how do you prove an angle is a right angle when the other 2 angles are complementary in a triangle theorem

The triangle created by the coordinate axes and the line with slope 3 has a 6 square unit area.

Given that the height (distance of the line from the origin) is 2 units, the area of the triangle is equal to

= (1/2)×(hypotenuse)×(height),

=6.66 square units.

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

n = a/b = change in b/change in a

where "n" represents a line's slope.

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The triangle formed by the coordinate axes and the line with slope 3 has a surface area of 4.44 square units.

As per data, we have,

Given a height of 2 units (distance of the line from the origin), the area of the triangle is equal to = (1/2)(hypotenuse) (height)

The solution is the same whether the line passes by the origin on the right or the left.

The sloping line will be the hypotenuse of a triangle whose other two sides are x or y-axis segments terminating at the origin.

The triangle's angles are 71.56 degrees (arctan3), 90 degrees, and 18.44 degrees.

The value of the length of the side opposite the tiny angle will be = 2/sin18.44 = 6.32 units

The hypotenuse length is 6.32/cos18.44 = 6.66.

The area of the triangle is calculated as (1/2)*(hypotenuse)*(height) = 4.44 square units.

The formula for the change in the y-coordinate with respect to the change in x-coordinate is: n = a/b = change in b/change in a

where "n" represents a line's slope.

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An equation to determine the radius of the hula hoop is diameter/2 and the  radius is 0.35.

The term called equation in math is known as a mathematical statement that is made up of two expressions connected by an equal sign.

Here we know that the Sandra measures the diameter of a hula hoop as 0. 7 m.

Here we need to write and solve an equation to determine the radius of the hula hoop.

As we all know that radius is defined as the distance from the center of the circle to any point on it's circumference.

And the term diameter is defined as a straight line passing through the center of a figure or body.

So, the diameter is calculated by using the formula,

=> d = 2r where r refers the radius.

Then the equation to calculate the radius is written as,

=> r = d/2

then the equivalent radius value is,

=> r = 0.7/2 = 0.35

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Some steps you might take after coming to a solution include all of the following:

A. Create a logical name for the variable.

E. Present your answer with units.

In Computer technology and Mathematics, a problem solving process can be defined as a systematic approach that is used typically for identifying and determining the optimal and effective solution to a particular problem.

Generally speaking, you must ensure that a logical name for the given variable is created after developing a solution to any mathematical or scientific problem.

In conclusion, the final answer (solution) must be presented with the correct and appropriate unit of measurement.

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The given system is :

a) Linear

b) Time-invariant

c) Casual

d) Impulse response function is h(n) = 2δ(n-1) + δ(n-2).

a) Linear: A system is considered linear if it satisfies the superposition principle, meaning that if the inputs x1(n) and x2(n) produce outputs y1(n) and y2(n), respectively, then the output of the system to a weighted sum of inputs is equal to the weighted sum of the outputs. In this system, 2x(n-1) and x(2n) are both linear operations, and the sum of two linear operations is also a linear operation. Therefore, this system is linear.

b) Time-invariant: A system is considered time-invariant if the output is not dependent on the current time, but only on the input and its previous values. In this system, the coefficients 2 and 1 do not change with time, and the system does not depend on the current time. Therefore, this system is time-invariant.

c) Causal: A system is considered causal if the output only depends on the present and past inputs, and not on future inputs. In this system, x(2n) only depends on the past and present inputs, and x(n-1) only depends on past inputs. Therefore, this system is causal.

d) Impulse response function: The impulse response function of the system can be found by taking the unit impulse as the input, solving for the output and normalizing it.

h(n) = 2δ(n-1) + δ(n-2)

where δ(n) is the unit impulse function and h(n) is the impulse response function of the system.

Correct Question :

y(n) = 2x(n-1) + x(2n). is the system linear or non-linear? you need to justify your answer. b) is the system time-varying or time-invariant? you need to justify your answer. c) is the system causal or not causal? you need to justify your answer. d) find the impulse response function of the system

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The entropy produced by the heat source is 2.17 J/K per hour.

