A shadow is cast by a pole. The angle of elevation from the end of the shadow to the top of
the pole is 35 degrees. If the distance from the base of the pole to the end of the shadow is 22
feet, how far is it from the end of the shadow to the top of the pole?

The exponent 0 refers to the number being raised to the power of 0.

When any number, except 0, is raised to the power of 0, the result is always 1. This is known as the "zero power property" and it is true for any non-zero number a. The mathematical statement can be represented as:

a^0 = 1

For example, 2^0 = 1, 5^0 = 1 and so on. This property holds true for any base a, including real numbers, complex numbers, and even matrices.

The exponent 1 refers to the number being raised to the power of 1. When any number is raised to the power of 1, the result is always the same as the number itself. This is known as the "identity property" and it is true for any non-zero number a. The mathematical statement can be represented as:

a^1 = a

For example, 2^1 = 2, 5^1 = 5 and so on. This property holds true for any base a, including real numbers, complex numbers, and even matrices.

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Answer:

Marshall saves 1/4 of his money and spends 1/4 of his money on fun. Therefore, he saves and spends 1/4 + 1/4 = 1/2 or 50% of his money on those two categories.

Step-by-step explanation:

Although part of your question is missing, you might be referring to the question :

Given that 2x+3y / 3x+4y = 5, find the ratio of y:x

Given : 2x+3y / 3x+4y =5

To find : y : x

Solution :

(2x+3y) / (3x+4y) = 5, or

2x + 3y = 15x + 20y, or

-15x + 2x = 20y - 3y, or

-13x = 17y

Therefore, x/y = -17/13

Hence, y/x = -13/17

y : x = -13 : 17.

The answer is -13 : 17.

Euclid is the father of geometry

Euclid and René Descartes was often called the father of modern mathematics because he created analytic geometry and the Cartesian coordinate system.

What is modern mathematics?

Different methodologies have been used in contemporary mathematics. It focuses mostly on entities, whereby interconnections follow themes and patterns.

René Descartes was a person who was very famous for his philosophy of science and mathematics. He was considered a person who evaluate and made various new development in the field of math as well as time in separate fields like geometry and algebra with new properties that is developed by him.

He had the main idea of having finite and infinite particles or numbers in geometry. And also used various scientific methods to prove that.

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The compound inequality says that x+1 is greater than 3 and less than 6.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than the relation between variables and the numbers.

Given that the compound inequality is 6 > x + 1 > 3. The compound inequallity says that the value of x +1 is greater than 3 and is less than 6.

The inequality can be written as,

6 > x + 1 > 3

x + 1 > 3

x +1 < 6

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In optics, an image is defined as the group of focus points of light rays coming from an object. A real image is a collection of focus points actually made by converging rays, while a virtual image is a collection of focus points made by extensions of diverging rays.

The real image is produced by the intersection of light rays. It can be obtained on a screen. Hence, projectors form real images.

The virtual image is formed when the light rays appear to be originating from a point but do not actually meet. It can be seen by human eyes.

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Answer:

29 is the correct answer

When the length of JK is 9.5 feet and the angle L is 61 degrees  trigonometric ratio of the tangent, solving yields: KL=9.5ft/1.804 KL=5.27 ft.

The relationship between triangle side lengths and angles is investigated in the branch of mathematics known as trigonometry. The application of geometry in astronomical study gave rise to the area's first appearance during the Hellenistic era, roughly in the third century BC. Exact methods mathematics focuses on certain trigonometric functions and how they might be applied to calculations. In trigonometry, there are six widely used trigonometric functions. Their respective names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, especially of right triangles. The features of all geometric shapes are studied in geometry, though.

given

△JKL

JK=9.5ft

∠L=61∘

Find:KL

We may determine the outcome using the tangent's trigonometric ratio.

Tan = JK/KL = 61

When we separate KL, we get KL=9.5ft/tan61.

When the length of JK is 9.5 feet and the angle L is 61 degrees  trigonometric ratio of the tangent, solving yields: KL=9.5ft/1.804 KL=5.27 ft.

