What are the 4 trigonometric functions?

At Nation Office Supply, Marley purchased 9 dozen notepads.

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

We have to given that;

At Nation Office Supply, pens are $1.69 per dozen and notepads are $4.59 per dozen.

Here, Marley purchases 9 dozen pens, and spend total $56.52.

Let number of notepads can she purchase = x

So, We can formulate;

⇒ 9 × $1.69 + $4.59x = $56.52

⇒ 15.21 + 4.59x = 56.52

⇒ 4.59x = 56.52 - 15.21

⇒ 4.59x = 41.31

⇒ x = 41.31 / 4.59

⇒ x = 9

Thus, Marley purchased 9 dozen notepads.

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The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.

To determine the domain of a function, look at the equation defining the function and identify any restrictions on the input values. For example, if the function is a square root, the input (x) value can not be negative.

To determine the range of a function, you can use the equation of the function and test several input values to find the corresponding output values. You can also use the graph of the function to identify the range. If the function is continuous, you can use the graph to see the range of the function.

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Answer:

192.5 miles

Step-by-step explanation:

let h be number of hours Anne takes to drive to her friend's house

[tex](55mph)(h) = (35mph)(h+2)[/tex]

Both sides of this equation represent the miles to her friend's home. (speed * time = distance)

We add 2 to h on the right side because the way back takes 2 hours longer than the way to her friend's home.

Now we can solve.

[tex](55)(h) = (35)(h+2)\\55h = 35h+70\\20h = 70\\h = \frac{7}{2} = 3.5[/tex]

Now that we have how long the trip to her friend's house takes, we can solve for the distance to her friend's house by using either side of our equation. I will use the left side because it is simpler.

[tex](55)(h)\\(55)(3.5)\\\boxed{192.5}[/tex]

That is the answer

- Kan Academy Advance

The value of x is 13.74 units.

Consider the following figure.

In this question we have been given a right triangle with the length of hypotenuse = 47 units.

From figure we can observe that the dotted line segments are parallel to the legs of right triangle.

So, the vertical side of right triangle = x units

And the angle opposite to side 'x' would be 17°  as they are the alternate angles formed by parallel lines and transversal.

Consider the cosider the sine of angle 17°

sin(17°) = x/47

0.2924 × 47 = x

x =  13.74 units

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The rational expression is

[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]

for x ∈ R - {1}

The ratio of two polynomials is a rational expression. If an expression is rational, it may be expressed in the form p/q, where p and q are polynomials.

When the numerator and denominator of an equation are both polynomials, the expression is said to be rational. The lowest form of the numerator and denominator is used to simplify rational formulas. An algebraic fraction is another name for a rational expression.

The value of a logical statement is diminished to its simplest form or lowest terms when it is simplified. Similar to how we simplify fractions, we can simplify a rational equation. In fractions, a rational number is said to be in its simplified form if its numerator and denominator share no factors other than 1. The only distinction is that when simplifying rational expressions, the same strategy also applies because the fraction contains polynomials.

The expression is

[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]

for x ∈ R - {1}

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Use the section formula to get the coordinates of a point that separates a line segment outside or internally in a specific ratio.

By building two right triangles and applying AA similarity, the section formula can be obtained. After determining the ratio of the triangle's side lengths in terms of the supplied ratios, we may solve for x and y to determine the coordinates of the point that divides the line segment.

To determine the coordinates of a point that splits a line segment externally or internally in a certain ratio, apply the section formula. A line segment's midpoint can be determined using this technique as well.

By section formula, we have, if (x, y) divides the line segments joining [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] internally in the ratio m: n then,

[tex]$x=\frac{m x_2+n x_1}{m+n}$[/tex] and [tex]$y=\frac{m y_2+n y_1}{m+n}$[/tex]

Here,

[tex]\left(x_1, y_1\right)=(8,-1) \\\\ \left(x_2, y_2\right)=(2,5) \\\\ (x, y)=(4, 3) \\[/tex]

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The correct value of "x" is equal to 4

Step-by-step solution:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Using Pythagoras's Theorem:-

[tex](Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}[/tex]

[tex](x+1)^{2} -x^{2} =3^{2}[/tex]

[tex](x+1)^{2} -x^{2} =3^{2}[/tex]

[tex](x+1+x)(x+1-x) =3^{2}[/tex]

[tex](2x+1)(1) =3^{2}[/tex]

[tex](2x+1)(1) =9[/tex]

[tex](2x+1) =9\\2x=9-1\\2x=8\\x=4\\[/tex]

Therefore, the value of "x" is: x=4

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A perpendicular bisector of a triangle is a segment that is perpendicular to the side of a triangle at its midpoint. So option A is the correct answer.

