what’s the equation of a line?

The slope of an angle 30 which in the positive x direction is tanФ = tan30= 1/√3

Slope:

Slope describes the steepness of a line and it also remains constant with the line it also gives us information about the direction. If the slop is negative then the line will be in the negative x-axis if the slop is positive the line will be in the positive x-direction.

A slope of a line is the change in the y coordinate w.r.t the change in the x coordinate.

m = Δy/Δx

m=tan θ = Δy/Δx

m=tan 30 = 1/[tex]\sqrt{3}[/tex]

Therefore the slope of a line that makes an angle of 30 with the positive x direction will be 1/√3

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Answer:

46 students

Step-by-step explanation:

20 female prefers dogs + 26 female prefer cats + 6 female no preference = 46 female total.

The solution of the equation is ( x - 5 )² +23 = 0.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant.

Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping, as well as the order of operations and other features of logical syntax.

Given that the equation is x²-10x = 3. The equation will be solved by completing the square method as below,

x²-10x = 3

x² - 10x - 3 = 0

( x - 5 )² - 3 + 5² = 0

( x - 5 )² - 3 + 25 = 0

( x - 5 )² + 23 = 0

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Answer:

5

Step-by-step explanation:

-5*-1 = 5

To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. This will shift the triangle in the desired direction.

To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. For example, if you wanted to translate the triangle with coordinates (1,2), (3,4), and (5,6) by two units to the right and two units up, you would add two to each x-coordinate and two to each y-coordinate. The new triangle would have coordinates (3,4), (5,6), and (7, 8).

1. Identify the coordinates for the triangle: (1,2), (3,4), and (5,6).

2. Decide how much you want to translate the triangle: two units to the right and two units up.

3. Add two to each x-coordinate and two to each y-coordinate: (3,4), (5,6), and (7,8).

4. The triangle is now translated two units to the right and two units up.

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Answer:

orthocentre

Step-by-step explanation:

A triangle's three altitudes intersect at the orthocentre

As asked by the question, the value of K for a given equation of a line is equal to the slope of the line.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

The value of K for a given line is equal to the slope of the line. Since lines are generally expressed in the form of y = mx +b , where m is the slope of the line and b is the y-intercept of the line. Here , the value of K will be equal to the slope m of the line.

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The function y = - 2(x - 1)² + 5 is reflected along the y-axis, shifted horizontally to the right by 1 unit, and then shifted vertically by 5 units.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, The parent function is y = x² which is quadratic.

Now, y = - 2(x - 1)² + 5,

First is reflected along the y-axis (-) sign,

(x - 1) is shifted by 1 unit to the right horizontally and (+5) is shifted vertically 5 units up.

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The function rule that represents each situation is $8.75 * n.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here, we have

A worker's earnings E are a function of the number of hours N worked at a rate of $8.75 per hour.

We have to create an incognita that represents a worker's salary based on how many hours he or she works.

G: Worker's salary

n: number of hours worked

G=f(n)

Then using the data that the worker earns $8.75 per hour worked, we must formulate f(n) so that with this data we can calculate G.

G = f(n) = $8.75 * n

If the worker performs 1 hour of work (n=1), then his salary will be:

G = $8.75 * 1 = $8.75

If the worker performs 10 hours of work (n=10), then his salary will be:

G=$8.75 * 10 = $87.5

Hence, the function rule that represents each situation is $8.75 * n.

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The two variables involved in the graph are: input variable (x - value) and output variable (y- value)

We know that many types of problems require  two variables at the same time. such relation can be described algebraically by a two variable function or equation.

To represent such function graphically we use two perpendicular lines called axes and their point of intersection is called as the origin. This method of representation is known as the Cartesian coordinate system. The numerical value of one variable is measured along the horizontal axis called the x axis. Whereas the numerical value of the other variable is measured along the vertical axis called the y axis.

The four sections formed due to these axex are called quadrants.

