Use the Pythagorean to find the missing side of this right triangle.​

To convert 1/5 to a decimal number by long division, we divide 1 by 5 and keep adding 0s to the dividend until we have enough decimal places and 1/5 as a decimal number is 0.2.

0.2 | 1.0000

   |-------

   | 0

   |----

     1

So, 1/5 as a decimal number is 0.2.

Part O:

If we keep repeating the division process in part N, we will get the same result of 0.2 because 1/5 has a finite decimal representation.

Part P:

From the three long-division calculations we have completed, we can conclude that the quotient, or result, from the long-division process can either end or continue indefinitely.

In part N, we found that 1/5 has a finite decimal representation, so the long division process ended.

However, for other fractions, such as 1/3, the long division process will continue indefinitely because the quotient has a repeating pattern of digits.

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Answer:

20cm

Step-by-step explanation:

90cm ÷ 1/2 the length 90 = 20cm

The quadratic equation 2x^2 - x + 10 = 0 can be solved using the quadratic formula, which is:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Here, a = 2, b = -1, and c = 10. Substituting these values, we get:

x = [-(-1) ± sqrt((-1)^2 - 4(2)(10))] / 2(2)

x = [1 ± sqrt(1 - 80)] / 4

x = [1 ± sqrt(-79)] / 4

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is "No solution".

Answer: find an alength times a weight

Step-by-step explanation:

What is the Area of a Rectangle?

a Definition: The area of the rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area. But in the case of a square, since all the sides are equal, therefore, the size of the court will be equal to the court of side length.

the

1. Find the length of the rectangle. In most cases, you will be given the length; if not, you can find it using a ruler.

Note that the double hash marks on the long sides of the rectangle mean that the lengths of the two sides are the same.

2. Find the width of the rectangle. Use the same methods to find it.

Note that the single hash marks on the wide sides of the rectangle mean that the two widths have equal lengths.

3. Write the length and width next to each other. In this example, the length is 5 cm and the width is 4 cm.

4. Multiply the length times the width. Your length is 5 cm and your width is 4 cm, so you should plug them into the equation A = L * W to find the area.

A = 4 cm * 5 cm

A = 20 cm^2

5. State your answer in square units. Your final answer is 20 cm^2, which means "twenty centimeters squared.

You can write your final answer in one of two ways: either 20 cm. sq. or 20 cm^2.

Binomial expansion of the given algebraic expression is:

729x⁶ − 1458x⁵y + 1215x⁴y² - 540x³y³ + 135x²y⁴ - 18xy⁵ + y⁶

The binomial theorem is one that states the principle for expanding the algebraic expression (x + y)ⁿ and expresses it as a sum of the terms involving individual exponents of variables x and y.

Thus, for example (x + y)³ will be expressed as:

1(x³)(y⁰) + 3(x²)(y¹) + 3(x¹)(y²) + 1(x⁰)(y³)

Similarly, for (3x - y)⁶, using pascals triangle, we have:

1(3x)⁶ + 6(3x)⁵(-y)¹ + 15(3x)⁴(-y)² + 20(3x)³(-y)³ + 15(3x)²(-y)⁴ + 6(3x)¹(-y)⁵ + 1(-y)⁶

= 729x⁶ − 1458x⁵y + 1215x⁴y² - 540x³y³ + 135x²y⁴ - 18xy⁵ + y⁶

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Answer:

82.8 in.

Step-by-step explanation:

Table B has inputs 6, 7, and 8, and each input has a unique output, so table B does represent a function.

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range) with the property that each input is related to exactly one output. Functions are used to model various real-world situations, from the growth of populations to the movement of celestial bodies. They play a central role in many areas of mathematics, including calculus, differential equations, and number theory. Functions are often represented using equations, graphs, and tables, and are studied in depth in the field of mathematical analysis.

Here,

A function is a relationship between an input set (usually called the domain) and an output set (usually called the range) such that for each input, there is exactly one output. To determine if a table represents a function, we need to check if each input has only one corresponding output.

Table A has inputs 1, 2, 3, and 4, but the output for input 2 is 9 and the output for input 3 is also 9. Therefore, table A does not represent a function.

