-136 = 8(m - 1)
\( - 136 = 8(m - 1)\)
​

In answering the question above, the solution is If you know the lengths Pythagorean theorem of the other two sides of the right triangle, you may use these formulae to determine the length of the missing side.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

c = √\((a^2 + b^2)\)

You may rewrite the formula as follows to get the length of one of the other sides:

a = √\((c^2 - b^2)\)

b = √\((c^2 - a^2)\)

If you know the lengths of the other two sides of the right triangle, you may use these formulae to determine the length of the missing side.

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Answer:

12j^3-12j^2+48)

Step-by-step explanation:

Any coefficients with the same power/exponent get added together. (18k^2-6k^2=12k^2).

Mary will have to take a sample of 30 to 40 students to treat observations as independent.

According to the central limit theorem, one condition for performing a hypothesis test is that the observations are independent. Mary is going to take a sample from a population of 500 students.

According to the requirement of the central limit theorem, when performing a hypothesis test, the observations should be independent. In order to treat observations as independent, Mary will have to take a sample without replacement.

For a sample to be independent, each of the students in the population should have an equal chance of being selected. Since the total population of students is 500, Mary should pick any number of students that will represent the entire population.Usually, a sample size of about 30 to 40 students is enough to represent the entire population.

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It is uncertain whether the corresponding 98% CI (Confidence interval), using the same data will contain zero. It is Possible that the new 95% CI will not contain zero due to different data, or still contain zero depending on data and distribution.

It is not possible to determine with certainty whether the corresponding 98% confidence interval (CI) will contain the number zero without knowing the underlying distribution and the sample size. However, it is possible for the 98% CI to not contain the number zero, even if the 95% CI did contain the number zero.

This is because the 98% CI will be wider than the 95% CI, and therefore, it is possible for the range of values to exclude the number zero.

If new data is collected and a 95% CI is constructed using this data, it is possible that the interval will not contain the number zero, even if the previous 95% CI did contain the number zero. This is because the new data may provide a different estimate of the population mean, resulting in a different confidence interval.

However, it is also possible that the new 95% CI will still contain the number zero, depending on the new data and the underlying distribution.

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Answer:

Step-by-step explanation:true

Answer:

Step-by-step explanation:

if we have a right triangle, and isosceles

c^2=a^2+b^2 , in this case of isosceles, a=b

c^2=2a^2

1^2=\(\sqrt{2a^2}\)

1=a\(\sqrt{2}\)

a=1/\(\sqrt{2}\)=\(\sqrt{2}\)/2

Answer:

The dimensions of the right triangle are 9 meters by 7 meters.
or
The base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base).

Step-by-step explanation:

To find the dimensions of the right triangle, we can use the formula for the area of a triangle, which is:

A = 1/2 * b * h

Where b is the base and h is the height of the triangle. In this case, we know that the area of the triangle is 40 square meters, and the height is 2 meters less than the base, so we can write the equation as:

40 = 1/2 * b * (b - 2)

To solve for b, we can rearrange the equation to get b by itself:

40 = 1/2 * b^2 - b

Then, we can move all the terms involving b to the left-hand side of the equation and all the constants to the right-hand side:

1/2 * b^2 - b - 40 = 0

Next, we can use the quadratic formula to solve for b:

b = (-(-1) +/- sqrt((-1)^2 - 4 * (1/2) * -40)) / (2 * (1/2))

Which simplifies to:

b = (1 +/- sqrt(1 + 80)) / 1

Since b must be a positive number, we take the positive solution:

b = (1 + sqrt(81)) / 1

Therefore, the base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base). Thus, the dimensions of the right triangle are 9 meters by 7 meters.

Answer:

Correct option: second one -> 141.3 cm3

Step-by-step explanation:

To find the volume, we can calculate the volume of two separates parts (one half sphere and one cone) and then sum the volumes.

Volume of half sphere:

V1 = (2/3) * pi * r^3

The radius is 3 cm, so:

V1 = (2/3) * pi * 3^3 = 56.5 cm3

The volume of the cone is:

V2 = (1/3) * pi * r^2 * h

The radius is 3 cm and the height is 9 cm, so:

V2 = (1/3) * pi * 3^2 * 9 = 84.8 cm3

Then, the total volume is:

V = V1 + V2 = 56.5 + 84.8 = 141.3 cm3

Correct option: second one

Answer:

82(-x-5)=26

-82x-410=26

-410-26=82x

-436/82=x

x=-218/41

The 4th proportional of the given ratio is 4/3. option C

The range of the data 112, 121, 184, 189, 177, 190 is 78. option A

It follows from the concept of proportions that the ratios can be represented as follows;