Therefore, the two variables involved in the graph are input variable which  measured along x-axis and output variable which  measured along y-axis.

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The commission for $750 at 3% is:

Commission can be defined as the fees or extra fees that is been paid to someone for a job well done or for rendering a service.

Now let find the commission amount using this formula

Commission = Earnings × rate

Where:

Earnings = $750

Rate =3%

Commission = $750 × 3%

Commission = $22.50

Therefore the commission is $22.50.

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The complete question is:

Find the commission.

Earning Commission

Sales Commission Rate Commission

$750

3%

?

The commission is $

Answer:

31800.997945142

or

31800 24407400⁄24457657

S

If the function for the total rental cost for vacuum cleaner is f(x) = 6x + 14 , then the cost for using it for 10 hours is  $74   .

A hardware store rents vacuum cleaner for a part of a day ,

the function that models the total rental cost for the vacuum cleaner is given as : f(x) = 6x + 14 ;

where , x is the number of hours the cleaner is used .

given that the vacuum cleaner is used for 10 hours , So x = 10 .

the total cost is f(10) = 6×10 + 14  ;

f(10) = 60 + 14 ;

f(10) = 74 ;

Therefore , the total rental cost for using the vacuum cleaner for 10 hours is $74  .

The given question is incomplete , the complete question is

A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner. What is the total cost for using the vacuum cleaner for 10 hours  .

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The four Inverse operations are :

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. In most cases, a number's inverse refers to its reciprocal, as in x /1 Equals 1 / x. One results from multiplying a number by its reciprocal, or inverse.

To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.

The definition of a cube is the process of multiplying a number by itself three times, while a cube root is the opposite of a cube. Alternately, we may state that a number's cube root gives us a number that, when cubed, gives us the same number and is referred to as a perfect cube.

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The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

V=b*h

b=base area of prism

h=height of prism

The volume of a prism is calculated as V=Bh, where B is the base area and h is the height.

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Answer:

The number of unit cubes are 6, its volume is 6 cu cm.

Step-by-step explanation:

Based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8

y = 4

Two right triangles are congruent to each other by the Hypotenuse-Length Congruence Theorem (HL) if the hypotenuse length and one leg of a right triangle is congruent to the hypotenuse length and leg of the other right triangle.

Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.

Use this to create two equations and solve to get the value of x and y.

Equal Hypotenuse:

(eqn. 1)

Equal legs:

(eqn. 2).

Find the value of y, by substituting x = (y + 4) into eqn. 1.

(eqn. 1)

Substitute

Find the value of x, by substituting y = 4 into eqn. 2.

X=y+4

X=4+4

X=8

Therefore, based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8

y = 4

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The domain and range calculator is a tool that allows us to enter the necessary data and have it compute and output the domain and range.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input.

After we enter an x value, the function outputs this sequence of values.

We simply solve the equation y = f to determine the values of the independent variable x and obtain the domain (x).

Simply put, after determining g's domain, x=g(y) will calculate the function's range (y).

The domain and range calculator is a tool in which we put in the required values and it calculates and gives out the domain and range as an output.

Therefore, the domain and range calculator is a tool that allows us to enter the necessary data and have it compute and output the domain and range.

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According to Pythagoras theorem, the value of the third side of the triangle is 38.6mm

In math Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Here we have given that the triangular pendant has two sides of length 23 mm and 31 mm.

And we need to find the possible lengths (in whole mm) for the third side.

Here in the given question, we have the values of the two sides are 23mm and 31mm.

Then we have to apply the values on the Pythagoras theorem formula,

=> hypotenuse² = adjacent² + opposite²

Now, we have to apply the values as opposite and adjacent on it, then we get,

=> hypotenuse²= 23² + 31²

=> hypotenuse² = 529 + 961

=> hypotenuse² = 1490

Therefore, the value of the third side is 38.6mm

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Answer: I think it is between 3rd and 4 lines of number 2 and 3

Step-by-step explanation:

Because it line here is 0.20

so 2.7 will be some where between 3rd and 4 lines of number 2 and 3

Critical values of the function f(θ) = 2cos(θ) +(sin(θ))² on the interval 0≤ θ < 2π is 0 and π.

