How is a complex number expressed?.

When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be [tex]\sqrt{2164}[/tex] .

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

Since we have a right-angled triangle, we can use the Pythagorean Theorem to find our answer. The Pythagorean Theorem states the following:

[tex]a^{2} +b^{2} =c^{2}[/tex]

In this formula a and b represent the legs of the triangle and c represents the length of the hypotenuse.

Let's substitute our data from the question.

[tex]42^{2} +20^{2} =c^{2}[/tex]

Square.

1764 + 400 = [tex]c^{2}[/tex]

And finally take the root of both sides. We only need to use the positive solution, since the length of the hypotenuse can't be negative.

[tex]c = \sqrt{2164}[/tex]

When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be [tex]\sqrt{2164}[/tex] .

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Answer: 53

Step-by-step explanation:

The length and width of the garden represent the legs of a right triangle, and the diagonal path represents the hypotenuse.

The Pythagorean Theorem states that a squared plus b squared equals c squared, where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.

Let p equal the length of the diagonal path in yards.

Applying the Pythagorean Theorem gives us p squared equals forty-five squared plus twenty-eight squared.

Now square forty-five and twenty-eight to get p squared equals two thousand twenty-five plus seven hundred eighty-four.

Next, find the sum of two thousand twenty-five and seven hundred eighty-four, which is two thousand eight hundred nine.

Finally, calculate the square root of two thousand eight hundred nine to find that p equals fifty-three.

So the length of the diagonal path is fifty-three yards.

The time to complete one swing or period is 16.4 seconds and the length is 3.3 meters

From the question, we have the following parameters that can be used in our computation:

L = 67 meters and g = 9.81 m/s²

The time, t, in seconds, that it takes for one swing or period of the pendulum can be modeled by the equation:

t = 2π(√(L/g))

Substitute the known values in the above equation, so, we have the following representation

t = 2π(√(67/9.81))

Evaluate

t = 16.4 seconds (approx)

Here, we use the same equation and solve for L

In this case, t = 9.6

t = 2π(√(L/g))

substitute the known values in the above equation, so, we have the following representation

9.6 = 2π(√(L/9.81))

So, we have

L = (9.6/(2π))² * 9.81

Evaluate

L = 3.3 meters (approx)

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The distance between points B and C is 10.3 miles.

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional figures. Trigonometry is made up of trigonometric functions (also known as circular functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

If we have a triangle with a right angle,

Then, tan = Opposite/Adjacent side

To find the distance,

In the ABC right angle triangle,

5.7 miles on the adjacent side = AB

θ = 61°

We must locate the BC.

tan = Opposite/Adjacent side

tan61°= BC/5.7

BC = 5.7×tan61°

BC = 10.283 = 10.3 (to the nearest tenth).

The figure is attached below.

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Answer:

f = 21

Step-by-step explanation:

since the rectangles are scaled copies then the ratios of corresponding sides are in proportion, scaled copy to original, so

[tex]\frac{f}{28}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )

12f = 28 × 9 = 252 ( divide both sides by 12 )

f = 21

Answer: 33

Step-by-step explanation:

66 - 33

Answer:

x is 33...........................

Step-by-step explanation:

33 +x =66

66-33=x

The locations (0, 17) and are traversed by an exponential function of the type y = abx, where a and b are constants (2, 153). We can utilise these points to solve for the values of a and b in order to determine the equation of the exponential function.

Since we now know that y = abx when x = 0, we can change the first point to read as follows:

17 = a(b^0)

We can simplify this to: since anything raised to the power of 0 is 1,

17 = a

We can now determine b using the second point (2, 153):

153 = ab^2

By applying the formula:

153/a = b^2

taking square root

b = sqrt(153/a)

Substitute a = 17

b = sqrt(153/17)

The equation will now look like this when we add the value of a back in:

y = a * b^x

y = 17 * sqrt(153/17)^x

y = 17 * sqrt(9)^x

Consequently ,y = 17 * 3^x, is the exponential function that passes between the positions (0, 17) and (2, 153).

Therefore , the exponential function is y = 17 * 3^x .

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Answer: x=56 you can just look it up on

Answer:

[tex]x=56[/tex]

Step-by-step explanation:

[tex]\frac{x}{4}+11=25\\\\[/tex]

Mutiply by 4 every each number you see.

[tex]x+44=100[/tex]

Subtract -44 in both sides.

[tex]x+44-44=100-44[/tex]

So,

[tex]x=56[/tex]

Hope this helps :D

The equation g(x) by translating the following function 4 units to the right would be g(x) = (x+4)² - 3(x+4) - 10.

What is a function?

A function is a mathematical relationship between a set of inputs and a set of outputs. More formally, a function is a rule that assigns to each input exactly one output. In mathematical notation, a function is typically represented by an equation of form f(x) = y, where x is the input and y is the output. The symbol f(x) is called the function notation, and x is called the independent variable, and y is called the dependent variable.