21 : 7 = 4 : 3a + 1

21/7 = 4 / (3a + 1)

cross product

21 × (3a + 1) = 4 × 7

63a + 21 = 28

subtract 21 from both sides

63a = 28 - 21

63a = 7

a = 7/63

a = 1/9

So,

3a + 1

= 3(1/9) + 1

= 3/9 + 1

= 1/3 + 1

= 1 ⅓

= 4/3

21 : 7 = 4 : 4/3

Range of the data:

112, 121, 184, 189, 177, 190

Recall, the range of a dataset is the difference between the maximum and minimum data values and hence, we have;

Range = Highest data value - Lowest data value

= 190 - 112

= 78

Therefore, the range of the given set of data is 78.

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Answer:

y = 7/2x - 5/2 ; gradient is 7/2

y = 5/3x - 4/3 ; gradient is 5/3

y = -2/3x - 10/3; gradient is -2/3

Step-by-step explanation:

2y = 7x-5

5x - 3y=4

10 - 2x+3y = 0

NOTE: The gradient is the slope

The number of square kilometers of saltwater in scientific notation is \(3.619* 10^{8}\) square kilometers.

The number of square kilometers of saltwater can be written in scientific notation as:

\(3.619* 10^{8}\) square kilometers

In this representation, the coefficient 3.619 is between 1 and 10, and the exponent 8 represents the number of places the decimal point must be moved to the right to obtain the original number.

Scientific notation is a convenient way to represent very large or very small numbers in a compact and easily readable form. It is commonly used in fields such as physics, engineering, and mathematics.

In scientific notation, a number is represented as a coefficient multiplied by 10 raised to a power. The coefficient is a number between 1 and 10, and the power is an integer that represents the number of places the decimal point must be moved to obtain the original number.

For example, the number 361,900,000 can be written in scientific notation as \(3.619* 10^{8}\). The coefficient 3.619 is between 1 and 10, and the exponent 8 represents the number of places the decimal point must be moved to the right to obtain the original number.

In general, scientific notation makes it easier to perform arithmetic operations with large or small numbers, as well as to compare the magnitude of numbers with different orders of magnitude.

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Answer:

Okay, here are the GCF (Greatest Common Factor) and LCM (Lowest Common Multiple) for each pair of numbers:

   6,15 ________

   GCF = 3

   30,48 __________

   GCF = 30

   6 and 9 _________

   LCM = 18

   12 and 30 ____________

   LCM = 60

KEY:

240=i 3=g 18=d 30=e 20=t 60=l 6=a

#1 #2 #3 #4

Let me walk through the steps for each problem:

   To find the GCF of 6 and 15:

   Find all factors of 6: 1, 2, 3, 6

   Find all factors of 15: 1, 3, 5, 15

   The greatest common factor is 3.

   The GCF of 30 and 48 is 30.

   To find the LCM of 6 and 9:

   Find all factors of 6: 1, 2, 3, 6

   Find all factors of 9: 1, 3, 9

   The lowest common multiple that contains all factors is 18.

   The LCM of 12 and 30 is 60.

Does this help explain the steps and solutions? Let me know if you have any other questions! I can also show additional examples if needed.

Let me know if you understand the GCF and LCM concepts and are able to proceed to the key. I can explain that part in more detail.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of y is given in equation 2

Putting value of y = 3x in equation 1

Y = - x + 4

3x = - x + 4

Bringing like terms on one side

3x + x = 4

4x = 4

x = 4/4 = 1

Now putting value of x = 1 in equation 2

Y = 3x

Y = 3(1) = 3

9514 1404 393

Explanation:

You can use the addition property of equality to "move" a term from one side of the equation to the other. For example, if you want to move the cos²α term, you can add cos²α to both sides of the equation:

  sin²α -cos²α +cos²α = 2sin²α -1 +cos²α

When this is simplified, it becomes ...

  sin²α = 2sin²α +cos²α -1 . . . . . . the cos²α term is gone from the left

__

The equation you have is an identity. The left and right sides are equal for any value of α. When you have such an equation as a trig problem, you are often being asked to prove it is true. The way you do that is to make use of other trig identities to transform one side so that it matches the other side.

Here, you can use the trig identity ...

  sin²α +cos²α = 1

If you use this to substitute for 1 on the right, you have ...

  sin²α - cos²α = 2sin²α - (sin²α +cos²α)

Now, when you collect terms, you get ...

  sin²α - cos²α = 2sin²α - sin²α -cos²α . . . eliminate parentheses

  sin²α - cos²α = sin²α - cos²α . . . . . proof of your identity

Answer:

  (x -1)(12x +13)

Step-by-step explanation:

You are looking to rewrite the middle term as the sum of terms that have factors of (12)(-13) that have a total of +1. Those factors are -12 and +13, so the expression you are factoring by grouping is ...