Therefore, the answer is 0 and π.

f(θ) = 2cos(θ) +(sin(θ))²

f'(θ) = -2sin(θ) +2sin(θ)cos(θ)

Critical values of f are points at which f' is zero or not defined.

For all values of θ, we can find that f'(θ) is defined.

f'(θ) = 0

-2sin(θ) +2sin(θ)cos(θ) = 0

cos(θ) - 1 = 0 or sin(θ) = 0

cos(θ) = 1

θ = nπ, n = 0, 1, 2, ...

sin(θ) = 0

θ = nπ, n = 0, 1, 2, ...

Therefore in the interval 0 ≤ θ < 2π, critical values are 0 and π.

2π is not there as it is not included in the interval.

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Answer:

The answer is False.

Step-by-step explanation:

Check the explanation below

The graph of the function f(x) = x^4 - 6*x^7 + 5 crosses the x-axis at x = 0 and x = 5.

The graph of the function f(x) = x^4 - 6*x^7 + 5 is a polynomial function. The roots of a polynomial are the values of x for which the polynomial is equal to zero. To find the roots of the polynomial, we must solve the equation f(x) = 0. To solve this equation, we will use polynomial division.

We will divide the polynomial by (x - 5), which will give us the following result:

f(x) = x^4 - 6*x^7 + 5 = (x - 5)(x^3 + 7x^2 - 5x + 25).

We can now solve for the roots of the polynomial. Since (x - 5) is a factor of the polynomial, the root is x = 5. We can also solve for the other roots by setting the remainder of the polynomial division equal to 0. This gives us the equation x^3 + 7x^2 - 5x + 25 = 0. This equation can be solved by factoring and the result is x = 0, 1, and 5. Therefore, the graph of f(x) = x^4 - 6*x^7 + 5 crosses the x-axis at x = 0 and x = 5.

f(x) = x^4 - 6*x^7 + 5

Divide f(x) by (x-5):

f(x) = (x-5)*(x^3 + 7x^2 - 5x + 25)

Set remainder equal to 0:

x^3 + 7x^2 - 5x + 25 = 0

Factor:

x^3 + 7x^2 - 5x + 25 = (x - 5)*(x^2 + 5x + 5)

x = 0, 1, 5

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Answer:

Step-by-step explanation:

You can use Pythagoras theorem for this

[tex]16^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]

256 = 36 + [tex]x^{2}[/tex]

220 = [tex]x^{2}[/tex]

[tex]\sqrt{220}[/tex] = x

14.8323.... = x

we also have to remember that it could be negative, but,  negative distances are just the same distance but in the other direction, so they are the same length here.

14.8 feet = x    to the nearest 10th

If the limit is infinity minus infinity it is undefined because the result would be a number that is not a real number.

In mathematics, a limit is the value that a function approaches as the independent variable approaches a certain value. Limits are used to study the behavior of a function as the independent variable approaches a certain point.When the limit is infinity minus infinity (∞ - ∞), it is undefined because the result is not a real number. Infinity minus infinity is an indeterminate form, which means that the limit could approach any real number or it could approach infinity or negative infinity. In other words, the result of infinity minus infinity is an unknown quantity.To understand why infinity minus infinity is undefined, you must understand the concept of infinity. Infinity is not a number, but rather an idea of something that is larger than any number. Therefore, when subtracting infinity from infinity, there is no set answer since the two concepts are not numbers. To calculate the limit, the two infinities must be replaced with real numbers. In conclusion, when the limit is infinity minus infinity, it is undefined because the result is not a real number. Infinity is an idea and not a number, so the result of infinity minus infinity can not be determined. To calculate the limit, the two infinities must be replaced with real numbers.