Specifically, it is a line which passes through the midpoint of a side of the triangle, and is perpendicular to that side. It crosses the side at a 90 degree angle, and divides the side into two equal parts.

It can also be thought of as a line which connects the vertex and the opposite side at 90 degrees. In order for a triangle to be equilateral, the three perpendicular bisectors must all intersect at the same point, which is the center of the triangle.

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Answer:

Step-by-step explanation:

using the rise over run method:

1 up and three to the right

the slope is 1/3
m = 1/3

In the given expression, 7^x=28, as there is variable in one side while in other side there is constant, also there is no logarithmic value, so it is not possible to  solve the equation by changing the base of both sides

The basic formula has been changed to logb b a = [logc c a] / [logc c b]. It simply implies that to alter the base of a logarithm logb b a, we divide [log a] / [log b], where these logarithms might have any (same) positive number as a basis.

The change of base formula gives you the answer of a log with a different base by utilizing only log computations with a base of 10. The formula instructs you to divide the log of the number in parentheses by the log of your base.

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Karen adds up 4 consecutive odd integers ,the sum if the smallest one is 2m-1 is 8m + 8.

Since they are odd numbers, each time it must be +2 (since +1 goes odd, even, odd, even, etc.), therefore the result will be:

(2m - 1) + (2m + 1) + (2m + 3) + (2m +5) = 8m + 8

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Formula used to calculate the y-intercept when coordinates of two points are given is as follow: y = mx + c where 'm' represents the slope and 'c' represents the y-intercept.

As given in the question,

Let us consider points of two coordinates be equal to

( x₁ , y₁ ) =  ( 2, 3 )

( x₂ , y₂ ) = ( 4, 7 )

Equation of the line is equal to :

( y - y₁ ) / ( x - x₁ )  = ( y₂ - y₁ ) / ( x₂ - x₁ )

⇒ ( y - 3 ) / ( x - 2 ) = ( 7 - 3 ) / ( 4 - 2 )

⇒ ( y - 3 ) / ( x - 2 ) = 2

⇒ y - 3 = 2x - 4

⇒ y = 2x - 1

Same as y = mx + c

Here c = -1

Here y-intercept is equal to -1 by substituting x = 0 we can get                 y - intercept.

Therefore, the value of y-intercept can be calculated with the coordinates of the given points using formula given by :

y = mx + c where 'c' represent y-intercept.

The given question is incomplete, I answer the question in general according to my knowledge:

If you're given coordinates of 2 points, how do you find the y-intercept?

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y = -5x - 23, is the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3).

What is the slope intercept?

The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3), we can use the point-slope form of a line which is y - y1 = m(x - x1), where m is the slope of the line, (x1,y1) is a point on the line.

We know the slope of the line is -5 and the point is (-4,3), so we can substitute these values into the point-slope form to get:

y - 3 = -5(x + 4)

Simplifying this equation gives:

y = -5x - 23

Hence, y = -5x - 23, is the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3).

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Yes, George can be claimed as a dependent by his parents.

A dependent is a person who qualifies for a dependency exemption but is not the taxpayer or the taxpayer's spouse. Every exemption for a dependent reduces the amount of taxable income by the exemption amount.

If a full-time student, your child must be younger than 24 or younger than 19 years old. If your child is totally and permanently incapacitated, there is no upper age restriction. Are these your roommates? There are a few situations where your child does not need to live with you for more than half the year.

Your child must be younger than you and either be a "student" younger than 24 years of age as of the end of the calendar year, or be younger than 19 years old.

