan y = 3/4

Also since csc x = 13/5

1/sin x = 13/5

sin x = 5/13

Since sin x = opp/hyp

opp = 5

hyp = 13

Get the adjacent

hyp² = opp²+adj²

13² = 5²+adj²

adj² = 13² - 5²

adj² = 169 - 25

adj² = 144

adj = 12

cos x = adj/hyp

cos x = 12/13

tan x = sin x/ cos x

tan x = (5/13)/(12/13)

tan x = 5/13 * 13/12

tan x = 5/12

tan(x-y) = tan x - tan y/1 + tan x * tan y

tan(x-y) = (5/12 - 3/4) / 1 + (5/12) (3/4)

tan(x-y) = (5-9/12) / 1 + 5/16

tan(x-y) = -4/12/(21/16)

tan(x-y) = -1/3 * 16/21

tan(x-y) = -16/63

the value of tan(x-y) is -16/63

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Answer:

Step-by-step explanation:

Finding an equation of a line can be condensed into 2 easy steps.  Step one is to establish the basic form of the equation, including it's slope.  

1)  Lets use y=mx + b as the basic form, where m is the slope and b is the y-intercept (the value of y when x is zero).  We are told the line is parallel to y = 3x - 1, which is a line with a slope (m) of 3.  Parallel lines have the same slope, so our kline will also have a slope of 3, bringing us to:

   y = 3x + b.

2)  The second step is finding the value of b.  We are told the line must go through point (1,5), so we need a value of b that will shift the line to (1,5).  Easy:  just enter this point in the equation we have so far:  y = 3x + b:

y = 3x + b

5 = 3*(1) + b for point (1,5)

b = 2

The equation becomes y = 3x + 2

See the attached graph.  [Extra credit]

The lines are parallel, and the y-intercept for the second line (b) is (0,2).

Answer:

72 [tex]ft^{2}[/tex]

Step-by-step explanation:

a = 1/2(24)(6)

a = 72

The pitch of the roof is roughly 35.3 degrees, and the middle height of the roof is 19.3 feet.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.

Here,

To find the pitch of the roof, we need to use the Pythagorean theorem to determine the height of the roof at the center. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

In this case, the height of the roof at the center is the hypotenuse, and the two shorter sides are the width of the house (32 feet) and half of the length of the rafter (22 feet / 2 = 11 feet). So, using the Pythagorean theorem, we can set up the following equation:

h² = (32 / 2)² + 11²

h² = 16² + 11²

h² = 256 + 121

h² = 377

h = √377

h = 19.3 feet

Next, we use the tangent function to find the pitch of the roof. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roof (19.3 feet), and the adjacent side is half of the rafter length (11 feet). So, we can set up the following equation:

tan(pitch) = 19.3 / 11

We can use the inverse tangent function (tan^-1) to find the angle, which will give us the pitch of the roof in degrees.

pitch = tan^-1(19.3 / 11)

The pitch of the roof is approximately 35.3 degrees and height of the roof at the center is 19.3 feet.

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If the current is 2.2 A, it falls within the 2% tolerance range of 2.156 A to 2.244 A and would be considered correct.

To determine if 2.2 A falls within the 2% tolerance range, we first need to establish what the expected current value is. If the expected current value is not specified, it's best to use the maximum rated current value as the expected value.

Once we have the expected current value, we can calculate the tolerance range. Tolerance is expressed as a percentage of the expected value, and in this case, it's 2%.

