Use a trigonometric ratio to solve for a. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?

Two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.

The sine graph or sinusoidal graph is an up-down graph and repeats every 360 degrees i.e. at 2π.

The general form of a cosine function is:

y = a cosb (θ±c) ± d

Here, amplitude, a  is = 1

For b, period is = π

2π/b = π

b = 2

c = 0

vertical shift = D = -3

Putting the value into formula

y = 1 cos2 (θ + 0) - 3

y = 1 ×−0.416(θ + 0) - 3

y = −0.416θ−3  

y = −0.416x −3  (cosine function)

y = 1 sin2 (θ + 0) - 3

y = 1 ×0.909(θ + 0) - 3

y = 0.909θ−3

y = 0.909x−3 (sine function)

Thus, two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.

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Answer:

2

Step-by-step explanation:

A dilation of a line is a transformation that changes the size of the line but preserves its shape.

It is a type of similarity transformation. A dilation can either be a reduction, in which the line is made smaller, or an enlargement, in which the line is made larger. In both cases, the line's shape is preserved, but the size is changed.

The center of dilation, also known as the scale factor, is a fixed point around which a dilation takes place. The scale factor is a value that represents the amount of change in size, it can be greater than 1 for an enlargement or less than 1 for a reduction.

In geometry, a dilation is represented by a multiplication of the coordinates of a point by a scale factor. For example, a dilation of a line with a scale factor of 2 will result in the line being twice as long as the original line.

In conclusion, a dilation of a line is a transformation that changes the size of the line but preserves its shape. The center of dilation or scale factor is a fixed point around which a dilation takes place and is represented by a multiplication of the coordinates of a point by a scale factor.

It can be either an enlargement or a reduction depending on the scale factor value.

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The correct options for the line are-

Coordinate are: (−2, 0) and (2, −4)

Slope m = y2 - y1 / x2 - x1

m = (-4 + 0)/(2 + 2)

m = -4/4 = -1

Slope is -1 , option A incorrect.

For the y-intercept

Use point (-2, 0) and slope m = -1

0 = -1(-2) + b

b = -2

As, y-intercept is -2.  

Option B correct.

Find equation of the line.

y = mx+ b

y = -x + (-2)

y = -x - 2

Thus, equation of the line is y = −x − 2.

Option C is also correct.

Find the x-intercept.

if y = 0

0 = -x - 2

x = -2

Thus, line intersects the x-axis at (−2, 0).

The option D is also correct.

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The complete question is-

Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.

A. The slope of the line is 1.

B. The line intersects the y-axis at (0, −2).

C. The equation of the line is y = −x − 2.

D. The line intersects the x-axis at (−2, 0).

Therefore , the solution to the given problem of expression comes out to be 80.

Math allows for addition, subtraction, multiplication, and division. Following is the structure of an expression: Calculator, number or variable, and expression The components of a mathematical expression include numbers, variables, and operations (such as subtraction, multiplication , addition, or division etc.) You can contrast phrases and expressions.

Here,

The formula for the number of points Han's team scores in a single round if each player has a perfect score is 20 4.

Each player is limited to a maximum of 20 points.

Han's team has four members.

Thus, assuming each participant receives a perfect score, the expression that will indicate the total points that Han's team receives in one round is:

= 20 × 4

= 80

Therefore , the solution to the given problem of expression comes out to be 80.

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A quadratic regression equation for the stream of water is,

⇒ y = -0.139x² + 1.667x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, The vertex = (6, 5)

Axis of symmetry is line, x = 6

And, A third point in the parabola is, (12, 0)

Hence, The quadratic regression equation for the stream of water is,

⇒ y = - a(x - 6)² + 5

      = -a(x² - 12x + 36) + 5

      = -ax² + 12ax - 36a + 5

Since the parabola passes through point (0, 0),

i.e. -36a + 5 = 0

⇒ a = 5/36

⇒ a = 0.139

Therefore, The equation is,

⇒ y = -0.139x² + 12(0.139)x

⇒ y = -0.139x² + 1.667x

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Answer:

Its A

Step-by-step explanation:

As the triangle cannot be equilateral since the sides are not equal. So the obtuse triangle has side lengths 5, 7 and 11.

