why is y=3x proportional

The values would be

sin2x = -3/5

cos2x = -4/5

tan2x = 3/4

What are double angles in trigonometry?

The double angle formulas are used to find the values of double angles of trigonometric functions using their single angle values. For example, the value of cos 30° can be used to find the value of cos 60°. Also, the double-angle formulas can be used to derive the triple-angle formulas.

Given: tanx = -3

Now as we know,

                  [tex]sin2x=\frac{2tanx}{1+tan^2x}\\\\sin2x=\frac{2(-3)}{1+(-3)^2}\\\\sin2x=\frac{-6}{10}\\\\sin2x=\frac{-3}{5}[/tex]

Now

               [tex]cos2x=\frac{1-tan^2x}{1+tan^2x}\\\\cos2x=\frac{1-(-3)^2}{1+(-3)^2}\\\\cos2x=\frac{1-9}{1+9}\\\\cos2x=\frac{-8}{10}\\\\cos2x=\frac{-4}{5}[/tex]

And similarly, we can find the value of tan2x, as

                  tan2x = sin2x/cos2x

                             = (-3/5)/(-4/5)

                             = 3/4

Hence,

The values would be

sin2x = -3/5

cos2x = -4/5

tan2x = 3/4

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On solving the provided question, we got that - 0.8 > 0.3, 0.8 is greater as , it is more closer to 1 than 0.3.

The term "number line" refers to a horizontal line with numbers placed equally apart. Depending on the numbers present, you can choose how to respond to the numbers on the line. The corresponding question dictates how to use numbers. B. When arranging the points.

From the provided question,

we  have to compare between 0.3 and 0.8.

Here,

Obviously, 0.8 is greater than 0.3.

as on number 0.8 is closer to 1 than 0.3,

and 0.3 is more closer to 0 than 0.8.

Therefore,

0.8 > 0.3.

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The equation Vy = a sin(k(x - d)) + c is an equation for a sine wave. A sine wave is a periodic function that describes a periodic oscillation or vibration. It is commonly used to model periodic phenomena in many fields, such as sound, light, and electricity.

In this equation, Vy is the vertical position of the sine wave at a given point in time (x), a is the amplitude of the sine wave (the maximum distance from the midline), k is the wave number (the number of complete cycles per unit distance), x is the horizontal position (time or distance), d is the phase shift (the horizontal shift of the wave), and c is the vertical offset (the distance from the midline).

The equation y = a cos(k(x - d)) + c is similar to the equation for a sine wave, but it describes a cosine wave instead. A cosine wave is also a periodic function, but it is shifted by 90 degrees in phase compared to a sine wave.

Like a sine wave, a cosine wave can be used to model periodic phenomena and is commonly used in many fields. In this equation, y is the vertical position of the cosine wave at a given point in time (x), a is the amplitude of the cosine wave, k is the wave number, x is the horizontal position, d is the phase shift, and c is the vertical offset.

What is sin and cosine sum?

sin(x) + cos(x) = √2 * sin(x + 45°)

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Answer: -9

Step-by-step explanation: If you subtitutie -2 in for x, ask yourself , what is 4*-2 which is -8 which is then subtracted by 1 which gets you -9 so, this means f (-2)=-9

Hope this helped!

Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].

What is the system of equation?

A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions.

Here given that,

Nolan is going to a carnival that has games and rides. Each game costs $[tex]2.50[/tex] and each ride costs $[tex]3.50[/tex]. Nolan spent $[tex]52.50[/tex] altogether on [tex]17[/tex] games and rides.

So, let us assume that the number of games are [tex]x[/tex] and the number of rides are [tex]y[/tex].

So, the equation is of the form

[tex]2.5x+3.5y=52.50 ........(1)[/tex]

And Noaln spent altogether $[tex]52.50[/tex] on [tex]17[/tex] games and rides.

So,

[tex]x+y=17[/tex]

Then,

[tex]2.5x+2.5y=2.5(x+y)\\As,\\x+y=17\\So,\\=2.5(17)\\\\=42.5.....(2)[/tex]

Now, subtract equation [tex](2)[/tex] from equation [tex](1)[/tex], we get

[tex]x=52.5-42.5\\\\x=10[/tex]

[tex]y=17-10\\y=7[/tex]

So the equation is of the form

[tex]2.5(7)+3.5(10)=52.50\\17.5+35=52.50\\52.50=52.50[/tex]

Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].

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Using square roots, we know that there are (A) 15 cubes in a row.

The value that a number produces when it is multiplied by itself is known as the square root of the number.

The square root is denoted by the radical sign. For instance, √16 = 4.

The root symbol or surds is another name for the radical symbol.

So, let x be the total number of cubes in a row.

The number of cubes in each row and column is equal because they are organized in a pattern with the same number of cubes in each.