Table B has inputs 6, 7, and 8, and each input has a unique output, so table B does represent a function.

Therefore, only table B represents a function, and the answer is "Only B".

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The area of the sidewalk of the circular flower bed is approximately 251.2 square meters.

All points on a plane that are equally spaced from a fixed point known as the center make up a circle, which is a geometric object. The diameter of a circle is the distance through its center; the radius is the distance from any point on the circle to that point. One of the many significant characteristics of circles is the constant ratio of circumference to diameter, indicated by the mathematical constant (pi).

Given, the diameter of the flower bed is 16m, thus:

radius = 16/2 = 8m.

Now,

Area of the flower bed = π(8m)^2 = 64π square meters

Area of the outer circle (sidewalk) = π(12m)^2 = 144π square meters

Area of the sidewalk = Area of the outer circle - Area of the flower bed

= 144π - 64π

= 80π square meters

≈ 251.2 square meters

Hence, the area of the sidewalk is approximately 251.2 square meters.

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Answer: geometric because it has a steady rate of multiplying by 4.5.

Step-by-step explanation:

The Practice Operations with radical expressions is simplified using the basic of the Algebra:

Algebraic expressions incorporating radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root might be an nth root, a square root, or a cube root. Radical expressions can be made simpler by taking them down to their most basic form and, if feasible, getting rid of all of the radicals.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. An algebraic expression's numerator and denominator are multiplied by the appropriate radical expression if the denominator contains a radical expression.

Practice Operations with radical expressions are:

1) [tex]\sqrt{540}[/tex] = [tex]\sqrt{36 * 15 }[/tex]

= 6√15

2) [tex]\sqrt[3]{432}[/tex] = [tex]\sqrt[3]{216*2}[/tex]

= [tex]6\sqrt[3]{2}[/tex]

3) [tex]\sqrt[3]{128}[/tex] = [tex]\sqrt[3]{64*2}[/tex]

= [tex]4\sqrt[3]{2}[/tex]

4) [tex]-\sqrt[4]{405}[/tex] = [tex]-\sqrt[4]{81*5}[/tex]

= [tex]-3\sqrt[4]{5}[/tex]

5) [tex]\sqrt[3]{-5000}[/tex] = [tex]-\sqrt[3]{1000*5}[/tex]

= [tex]-10\sqrt[3]{5}[/tex]

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The final answer is "2.2" < x  < 6.4 which is the pοssible length οf x.

The triangle inequality theοrem is a cοrnerstοne οf geοmetry and states that any triangle's sum οf its first twο sides is always greater than its third side. Fοr a triangle with sides a, b, and c, a + b > c, b + c > a, and a + c > b.

Accοrding tο the Triangle Inequality Theοrem, the length οf the third side must be greater than the sum οf the lengths οf the triangle's twο sides.

Therefοre, the pοssible length οf a triangle is equal tο the prοduct οf the sum οf the twο sides and the difference οf the twο sides.

Therefοre,

4.3 - 2.1 <  x < 4.3 + 2.1

2.2 < x < 6.4

Since "2.2" x 6.4 is a pοssible length fοr f x, that is the final answer.

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Complete Question:

What is the range of possible sizes for side xxx? < x <

Using graphs, the measure of the angle XYZ after the rotation on the coordinate plane about its origin is option E, 150°.

An ordered set of facts or values is shown visually in a graph, which is a diagram in mathematics. Often, the points on a graph serve as a representation of the relationships between two or more things.

An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. The numerical information gleaned via observation is referred to as data.

The Latin word Datum, which means "something delivered," is where the word data originated originates.

Following the formulation of a study question, data are continuously gathered through observation. The information is subsequently categorised, organised, and visually portrayed.

Here in the question,

When the given angle of 60° is rotated 90° on its origin:

The angle created = 60+90 = 150°

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The equation whigh relates x and y points along the incline is: y = 2x - 3

We know that the general form of a slope - intercept form of equation of line is :

y = mx + c

m = slope

and c = y-intercept

We know that slope is nothing but angle of incline.