Assume that a triangle has sides that measure 5, 7, and 11.

Finding the sum of the squares on the triangle's two shorter sides and comparing it to the square on the longest side will reveal the type of triangle.

A triangle must be sharp in order to:

Let a = 5, b = 7 and c = 11

a^2 + b^2 =  (5)^2 + (7)^2 = 25 + 49 = 74

c^2 = (11)^2 = 121

(1) If the triangle is

a^2 + b^2 > c^2

Therefore, the triangle is not acute.

(2) Eqviangular means that each internal angle must be 60 degrees in length.

As a result, the triangle is not eqviangular.

(3) The triangle cannot be equilateral since the sides are not equal.

(4) We note that a^2 + b^2 = c^2.

The triangle is hence obtuse.

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Statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday

A number system is defined as a system of writing to express numbers.

In the given number line each unit is 10⁰ F

On Monday at 11:00 p.m. the temperature is 40⁰ F

Tuesday at 11:00 p.m. the temperature is -10⁰ F

The difference between two temperatures is 40⁰ F-( -10⁰)

40⁰ F+10⁰F

50⁰ F

The temperature on Monday is 50⁰ F lesser than Tuesday

Hence, statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday

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Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.

An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 6 + 6 = 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Assumed: expressions

Finding the expression with a value that is closest to e

Solution:

e is worth 2.718, which equals (1 + 1/19).

(1 + 1/19)^19

=> (20/19)^19 = 2.65

=> (1+ 1/22)^22

= >(23/22)^22 = 2.659

=> (1 + 1/20)^20

= >(21/20)^20 = 2.653

=>(1 + 1/21)^21

= > (22/21)^21 = 2.656

As a result, the value of e is closest to the value of 2.659.

Option B is hence the appropriate choice.

Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.

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The value of K that will make the expressions equivalent is 10.

Considering the two expressions:

7 + (1/2)x - 3 + (3/4)x and 1 whole number (1/4)x + k - 6

we shall write the expression 7 + (1/2)x - 3 + (3/4)x in the form of the expression having k and then compare to know the value of k as follows;

(1/2)x + (3/4)x = (2x + 3x)/4

(1/2)x + (3/4)x = 5x/4

7 - 3 = 10 - 3 - 3

7 - 3 = 10 - 6

so;

7 + (1/2)x - 3 + (3/4)x = 5x/4 + 10 - 6

by comparison;

5x/4 is equal to the mixed fraction 1 whole number (1/4)x

k = 10 as obviously -6 is equal to -6.

Therefore, 10 is the value of k that will make expressions equivalent.

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The gear ratio for the bike based on the information is 3:1.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

From the information, the gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket. If a bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket,

The gear ratio for the bike will be:

= 36 / 12

= 3 / 1

= 3:1

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The total area of the patio will be 20 * 40 = 800 square feet.

The proportionate relationship between a linear dimension of a feature on a model, map, or drawing of an object and the same feature on the genuine thing. A scale model is a physical representation of an object that is geometrically equivalent (known as the prototype).

Since the scale drawing is 3 inches : 10 feet, this means that every 3 inches on the drawing represents 10 feet in real life. Hence, 1 inch on the drawing represents 10/3 = 3.33 feet in real life.

So the patio measures 6 inches by 12 inches on the drawing, which corresponds to 6 * 3.33 feet by 12 * 3.33 feet in real life, or 20 feet by 40 feet.

Therefore, the total area of the patio will be 20 * 40 = 800 square feet.

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Answer:

The correct answer is D. 225pi cm^3.

To find the volume of a cylinder, you use the formula:

V = πr^2h

Where V is the volume, π is pi, r is the radius of the base, and h is the height of the cylinder.

In this case, the height is 9cm, and the width is 10cm. To find the radius, we divide the width by 2:

r = 10cm / 2 = 5cm

Now we can plug in the values into the formula:

V = πr^2h

V = π(5cm)^2(9cm)

V = π(25cm^2)(9cm)

V = 225π cm^3

So the volume of the cylinder is 225π cm^3

Step-by-step explanation:

Answer: D)  225pi cm^3.