Now,

Total cubes = x * x

Total cubes = x²

We know that the total number of cubes is 225.

So, we got:

x² = 225

Taking square roots:

x² = 225

x = √225

x = 15

Therefore, using square roots, we know that there are (A) 15 cubes in a row.

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Complete question:
A group of cubes is arranged in a pattern with the same number of cubes in each row and column. There are 225

cubes in the shape. How many cubes are in one row?

A) 15

B) 25

C) 56

D) 75

The  equation  for the length, h is h= ( 2V ) / ( πr² )

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

Volume of a half-cylinder:

V= (1/2)πr²h

Move 2 to the left

=> 2V= πr²h

Solve for h

=> 2V/πr² = h

=> h= ( 2V ) / ( πr² )

Thus, the  equation  for h is h= ( 2V ) / ( πr² )

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3-year treasury securities as calculated from the data will now have a rate of 3.70%.

Current interest rate is calculated as Current Interest Rate + Liquidity Premium.

Average interest for 3 Year = (3.45% + 3.95% +3.25%)/3   = 3.55

3 year security liquidity premium = 0.15%

3 year Treasury security's current rate is 3.55% +0.15%.

= 3.70%

Therefore, The current rate be on 3-year treasury securities is 3.70%.

Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is often reported as an annual percentage rate, interest expense or revenue is sometimes expressed as a dollar figure (APR).

The compensation a lender or financial organisation receives for giving out money is called interest. The percentage of a stockholder's ownership in a corporation that is also referred to as interest.

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The new mean for the given data would be 80.

What is the mean of the numbers?

The average (mean) is equal to the sum of all the data values divided by the number of values in the data set.

Mean = Sum / Count

Firstly 18 students took the test and the mean was 81.

By using the definition of mean we can write

        Mean = sum of scores/number of students

         81 = sum of scores / 18

    Sum of scores = 81 * 18

                             = 1458

Now later the four absent kids made it up and scored 77, 85, 68, and 80.

Now new sum of the scores would be = 1458 + 77 +  85 + 68 + 80

                                                               = 1768

And the total number of students will be = 18 + 4 = 22

New mean = new score/number of students

                  = 1768/22

                   = 80.36

                   ≈ 80

Hence, the new mean for the given data would be 80.

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Answer:

2y4−4y3−3y2+8y :)

The equation of a polynomial that has zeros at x = 2i and x = 3 is given as follows:

x³ - 3x² + 4x - 12.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros are given as follows:

Then the polynomial is obtained as the product of it's linear factors, due to the Factor Theorem, as follows:

(x - 2i)(x + 2i)(x - 3)

(x² + 4)(x - 3)

x³ - 3x² + 4x - 12.

(as the base complex number relation is i² = -1).

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Answer: 21

the hcf of 315 and 42 is 21.

Answer:

HCF of 315 and 42:

Your answer is 21 !

Answer:

(5,0)

Step-by-step explanation:

When graphed the x-intercept meaning the line touching x

is 5 so then your answer is  (5,0) because the x-value comes first so then you'd put the 5 in front.

Answer:

Line down the middle

Step-by-step explanation:

There is only one line of symmetry in this shape because there is no rotational symmetry. Its a line down the middle.

Answer:

Step-by-step explanation:

68 Ounces B - 61.2

92.4 Ounces A - 60.06

70% of 160 = 112

A+B estimated 112

Answer:

178.7 miles

Step-by-step explanation:

First, determine the miles per gallon:

[tex]\frac{302.9\ miles}{23.3\ gallons}\\13.0\frac{miles}{gallon}[/tex]

Then, use that value to find miles traveled on 13.7 gallons:

[tex]13.7\ gallons(\frac{13\ miles}{1\ gallon})\\178.7\ miles[/tex]

Answer:

Answer = 8 days

Step-by-step explanation:

Step 1: Find how long one machine takes to finish

    1. 6 ∙ 4 = 24 days

Step 2: Divide 24 by 3 to get the rate of speed of 3 machines

    2. 24 / 3 = 8 days

The value of the cos(A - B) in simplest form would be 273/100.

What are the trigonometric angles?

Trigonometry angles are the angles given by the ratios of the trigonometric functions. Trigonometry deals with the study of the relationship between angles and the sides of a triangle. The angle value ranges from 0-360 degrees. The important angles in trigonometry are 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°.

sin B = 3/5

tan A = 5/12

We have find cos(A - B)

first, let’s hope these are both all-integer triangles:

In a 3-4-5 Right triangle,

sinB = 3/5, cos B = 4/5

For tanA = 5/12 the hypotenuse turned out to be 13.

sin A = 5/12

cos A = 12/13

So now we just use the identity for cos ( A +  B )

cos(A - B) = cosAcosB + sinAsinB

                = (12/13)(4/5) + (5/12)(3/5)

                = (60 + 52/65) + (25 + 36/60)

                = (112/65) + (61/60)

                = 273/100

Hence, the value of the cos(A - B) in simplest form would be 273/100.