  12x^2 +13x -12x -13

  = x(12x +13) -1(12x +13)

  = (x -1)(12x +13)

Answer:

We start at:

|X+6|- 12 < 13

Here we can add 12 to both sides:

|X+6| <13 + 12 = 25

|X+6| < 25

We can separate it in two equations:

if x > -6, then |X+6|  = x + 6

        (x + 6) < 25

         x < 25 - 6

          x <  19

if x < -6, then |X+6|  = -(x + 6)

         -(x + 6) < 25

          -x < 31

            x > -31

And with those two equations we get:

-31 < x < 19

The inequality Amber should graph is:

-31  <  x  <  19

The given inequality is:

|x  +  6| -  12  <  13

This can be simplified as:

|x  +  6|  <  12 +  13
|x  +  6|  <  25

This has two solutions:

x  +  6  <  25

x  <  25 - 6

x  <  19

Also:

x  + 6 > -25

x    > -25 - 6

x  > -31

Therefore, the inequality that Amber will graph is:

-31  <  x  <  19

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Answer:

y = x - 4

Step-by-step explanation:

Given:

Passes through (6, 2)

m = 1

Slope-intercept:

y - y1 = m(x - x1)

y - 2 = 1(x - 6)

y - 2 = x - 6

y = x - 4

Answer:

Yes

Step-by-step explanation:

Anything muliplied by zero end up equalling zero. So with this in mind we can put 0 in for x and find out what each eqautian equals.

2(0) + 6(0) = 0; Once we multiply both sides we end up adding 0 and 0, so it equals 0

9(0) = 0

Since, 0 = 0 they are both equal.

Hope this helps!

Let's see

#a

Take 28

#2

Take 9,10

Answer:

Two-digit number greater than 25:   32

Rewrite 32 as the difference of 2 numbers: 40 - 8

Therefore, x = 40  and  y = 8

\(\begin{aligned}\implies (40-8)^2 & =40^2-2(40)(8)+8^2\\ & = (4 \cdot 10)^2-(80)(8)+64\\ & = 4^2 \cdot 10^2-640+64\\ & = 16 \cdot 100-640+64\\ & = 1600-640+64\\ & = 960+64\\ & = 1024\end{aligned}\)

Let a = 10

Let b = 11

\(\begin{aligned}\implies 10^3+11^3 & =(10+11)(10^2-10 \cdot 11+11^2)\\& = 21(100-110+121)\\ & = 21(-10+121)\\ & = 21(111)\\& = 21 (100 + 10 + 1)\\ & = (21 \cdot 100)+(21 \cdot 10)+(21 \cdot 1)\\ & = 2100 +210+21\\ & = 2310 + 21\\ & = 2331\end{aligned}\)

ANSWER

x = 4; 5x + 1 = 21

EXPLANATION

First, we have to find the value of x using the given equation,

To do so, divide both sides by 2,

Now, with x = 4, replace it into the expression given to find its value,

Hence, the value of the expression is 21.

Answer:

x = 28

Step-by-step explanation:

4 + 2 ( x - 8) = 44

4 + 2x - 16 = 44

2x - 12 = 44

2x - 12 + 12 = 44 + 12

2x = 56

x = 28

Given the equation of a line as shown below :

To determine the slope and the y - intercept of the line, compare the equation with straight line equation

After comparing the equation of a line

Therefore slope = -3 and y - intercept = -2

Answer:

10

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

Since the triangles are similar, the ratio of the pair of each corresponding side must be the same as the ratios of other corresponding sides.

The work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

To calculate the work required to pump all the water over the edge of the tank, we need to consider the weight of the water in the tank and the height it is lifted.

First, let's find the volume of the water in the tank. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Plugging in the values, we have:

V = (1/3)π(3²)(12)

= (1/3)π(9)(12)

= 36π

Next, we need to find the weight of the water. The weight of an object is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity. The mass of the water can be found by multiplying its volume by the density of water, which is approximately 62.4 pounds per cubic foot:

m = (36π)(62.4)

≈ 22619.47 pounds

Now, we can calculate the work done by multiplying the weight of the water by the height it is lifted. In this case, the height is 12 feet:

W = (22619.47)(12)

≈ 271433.64 foot-pounds

Therefore, the work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

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The work required to pump water out of an inverted conical tank involves calculating the pressure-volume work at infinitesimally small volumes within the tank and integrating this over the entire volume of the tank. This provides an interesting application of integral calculus in Physics.

