Can the sine ratio of an acute angle be greater than 1?

a. The trigonometric ratio tanθ = -√(sec²θ - 1)

b. The trigonometric ratio secθ = -1/√(1 - sin²θ)

Trigonometric ratios are the following mathematical expressions sinθ, cosθ, tanθ,secθ,cosecθ and cotθ.

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

tan²θ + 1 = sec²θ

Making tanθ subject of the formula, we have that

tan²θ = sec²θ - 1

tanθ = ±√(sec²θ - 1)

Since in Quadrant II, tanθ is negative, we choose the negative answer.

So, tanθ = -√(sec²θ - 1)

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

secθ = 1/cosθ and

sin²θ + cos²θ = 1

Making cosθ subject of the formula, we have that

cos²θ = 1 - sin²θ

cosθ = ±√(1 - sin²θ)

So, secθ = 1/cosθ

= ±1/√(1 - sin²θ)

Since in Quadrant III, secθ is positive, we choose the positive answer.

So, secθ = -1/√(1 - sin²θ)

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None of the listed methods are used for enumerating sample points in a multiple-step experiment. So, option D is the correct answer.

Graphical methods are important mathematical tools that are very helpful when it comes to managing a vast amount of data. These also help when we need to visually represent data. These methods help quite a lot since they make it easier to keep track of data and understand it as well.

A bar chart and a histogram are similar tools that are used to represent data by plotting them as rectangular bars. These can be either vertical or horizontal. A pie chart is also a tool that uses a shape for data visualization. In its case, it represents data in the shape of a circle and all categories/data sets have their slices. So, this means that these three are not methods that can be used for enumerating sample points in a multiple-step experiment. Hence, option D is the correct option.

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The solution for given differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)

This is a second-order linear differential equation with constant coefficients. To solve this equation, we can use the method of an auxiliary equation, which is 3r^2 + 6r + 1 = 0. This equation has two complex conjugate roots, r = -3 ± i√3. Therefore, the solution of the differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)cos(√3x^2/2) + c3xe^(-x^3/3)sin(√3x^2/2), where c1, c2, and c3 are arbitrary constants.

The method of an auxiliary equation is a popular way to solve second-order linear differential equations with constant coefficients. It involves finding the roots of an auxiliary equation, which is found by setting the coefficient of the second derivative equal to zero.

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The value of YZ = 2 units.

The Latin words "col" and "linear" are combined to form the word "colinear." "Col" stands for "together," and "Linear" is a line. Collinear points are hence points that are situated along a single line. Numerous instances of collinearity can be observed in daily life, such as a line of pupils standing together.

Given X, Y, and Z are collinear. Y is between X and Z.

so XY + YZ = XZ

given XY = 12 units and XZ = 14 units

XY + YZ = XZ

12 + YZ = 14

YZ = 14 - 12

YZ = 2 units

Hence measure of YZ is 2 units.

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Intercept = 1

Equation - y = -(2/5)x + 1

Answer:

----------------------------

We see two sides and one angle marked as congruent on both triangles.

The congruent angle is not included.

It means we can neither state it is ASA nor SAA as both of these require two congruent angles.

On solving the provided question we can say that - here in equation we have [tex]y = 160+ 2 *t= > y = 160 + 2X 30 = > y= 160+ 60 = > y = 220 pounds[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]

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The final answer after solving the given equation could be 14.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.

Given,

Given equation,

2x + 6 = 3x -8

separating the value into a similar term:

2x-3x = -8 - 6

subtracting the equation:

-x = -14

remove negative sign:

x = 14

Therefore , the final answer could be 14.

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Answer:

y = 72 and x = 36

Step-by-step explanation:

So firstly, the outside angle is 108, right? And the total of all angles in a triangle is 180 degrees. So:
180 - 108 = 72
Then the other angle, angle x, is also 72 degrees. That's because they are supplementary angles.
Now that we know x = 72 degrees. To find the y angle, you add 72 and 72 together. Which is 144.
Then you do 180 - 144. Which is 36. So, x = 72 and y = 36

I hope it helped you!