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The correct question is :-

Given triangle JKL, find the length of KL. The length of JK is 9.5 ft and the angle L is 61 degrees.

In part A; The graph of inequality y > 2x - 9 shows the dashed line.

And, In part B; The graph of inequality y - 6 ≤ x shown the solid line.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality are,

Part A: y > 2x − 9

Part b; y − 6 ≤ x

Now,

In part A; The inequality '<' used which represent the dashed line

And, In part B; The inequality ≤ used which represent the solid line.

Hence, The graph of inequality y > 2x - 9 shows the dashed line.

And, The graph of inequality y - 6 ≤ x shown the solid line.

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Answer:

I think the answer is A

1,2

The proof is given below

We can start by using the definition of the trigonometric functions cosec(A), tan(A), and cot(A):

cosec(A) = 1/sin(A)

tan(A) = sin(A)/cos(A)

cot(A) = 1/tan(A) = cos(A)/sin(A)

Now, we can substitute these definitions into the equation:

cosec(A)/(tan(A) + cot(A)) = 1/sin(A) / (sin(A)/cos(A) + cos(A)/sin(A))

Simplifying the right-hand side gives us:

1/sin(A) / (sin(A)(1/cos(A) + 1/sin(A))) =

1/sin(A) / (sin(A)/sin(A)cos(A) + sin(A)) =

1/sin(A) / (1 + sin(A))

Finally,

multiplying both sides by sin(A) (which is not 0 because A is not a multiple of pi/2)

cosec(A)/(tan(A) + cot(A)) * sin(A) = 1/sin(A) / (1 + sin(A)) * sin(A) = 1 / (1 + sin(A)) * sin^2(A) = cos(A)

Therefore, cosec(A)/(tan(A) + cot(A)) = cos(A)

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Lisa's book has 10,600 pages.

Multiplication is an operation that represents repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication is the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.

Tim's book has 50 pages, if Lisa's book has 212 times as many pages, therefore;

Lisa's book has 212 x 50 pages

Lisa's book has 10,600 pages.

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Answer: 3

If you look at the left-most side on figure A, youll notice that it is 2 units long. On figure B, it is 6 units long. 2*x=6 where X is the scale factor. You'll find that X=3. YW BRO

Speed = 7.7miles/2.2hours = 3.5miles/hour

In physics, the average speed is defined as the ratio of distance traveled during a certain time period.

Distance/Time = Speed

If the problem stated that the two groups’ average speeds are equal,

Mark’s Group Speed Equals Sally’s Group Speed

The problem now suggests that the time is likewise equal. That means Sally’s group took t = 4.7 – 2.5 = 2.2 hours to travel the remaining 7.7 miles.

That implies that the speed is,

7.7 miles/2.2 hours = 3.5 miles/hour.

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The positive exponent for the given expression is 1/5.

A positive exponent tells us how many times to multiply a base number, and a negate

ve exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.

The given exponent is [tex]25^{-\frac{1}{2}[/tex].

Now, [tex]25^{-\frac{1}{2} }=(5^2)^{-\frac{1}{2}[/tex]

= 5⁻¹

= 1/5

Therefore, the positive exponent for the given expression is 1/5.

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Answer:

the equation of the line = y + x -3 -3 = 0

Step-by-step explanation:

Equation of the line is give n by the formula

y - y¹ = m

x - x¹

note: m is the gradient.

Point = (3, 3) and (-1, 7).

Gradient =m= y2 - y1 = 7 - 3 = 4 = -1

x2 - x1 -1 -3 -4

the equation of the line

y - y1 = m

x - x1

y - 3 = -1

x - 3

note: Perform cross multiplication also remember every whole number is over one.

=y - 3 = -1 (x - 3)

=y - 3 = - x + 3

y + x - 3 - 3 = 0.

ans is 90 and 30

Step-by-step explanation:

LN=90° (right angle)

MN=30°(DO THE MATH)

The distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.

The length along a line or line segment between two points on the line or line segment.