The question requires the concept of work in Physics applied to a fluid, in this case, water lying within an inverted conical tank. Work is done when force is applied over a distance, as stated by work = force x distance. In the fluid analogy, the 'force' link is the pressure exerted on the water and the distance is the change in volume of the fluid. Therefore, work done (W) = Pressure x Change in Volume (ΔV).

In this scenario, you are required to pump out water from an inverted conical tank, hence, the work you do is against the gravitational force pulling the water downwards. To calculate the total work done, you have to consider the work done at each infinitesimally small (hence, constant pressure) strip of volume and integrate over the entire volume of the tank.

The detail of calculation would require the knowledge of integral calculus and the formula for volume of a cone. I recommend considering this as an interesting application of integrals in Physics. Also remember that the volume of a cone = 1/3πr²h, where 'r' is the radius of base and 'h' is the height of cone.

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Matrix A that stratifies the condition is  \(\left[\begin{array}{cccc}1&-1&0\\3&1&2\\-1&2&-3\\-3&3&1\end{array}\right]\) .

To find matrix A such that the given set is col(A), we need to express the given set as a linear combination of the columns of A.

Let's consider the set {[r - s, 3r + s + 2t, -r + 2s - 3t, -3r + 3s + t] : r, s, t are real}.

We can rewrite each element of the set as follows:

[r - s, 3r + s + 2t, -r + 2s - 3t, -3r + 3s + t] = r[1, 3, -1, -3] + s[-1, 1, 2, 3] + t[0, 2, -3, 1]

Now, we can see that each element of the set can be expressed as a linear combination of the columns of the following matrix A:

A =\(\left[\begin{array}{cccc}1&-1&0\\3&1&2\\-1&2&-3\\-3&3&1\end{array}\right]\)

Therefore, matrix A = [1 -1 0; 3 1 2; -1 2 -3; -3 3 1] satisfies the condition, and the given set is col(A).

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The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral \(\( \int_{1}^{2} x \ln x \, dx \)\) is approximated using \(\( n = 4 \)\)subintervals. In part (b), the integral\(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) is given with incorrect limits, so it cannot be evaluated.

To approximate \(\( \int_{1}^{2} x \ln x \, dx \)\) using the Composite Trapezoidal rule, we divide the interval \(\([1, 2]\) into \( n = 4 \)\) subintervals. The step size, \(\( h \)\), is calculated as\(\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)\). Then, we evaluate the function \(\( x \ln x \)\)at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: \(\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\]\)

Using this formula, we can calculate the approximation for the given integral. The limits of the integral \(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) are given as \(\( 2 \)\) to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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D and F are functions on an appropriate domain. A, C, and D are functions that take in a real number and output a real number, so they are valid functions on the domain of real numbers.

A domain is a set of names or IP addresses that are associated with a particular website or web server. It is what allows users to access a website's content using a web browser. Domains are typically purchased from a domain registrar and can be used to host websites, email accounts, and other services.

B and F are invalid functions because they take in a real number and output something that is not a real number.

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Al-Fatihah is an Islamic prayer recited during the five daily prayers. Comparing radio and television in reading Al-Fatihah from its beginning requires an analysis of how each medium conveys the prayer to its audience. Radio precedes television in reading Al-Fatihah from its beginning.

This is because radio broadcasting began in the early 1900s while television broadcasting began in the late 1940s.

This delay can range from a few seconds to a few minutes depending on several factors such as the geographical location of the audience, the strength of the signal, and the quality of the receiver. Therefore, the time difference between radio and television in reading Al-Fatihah can vary depending on the factors mentioned above.

Mathematically, the time difference between radio and television can be calculated using the formula: d = s / tWhere d is the distance between the transmitter and the receiver, s is the speed of the signal, and t is the time it takes for the signal to reach the receiver.

In this case, d is the distance between the broadcasting station and the audience, s is the speed of the signal which is constant (i.e., the speed of light), and t is the time it takes for the signal to reach the audience. Since the speed of light is approximately 299,792,458 m/s, the time it takes for the signal to reach the audience can be calculated using the following formula:t = d / s

Therefore, the time difference between radio and television in reading Al-Fatihah can be calculated by subtracting the time it takes for the radio signal to reach its audience from the time it takes for the television signal to reach its audience. This difference can range from a few milliseconds to a few minutes depending on the factors mentioned above.

In network concepts, the time difference between radio and television in reading Al-Fatihah can be affected by the bandwidth of the network. The bandwidth is the amount of data that can be transmitted over a network in a given time. If the bandwidth is low, it can cause a delay in the transmission of the signal which can affect the time difference between radio and television.

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