Step-by-step explanation:

6 with an exponent of 2 is 36. 6 with an exponent of 2 means 6 multiplied by 6.

When a number is raised to a certain power, it means that the number is multiplied by itself that many times.

Exponents are a way of shorthand for repeated multiplication. When a number has an exponent of 2, it means that the number is multiplied by itself once. When a number has an exponent of 3, it means the number is multiplied by itself twice.

In this case 6 with exponent of 2, means 6 multiplied by itself twice, which is equal to 36.

It's important to note that the exponent is also known as the power, so 6^2 is also read as 6 to the power of 2.

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The lower bound of c-d is 42.70 and the upper bound of c-d is 42.69.

In the given question, a number, c, rounded to 1 d.P. is 47.3.

A number, d, rounded to 1 d.P. is 4.6.

We have to find the lower and upper bound of c-d.

The maximum and smallest values that a number may have before it was rounded are known as upper and lower limits. They are also known as accuracy limits.

Error intervals are a useful tool for expressing the upper and lower bounds.

This is the lower bound for c; the smallest integer that will round to 47.3 is 47.25.

47.33999... is the highest number of c that may be rounded down to 47.3. Therefore, we define 47.34 as the upper bound.

This is the lower bound for d; the smallest integer that will round to 4.6 is 4.55.

4.64999... is the highest number of c that may be rounded down to 4.6. Therefore, we define 4.65 as the upper bound.

So, the lower bound of c-d = 47.25-4.55 = 42.70

So, the upper bound of c-d = 47.34-4.65 = 42.69

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Polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.

What is a complex number?

A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Polynomial identities are equations that are always true for any values of the variables, regardless of whether the variables represent real numbers or complex numbers. Complex numbers can be represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit.

For example, the identity[tex](x + y)^2 = x^2 + 2xy + y^2[/tex] is true for any real numbers x and y, and it also applies to complex numbers a + bi and c + di. The identity becomes [tex](a + bi + c + di)^2 = (a + c)^2 + 2(a + c)(bi + di) + (bi + di)^2[/tex]

Another example is the identity [tex](a+bi)^2 = a^2 + 2abi - b^2[/tex] which is always true for any complex number a+bi. This identity applies to any complex number and can be used to simplify polynomials involving complex numbers.

Hence, polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.

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The coordinate (2, 3) lies in the first quadrant of a Cartesian plane, which is the upper-right quadrant when the origin (0, 0) is the center.

The coordinate (2, 3) lies in a Cartesian plane, which is a two-dimensional plane with an origin (0, 0) at the center. There are four quadrants on the Cartesian plane. To find which quadrant the coordinate (2, 3) lies in, we must look at the signs of the x- and y-coordinates. The x-coordinate is 2, which is a positive number, and the y-coordinate is 3, which is also a positive number. This means that the coordinate (2, 3) lies in the first quadrant, which is the upper-right quadrant when the origin is the center. The other quadrants are numbered in a clockwise direction, starting with the first quadrant, which is the upper right. The second quadrant is the upper left, the third quadrant is the lower left, and the fourth quadrant is the lower right.

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The equation that can be used to find the car's distance, d, at any time is  d = 30 × t.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given that;

First, we determine the speed of the car.

Speed = Distance ÷ time

Speed = 180 / 6

Speed = 30 m/s

Now, to get the distance traveled at any time, plug the value of the speed of the car into the speed formula and solve for distance d.

Speed = Distance ÷ time

Speed = d / t

d = Speed × t

d = 30 × t

Therefore, the equation is d = 30 × t.