The coordinates of A are (-18, -18)

coordinates of B are (20, 0)

coordinates of C are (-12, 16)

The formula for distance is Distance=√(x₂-x₁)²+(y₂-y₁)²

Distance AB=√(20-(-18))²+(0-18)²

=√(20+18))²+(0-18)²=√38²+18²

AB=√1444+324=√1768=42.04 units

Distance BC=√(-12-20)²+(16)²

=√(-32)²+(16)²=√1024+256

=√1280

=35.77

Distance CA=√(-12-(-18))²+(16+18)²

=√(6)²+(34)²

=√36+1156=34.5

Hence, the distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.

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2 dilated means that the measurement of an area has increased or expanded in size.

This can be a linear measurement such as the diameter of a circle, or the area of a square or rectangle. The formula for the area of a circle is A=πr2 where r is the radius of the circle. A 2 dilated measurement would mean that the radius has doubled, so the formula would be A=π(2r)2 A=4πr2. This would mean that the area of the circle has increased by a factor of 4. Similarly, if the length and width of a rectangle were 2 dilated, the area would be A=2L2W, which would be four times the original area.

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The unit rate of the 76th player is [tex]1\frac{1}{3}[/tex] miles per hour.

The unit rate of the 91st player is [tex]1\frac{1}{9}[/tex] miles per hour.

The unit rate of the 44th player is [tex]1\frac{1}{2}[/tex] miles per hour.

What is an improper fraction?

An improper fraction is one in which the denominator is greater than or equal to the numerator. 5/2 and 8/5, for example, are incorrect fractions. Every fraction is made up of two parts: the numerator and the denominator. Proper fractions and improper fractions are the two main types of fractions in mathematics based on the numerator and denominator values.

For 76 number of players:

In 1/4 hour he can run 1/3 mile

In 1 hour he can run (1/3)/(1/4)mile

                                 =4/3 miles

Convert it into a mixed number:

                                = [tex]1\frac{1}{3}[/tex] miles per hour  

For 91 number of players:

In 3/4 hour he can run 5/6 mile

In 1 hour he can run (5/6)/(3/4)mile

                                 =10/9 miles

Convert it into a mixed number:

                                = [tex]1\frac{1}{9}[/tex] miles per hour

For 44 number of players:

In 1/2 hour he can run 3/4 mile

In 1 hour he can run (3/4)/(1/2)mile

                                 =6/4 miles

                                 =3/2 miles

Convert it into a mixed number:

                                = [tex]1\frac{1}{2}[/tex] miles per hour  

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In the  of 76th player's unit rate is 1 1/3 miles per hour , 91st player's unit rate is 1 1/9miles per hour and the 44th player's unit rate is 1 1/2miles per hour.

When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.

For a total of 76 players:

He can run 1/3 mile in 1/4 hour.

He can run (1/3)/(1/4) mile in 1 hour.

= 4/3 miles

Change it to a mixed number:

= 1 1/3 miles per second.

For a total of 91 players:

He can run 5/6 mile in 3/4 hour.

He can run (5/6)/(3/4) mile in an hour.

= 10/9 miles

Change it to a mixed number:

= 1 1/9 miles per hour.

For a total of 44 players:

He can run 3/4 mile in half an hour.

He can run (3/4)/(1/2) mile in 1 hour.

=6/4 miles

=3/2 miles

Change it to a mixed number:

= 1 1/2 miles per hour.

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Answer:

[tex] \frac{23}{3} ....in \: fraction \: or \\ 7.666666...in \: decimal[/tex]

Step-by-step explanation:

Greetings!!!

look at the image attached

Hope it helps!!!

