What is a sum example?.

When you are skiing on a mountain with an altitude 12 meters and angle of depression is 21 degrees then you will ski down for a distance of 31.57 meters.

Solution:

Here we have ,

Height i.e altitude of mountain (h) = 12 meters

Angle of depression (∅) =21°

And let the distance coverd be (b)

Using theorm of trigonometery,

tan∅ = [tex]\frac{height}{base}[/tex]

       = [tex]\frac{12}{b}[/tex]

Therefore,

tan(21°) = [tex]\frac{12}{b}[/tex]

b = [tex]\frac{12}{tan(21)}[/tex]

b = [tex]\frac{12}{0.38}[/tex]

b = 31.57 meters

Hence ,

You will ski down 31.57 meters.

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The slope of the line is a measure of the rate of change between two points and is calculated by dividing the change in y-values by the change in x-values. In this case, the slope is -6, which means that for every 1 unit increase in x, there is a 6 unit decrease in y.

The slope of the line is a measure of the rate of change between two points. It is calculated by dividing the change in y-values by the change in x-values. To find the slope of the line represented by the table of values, we need to first identify two points on the line. We will use the points (x1, y1) and

(x2, y2).

We can choose any two points, but for this example, we will use

(x1, y1) = (-7, 9) and (x2, y2) = (8, -15).

The slope of the line is then calculated by finding the difference between the y-values

(y2 - y1 = -15 - 9 = -24)

and the difference between the x-values

(x2 - x1 = 8 - (-7) = 15)

and dividing these two values:

-24/15 = -6.

This means that for every 1 unit increase in x, there is a 6 unit decrease in y.

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The main difference between a true solution and a colloidal solution is the particle size of the dispersed substance. In a true solution, the particles are so small that they cannot be seen with the human eye, while in a colloidal solution, the particles are intermediate in size and are visible under microscope.

A true solution is a homogeneous mixture of two or more substances where one substance is completely dissolved in the other. The particles of the dissolved substance, called solute, are so small that they cannot be seen with the human eye and are evenly distributed throughout the solution. A true solution is transparent, and the particles of the dissolved substance do not scatter light, thus not visible under a microscope. Examples of true solutions are sugar dissolved in water, and salt dissolved in water.

On the other hand, a colloidal solution is a type of mixture where one substance is dispersed throughout another substance in small particles that are not large enough to settle out but are large enough to scatter light. The particles of the dispersed substance, called the dispersed phase, are intermediate in size between those of a true solution and a suspension. The particles are visible under microscope, but not to the human eye, and the mixture is usually cloudy or opaque. Examples of colloidal solutions are milk, fog, and blood.

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Equivalent 4/5 is equals to 20/25 in fractions.

In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.

The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.

= 4/5 ( multiply by 5/5)

= 4/5 * 5/5

= 20/25

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Correct Question:

What is 4/5 as an equivalent fraction?.

The mirror image of (4,5) is (4,-5) or (-4,5)

The term mirror image in math is defined as a reflected duplication that appears identical but in reverse.

Here we need to find the mirror image of (4,5).

As we all know that the rule used here is written as the image of (x, y) in the y-axis is (–x, y).

Then according rule here the given that the mirror image of (4,5) along x axis is written as (4,-5).

Then as per the point lies in fourth quadrant.

Then the another form of the mirror image of ( 4,5) along y axis is written as (-4,5) and then the point lies in second quadrant.

Complete Question:

What is the mirror image of the coordinate (4,5)?

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Step-by-step explanation:

let the mid point be (x, y)

x= (-2-2)/2; y=(1-(-3))/2

please comletd the rest by yourself

Answer: I believe the midpoint of the side AB would be (0.3,0)

Step-by-step explanation:

I hope that helps!

Answer:83

Step-by-step explanation: sum of the angles should be 180

44+53+x=180

x=180-97

x=83

Answer:

Step-by-step explanation:

The addition of three angles in a triangle is 180°.

Therefore, if we add all the angles, it's

180°                   = x + 53° +44 °

180° - ( 53°+44° ) = x

        180°-97°   = x

         83 °        = x

Then the answer is obvious, it's 83°.

The three angles of the triangle can be found by using the formula for the sum of angles of a triangle, which is 180°. Then, the measure of angle A + angle B + angle C = 180°.

1. Using the sum of angles formula, angle A + angle B + angle C = 180°

2. Use the Law of Cosines to calculate the angle between two sides of the triangle.

3. Subtract the sum of those two angles from 180° to find the measure of the third angle.

The three angles of a triangle can be found using the sum of angles formula, which states that the sum of the angles of a triangle equals 180°. This means that angle A + angle B + angle C = 180°. To find the individual angles, we can use the Law of Cosines which states that c2 = a2 + b2 - 2ab cos C, where C is the angle between two sides of the triangle. This formula allows us to calculate the angle between two sides of the triangle. Once we have calculated the sum of the two angles, we can subtract this sum from 180° to find the measure of the third angle. For example, if the sum of the two angles is 120°, then the third angle would be 180° - 120° = 60°. This method allows us to find the three angles of the triangle with the given vertices.