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supposed to questions

Step-by-step explanation:

people say the climate is changing

Point= (1, -1)

Hence, this is not the solution of the desired answer.

inequality is defined as declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or the algebraic expressions. Either queries or the declarations of fact in the form of theorems can be used to formulate and solve inequality problems.

Shaded Region represents y<2x-3

Given Point= (1, -1)

Hence, this is not the solution of the desired answer,

As it not defines the equality part.

As for example (2,-2) is the solution of the desired inequality and it satisfies the condition y<2x-3.

And given point (1, -1) is not the solution of the desired equation as it does not satisfy the inequality portion.

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Answer: 104%

Step-by-step explanation:

75/78=1.04

The system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Total money Anthony and Joan have to buy apples and oranges = $10

Total pieces of fruit the Anthony and Joan buy is = 25 pieces of fruit

Each Apple's cost = 50 cents

Each orange's cost = 25 cents

Let, x = be the apples

and, y = be the oranges

The equation applied for the number of pieces of fruit they will buy,

x + y = 25

And, the equation applied for cost is,

0.50x + 0.25y = 10.00     (Keep everything in same decimal places)

Hence, the system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10

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By ASA property

Therefore, if all three sides of two triangles are the same, then the triangles are said to be congruent. If we have a side, an angle between the sides, and then another side that is congruent, we know they are congruent. In other words, side, angle, side.

We are asked that will property will show that Δ NKL ≅Δ LMN

It is given that NL  bisect KNM and KLM

∠ KNL≅ ∠ MNL (by bisect property)  (angle)

∠ KLN ≅∠MNL (by bisect property)    (angle)

line NL   (common)

Thus by ASA property we can say that Δ NKL ≅ΔLMN

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Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

Answer: angle EHF = 31 degrees

Step-by-step explanation:

Complementary angles mean either of two angles whose sum is 90°.

So the equation is 6x-1+3x+1=90

combine like terms

9x=90

x=10

Substitute in 10 to EHF or 3x+1

3(10)+1

angle EHF = 31

The probability that a randomly selected student has a brother given they have a sister is 8/30.

We have provided that.

A class of 30 pupils has 13 brothers, 8 sisters, and 3 students who have both brothers and sisters.

The probability of an occurrence is calculated by dividing the total number of outcomes in the sample space by the proportion of favorable events.

Considering that there are 30 pupils overall and that 8 of them have both a brother and a sister,

The probability of a student having a brother given that they have a sister would then be 8/30 (8 out of the 30 students).

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Answer:

4

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{4}{2}[/tex] = 2

then

a₂₈ = 2 [tex](2)^{27}[/tex]

a₂₆ = 2 [tex](2)^{25}[/tex]

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then

[tex]\frac{a_{28} }{a_{26} }[/tex]

= [tex]\frac{2(2)^{27} }{2(2)^{25} }[/tex] ( cancel 2 on numerator/ denominator )

= [tex]\frac{2^{27} }{2^{25} }[/tex]

= [tex]2^{(27-25)}[/tex]

= 2²

= 4

Answer:

x= -2

Step-by-step explanation:

since we know what y equals we fill it into the second equation

3(x+4)= -2x+2

3x+12=-2x+2

   -12.      -12

3x=-2x-10

+2x +2x

5x=-10

/5. /5

x= -2

hopes this helps please mark brainliest

Using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.

So, it is a given that the distance between the home plate and the pitcher's mound on a softball field is 43 feet.

27° east of the pitcher's mound is the angle at which a ball is struck.

Before an outfielder catches the ball, it travels 162 feet.

Using the law of cosines, we may now:

a² = b² + c² - 2bcosA

When b=43, c=162, and A=27° are entered, we get:

a² = 43² + 162² - 2(43)(162)cos27°

a² = 1849 + 26244 - 12413.4

a² = 15679.6

a = 125.21

a = 125ft

Therefore, using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

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Complete question;
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

The total number of pairs sold by SoccerWorld is 57

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

The above parameters means that

s = 3j

d = 5 + j

70(s + d + j) = 7000

Where

j = JP Sports

s = SoccerWorld

d = DirectSportz

Divide both sides of 70(s + d + j) = 7000 by 70

s + d + j = 100

Substitute s = 3j and d = 5 + j

3j + 5 + j + j = 100

Evaluate the like terms

5j = 95

Divide by 5

j = 19

Substitute j = 19 in s = 3j

s = 3 * 19

So, we have

s = 57

Hence, the number of pairs is 57

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