Answer:

Outputs are-

f(-2) = 7

f(-1) = 5

f(0) = 3

f(3) = -3

Step-by-step explanation:

Given, f(x) = -2x+3

To find, 1) f(-2)

2) f(-1)

3) f(0)

4) f(3)

Solution,

1) Substituting x for -2,

f(-2) = -2 x -2 + 3 = 7

2) Substituting x for -1,

f(-1) = -2 x -1 + 3 = 5

3) Substituting x for 0,

f(0) = -2 x 0 + 3 = 3

4) Substituting x for 3,

f(3) = -2 x 3 + 3 = -3

The total cost of the fencing as a function of the length of the x side is 11x

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the total cost:

Total cost = (southern + east + west) * side

Total cost = (5 + 3 + 3)*x

Total cost = 11x

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A line can be represented in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Given that m = −72 and the y-intercept is 12, we can represent the line as y = −72x + 12

We are also given that the point (x, 5) lies on the line. So we can substitute the x and y values of the point into the equation of the line to find the value of x.

y = −72x + 12

5 = −72x + 12

-7 = -72x

x = 7/72

So the value of x is 7/72.

We can also get this by solving the equation of the line for x.

y = -72x + 12

y - 12 = -72x

(y - 12)/-72 = x

x = (y - 12)/-72

So for any point (x, y) on the line, the value of x can be obtained by substituting y and the slope-intercept form equation.

Answer: To get another turn, Sydney's score must be greater than 1. Therefore, to find the lowest number that Sydney can roll to get another turn, we need to find the smallest number that, when multiplied by the fraction on the card, will give a result greater than 1.

It's not mentioned which fraction card Sydney drew, so we can assume any fraction.

Let's assume the fraction card is labeled 1/4.

To get another turn, Sydney's score must be greater than 1. Therefore, we need to find the smallest number that, when multiplied by 1/4, will give a result greater than 1.

1/4 * x >1

x > 4

so the smallest number that Sydney can roll to get another turn is 5.

It should be noted that this is assuming that the fraction card is labeled 1/4 , if the fraction card is labeled with any other fraction the answer would be different.

Step-by-step explanation:

The linear combination method will be used to resolve a system of three equations in three variables.

Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal." The slope-intercept form, standard form, and point-slope form are the three primary formats for linear equations. A mathematical expression known as an equation has an equals sign. Many equations contain algebra. When you don't know the exact number to compute in math, algebra is used.

given

The linear combination method will be used to resolve a system of three equations in three variables.

This time, we will consider two equations at a time, eliminate one variable using the resulting equations in two variables, then solve for the third variable. with respect to this instance.

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A 4 polygon is a two-dimensional shape with four sides and four angles.

Polygon is a closed figure in a plane made up of straight lines or curved lines that intersect in pairs. A polygon has at least three sides and angles. The sides can be of any length and the angles can be of any measure. Polygons are classified according to the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), etc. Polygons are used in many fields, from mathematics to engineering.

It is a type of quadrilateral, which is a polygon with four sides. Examples of 4 polygons include squares, rectangles, rhombuses, and trapezoids. All 4 polygons have four sides of equal length, and all their interior angles add up to 360 degrees.

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Answer:

There are 14 pizza rolls and 2 mini hot dogs in the combination meal.

Step-by-step explanation:

From the question, we have the following parameters

Pizza roll = 55 calories each

Mini hotdog = 70 calories each

Combination meal = 910 calories in total

Let the pizza roll be x and the mini hotdog be y

So, we have

55x + 70y = 910

x = 12 + y

Make x the subject in x = 12 + y

x = 12 + y

Substitute x = 12 + y in 55x + 70y = 910

55(12 + y) + 70y = 910

Evaluate

660 + 55y + 70y = 910

So, we have

125y = 250

This gives

y = 2

Recall that

x = 12 + y

So, we have

x = 12 + 2

x = 14

Hence, there are 14 pizza rolls and 2 mini hot dogs

The value of the equation on x = 2 is 0.5

Given Quadratic equation,

[tex]= \frac{11}{12} x - \frac{5}{6}( x - \frac{2}{5})[/tex]

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

[tex]= \frac{11}{12} *2 - \frac{5}{6}( 2 - \frac{2}{5})[/tex]

[tex]= \frac{11}{6} - \frac{5}{6} * \frac{8}{5}[/tex]

[tex]= \frac{11}{6} - \frac{4}{3}[/tex]

[tex]= \frac{1}{2}[/tex]

= 0.5

Therefore, the value of the equation on x = 2 is 0.5

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Answer:

7

Step-by-step explanation:

7