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The length of the side is greater than equal to 35 and less than equal to 46 such that the perimeter of square lies in the given range.

let the length of each side of square be x units

the perimeter of the square = x +x +x +x

=> 4x

so the boundation on the perimeter is given in the question

given:

138 < 4x < 186

138/4 < x < 186 /4

34.5 < x < 46.5

so the length of the side is greater than equal to 35 and less than equal to 46

The range of the possibel sides is [35 ,46]

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The equation of the function shown in the provided graph is y = 1

                                                                                                         (x+3)²  

The parent function is f(x) =  1

                                              x²

Graph can be defined as a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things

How horizontal shifting of the graph takes place

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+k) where k>0

Since the graph is shifted towards the negative x-axis by 3 units

So, the parent function f(x) will become f(x+3)

 f(x)=  1

         x²

f (x+3)= 1    

           (x+3)²

So, the equation of the function will be y = 1    

                                                                       (x+3)²  

Therefore, The equation of the function shown in the provided graph is  

y = 1

    (x+3)²                                          

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Answer: C: y=6×6^x

Step-by-step explanation:

Hope this helps! Good luck!

Answer:

Step-by-step explanation:

1 st Q:  answer is -2 (choice C)

2nd Q:  answer is (8,1)  (choice D)

The solution is where the 2 lines intersect

The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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Answer:

x = 8, y = 9

-3x + 44 - x = 12

-3x - x = 12 - 44

-4x = -32

x = 8

-3(8) + 4y = 12

-24 + 4y = 12

4y = 12 + 24

4y = 36

y = 9

The value of the equation on x = 2 is 5. Thus, Option D is the correct answer.

Given Quadratic equation,

[tex]=\frac{1}{2} x^{4} - \frac{3}{4}x^{2}[/tex]

Put the value of x = 2 in the above equation and we get

[tex]=\frac{1}{2} x^{4} - \frac{3}{4}x^{2}[/tex]

[tex]=\frac{1}{2}* 2^{4} - \frac{3}{4}*2^{2}[/tex]

= 8 - 3

= 5

Therefore, the value of the equation on x = 2 is 5.

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After solving, the slope of equation 3x + y = -3 is -3.

In the given question, we have to find the slope for 3x + y = -3.

The given equation is 3x + y = -3.

The general equation of line is y = mx + c, where m = slope of line and c is the y-intercept of line.

To find the slope we have to convert the given equation in the form of general equation.

To convert in general form we have to isolate the y.

3x + y = -3

Subtract 3x on both side, we get

y = -3x - 3

Now comparing with y = mx + c, we get

m = -3

Hence, the slope of equation 3x + y = -3 is -3.

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The complete question is:

What is the slope for 3x + y = -3?

Gallons of gas used 40 gallons.

The given equation, m = pace / 40g, represents the distance in miles (m) that a car can travel using a certain number of gallons (g) of gas. The variable "pace" represents the miles per gallon (mpg) of the car. To find the number of gallons used, we need to solve for g in the equation.

Here are the key steps:

Finally, we can solve for g and we get the answer that the car used 40 gallons of gas.

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Yes, AB ≅ DE, EF ≅ DE, then AB ≅ EF. The property of congruence illustrated in the question is the transitive property.

The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.

In the statement "If AB ≅ DE, EF ≅ DE, then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.

The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.

--The given question is incorrect; the correct question is

"Is AB ≅ DE, EF ≅ DE then AB ≅ EF? explain"--

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Step-by-step explanation:

(6×(-4) - 1 )/ 4=-24-1/4= -25/4= -6.2

We can calculate it by using a long multiplication method where you multiply every digit of 12 by 12. 144 = 1 x 12 + 4 x 1 = 12 + 4 = 16. So, the value of 144 is 16

Calculating the value of 144 is a simple mathematical operation that can be done in several ways. The most straightforward method is to multiply 12 by 12, as 144 = 12 x 12. Another way to calculate the value of 144 is to find the square of 12, as 144 = 12^2. An alternative method is to use long multiplication where you multiply every digit of 12 by 12. The result of this will be 144 = 1 x 12 + 4 x 1 = 12 + 4 = 16.

In summary, the value of 144 is 16, regardless of the method you choose to calculate it. It is a well-known fact and can be easily looked up in mathematical tables as well.