From figure we can observe that the line passes through points (3, 3) and (6, 9)

Using the formula of slope,

m = (9 - 3) / (6 - 3)

m =  6/3

m = 2

So the equation of line would be

y = 2x + c

As line passes though point (3, 3),

3 = 2(3) + c

3 = 6 + c

c = - 3

So, the equation that relates x and y for points along the incline is:

y = 2x - 3

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The complete question is:

All three points displayed are on the line. you'll need to write an equation that relates x and y for points along the incline. what is this equation?

The answer is C. To Solve i just used desmos.

Step-by-step explanation:

Box volume = 2880  cm^3    <=====correct

Cylinder volume = pi * r^2 * h = 3.14 * (6^2) (20) = 2260.8 cm^3

                 (radius, r = 1/2 diameter = 6 cm)

Box can hold this much more:  2880 - 2260.8 = 619.2 cm^3

Keelin's hourly rate increased by 7.89%. To calculate the percentage increase in Keelin's hourly rate, we need to determine the difference between the new and old rates and express that difference as a percentage of the old rate.

First, we find the difference between the two rates:

$10.25 - $9.50 = $0.75

This means that Keelin's hourly rate increased by $0.75 per hour.

Next, we need to express this increase as a percentage of the old rate:

($0.75 / $9.50) x 100% = 7.89%

Therefore, Keelin's hourly rate increased by 7.89%.

A percent increase is a measure of the increase in a quantity compared to the original value. In this case, the original value is Keelin's hourly rate of $9.50, and the new value is $10.25. The percentage increase is calculated by finding the difference between the new and old values and expressing that difference as a percentage of the original value.

A percentage increase is useful in analyzing changes over time or comparing changes in different variables. In this case, knowing the percentage increase in Keelin's hourly rate can help her understand how much her pay has increased and plan for future financial goals. It can also be helpful for an employer to calculate percentage increases in employee salaries when determining raises or promotions.

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Answer: 40 degrees

Step-by-step explanation:

There are 9 sides in a nonagon and 360 degrees make the shape up.

360 degrees divided by  9 EQUAL SIDES of a nonagon = 40 degrees

The new weight of wrestler 1 is w_{(n+2)/2} = w_{(n+3)/2} - 1

The new weight of wrestler 2 is w_{(n+4)/2} = w_{(n+3)/2} + 2.

Let's suppose the weights of the wrestlers before the two new wrestlers joined the team are arranged in increasing order as follows:

w_1 ≤ w_2 ≤ w_3 ≤ ... ≤ w_n

where;

Since the mean weight remains unchanged, we have:

(w_1 + w_2 + w_3 + ... + w_n) / n = (w_1 + w_2 + w_3 + ... + w_n + x + y) / (n+2)

where x and y are the weights of the two new wrestlers.

Simplifying the above equation, we get:

2(w_1 + w_2 + w_3 + ... + w_n) = nw_1 + nw_2 + nw_3 + ... + nw_n + 2x + 2y

which can be further simplified as:

2(w_1 + w_2 + w_3 + ... + w_n) - 2nw_n = (n-2)w_1 + (n-2)w_2 + (n-2)w_3 + ... + (n-2)w_{n-1} + 2x + 2y

Since the median weight increases by 3 pounds, the new median weight is the weight of the (n+3)/2-th wrestler.

where;

We can express this in terms of the weights of the original wrestlers and the weights of the new wrestlers as follows:

If n+2 is even, then the new median weight is the average of the (n+2)/2-th and (n+4)/2-th weights.

If n+2 is odd, then the new median weight is the (n+3)/2-th weight.