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Answer:

Below

Step-by-step explanation:

It is just the angles that are next to GHI  

  this would be IHJ   and  FHG  

Using linear regression to calculate the line of best fit is ŷ = 25.91429X + 553.13333

A line of best fit is a straight line that is used to describe the relationship between two variables in a scatter plot. The line of best fit is also known as the "trend line" or "regression line" and is used to make predictions about the values of one variable based on the values of the other variable.

Linear regression is a statistical method used to find the line of best fit for a set of data. Linear regression analysis is used to determine the linear relationship between two variables.

In the given data;

Sum of X = 21

Sum of Y = 3863

Mean X = 3.5

Mean Y = 643.8333

Sum of squares (SSX) = 17.5

Sum of products (SP) = 453.5

Regression Equation = ŷ = bX + a

b = SP/SSX = 453.5/17.5 = 25.91429

a = MY - bMX = 643.83 - (25.91*3.5) = 553.13333

ŷ = 25.91429X + 553.13333

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A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.

Inverse relationship means that the two variables are directly proportional to each other; if one increases, the other decreases. An example of an inverse relationship is the relationship between the temperature outside and the amount of ice cream sold. As the temperature outside rises, the amount of ice cream sold decreases. This is because people are less likely to buy ice cream when it is hot outside.

A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.

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The number of gallons of gasoline pumped by a filling station during a day represents a B: "quantitative " type of variable.

Quantitative variables are data about numeric values such as how much; how often; or how many.  In other words, quantitative variables are referred to as any variables that represent amounts, such as age, height, or weight.

In the given case, it is talked about the number of gallons of gasoline filled during a day; since it represents the quantity or number of gallons so it is a type of quantitative variable, representing the number of gallons of gasoline to be pumped.

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No matter how far they reach, parallel lines are those that do not have a shared meeting point in the same plane.

If two lines cannot collide when extended in both directions to infinity, they are said to be parallel in a plane. Throughout the entire length, there remains a constant gap between two lines.

|| is the symbol used to represent the parallel lines. Assuming that lines "a" and "b" are parallel to one another, we may indicate this using the symbol "a||b," which means "a is parallel to b."

We need a ruler and a compass to create a line parallel to the other line starting from an outside point. The diagram of parallel line is given below:

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Answer:

The diameter of the circle is 7/2.

Step-by-step explanation:

⭐What is the radius of a circle?

⭐What is the diameter of a circle?

Thus, the diameter of said circle is twice the radius of said circle.

diameter = 2(radius)

diameter = 2(7/4)                   . . . . substitute known values

diameter = 14/4                      . . . . multiply the numerator & denominator

diameter = 7/2                       . . . . simplify

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The equation for the horizontal asymptote of the function f is y=Lim x→∞ f(x).

In algebra and calculus, a horizontal asymptote is a horizontal line that the graph of a function approaches as the x-values or input values increase or decrease without bound.

The equation for the horizontal asymptote of a function f is:

Lim f(x) → ∞ = c

Where c is the horizontal asymptote.

Example:

f(x) = x2 + 3x + 2

Horizontal Asymptote:

Lim f(x) → ∞ = ∞

numeric value in equation

For example, if x = 5:

f(5) = 5^2 + 3*5 + 2 = 32

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Answer:

3

Step-by-step explanation:

x = the third side

x² + ([tex]\sqrt{55}[/tex])²= 8²

x² = 64 - 55 = 9

x = [tex]\sqrt{9}[/tex] = 3

The value of y after solving the given equation is -8.

We can calculate the value of y through the following method,

We have been provided with an exponential equation [tex]8^{y} = 16^{y+2}[/tex]

As we know, an exponential equation is an equation whose exponent or part of the exponent is a variable.

For solving an exponential equation, we need to use logarithms and their properties.