So the tolerance range is:

(Expected Value) * (Tolerance Percentage) = Tolerance Range

For example, if the expected value is 2.2 A, then the tolerance range would be:

2.2  * 0.02 = 0.044

The tolerance range represents the amount by which the actual current can deviate from the expected value and still be considered acceptable. In this case, the tolerance range is 0.044 A, so the acceptable range for the current would be:

(Expected Value - Tolerance Range) to (Expected Value + Tolerance Range)

2.2 - 0.044 to 2.2 + 0.044 = 2.156 to 2.244

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x = 4

-- All angles of a triangle add up to 180° --

-- the inverse of a trianglenis equal to its opposite angle of intersection--

1) build equation

180° = 20° + (4 + 6x) + (32x + 4)

2) solve

180-20 = 4 + 6x + 32x + 4

160 = 8 + 38x

152 = 38x

152/38 = x

x = 4

verify

180 = 20 + (4 + 6x) + (32x + 4)

180 = 20 + (28) + (132)

180 = 180 so x = 4

[tex]\stackrel{\textit{for bills}}{1500\cdot \cfrac{1}{2}}~~ + ~~\stackrel{\textit{for savings}}{1500\cdot \cfrac{1}{5}}~~ + ~~\stackrel{\textit{food and ET}}{x}~~ = ~~\stackrel{total}{1500} \\\\\\ 750+300+x=1500\implies 1050+x=1500\implies x=450[/tex]

so let's take a peek at the triangular pyramid, hmm it has a base of well, the base is a triangle, so we can say the triangle has a base of 10 and a height of 8, thus and area of (1/2)*10*8, and the pyramid has a height of 9.

[tex]\textit{Volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(10)(8)\\[1em] h=9 \end{cases}\implies V=\cfrac{1}{3}\left[ \cfrac{1}{2}(10)(8) \right](9) \\\\\\ V=\cfrac{1}{3}(40)(9)\implies V=\cfrac{360}{3}\implies V=120~m^3[/tex]

The solution is x^2-5x+22<0.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

2x-5/ x^2-6x-7< 1/x-3,

so, we get,

⇒2x-5/x^2-7x+x-7 <  1/x-3

⇒2x-5/(x-7)(x+1) < 1/x-3

⇒2x-5 * x-3 < (x-7)(x+1)

⇒2x^2-11x+15 < x^2-6x-7

⇒x^2-5x+22<0

Hence, The solution is x^2-5x+22<0.

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Answer:

Step-by-step explanation:

Since the base x is consistent with all terms of this complex fraction, all you need to do is add the two exponents found in the numerator and from that, subtract the exponent in the denominator.

This gives us x^(3/5) divided by x^(4/5), which is x^(-1/5). This gives 1/x^(1/5), which is 1 divided by the fifth root of x.

Answer:

120%

Step-by-step explanation:

3,600,000 divided by 3,000,000, times 100 = 120%

So, 120% of 3,000,000 is equal to 3,600,000

Answer:

120 %

Step-by-step explanation:

To solve for this percentage problem, we set up an equation:

[tex]3,000,000 * \frac{x}{100} = 3,600,000[/tex]

[tex]30,000 * x = 3,600,000[/tex]

x = 120

The age that she must work till she is qualified to receive Social Security benefits when she retires is: 56 years

Social Security benefits provide partial replacement income for retired beneficiaries and disabled persons, as well as their spouses, children and survivors.

To be eligible for Social Security benefits, you must be enrolled in the Social Security program and accumulate 40 credits while employed.

Benefits are based on your income history, year of birth, and age at which you began applying for Social Security.

If your spouse is unemployed or has not reached the required number of credits, you can receive benefits according to your spouse's work performance.

Benefits may likely be taxed based on the specific income and tax return status.

She will be required to earn a total of 40 credits in order to qualify to be able to receive social security benefits, due to the fact that she earns the maximum number of 4 credits per year, she therefore has to work for at least a minimum of ten years or until at least she is 56.

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In a case whereby A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet the expression that best represents the value of pi is  43.96 feet/ 14 feet.

The concept that will be use here is Circumference. we were given Circumference of the circle  as 43.96 feet

where the Diameter of the circle is  14 feet, then we can find the Circumference of the circle  as( πd)

Then ( πd) = 43.96 feet

π= 43.96 feet/ 14 feet

Therefore, option C is correct.

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Answer:

3.25

Step-by-step explanation:

total 18.25 - 2.00 tip = 16.25

16.25/5=3.25

An amount of $ 13,200 has a total comission of 856.