In either case, we have:

w_{(n+2)/2} + w_{(n+4)/2} = 2(w_{(n+3)/2} - 3)

Substituting the weights of the original wrestlers and the new wrestlers using the equation we derived earlier, we get:

[(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2} + 2x + 2y] + [(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2}] = 2[(n+2)w_{(n+3)/2} - 6]

Simplifying and rearranging the terms, we get:

4w_{(n+3)/2} - 2w_{(n+2)/2} - 2w_{(n+4)/2} = x + y - 3

Substituting x + y = 2w_{(n+3)/2} - 3, we get:

w_{(n+4)/2} - w_{(n+2)/2} = 3 - w_{(n+3)/2}

Since the weights are arranged in increasing order, we have:

w_{(n+2)/2} ≤ w_{(n+3)/2} ≤ w_{(n+4)/2}

Therefore, the only possible solution is:

w_{(n+2)/2} = w_{(n+3)/2} - 1

w_{(n+4)/2} = w_{(n+3)/2} + 2

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Answer:

Step-by-step explanation:

Its 4.24 to the nearest hundredth because I input the square root of 18 in my caclulator.

Mr. Nelson took 35 students on the trip.

The equation that can be used to solve this problem is:

100 + 6.50n = 327.50

Where n is the number of students. To solve this equation, we need to subtract 100 from both sides of the equation:

6.50n = 227.50

Next, we need to divide both sides by 6.50:

n = 35

Therefore, Mr. Nelson took 35 students on the trip.

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The area of the square is increasing at a rate of 8 cm²/s when the area of the square is 16 cm².

When the side length of a square increases, the area of the square also increases. The formula for area of a square is side length multiplied by itself.

Therefore, when the side length of a square increases at a rate of 2 cm/s, the area of the square increases at a rate of 2 cm/s multiplied by 2 cm/s, or 4 cm²/s.

However, since the side length of the square is 16 cm when the area of the square is 16 cm², the rate at which the area of the square increases is 2 cm/s multiplied by 16 cm, or 8 cm²/s.

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The equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

To find the equation of the line passing through the two given points (–6, 1) and (6, –9) in slope-intercept form, we need to first find the slope of the line.

The slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]

Substituting the values of the given points, we get:

m = (-9 - 1) / (6 - (-6))

m = -10 / 12

m = -5 / 6

Now that we know the slope of the line, we can use the point-slope form of the equation of a line to find its slope-intercept form. The point-slope form of a line passing through a point [tex](x_1, y_1)[/tex] with slope m is given by:

[tex]y - y_1 = m(x - x_1)[/tex]

Substituting the values of the slope and one of the given points (–6, 1), we get:

y - 1 = (-5 / 6)(x - (-6))

y - 1 = (-5 / 6)(x + 6)

Simplifying this equation, we get:

y = (-5 / 6)x - 1/6

Therefore, the equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

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The answer of the given question based on Quadrilateral ABCD is inscribed in the circle on finding the measure of the angle ∠B is  70°.

A quadrilateral is a geometric shape that consists of four straight sides, connected end-to-end to form a closed figure. Examples of the quadrilaterals are rectangles, squares, parallelograms, trapezoids, and rhombuses. In a quadrilateral, the interior angles add up to 360° degrees. Quadrilaterals can have opposite sides parallel (as in parallelograms) or opposite sides equal in length (as in kites). They are widely used in geometry and mathematics in general.

In a circle, the opposite angles of a quadrilateral inscribed in the circle are supplementary. Therefore, we have:

m∠B + m∠D = 180°

We are given that B = (4x - 20)°, so we can substitute this into the equation above and solve for x:

m∠B + m∠D = 180°

(4x - 20)° + 115° = 180° (Note that m∠D is given as 115° in the diagram)

4x - 20 + 115 = 180

4x + 95 = 180

4x = 85

x = 21.25

Now that we know x, we can find the measure of angle ∠B:

m∠B = 4x - 20°

m∠B = 4(21.25) - 20°

m∠B = 70°

Therefore, the measure of angle ∠B is 70°.

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Answer:

(x,y) = (-5,-8)

Answer:

Step-by-step explanation:3x+7=x-3. 3x-x=-3-7. 2x=-10. X=-5. but y=x-3. So. Y=-5-3=-8

Thus, the angle of depression from the plane to the building is found as:

Ф = 27.90°.

The angle of depression is indeed the angle formed by a line drawn from the observer's line of sight down to an object below it.

It is frequently used in navigating, surveying, and trigonometry to describe its position of an object in relation to an observer's point of view. Degrees are used to express the depression's angle.