We can write [tex]8^{y}[/tex] also as [tex]2^{3y}[/tex] since we know that 2³ = 8

Similarly, we can write [tex]16^{y+2}[/tex] also as [tex]2^{4(y+2)}[/tex] since we know that [tex]2^{4}[/tex] = 16

Therefore we get the new equation as,

[tex]2^{3y}[/tex] = [tex]2^{4(y+2)}[/tex]

Now we will add log with base 10 on both the sides

Therefore the equation will become,

log₁₀ [tex]2^{3y}[/tex] = log₁₀ [tex]2^{4(y+2)}[/tex]

Since, according to the property of logarithm,

log₁₀ aᵇ = b log₁₀ a

Therefore,

3y log₁₀ 2 = 4(y + 2) log₁₀ 2

We can cancel out log₁₀ 2 on both sides

We get the equation as,

3y = 4(y + 2)

3y = 4y + 8

y = -8

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The value of x is 2 and NM = OL = 7

Now, According to the question:

What is a parallelogram?

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, LMNO is a parallelogram and NM = x + 5 and OL = 2x + 3,

Since, we know that, opposite sides of a parallelogram are equal,

Therefore,

NM = OL

x+5 = 2x+3

x = 2

Therefore, NM = OL = 7

Hence, the value of x is 2 and NM = OL = 7

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The inverse meaning in math is a function or operation which reverses the order or operation of another function or operation.

Let us take an inverse math example, The inverse operation of addition is subtraction, and the inverse operation of multiplication is division.

For example, The multiplication of two numbers 3 and 6 is 3 × 6 = 18. The inverse operation of this is a division which is as follows: 18/6 = 3.

The Inverse of a Number

Consider a number y where y is not equal to zero. Then the inverse of a number y is the reciprocal of the number that is 1/y.

For example, The inverse of the number 200 is 1/200, and the inverse of the number 32 is 1/32.

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The 30, 60, and 90 are special right triangles. the perimeter of the triangle is = [tex]a+b+c[/tex] =[tex]x+2x+x\sqrt{3}[/tex]

30,60,90 special right triangles because there is a relation between height, base, and the hypotenuse.

Point to be noted

the opposite side of [tex]30^o[/tex] is height, the opposite side of [tex]60^o[/tex] is base, and the opposite side of [tex]90^o[/tex] is the hypotenuse.

Assume the height of the triangle = [tex]x[/tex]

In this type of triangle, the hypotenuse is double of height,

so, hypotenuse = [tex]2x[/tex]

and the base of the triangle is [tex]\sqrt{3}[/tex] of the height.

Therefore, base = [tex]x\sqrt{3}[/tex]

so that, The perimeter of the triangle = [tex]x+2x+x\sqrt{3}[/tex]

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The result of dividing 2x^3 + x^2 - 2x + 8 by x + 2 is:

Quotient: 2x^2 - 3x + 4

Remainder: 0

The given polynomial is 2x^3 + x^2 - 2x + 8.

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.

(x)(2x^2) = 2x^3

Thus, we multiply the divisor (x + 2) by 2x^2 which gives 2x^3 + 4x^2.

Now we subtract this from the polynomial which gives -3x^2 - 2x +8.

Next we multiply the divisor by -3x which gives -3x^2 - 6x. Again we subtract the same from the remaining polynomial -3x^2 - 2x +8 and get 4x + 8.

Repeating the same we multiply the divisor by 4 which gives 4x + 8. Subtracting the same from the remaining polynomial 4x + 8 we get the remainder 0.

Thus, the quotient is 2x^2 - 3x + 4.

The question is incomplete, the complete question is:

What is the result of dividing 2x^3 + x^2 - 2x + 8 by x+2?

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The length of arc COD is approximately 12.56 units.

To find the radius of the circle, we can use the area of sector COD and the angle COD.

We know that the area of a sector is (angle/360) * pi * r^2, and we know that the area of sector COD is 50.24 square units. We also know that the angle COD is 90 degrees.

So we can set up the following equation:

50.24 = (90/360) * 3.14 * r^2

Solving for r, we get:

r = sqrt(50.24 / (90/360) * 3.14) = sqrt(50.24 / (0.25 * 3.14)) = sqrt(50.24 / 0.785) = sqrt(64.28) = 8 (approximately)

So the radius of the circle is approximately 8 units.

To find the length of the arc, we can use the formula of arc length which is Arc Length = (Angle/360) * 2πr

So the length of the arc COD is (90/360) * 23.148 = 4*3.14 = 12.56 (approximately).

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