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Answer:

A could finish the whole work in 60 days

Step-by-step explanation:

Both A and B can finish the work in 30 days.

That means both A and B can finish 1/30 part of the work in 1 day.

So in 20 days, both A and B can finish 20/30 = 2/3 part of the work.

Both A and B worked together for 20 days and completed 2/3 part of the work. Now 1/3 part of the work is remaining.

But after 20 days B left the work. Now A finished the remaining 1/3 part of the work alone.

Given A has completed the remaining 1/3 part of the work in 20 days. We are asked to find in how many days A could finish the whole work.

Let A could finish the whole work in x days.

That means A could finish 1/x part of the work in 1 day.

So in 20 days, A could finish 20(1/x) = 20/x part of the work.

But it's given that A finished the remaining 1/3 part of the work in 20 days.

Thus we are able to equate 20/x and 1/3.

[tex]\longrightarrow\dfrac{20}{x}=\dfrac{1}{3}[/tex]

[tex]\Longrightarrow\underline{\underline{x=60}}[/tex]

Hence A could finish the whole work in 60 days.

 Two shapes are congruent if they have the same shape and size. We can also say if two shapes are congruent, then the mirror image of one shape is the same as the other.

  Geometric figures that are congruent share the same size and shape. In other words, figures are congruent if they can be transformed into one another through a series of transformations, rotations, and/or reflections. When the sides and angles of two triangles match, the triangles are said to be congruent. 

Triangles that have comparable sides and equal angles are said to be congruent. Indicating congruence is the sign “≅”.

identical in size and shape.  

Congruent refers to objects that are exactly the same size and shape. Even if we flip, turn, or revolve the shapes, the shape and size must remain the same.

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The graph G represents the solution set for 8x + 5y ≤ 100.

What is Solution set ?

A solution set in mathematics is the collection of values that satisfy a particular set of equations or inequalities. The set of solutions to a constrained optimization problem represents the viable zone.

We have, 8x + 5y ≤ 100

Let's assume it as 8x + 5y = 100,

when x = 0,

   5y = 100

    y = 20

when y = 0,

   8x = 100

    x = 12.5

So, The line touches x-axis and y-axis at 12.5 and 20.

Now, Putting (0, 0) in  8x + 5y ≤ 100,

We get, 0 ≤ 100 which is true.

Hence, The region below the line should be the solution set for 8x + 5y ≤ 100.

So, Graph G represents the solution set for 8x + 5y ≤ 100.

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Answer:

Step-by-step explanation:

The perimeter is P = 26x - 62.

P = 2(L + B)

P = 2(5x + 12 + 8x - 43)

P = 2(13x - 31)

P = 26x - 62

Z-score of the manufacturer's claim is 0.25.

It is a statistical expression that refers the difference between observed value and standard deviation.

we calculate the Z-score from the following equation.

Z-score= X-μ/σ

           (Observed value- mean value)/standard deviation

as per the question= (manufacturer's claim - sample mean)/standard deviation

                               (1500-1480)/80=0.25

hence, Z-score is 0.25

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Z-score of the manufacturer's claim is 0.25.

It refers to the difference between the observed value and standard deviation and is a statistical statement.

The standard score, also known as a z-score, is a highly helpful statistic since it lets us compare scores from different normal distributions and assess the likelihood that a given score will fall within our normal distribution.

The 90th percentile's z-score is 1.2816, as calculated by the Percentile to Z-Score Calculator. Therefore, a student's z-score would be deemed "excellent" if it was greater than or equal to 1.2816.

we calculate the Z-score from the following equation.

Z-score= X-μ/σ

(Observed value- mean value)/standard deviation

as per the question= (manufacturer's claim - sample mean)/standard deviation

 (1500-1480)/80=0.25

hence, Z-score is 0.25

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