To translate a function 4 units to the right, we can add 4 to the input variable (x) inside the function. Therefore, the equation for g(x) would be:

g(x) = (x+4)^2 - 3(x+4) - 10

Hence, the equation g(x) by translating the following function 4 units to the right would be g(x) = (x+4)² - 3(x+4) - 10.

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The equation of the parabola with vertex (-1,-3) and the origin as zero point is given by y = (x + 1)2 - 3.

An equation is a mathematical statement that expresses two expressions as being equal. It consists of two expressions, one on either side of an "equals" sign, and indicates that the expressions have the same value. For example, the equation "2 + 2 = 4" states that the value of the expression "2 + 2" is equal to the value of the expression "4".

This equation can be derived by transforming the standard form of a parabola, which is y = ax2 + bx + c, into a form where the vertex of the parabola lies at the origin of the coordinate system. The standard form of the equation can be written as y = (x - (-1))2 -3. When the terms inside the parentheses are multiplied out, the equation becomes y = (x + 1)2 – 3.

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The system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions when the coefficients of x and y are the same ratio on both equations,

2x + 3y = 4

6x + 27y = 12

For the system of equations to have infinite solutions, the ratio of the coefficients of x and y must be the same. In this case, the ratio of the coefficients of x is 2/6 = 1/3 and the ratio of the coefficients of y is 3/27 = 1/9. Since the ratio of the coefficients is not the same, the system of equations does not have infinite solutions.

Hence, the value of k for which the system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions is not exist.

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The sum of frequencies for all classes will always equal to the number of element in a data set. Between 0-100 there will be 100 numbers.

So that it's 100 and correct option is b

What is frequencies ?

A frequency is a measurement of how frequently a certain value, occurrence, or feature takes place. It is employed in a wide range of disciplines, including science, engineering, mathematics, and statistics. Frequency is often expressed as a number, percentage, or ratio. For example, a frequency chart might show the number of times a particular product was purchased over a certain time period. Frequency can also refer to the number of times a particular wave pattern occurs in a given time period. In physics and engineering, frequency is used to measure the number of cycles per second of a wave or periodic phenomenon. For example, a wave with a frequency of 440 hertz (Hz) has 440 complete cycles per second.

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A commutative property in math is

Commutativity says that the numbers we are dealing with can be shifted or swapped without affecting the answer. This property applies to addition and multiplication, but not to subtraction and division.

a + b = b + a; where a and b are

integers. Example: 3 + 4 = 4 + 3 = 7.

a × b = b × a; where a and b are

non-zero integers. Example :

2×3 = 3×2 = 6

So this rule simply states that you can change the order of numbers in a question by adding or multiplying them without affecting the answer.

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By setting one side of a quadratic equation to zero, factoring the resulting polynomial, and then using the Zero Product Property, you can obtain the solutions, or roots, of these equations.

According to the Principle of Zero Products, if ab = 0, then either an or b, or both a and b, are 0, or both are 0. The roots of a function (f (x) can be any function) are the answers to y = f (x) when y = 0. These are the locations where an equation's graph crosses the x-axis.

To use factoring to solve a quadratic equation:

1. Convert the equation to standard form with a zero on one side.

2. Factor the non-zero side.

3. Reset each component to zero.

4. Solve each of the ensuing equations.

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The modal  number of the pairs of shoes owned by the children is 3 pairs of shoes.

In mathematics, the modal number or mode, is the number that appears on the data set the most times out of all the numbers that appear on a set of numbers or data.

In the case of this line graph on the number of pairs of shoes that children own, the modal number would be 3 pairs of shoes as this is the highest number according to the fact that 5 students own 3 pairs of shows.

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The question is:

What is the modal number of pairs of shoes owned by the children?

Answer:

C) 12%

Step-by-step explanation:

Answer: The answer is B.

Step-by-step explanation:

Add all of the students who chose English together and u get 24 and 12 is 50% of 24

Answer:

Step-by-step explanation:

42 : x = 12 : 14

x = 42 x 14 : 12

x = 49

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

Gross profit is the profit that a business makes after the manufacturing and selling costs are subtracted from the total sales.

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The solutions to the equation are x = 2.61 and x = -0.61

To solve the quadratic equation 3x² - 16x + 6 = 0, we'll use the quadratic formula:

x = (-b ± √(b²-4ac)) / 2a

Where a = 3, b = -16 and c = 6.

x = (-(-16) ± √((-16)²-4(3)(6)))/2(3)

x = 16 ± √(256-72) / 6

x = 16 ± √(184) / 6

x = 16 ± √184 / 6

x = (16 ± 4√23) / 6

So the solutions are:

x = (16 + 4√23) / 6 ≈ 2. 61 or x = (16 - 4√23) / 6 ≈ -0.61

Therefore, the solutions to the equation are x = 2.61 and x = -0.61.

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When we say "0" or "infinity," what we're really saying is that the number has no end.