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Answer:1096.6332

Step-by-step explanation:

Answer: Use

1096.6332

Step-by-step explanation:

The Slope Intercept Form Of 2x + 3y = 8 Is y = -2x/3 + 8/3

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

2x + 3y = 8

Make 3y the subject of the formula

So, we have the following representation

3y = -2x + 8

Divide through by 3

This gives

y = -2x/3 + 8/3

Hence, the equation is y = -2x/3 + 8/3

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Complete question

contents

The Slope Intercept Form Of 2x + 3y = 8 Is

The boxes of oranges that Tim need to sell in order to sell 60 boxes will be 13 oranges.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this situation, Tiana sells 47 boxes of orders for a fundraiser. Therefore, the boxes of oranges that Tim need to sell in order to sell 60 boxes will be:

= 60 - 47

= 13

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The probability of having a flip flop is 4/9.

In the question, we can see from the data that we have that Xavier's mother has a large collection of shoes. the table shows flip flop 8, boots 4, and clogs 6.

Recall that probability deals with the possibility that an event may occur or not occur under a given circumstance. We know that;

Total number of the shoes = 4 + 6 + 8 = 18

Probability of a flip flop = 8/18 = 4/9

This is the possibility that what would be picked is a flip flop.

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Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

The value for Simple Interest is given as = $180

The value for rate is given as = 4.5%

The value for time is given as = 3 years

To find the value for Principal amount, follow the formula for Simple Interest -

SI = P R T/100

Where P is the principal amount, R is the rate and T is the time.

Substitute the values in the equation -

180 = (P × 4.5 × 3)/100

180 = 13.5P / 100

P = (180 × 100) / 13.5

P = 18000 / 13.5

P = 1333.33

Therefore, the value for principal amount is $1333.33.

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A factor of a polynomial function is a polynomial that divides the function evenly when using polynomial division.

To check if x - 8 is a factor of the function f(x) =[tex]2x^3 - 17x^2 + 64[/tex]  , we can use polynomial division.

When dividing f(x) by x - 8, the remainder should be zero.

x - 8 is a factor of the function when the remainder is zero.

In this case, the quotient is [tex]2x^2 + x + 8[/tex] , and the remainder is zero, so x - 8 is a factor of the function f(x) = [tex]2x^3 - 17x^2 + 64.[/tex].

So we can say [tex]f(x) = (x-8)(2x^2 + x + 8)[/tex]

Alternatively, we can also use synthetic division to check if x - 8 is a factor of the function.

Synthetic division is a shorthand method of dividing a polynomial by a linear factor such as x - 8.

If the remainder is zero, then x - 8 is a factor of the function.

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The inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].

A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is denoted by f-1 or F-1 if the function is represented by  [tex]f^{-1}(x)[/tex].

The given function is:

f(x) = 7x -2

Write the function in the form of a function:

y = 7x - 2

Interchange the variables in the equations:

x = 7y - 2

Isolate the value of y:

y = x/7 + 2/7

Replace y with [tex]f^{-1}(x)[/tex]:

[tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex]

Hence, the inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].

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∠6 and ∠7 are the angles which are supplementary to ∠1.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

In the given figure lines l and m are parallel lines.

A transversal passed through parallel lines.

∠1+∠2=180 degrees

∠1+∠3=180 degrees.

∠2 is corresponding angle of ∠6.

∠1+∠6=180 degrees.

∠3 is corresponding angle of ∠7.

∠1+∠7=180 degrees.

Hence, ∠6 and ∠7 are the angles which are supplementary to ∠1.

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D) The example (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials.

The commutative property of addition for polynomials states that the order in which polynomials are added does not affect the result of the sum. In other words, it states that if we have two polynomials A and B, the result of adding A and B (A+B) will be the same as adding B and A (B+A).

For example, consider the polynomials (2x^2 + 5x) and (4x^2 - 4x). If we add these two polynomials in the order given, (2x^2 + 5x) + (4x^2 - 4x) = 6x^2 + x. Now, if we add these two polynomials in the reverse order, (4x^2 - 4x) + (2x^2 + 5x) = 6x^2 + x. We can see that the order of the polynomials does not affect the result of the sum, and thus it holds the commutative property of addition.

Option (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials, because it shows that the order of the polynomials does not matter and it gives the same answer.

It is important to note that the other options does not illustrate the commutative property.

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Answer: (5x^2-7)(x-4)

Step-by-step explanation:

5x^2(x-4)-7(x-4)

= (5x^2-7)(x-4)