In order to calculate the amount of entropy produced by a heat source, we need to use the formula for entropy change: ΔS = Q/T,

where Q is the amount of heat transferred and T is the temperature of the surroundings in kelvins.

To convert the temperature to Kelvin, we add 273.15 to the temperature in degrees Celsius.

In this case, the heat source generates 70.0 W of heat and the temperature of the surroundings is 28.5 °C.

So, to find the entropy change per hour, we need to multiply the power generated by the time:

ΔS = (70.0 W) * (3600 s/h) / (28.5+273.15)

This calculation results in approximately 2.17 J/K * h or 2.17 J/K per hour.

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The initial height of the ball is the y-intercept of the function. The initial height she threw the ball from was 35.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient, and 'c' is called the absolute term of f (x).

The function is as follows:

h(x) = -16x² + 3x + 35

Substitute the value of x = 0.

So, we have:

h(0) = -16(0)² + 3(0) + 35

Evaluate the exponent

h(0) = -16(0) + 3(0) + 35

Evaluate the products

h(0) = 0 + 0 + 35

Evaluate the sum

h(0) = 35

Hence, the initial height she threw the ball from was 35.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{9}{8}}x-9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{9}{8}} ~\hfill \stackrel{reciprocal}{\cfrac{8}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{8}{9} }}[/tex]

so we're really looking for the equation of a line whose slope is -8/9 and it passes through (-2 , 2)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{8}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{8}{9}}(x-\stackrel{x_1}{(-2)}) \implies y -2= -\cfrac{8}{9} (x +2) \\\\\\ y-2=-\cfrac{8}{9}x-\cfrac{16}{9}\implies y=-\cfrac{8}{9}x-\cfrac{16}{9}+2\implies {\Large \begin{array}{llll} y=-\cfrac{8}{9}x+\cfrac{2}{9} \end{array}}[/tex]

The correct statement is parameter because the value is a numerical measurement describing a characteristic of a population.

A parameter is a numeric value that describes a population feature in probability and statistics. It is a fixed value that is typically unknown and used to define or describe a probability distribution. The population's mean, variance, and standard deviation are a few examples of parameters.

Typically, these parameters are calculated using statistical techniques like maximum likelihood estimation from a sample of data. One can learn something about the entire population from a parameter. In the case of a given question, this implies that after asking everyone in that group, one will know something. All 1506 seniors at college were included in the survey and it was discovered that 65% of them own a television.

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The cor() returns the correlation between two variables.

Correlation shows us how strong the relationship is between two variables.

Hence, option (c) is the correct choice.

Correlation quantifies the intensity of a link between two variables and is symmetrical, meaning that the correlation between A and B is the same as the correlation between B and A.

Correlation is a statistical term that describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). It's a common way of explaining simple interactions without stating a cause and effect relationship.

In R, the cor() function is used to calculate the correlation coefficient between two vectors. Correlations may be generated using the cor() function, while covariances can be generated using the cov() function. The type of correlation is specified.

There are three options: Pearson, Spearman, and Kendall.

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The complete questions should be like:

A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?

A sd()

B mean()

C cor()

D bias()

The measure of the missing length in the figure, found using Pythagorean Theorem is; x = 37 mm

Pythagorean Theorem states the relationship between the lengths of the sides of a right triangle. According to Pythagorean Theorem, the sum of the squares of the leg lengths of a right triangle is equivalent to the square of the length of the hypotenuse side.

Please find attached a possible figure in the question, obtained from a similar question posted on the website.

The 13 mm side hypotenuse length of the right triangle on the left  indicates a other leg length of the right triangle can be found using Pythagorean Theorem as follows;

Square of the length of the hypotenuse side = Sum of the square of the length of the other two sides

13² = 5² + (second leg length)²

The second leg length of the right triangle on the left = √(13² - 5²) = 12

The 12 mm leg length of the right triangle on the left indicates that the leg length of the right triangle on the right which correspond with the 12 mm leg length on the left is 12 mm

The length of the hypotenuse of the right triangle on the right, which is the missing length, x is therefore;

x² = 12² + 35² = 1369

The measure of the missing length x is therefore;

x = √(1369) = 37

The missing length in the figure is; x = 37 mm

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Oliver runs a mile in 6 minutes. He runs 2 miles North and 3 miles east, so the total distance he ran is 2 + 3 = 5 miles.