The original value of zero corresponds to the logarithm, and the original value of infinity to the logarithm +. We consider the initial values 0 and infinity similarly when we treat both of the conceivable values and + as a single infinity. Georg Cantor, a mathematician, developed the concept of infinity into The Absolute Infinite. You can think of it as a number that is greater than any other possible or inconceivable amount, whether it be transfinite or finite. Infinity is the unfathomable end of the number line, according to mathematics. No actual number is bigger than infinity since it cannot be believed to exist beyond it.

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Answer:

The number is 6

Step-by-step explanation:

"Think of a number,"    [I'm thinking of x]

"double the number"    [OK, that would be 2x]

"and add 6 "                    [If you insist:  2x + 6]   ["The Answer"]

"The answer is 3 times the number"  [Answer = 3x]

We take the answer, 2x+6 and set it equal to 3x

         2x+6 = 3x

Answer: $9.50 per hour

Hope this helps :)

Step-by-step explanation:

Find the rate of change

76/8 = 9.5

8.50 cents per hour because 8.50 x 9 is close to 76

Answer:

28.8 days

Step-by-step explanation:

If. 15 scout = 24 days

than. 18 scout = ?

= 18/15 × 24 days

= 432/15

= 28.8 days.

If 15 scout can sell all their troops cookie's in 24 days than 18 scout too will sell cookies in 28.8 days.

To be a function, each x-value (or input) can only be used once.  Each x-value (or input) can only be paired with a single y-value (or output).

If any x-value (or input) is paired with more than one y-value (or output), it's not a function.

Top Left:

Not a function

"rock" and "leaf" are paired with two outputs.

Top Right:

Not a function

The one input goes to three outputs.

Bottom Left:

Function

Each x-value/input is used only once.

Bottom Right:

Not a function

The x-value of 4 is used twice and paired with two different y-values.

Answer:

42 feet

Step-by-step explanation:

Since they are similar, that means the rectangles are reduced copies of each other. So, to find the length, you have to do 60/(40/28), to get the length of the pool. 40/28 is the ratio. 60/(40/28) = 42, so the answer is 42 feet.

Answer: 42 feet

Step-by-step explanation:

Width of pool to patio = 28 : 40

28 : 40 = 7 : 10

Multiply both sides by 6:

42 : 60, so the length of the pool is 42 feet

At a local print shop, 20 copies can be made for $8. At this rate,  it would cost $30 to make 75 copies.

What is the equivalent ratio?

Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.

To solve this problem, we can set up a ratio between the number of copies and the cost:

20 copies / $8 = 75 copies / x

We can cross-multiply to find the value of x:

20 copies * x = 75 copies * $8

20x = 600

x = 30

Therefore, it would cost $30 to make 75 copies.

Here's the completed table of equivalent ratios:

Number of copies                        Cost

           20                                 $8

           75                                   x

We know that these ratios are equivalent, so we can set up a proportion:

20/8 = 75/x

Then we cross-multiply:

20x = 75 * 8

20x = 600

And solve for x:

x = 600/20

x = 30

Therefore, it would cost $30 to make 75 copies.

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The height of Tree A t years after being planted can be represented by the equation:

A = 30 + 2t

This equation states that the initial height of the tree (30 inches) plus the annual growth of the tree (2 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.

The height of Tree B t years after being planted can be represented by the equation:

B = 15 + 5t

This equation states that the initial height of the tree (15 inches) plus the annual growth of the tree (5 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.

To determine which tree is taller after 6 years, we can substitute t = 6 into each equation and compare the results:

A = 30 + 2(6) = 30 + 12 = 42 inches

B = 15 + 5(6) = 15 + 30 = 45 inches

Tree B is taller than Tree A after 6 years because 45 inches is greater than 42 inches.

Yes, 64 a cube number.

64 is the cube of 4.

As, 4 x 4 x 4 = 64

The cubes are made up of values that are obtained by multiplying integers by themselves three or four times. The cube's original number can be found by raising any natural number to the power of three.

Cubes are the numbers that are produced when an integer is multiplied by itself three times. We can find cubes for any number, whether it be an integer or a fraction. In order for the cube of a whole number (x) to produce a perfect cube, the cube root of x3 must equal x. The procedure of locating cubes is thus the opposite of locating the cube root.

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Answer:  x = 13, and the angle measures are 131, 49, 131, 49.

Step-by-step explanation:

7x + 40 = 10x + 1

40 = 3x + 1

39 = 3x

x = 13

The obtuse angle is 131, and the acute one is 49.

The equivalent expression of the given value is sqrt 9x/5. Option D

We have to note that when we are dealing with this expression, we have to bear in mind one of the rules of surd that states that; √P/√Q = √P/Q. This is the rule of surd that would guide our operation here.

We have that;

√9x^2/√5x

This would be the same as;

√9x^2/5x

According to the rule above, we now have;

√9x/5

Thus, by the use of the laws of surd we would have the expression √9x/5 as shown in the solution above.

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