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Answer:

$1.75

Step-by-step explanation:

We take

14 / 8 = $1.75

So, one product cost $1.75

It would take Lisa 3 hours to complete the painting as both Brennan and Lisa could end up charging the same amount of $63.

An hour is a unit of time that is traditionally calculated as 124 of a day and is scientifically estimated to last between 3,599 and 3,601 seconds, depending on how quickly the Earth rotates. There are 60 minutes in an hour and 24 hours in a day.

The concept of the hour was first developed in the ancient Near East as a flexible measurement of 1/12 of the night or day. Such seasonal, temporal, or uneven hours varied with latitude.

Equal or equinoctial hours were defined as 124 of the day, measured from noon to noon; the minor seasonal variations of this unit were eventually smoothed out by making it 124 of the mean solar day.

Flat rate quoted by Brennan = $63

Rate quoted by Lisa = $8 h + $47

The number of hours for Lisa to finish the painting = ($63 - $47)/$8

                                                                                    =  2 hours

The total cost that Lisa would charge is = ($8 x 2 + $47)

                                                                  = $63

Thus, It would take Lisa 3 hours to complete the painting as both Brennan and Lisa could end up charging the same amount of $63.

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Total money spent on a pass and lunch for each student = $29.9

A field trip is a journey by a group of people to a place away from their normal environment.

Given :

School spends $633.85 on passes for 31 students and 4 teachers.

School spends $300.08 on lunch for 31 students.

Calculation :

School spends on a pass for each student,

633.85

  35

=20.22$

School spends on a lunch for each student,

300.08

  31

=9.68$

Therefore, total money spent on a pass and lunch for each student

20.22 + 9.68

= $29.9

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y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex]  is the rational function  that has a horizontal asymptote of y = 0.

When the denominator of a polynomial has a degree of at least 1, it is said to be a rational function. Or to put it another way, the denominator must contain a variable.

When p(x) and q(x) are polynomials and q(x) ≠ 0, the general form of a rational function is p(x)/q(x).

Asymptotes are lines that the function graph approaches but never crosses. Both the x and y axes are asymptotes in the parent function f(x)=1x. The parent function's graph will approach the asymptotes steadily but never actually touch them.

If the degree of the denominator > degree of the numerator, there is a horizontal asymptote at y = 0.

Here, only y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex] has the degree of the denominator > degree of the numerator.  

Thus, y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex]  is the rational function  that has a horizontal asymptote of y = 0.

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The circumference of cylinder's circular face is 20.09 pi units.

The cylinder's lateral surface area is equal to the circumference of the circular base multiplied by the height. A circle's circumference is 2r and its height is h, so the lateral area is 2rh.

That is LSA =  2 × π × r × h where, r = base radius, and h = height of the cylinder.

Here given,

LSA = 824m²

Height = 40 m

By substituting

824 = 2 x 3.14 x r x 40

824 / 2 x 3.14 x 40 = r

r = 3.2m

Circumference of circular face = 2 π r

By substituting the values,

Circumference = 2 x 3.14 x 3.2

Circumference = 20.09 pi units.

Therefore the circumference of a cylinder with circular face is 20.09 pi units.

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Answer:

15

Step-by-step explanation:

(-6,-6)and (-9,-5) =15

A binomial is an algebraic expression containing two different terms connected by addition or subtraction.

An algebraic expression containing only two terms is called a binomial expression. This is called a binomial polynomial. Also called the sum or difference of two or more monomials. This is the simplest form of polynomial. Binomials are classified into algebraic expressions based on the number of terms they contain, along with monomials, trinomials, quaternions, etc. In other words, two different monomials of different degrees connected by a plus or minus sign form a binomial. For example, consider two monomials 2x and 5x¹⁰. Adding these monomials gives the binomial given by 2x + 5x¹⁰.

2) For example, 2xy + 7y is binomial because it has two terms.

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The number of students that were surveyed where 7 out 8 students own a bike is equal to 96.

Let the number of students surveyed be [tex]x[/tex] .

According to the question,

When 8 students were surveyed 7 owned a bike. So, when [tex]x[/tex] students were surveyed,

               Number of students who own bikes = [tex]\frac{7}{8} x[/tex]

                Number of students who don't own bike = [tex]\frac{1}{8} x[/tex]

 In question, it is given that:

                             [tex]\frac{7}{8} x - \frac{1}{8}x = 72\\\\\frac{6}{8} x = 72\\\\6x = 576\\x= 96[/tex]

Hence, the number of students that were surveyed is 96.

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After working 8 hours and grading 9 papers per hour, it is expected Autumn has 11 papers left.

To calculate the number of papers she can grade during this time, let's use the rate provided:

This means in 9 hours she can grade 72 papers.

Now, let's calculate the number of papers left:

Based on this, the total of papers left after working for 8 hours is 11 papers.

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