Answer:

5√2

Step-by-step explanation:

Hello!

To simplify the radical, we can identify perfect square factors in the radicand or the number inside the square root.

We know that 50 is 25 times 2, so we can expand the radical like this...

Now we can simplify each radical:

The simplified form is 5√2.

The required slope of the linear equation is -3 which values shown in the table.

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The table is given in the question as follows:

x          y

-4       -15

-2        9

0         3

2        -3

4         -9

As per the question, we take the given points are (0, 3) and (4, -9).

So we can substitute these values into the formula:

m = (-9 - 3) / (4 - 0)

m = -12 / 4

Apply the division operation, and we get

m = -3

Therefore, the required slope of the linear equation is -3.

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Answer:

B. x ≥ 1

Step-by-step explanation:

Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.

An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.

Here,

The halting problem, which claims that no program can be created that can anticipate whether or not any other program will halt after a finite number of steps, is an intractable algorithmic challenge.

The inability to solve the stopping problem directly affects software development.

Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.

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Answer:     -0.2      hope this answer helps you good luck                                

Answer:

-0.2

Step-by-step explanation:

[tex] \frac{ {5}^{ - 1} }{ { - 9}^{0} } = \frac{ \frac{1}{5} }{ - 1} = \frac{1}{5} \times \frac{ - 1}{1} = \frac{ - 1}{5} = - 0.2[/tex]

Answer:

F.

Step-by-step explanation:

y = k/x where k is a constant

given that x = 4 when y = 3, we have:

3 = k/4

So, k =12.

The equation of variation is:

y = 12/x

When x = 15

y = 12/15 = 4/5.

So not 12 so this is False,

The distance between town a and b is 175 mi.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given that, a map drawn move to the scale 2 cm : 100 mi. on the map town b is 3.5 centimeters from town a and town c is 2 centimeters past town b

Since, 2 cm = 100 mi

1 cm = 50 mi

Therefore, 3.5 cm = 50×3.5 = 175 mi

Hence, the distance between town a and b is 175 mi.

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A 45°-45°-90° triangle looks like Right Angle Triangle.

A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.

45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2 . The measures of the sides are x, x, and x√2.

In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg, and the Opposite side to 45 = 1/√2 * Hypotenuse.

The 45-45-90 triangle has three unique properties that make it very special and unlike all the other triangles.

Hence, a 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.

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The like terms in 3x (3 - 2y) and 2 (xy + x²) are -6xy and 2xy.

Like terms are terms which have the same variables and exponents. In this case, the like terms are -6xy and 2xy because they both have the same variable (xy) and exponents (1). In algebra, like terms can be added or subtracted to simplify an expression.  Like terms are terms which have the same variables and exponents.

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Answer: no question=no answer

Step-by-step explanation:

[tex]\huge\text{Hey there!}\\\\\\\mathsf{\dfrac{3}{21}}\\\\\mathsf{= \dfrac{3\div3}{21\div3}}\\\\\mathsf{= \dfrac{1}{7}}\\\\\huge\text{Therefore, your\ answer\ should\ be: \huge\boxed{\mathsf{\dfrac{1}{7}}}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Three true statements about the angles of the given figure are,

1. angle 1 and the 55 degree angle are adjacent.

5. angle 1 = 180 degree - 55 degree

6. angle 2 = 180 degree - 55 degree - 45 degree.

Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.

Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.

Analysing all the statements given in the question,the corrrect options are

Option 1, since angle 1 and 55 degree share the same vertex.

Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.

Option 6, since the sum of all the interior angles of a triangle is 180 degrees.

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The resulting polynomial in standard form (b)  –4g^4 –3g³ +4g² +5g +3

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

The simplification process is described and partially carried out. We are to finish by combining like terms and writing the result in standard form.