Herein we find the case of the calculation of a comission for an amount of money, where an interest rate of six percent is applied for first $ 10.000 and an interest rate of eight percent is applied for the excedent above $ 10.000. The total comission is determined by following mathematical equation:

C = 10,000 · (6 / 100) + (13,200 - 10,000) · (8 / 100)

C = 856

The graduate must pay a total comission of $ 856 for an amount of $ 13,200.

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Indicating whether the variable is relevant to the questions, and Identifying the variable as either categorical or quantitative.

Rather than straightforward explanations. Anything may be measured using it. It can also do mathematical calculations, which is essential for data analysis.

To completely understand all of the facets of quantitative data, statistical analysis—the discipline of obtaining, analysing, and presenting enormous volumes of data to uncover patterns and trends—is used. This calls for quantitative analysis employing a wide variety of data.

Categorical data is data that may be arranged into groups or categories using names or labels.

The approach is based on algorithms that assess each component of a data collection individually, compare them to other individual data sets, and look for particular similarities.

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Complete question:

identify and classify the variable(s) you will use.Here is the list of variables in the data set. Use the menu to the right of each variable to: Indicate whether the variable is relevant to the questions we are investigating, and Identify the variable as either categorical or quantitative. Group of answer choices

Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

1

Step-by-step explanation:

6 children that each want to eat half of a chocolate bar (0.5)

6 * 0.5 = 3 - chocolate bars will be eaten

They bought a package of 4 chocolate bars

4 - 3 = 1 - chocolate bar will be left

Answer:

  ㏒₅₄168 = (1+ab)/(8a-5ab)

Step-by-step explanation:

You want ㏒₅₄168 written in terms of a and b, where ...

The rules of logarithms are relevant here:

  [tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}\\\\\log(ab)=\log(a)+\log(b)[/tex]

In order to simplify the writing in what follows, we want to define ...

Now, we can write the equations ...

  a = log(12)/log(7) = (2p+q)/r . . . . . . . . . [eq1]

  b = log(24)/log(12) = (3p+q)/(2p+q) . . . [eq2]

Using these, we can solve for p and q:

  2p +q = ar . . . . . . . . . . . . . [eq3], from [eq1]

  (3 -2b)p +(1 -b)q = 0 . . . . . [eq4] from [eq2]

Using your favorite solution method for linear equations, you find ...

  p = ar(1 -b)/(2(1 -b) -(3 -2b)) = ar(1 -b)/(2 -2b -3 +2b) = ar(b -1)

  q = (-ar(3 -2b)/(-1) = ar(3 -2b)

Substituting these expressions into ...

  [tex]\log_{54}{168}=\dfrac{\log{(2^3\cdot3\cdot7)}}{\log{(2\cdot3^3)}}=\dfrac{3p+q+r}{p+3q}\\\\=\dfrac{3ar(b-1)+ar(3-2b)+r}{ar(b-1)+3ar(3-2b)}=\dfrac{3ab-3a+3a-2ab+1}{ab-a+9a-6ab}\\\\=\boxed{\log_{54}{168}=\dfrac{1+ab}{8a-5ab}}[/tex]

__

Additional comment

The calculator confirms the result.

Justice had the rented car for 22 days, when the rent per day is $20 with $50 deposit.

Rent is a periodic payment made by a tenant to a landlord in exchange for the use of land, building, apartment, office, or other property. A payment or series of payments made by a lessee to an owner in exchange for the use of machinery, equipment, etc. 

According to the information in the question:

Deposit = $50

Rent cost per day for the car = $20

Total amount that Justice has to pay = $490

∴ Total number of days that Justice kept the car = (490 - 50)/20

                                                                                 = 440/20

                                                                                 = 22 days

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The number of days did he have the car are 22.5 days.

a set monthly fee that you pay to utilise someone else's space, including their home, car, television, etc. Because my room is larger than the other renters', I pay a higher rent or more rent.