Since he ran the same distance back to his house, the total distance he ran is 52 = 10 miles.

Since he runs a mile in 6 minutes, the total time of Oliver's run was 106 = 60 minutes.

Therefore, Oliver's total run time is 60 minutes.

Answer:

Step-by-step explanation:=2/11+10/5

                                            =10/55+110/55

                                            =120/55

                                            =24/11

Answer:

1/16 gallons per minute

Step-by-step explanation:

The water level drops from 8 gallons to 6 gallons in 32 minutes

The volume of water that has leaked is 8 - 6 = 2 gallons

Since this volume of water has leaked in 32 minutes, rate of leak

+ 2/32 = 1/16 gallons per minute

If David spends $10, he may call for 50 minutes.

As per the data given in the above question are as bellow,

Let x represent the duration of David's phone calls.

The following linear equation can be used to express the call's cost:

Price = x + (x - 3) (0.10)

By setting the equation's value to 10 and finding the value of x, we can determine how long David will talk on the phone if he spends $10:

10 = 0.25x + (x-3)(0.10) (0.10)

The right side of the equation is first made simpler:

10 = 0.25x + 0.10x - 0.30

Next, we may combine related words as follows: 10 = 0.35x - 0.30

10 plus 0.30 equals 0.35x when applied to both sides.

Consequently, x = 50. David talks on the phone for 50 minutes.

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There must be some reason why Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12: I bought just enough packets of each to have the same number of each therefore the number of items which were on the receipt is eleven (11).

This is referred to as an operation that represents the basic idea of repeated addition of the same number and will be used to get the same number of each in this scenario.

Since Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12, to get the same number of each will be to look for values which when multiplied will give the same number which are 6 and 5 respectively to give equal number of 60 each. therefore the number of items on the receipt will be 6+5 = 11.

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If one column of dots on the dot plot is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week.

A dot plot is a simple graphical representation of data where each data point is represented by a dot or mark above a number line. In this context, the dot plot shows the number of pizzas sold at a local restaurant each day for one week. The height of the column of dots represents the number of pizzas sold on that particular day.

If one column of dots is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week. This could be due to a variety of reasons such as a special promotion, a holiday, or just a generally busy day.

Understanding which days are the busiest for the restaurant can help the management make decisions such as staffing levels, inventory management, and marketing strategies. For example, if a particular day of the week is consistently the busiest, the restaurant may want to offer a special promotion or discount on that day to attract more customers.

In terms of percents, if for example, the restaurant sold 100 pizzas on the day with the tallest column of dots, and the next highest day sold 60 pizzas, the day with 100 pizzas would be 166.6% higher than the day with 60 pizzas. It indicates the significance of the difference between the two days in terms of sales.

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In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class.

Cumulative frequency is a running total of the frequencies of a data set. It is used to keep track of how many observations fall within a certain range of values. It is the sum of the frequencies of all the classes up to a certain point.

The second class is 1150-1219 which means it includes the price of refrigerators that fall within the range of $1150 and $1219. To find the cumulative frequency of the second class, you would need to count the number of prices in the data set that fall within that range and add it to the cumulative frequency of the previous class.

In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class. Since the cumulative frequency of the first class is not provided, we cannot calculate the cumulative frequency of the second class without more information.

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Answer:

The slope of the line is -2.

Step-by-step explanation:

Rise/Run

you have 2 points on the graph since this is a negative slope you start on the top point

you count straight down up to your next point and you should get 8.

then you count to the right to your next point and should get 4.

that would give you 8/4 as your slope.

8/4 simplified is 2.

The slope is 2

Answer: There are 114 red marbles contained in the bag containing 120 marbles.

Step-by-step explanation:

To find the amount of red marbles in the bag:

From the question, we can presume that for every 19 marbles in a bag, there exist a single black marble. This is the same case for the total number of marbles (both red and black) in each set is 20 marbles

Set of marbles: 120/20

Red marbles:

19r = 19 x 6

19r  = 114 red marbles.