Given

Add: (g² – 4g^4 + 5g + 9) + (–3g³ + 3g² – 6)

Combine Like Terms

g²  + (–4g^4) + 5g + 9 + (–3g³) + 3g²  + (–6)

The like terms are the g² terms and the constants;

= (1 +3)g² + (–4g^4) +5g +(9 +(–6)) +(–3g³)

 = 4g² +(–4g^4) +5g +3 +(–3g³)

Write in Standard Form

In this form, the terms are written in order of decreasing degree.

= –4g^4 –3g³ +4g² +5g +3

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Linear graphs have the following form: y = mx + b, where m is the slope of the line and b is the y-intercept.

To calculate the slope, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Exponential graphs have the following form: y = ab^x, where a and b are constants. To calculate the constants, you can use the formula y = a + b^x, where (x, y) are two points on the graph and a is the y-intercept.

Quadratic graphs have the following form: y = ax^2 + bx + c, where a, b, and c are constants. To calculate the constants, you can use the formula y = ax^2 + bx + c, where (x, y) are two points on the graph and c is the y-intercept.

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9) x = 6

10) x = 1

11) x = 0

12) x = 6

This can be solved from the property of parallelogram.

A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.

Properties are:

9) As we know, from the property of parallelogram,

SR = TQ and ST = RQ

Now, 4 + 2x = 3x - 2

or, x = 6

10) As we know, from the property of parallelogram,

EF = DC and ED = FC

17x + 1 = 18x

or, x = 1

11)  As we know, from the property of parallelogram,

YZ = XW and YX = ZW

2x + 9 = 9

2x = 0

x = 0

12)  As we know, from the property of parallelogram,

TU = SV and TS = UV

6 + 2x = 4x - 6

or, 2x = 12

or, x = 6

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The total amount each member of the Nantucket recreation center have to pay after the discount is given by the equation A = $ 840

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount for each person after discount be represented as A

Now , the equation will be

The total number of people in the group = 36

The standard fare for each person = $ 1200

So , the total cost of the fare = total number of people x standard fare for each person

Substituting the values in the equation , we get

The total cost of the fare = 1200 x 36

The total cost of the fare = $ 43,200

Now , the discount percentage = 30 %

So , the amount after discount = total cost of the fare - total cost of the fare x discount percentage

Substituting the values in the equation , we get

The amount after discount = 43,200 - ( 30/100 ) x 43,200

The amount after discount = 43200 - 12960

The amount after discount = $ 30,240

Now ,

Total amount for each person after discount A =amount after discount / 36

Total amount for each person after discount A = 30,240 / 36

On simplifying the equation , we get

Total amount for each person after discount A = $ 840

Therefore , the value of A is $ 840

Hence , the amount is $ 840

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Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.

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The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

What is the null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Here,

We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.

We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.

Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

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Answer:

The two little blue boxes are going

Step-by-step explanation:

Lets start with the 0s.

Two zeros is 0. so its

_ _ _ _ 0.

Now we add 2 and 0 which is 2.

_ _ _ 2 0

now we add 6 and 4, which is 10. We have to put the 1 above the 7 and 5 and we are going to put 0 down below

_ _ 0 2 0

now we are going to add 7 +5, but dont forget the 1! Its going to be 13. Put the 3 down below and put the 1 above the 2!

_ 3 0 2 0

Now its 2 + 1 which is 3

your answer is

33020

The inverse of +5 as calculated is found to be +1 / 5.

To find the inverse of +5 we can simply reciprocate it and the result will be the required answer.

reciprocal of +5 = 1 / 5.

Therefore, the answer is 1 / 5.

The opposite or reciprocal of a number or term in math is known as it's inverse. There are two types of inverse in math, the additive inverse and the multiplicative inverse.

The multiplicative inverse of a number for any n is given as 1/n.  It is also called as the reciprocal of a number and 1 is called the multiplicative identity. On the other hand subtraction is the inverse of addition.

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