Justice rented a car for a deposit of $50 and a daily rate of $20. When he returned the car, he owed $490.

To find out how many days he had the car, we can set up an equation:

$50 + (number of days x $20) = $490.

Solving for the number of days: number of days = ($490-$50)/$20 = 22.5 days.

So Justice had the car for approximately 22.5 days.

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Answer:

we can find a + a^(1/2) by substitution:

a + a^(1/2) = 6/5 + √(6/5)

Step-by-step explanation:

We have the equation:

a² + a - 1/2 = 5

Adding 1/2 to both sides:

a² + a = 5 1/2

Factoring out a from the left-hand side:

a(a + 1) = 5 1/2

Taking the square root of both sides:

a + 1/2 = ±√(5 1/2 / a)

Since a^(1/2) - a^(1/2) > 0, we know that a is positive, so we can discard the negative root. Then we have:

a + 1/2 = √(5 1/2 / a)

Squaring both sides:

a² + a + 1/4 = 5 1/2 / a

Substituting the expression for a² + a from the first equation:

5 1/2 - 1/2 + 1/4 = 5 1/2 / a

Multiplying both sides by a:

5 1/2 a - 1/2 a + 1/4 a = 5 1/2

Simplifying:

5a - 1/2 = 5 1/2

Adding 1/2 to both sides:

5a = 6

Dividing by 5:

a = 6/5

Finally, we can find a + a^(1/2) by substitution:

a + a^(1/2) = 6/5 + √(6/5)

Answer:

Step-by-step explanation:

a-2

Answer:

d ≥ - 14

Step-by-step explanation:

6d ≥ - 84

Divide by 6 both sides

6d/6 ≥ - 84/6

d ≥ - 14

r = red tiles

b = blue tiles

b = r + 12 , whatever "r" is, "b" is 12 more than that

[tex]\stackrel{red}{3}~~ : ~~\stackrel{blue}{5}\qquad \implies \cfrac{r}{b}=\cfrac{3}{5}\implies \cfrac{r}{r+12}=\cfrac{3}{5}\implies 5r=3r+36 \\\\\\ 2r=36\implies r=\cfrac{36}{2}\implies r=18[/tex]

Answer:

18

Step-by-step explanation:

Because there are 12 more blue tiles than red, that means that we can write the equation 3x + 12 = 5x. By simplifying, the equation is boiled down to 12=2x. By dividing, we see that x=6. This means that we can multiply 3 by 6 to get 18 red tiles. To check our answer, we just multiply 6 by 5 to get 30, and the ratio 18:30 is equivalent to 3:5. Also, 30-18=12, so this must be correct.

Answer:

y= 13

Step-by-step explanation:

y+3x2+7

y=6+7

y=13

x     y

0     13

1       13

linear

Since 6100 is greater than 5600, nine refrigerators and eight pianos would overload the truck.

What is linear inequality?

A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.

Let "x" be the number of refrigerators and "y" be the number of pianos. The total weight of the refrigerators is 300 pounds per refrigerator, so the total weight of the refrigerators is 300x pounds. The total weight of the pianos is 425 pounds per piano, so the total weight of the pianos is 425y pounds. The total weight of the load must be less than or equal to 5600 pounds, so we can write an inequality as follows:

300x + 425y ≤ 5600

To graph this inequality, we can use the coordinates of points that satisfy the inequality and shade the region that represents the solutions.

To determine if nine refrigerators and eight pianos would overload the truck, we can substitute these values into the inequality and see if it still holds:

300 × 9 + 425 × 8 = 2700 + 3400 = 6100

Since 6100 is greater than 5600, nine refrigerators and eight pianos would overload the truck.

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Answer:

Step-by-step explanation:

Convert pounds to ounces:

2[tex]\frac{2}{3}[/tex] = 2.667

2.667 lb x 16 oz/lb = 42.7 oz

42.7 > 40, therefore Tuga has enough sweet potatoes to make chili