Give data:

Let the height  h = 420 ft.

Let the distance x = 896 ft.

angle of depression is found using the trigonometric formula:

tan Ф = height/distance

tan Ф = h/x

tan Ф = 420/896

tan Ф = 0.46875

Ф = tan⁻¹(0.46875)

Ф = 27.90°.

Thus, the angle of depression from the plane to the building is found as:

Ф = 27.90°.

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a) The residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

b) the equation y = 2x + 3 may not be a good fit for the given data.

What is the linear equation?

A linear equation is an equation that describes a straight line in a two-dimensional space. It is a mathematical expression that relates two variables, usually x and y, such that one variable is a function of the other. The general form of a linear equation is:

y = mx + b

a. To calculate the residuals, we need to find the predicted values of y using the given equation and then subtract them from the actual values of y.

For x = 1, y = 2(1) + 3 = 5, residual = 5 - 5 = 0

For x = 2, y = 2(2) + 3 = 7, residual = 8 - 7 = 1

For x = 3, y = 2(3) + 3 = 9, residual = 4 - 9 = -5

For x = 4, y = 2(4) + 3 = 11, residual = 5 - 11 = -6

For x = 5, y = 2(5) + 3 = 13, residual = 6 - 13 = -7

For x = 6, y = 2(6) + 3 = 15, residual = 16 - 15 = 1

For x = 10, y = 2(10) + 3 = 23, residual = 11 - 23 = -12

So, the residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

We can plot these points (x, residual) on a scatter plot.

b. The points on the scatter plot show a random pattern, which suggests that the model may not be a good fit.

The negative residuals for x = 3, 4, and 5 indicate that the actual values of y are lower than the predicted values, while the large negative residual for x = 10 indicates a much larger error.

Additionally, the residual for x = 6 is positive, which means the actual value of y is higher than the predicted value.

Therefore, the model may not be a good fit for the given data.

The points (1, 0), (2, 1), (3, -5), (4, -6), (5, -7), (6, 1), and (10, -12) show a random pattern on the scatter plot, which suggests that the model may not be a good fit.

Thus, the equation y = 2x + 3 may not be a good fit for the given data.

Hence, a) the residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

b) the equation y = 2x + 3 may not be a good fit for the given data.

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Answer and explanation:

Background info:

y = mx + b, where,

 If we look at the y-values in the table, we see that 4 ounces is added each time (16 + 4 = 20 + 4 = 24...).  Similarly, if we look at the x-values in the table, we see that 0.5 hours is added each time (0 + 0.5 = 0.5 + 0.5 = 1 ...).

Therefore, since the change in y is 4 (oz) and the change in x is 0.5 (hr), we divide 4 by 0.5 to find the slope:

4 / 0.5 = 8 = m

As we can see on the table, when x is 0, y = 16.  Thus, 16 is our y-intercept.

Thus, the general equation for the table is y = 8x + 16

Interpreting the slope and y-intercept:  When we consider our units, slope in context of this problem is change in ounces / change in hours.  We can think of 8 as the fraction 8 over 1.  

The measure of angle B is 24 degrees. We can calculate it in the following manner.

When two angles lie along a straight line, they form a straight angle which measures 180 degrees. Let's call the measure of angle B as x, then the measure of angle A can be expressed in terms of x as:

m∠A = 5(x + 7.2)

We can now use the fact that the sum of the measures of angles A and B is equal to 180 degrees, and substitute the expression for m∠A to get:

m∠A + m∠B = 180

5(x + 7.2) + x = 180

Simplifying the equation:

6x + 36 = 180

Subtracting 36 from both sides:

6x = 144

Dividing both sides by 6:

x = 24

Therefore, the measure of angle B is 24 degrees.

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Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, what is m∠B?

For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?

An equation that can be used to find the lightest and heaviest acceptable weights, x, for the filled canister include the following: B. |x − 42| = 0.9.

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by the following mathematical equation:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Based on the information provided about the desired weight of the canister and the popcorn, an equation that models the situation is given by;

|x − 42| = 0.9.

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