I hope this helps!

The difference between their heights in feet and inches is 6'6.3"

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

Robert Wadlow was 8’11” tall.

Pingping was 2’4.7" tall

The difference in their heights can be calculated by subtracting the smaller height from the larger

So, we have

Difference = 8’11” - 2’4.7"

Evaluate the difference

Difference = 6'6.3"

Hence, the difference is 6'6.3"

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The scale factors of the shapes are 1.25, 1.25. 5 and 2, respectively

To do this, we divide the side length of the larger shape with the corresponding side of the small shape

using the above as a guide, we have the following scale factors calculations

figure 7 = 15/12 = 1.25

figure 8 = 25/20 = 1.25

figure 9 = 40/8 = 5

figure 10 = 10/5 = 2

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f(x) = 4800 * 1.5^x is the equation to model the relationship between the number of weeks, x, and the number of site visits.

It is said that the number of visits increased by a factor of 1.5 each week, which means it multiplied by 1.5 every week.

So the equation can be modeled as:

f(x) = 4800 * 1.5^x

Where x is the number of weeks and f(x) is the number of site visits.

Note that this equation is only valid for the number of weeks after the new marketing plan has been launched, since before that the number of visits was 4,800.

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Answer:

24

Step-by-step explanation:

12*8*5 =480 current surface

double = 960

so make the 12 into 24 height.

done

To go from slope intercept form of line to standard form Ax + By + C = 0, collect all terms on the left side of the equation and multiply by the denominator B.

We know that the standard form of equation of line is Ax + By + C = 0. And the slope intercept form of line is y = mx +b, where m is the slope of the line, and b is the y-intercept i.e., the value of y when x = 0.

Converting from slope intercept form to standard form:

⇒ y = mx + b

⇒ y - mx = (mx - mx) + b           .........(subtract mx from each side)

⇒ y - mx = b

⇒ y - mx - b = b -b                    .........(subtract b from each side)

⇒ y - mx - b = 0

⇒ - mx + y - b = 0

Above equation is of the form Ax + By + C = 0

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The two expressions that add to get a sum of - n + 6 are

A. (-6n) + (6 + 2n) and

B. (- 10n + 2) + (6n + 4)

Now, According to the question:

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

The expression is :

-4n + 6

Now the expression as

A. (-6n) + (6 + 2n)

After adding, we have;

(-6n) + (6 + 2n) = -6n + 6 + 2n

= - 4n + 6

B. (- 10n + 2) + (6n + 4)

After adding we have;

(- 10n + 2) + (6n + 4) = - 10n + 2 + 6n + 4

= - 4n + 6

Hence, The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)

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Answer: -1.9d + 5.4h - 13

Step-by-step explanation:

The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

According to the question,

91 pts nine percent of Americans have rh-negative o blood type.

In a random sample of 200 Americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% = ?

by Using central limit theorem,

P(p cap < p) = P(Z<p cap-p/√p(1-p)/n)

so,

P(p cap < 0.12) = P(Z<0.12-0.09/√(0.09×0.91/200)

= P(Z<1.4825)

= 0.9309 (from Z table)

= 0.93 (Rounded to second decimal place)

so, The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

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The equation of the parabola with the given vertex and y-intercept is:

y = -(x - 3)² + 3

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

Where (h, k) is the vertex of the parabola, and a is a nonzero constant. To find the equation of the parabola that satisfies the given conditions, we can use the vertex and the y-intercept to find the values of a, h, and k.

The vertex of the parabola is (3, 3), so h = 3 and k = 3. The y-intercept of the parabola is (0, -6), which means that when x = 0, y = -6. Substituting these values into the equation of the parabola, we get:

y = a(x - 3)² + 3

When x = 0, y = -6. Plugging in the value of x and y, we get

-6 = a(0 - 3)² + 3

-6 = 9a + 3

-9 = 9a

a = -1

Therefore, the equation of the parabola that satisfies the given conditions is:

y = -(x - 3)² + 3

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