What is the value of the expression below? 34 - 9 x 2

Step-by-step explanation:

{(2 1/5) + (1 5/6)} /30

Step 1.

Convert all the entities in the numerator from a mixed fraction to an unmixed fraction. By so doing, we will have;

{(11/5) + 31/6)}/30

Step 2

Now, let us add the numerator together. To do this, we have to find the Least Common Factor (LCM) for the two entities on the numerator. To achieve that, we will have;

(5×6) = 30

Now, we can proceed with further extrapolation.

{(30/5) × 11} + {(30/6) ×31}

(6 × 11) + (5× 31)

66 + 155

= 221

Now, 221 is the numerator, and 30 is our denominator, putting both together becomes;

221/30.

So the answer to the question is 221/30.

The equation of a line perpendicular to y=2x-5 that passes through the point (2,-5) is y = -1/2x - 4.

The point slope form is given as y - y1 = m(x - x1). When a line's slope and a point on the line are known, the equation may be used to get the equation of the line. Just enter the specified point and slope into the equation and simplify as necessary to utilise the point-slope form.

A line graph can also be drawn using the point-slope form. Plot the provided point on the coordinate plane first before using this form to graph a line. As you move up or down and to the right or left from the starting point, depending on whether the slope is positive or negative, you may utilise the slope to identify more places along the line.

The given equation of the line is y = 2x - 5.

Here the slope is 2.

For a perpendicular line the slope is negative and reciprocal thus.

slope = - 1/2.

Now using the point slope form:

y - y1 = m(x - x1)

y + 5 = -1/2(x - 2)

y + 5 = (-1/2)x + 1

y = (-1/2)x - 4

Hence, the equation of a line perpendicular to y=2x-5 that passes through the point (2,-5) is y = -1/2x - 4.

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Answer:

32.67 square meters

Step-by-step explanation:

finding the area of the shaded region.

area of sector = (θ/360°) x πr²

where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.

Substituting the given values into the formula, we get:

area of sector = (60°/360°) x π(14m)²

area of sector = (1/6) x 3.14 x 196m²

area of sector = 32.67m² (rounded to two decimal places)

Therefore, the area of the section is 32.67 square meters

Answer:

First, we need to find the radius of the base of the cone. We can see from the grid that the diameter is 8 units, so the radius is 4 units (or 4 feet).

Next, we can use the formula for the volume of a cone to find the height:

V = (1/3)πr^2h

Substituting the given volume and radius, and using 3.14 for π, we get:

200.96 = (1/3) x 3.14 x 4^2 x h

Simplifying and solving for h, we get:

h = 200.96 / (1/3 x 3.14 x 4^2)

h = 200.96 / 53.02

h ≈ 3.79 feet (rounded to two decimal places)

To construct the cone vertically on the grid with respect to the center of the base, we can draw a circle with radius 4 units (or 4 feet) centered at the point (4,4) on the grid. Then, we can draw a line from the center of the circle (point (4,4)) up to a point above the circle that is 3.79 units (or 3.79 feet) away from the center. This line represents the height of the cone. Finally, we can connect the endpoint of the line to the points where the circle intersects the grid to complete the cone.

Answer:

0.0234

Step-by-step explanation:

please give brainliest

The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.

The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:

Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.

The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).

In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.

These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.

In the given triangle using the sum of interior angle of triangle we have:

180 - 90 - 29 = 61

The measure of the third angle is 61 degrees.

Now, tan(61) = XZ/XY

XZ = XY * tan(61)

XZ = 18 * 1.927 = 34.686

Now, using the Pythagoras theorem we have:

ZY² = XZ² + XY²

ZY² = 34.686² + 18²

ZY² = 1712.3996

ZY = 41.38

Now, the value of:

sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435

cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838

tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518

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Answer:

To calculate the expected return on the portfolio, we use the following formula:

Expected return = (weight of stock X * expected return of stock X) + (weight of stock Y * expected return of stock Y) + (weight of stock Z * expected return of stock Z)

Expected return = (0.35 * 0.09) + (0.2 * 0.15) + (0.45 * 0.12) = 0.0321 or 3.21%

To calculate the variance of the portfolio, we use the following formula:

Variance = (weight of stock X)^2 * variance of stock X + (weight of stock Y)^2 * variance of stock Y + (weight of stock Z)^2 * variance of stock Z + 2 * weight of stock X * weight of stock Y * covariance of stocks XY + 2 * weight of stock X * weight of stock Z * covariance of stocks XZ + 2 * weight of stock Y * weight of stock Z * covariance of stocks YZ

Assuming that the stocks are uncorrelated, the covariance terms will be zero. Also, we assume that the variances of the stocks are equal to the square of their standard deviations. Therefore, we can simplify the formula to:

Variance = (weight of stock X)^2 * standard deviation of stock X^2 + (weight of stock Y)^2 * standard deviation of stock Y^2 + (weight of stock Z)^2 * standard deviation of stock Z^2

Variance = (0.35)^2 * (0.09)^2 + (0.2)^2 * (0.15)^2 + (0.45)^2 * (0.12)^2 = 0.00060167 or 0.060167%

To calculate the standard deviation of the portfolio, we take the square root of the variance:

Standard deviation = sqrt(0.00060167) = 0.0245 or 2.45%

Therefore, the expected return of the portfolio is 3.21%, the variance is 0.060167% and the standard deviation is 2.45%.

