HELP QUICK!! Which set of side measurements could be used to form a right triangle?

Answer:

????

Step-by-step explanation:

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Step-by-step explanation:

The given equation is :

2x = 10

We need to find the value of x.

This equation has one solution as it is a linear equation having one variable i.e. x.

Dividing both sides by 2,

x = 5

So, the value of x is equal to 5.

Put x = 5. So,

2(5) = 10

10 = 10

Hence, this is the required solution.

when model building using the build-down method, you want to start with the complete 2nd-order model and build down to the most data model.

when working on a workbook which requires a team of people to work with you on the workbook, it is important you create transparency and also ensure you complete the workbook on time.

one very important way to complete the task on time is to share the workbook with your team so that they can input their own contributions towards the task, this practice ensures speedy completion of the task. and reduces the level of errors which might have occurred if you where working on it alone.

granting access to the workbook is a very good way to create trust and transparency.

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The key phase that we see in our response is "Divide the numerator by the denominator" (option C).

A key phrase refers to a phrase that contains words that define the most important part of a text. A key phrase serves as a summary of a paragraph or larger text.

In this case, the key phrase would serve to establish what was the mathematical procedure that we carried out to solve a mathematical problem. According to the above, it can be inferred that the key phrase must contain the most precise information to describe this procedure.

Based on the above, the correct answer is "Divide the numerator by the denominator" because it exactly describes the procedure that was performed.

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Answer:

$568.75.

Step-by-step explanation:

When \(n=0\), we have

\(5^{3^0} + 1 = 5^1 + 1 = 6\)

\(3^{0 + 1} = 3^1 = 3\)

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for \(n=k\), that

\(3^{k + 1} \mid 5^{3^k} + 1\)

Now for \(n=k+1\), we have

\(5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)\)

so we know the left side is at least divisible by \(3^{k+1}\) by our assumption.

It remains to show that

\(3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1\)

which is easily done with Fermat's little theorem. It says

\(a^p \equiv a \pmod p\)

where \(p\) is prime and \(a\) is any integer. Then for any positive integer \(x\),

\(5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3\)

Furthermore,

\(5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3\)

which goes all the way down to

\(5^{3^k} \equiv 5 \pmod 3\)

So, we find that

\(\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3\)

QED

1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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Answer:

C. 93 cars

Step-by-step explanation:

57 cars + 36 cars = 93 cars

Answer:

y=2

Step-by-step explanation:

A horizontal line can be represented as y = a number.

Therefore D. y=2 is a horizontal line.

The composite function for this problem is given as follows:

16.

The composite function of g(x) and f(x) is defined by the function presented as follows:

(g ∘ f)(x) = g(f(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is given as follows:

(g ∘ f)(x) = g(f(x)) = g(4) = 5(4) - 4 = 20 - 4 = 16.

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Answer:

3,098

Step-by-step explanation:

when you do the ,ath you will get it

Answer:

Surface Area = (2 • π • r²) + (2 • π • r • height)

Surface Area = 2 * 3.14 * 3*3 + 2 * 3.14 * 3 * 15

Surface Area = 56.52 +  282.60

Surface Area = 339.12

Formulas: http://www.1728.org/diamform.htm

Step-by-step explanation:

Using the given ratio, we will see that the width of the television is 24 inches.

We know that the length-to-width ratio is 4 to 3, then if the length of the television is L, the width will be:

W = (3/4)*L

In this case, we know that the length is 32 inches, so we can write:

L = 32in

Using the width equation we will get:

W = (3/4)*32 in = 24 in

So the correct option is the second one.

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Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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The Angle-side-angle postulate states that:

if two angles of a triangle and the side between them are congruent to two angles of another triangle and the side between them, then the two triangles are congruent.

In the image, there are indications that the triangles have two congruent angles and the respective sides between each pair of angles are also congruent.

Therefore, the triangles are congruent by the postulate Angle-side-angle, or just ASA.

Thus, option c is correct.

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time

Answer:

20 mins

Step-by-step explanation:

Answer:

18 minutes

Step-by-step explanation:

At the end of the 18th minutes, machine A would have completed 2 flagpoles and machine B will have completed 3 flagpoles. They both start producing another flagpole in the 19th minute

There are 2 correct statements- "The function is positive for all real values of x where x > 0" and "The function is negative for all real values of x where x < –3 or x > –1".

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Four main categories may be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

Here,

"The function is positive for all real values of x where x > 0" and "The function is negative for all real values of x where x -3 or x > -1" are both valid statements.

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Tape diagrams are models that used to represent ratios using rectangles

The area on the second tape diagram is 750 square cm.

From the tape diagram, we have the following area ratio

Ratio = 2cm : 3cm

revised we have

First: Second = 2cm : 3cm

When the area on the first tape is 500 cm², the ratio becomes

500cm : Second = 2cm x 250: 3cm x 250

This given us

500cm : Second = 500cm : 750cm

By comparison, we have
Second = 750cm²

This means that the area on the second tape diagram is 750cm²

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Answer:

20

Step-by-step explanation:

Answer:

XER (X are all real numbers)

Step-by-step explanation:

as;dbdjkdbusaj hfsvd

After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Answer:

sin = \(\frac{16}{20}\)

Step-by-step explanation:

given

cos = \(\frac{12}{20}\) = \(\frac{adjacent}{hypotenuse}\)

this is a right triangle with hypotenuse = 20 and adjacent = 12

using Pythagoras' identity to find the side opposite (opp ) , then

opp² + 12² = 20²

opp² + 144 = 400 ( subtract 144 from both sides )

opp² = 256 ( take square root of both sides )

opp = \(\sqrt{256}\) = 16

then

sin = \(\frac{opposite}{hypotenuse}\) = \(\frac{16}{20}\)

Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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