Answer:

Step-by-step explanation:

To calculate the expected return on the portfolio, we need to take the weighted average of the individual stock returns based on their proportions in the portfolio. The expected return on the portfolio can be calculated as follows:

Expected return on portfolio = (weight of stock X × expected return on stock X) + (weight of stock Y × expected return on stock Y) + (weight of stock Z × expected return on stock Z)

Expected return on portfolio = (0.35 × 9%) + (0.20 × 15%) + (0.45 × 12%)

Expected return on portfolio = 3.15% + 3.00% + 5.40%

Expected return on portfolio = 11.55%

To calculate the variance and standard deviation of the portfolio, we need to use the formula that takes into account the individual stock variances, covariances, and the weights of the stocks in the portfolio. Assuming the covariances between the stocks are zero, we can use the following formulas:

Portfolio variance = (wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2) + 2(wX * wY * σXY) + 2(wX * wZ * σXZ) + 2(wY * wZ * σYZ)

Portfolio standard deviation = sqrt(portfolio variance)

where wX, wY, and wZ are the weights of stocks X, Y, and Z in the portfolio respectively, σX, σY, and σZ are the standard deviations of returns on stocks X, Y, and Z respectively, and σXY, σXZ, and σYZ are the covariances between the returns on stocks X and Y, X and Z, and Y and Z respectively.

Since we assume the covariances between the stocks are zero, we can simplify the formulas as follows:

Portfolio variance = (wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2)

Portfolio standard deviation = sqrt[(wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2)]

Substituting the values, we get:

Portfolio variance = (0.35^2 * 0.09) + (0.20^2 * 0.15) + (0.45^2 * 0.12)

Portfolio variance = 0.0036475

Portfolio standard deviation = sqrt[(0.35^2 * 0.09) + (0.20^2 * 0.15) + (0.45^2 * 0.12)]

Portfolio standard deviation = sqrt(0.0036475)

Portfolio standard deviation = 0.06035

Therefore, the expected return on the portfolio is 11.55%, the portfolio variance is 0.0036475, and the portfolio standard deviation is 0.06035.

The completed statement with regards to the area of the square and the rectangle are;

The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.

The area of a square is the product of the side lengths which are congruent, therefore;

Area of a square = Side length, s × Side length, s = s²

The possible figure in the question includes;

A shaded square that is 125 square inches

An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches

Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.

Therefore;

The side length of the square = √(125) inches =  5·√5 inches

The estimated value of the side length of the square is; 5·√5 inches

The area of a rectangle = Length × Width

The length of the rectangle = 7·√5 inches

The width of the rectangle = 5·√5 inches

Therefore;

The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175

The estimated area of the unshaded rectangle is 175 square inches

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Answer:

-2 ( 2x - 3 )

Step-by-step explanation:

We know that,

( + ) × ( + ) = ( + )

( - ) × ( - ) = ( - )

( + ) × ( - ) = ( - )

Accordingly,

-4 ( x - 1 ) + 2

First, solve the brackets. That is, multiply each term inside the brackets by -4.

- 4x + 4 + 2

Combine like terms.

- 4x + 6

You can take the common factor out of the brackets.

-2 ( 2x - 3 )

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

In mathematics, reflection is a transformation that flips a figure over a line called the line of reflection. This line acts like a mirror, reflecting the original figure onto the opposite side of the line.

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

Reflections (also known as flips) change the orientation of a figure by flipping it across a line of reflection, which acts like a mirror.

Rotations change the orientation of a figure by rotating it around a fixed point. The figure stays the same shape and size, but its position and orientation in space changes.

Translations (also known as slides) change the position of a figure by sliding it along a straight line without changing its orientation or shape.

All of these transformations are important in geometry and other fields, such as physics and computer graphics, and can be used to describe the motion and properties of geometric objects.

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Answer:

Step-by-step explanation:

We need to find the number of teenagers in the group, given that the product of their ages is 18,727,200.

To solve this problem, we need to factorize the given number into its prime factors and then determine how many distinct factors there are.

18,727,200 can be factorized as:

18,727,200 = 2^6 × 3^2 × 5^2 × 13^2

To find the number of distinct factors, we add 1 to each exponent and then multiply them together:

(6+1) × (2+1) × (2+1) × (2+1) = 7 × 3 × 3 × 3 = 189

Therefore, there are 189 factors of 18,727,200, which means that there are 189 ways to multiply whole numbers together to get this number.

Since we want to find the number of teenagers in the group, we need to look for combinations of factors that result in whole numbers for the ages. We can start by dividing the total number of factors by 2 (since we are looking for pairs of factors) and then slowly increase the divisor until we find the smallest number that results in a whole number.

189 ÷ 2 = 94.5 (not a whole number)

189 ÷ 3 = 63 (not a whole number)

189 ÷ 4 = 47.25 (not a whole number)

189 ÷ 5 = 37.8 (not a whole number)

189 ÷ 6 = 31.5 (not a whole number)

189 ÷ 7 = 27 (a whole number)

Therefore, there are 27 pairs of factors that result in whole numbers for the ages. Each pair corresponds to a group of teenagers, and since each group has the same number of teenagers, there are 27 teenagers in the group.

The larger of the two acute angles is 58°.

The larger of the two acute angles in a right triangle is always opposite to the longer side of the triangle. This is because the longer side is always opposite to the larger angle, and the shorter side is always opposite to the smaller angle.

Let's start by using the identity cos(90°-x) = sin(x) for any angle x. This identity relates the cosine and sine of complementary angles, which are angles that add up to 90 degrees. In a right triangle, one of the angles is always 90 degrees, so the other two angles are complementary.

Applying this identity to the given equation, we get:

cos(90° - 8x) = sin(4x + 3)°

Using another identity, sin(90°-x) = cos(x), we can simplify the left-hand side of the equation:

sin(8x) = sin(4x + 3)°

Now we have two angles with the same sine, which means they differ by a multiple of 360 degrees. In other words, either:

8x = 4x + 3 + 360n (where n is an integer)

or

8x = 177 - (4x + 3) + 360n

Simplifying the first equation, we get:

4x = 360n - 3

x = 90n - 3÷4

Simplifying the second equation, we get:

12x = 177 + 360n

x = 59 + 30n

Since x is an acute angle, it must be between 0 and 90 degrees. Therefore, we can eliminate the solution x = 59 + 30n, because it exceeds 90 for n ≥ 2. This leaves us with:

x = 90n - 3÷4

Now we need to find the larger of the two acute angles in the right triangle. Let's call these angles A and B, with A being the larger one. Then:

A + B = 90

We know that one of the acute angles is 8x, and the other is 4x + 3 degrees. Without loss of generality, let's assume that 8x is the larger one (i.e., A = 8x and B = 4x + 3).

Substituting these values into the equation above, we get:

8x + 4x + 3 = 90

12x = 87

x = 7.25

Therefore, the larger acute angle is A = 8x = 58 degrees (rounded to the nearest degree).

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The following are the values for the side and angles for each right triangle using trigonometric ratios:

12). x = 30.41

13). ? = 19.47°

14). ? = 47.96°

15). ? = 55.15°

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

12). tan 58 = x/19 {opposite/adjacent}

x = 19 × tan 58 {cross multiplication}

x = 30.4064

13). sin ? = 6/18 {opposite/hypotenuse}

? = sin⁻¹(6/18) {cross multiplication}

? = 19.4712

14). tan ? = 41/37 {opposite/adjacent}

? = tan⁻¹(41/37) {cross multiplication}

? = 47.9357

13). cos ? = 8/14 {adjacent/hypotenuse}

? = tan⁻¹(8/14) {cross multiplication}

? = 55.1501

Therefore, the values for the side and angles for each right triangle using trigonometric ratios are:

12). x = 30.41

13). ? = 19.47°

14). ? = 47.96°

15). ? = 55.15°

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Answer:

Step-by-step explanation:

answer 42

how to explain but the answe is 42

The first and second equations satisfy standard form of the linear equation, hence they are linear. While, third, fourth, and fifth are non linear equations.

A group of two or more simultaneous solutions to linear equations is referred to as a system of linear equations. A collection of values that satisfy every equation in a system of linear equations is the solution. There might not be a unique solution if the number of equations in the system is less than or equal to the number of variables in the system. Systems of linear equations can be solved using various methods, such as substitution, elimination, or matrix algebra.

The standard form of linear equation is given as:

y = mx + b

The first and second equations satisfy, or represent the standard form of the linear equation, hence they are linear.

While, third, fourth, and fifth do not represent the standard form and hence are non linear equations.

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1. linear function 2. non linear function 3. linear function 4. non linear function 5. non linear function.

What is linear function?

In mathematics, a linear function is a type of function that can be represented by a straight line on a graph.

1.The equation m = 5.45p represents a linear function. It has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 5.45, which is a constant rate of change, and there is no other term involving p, so the equation is linear. When p increases or decreases by 1 unit, m increases or decreases by 5.45 units, respectively.

2.The equation 1=56.01+5 is not a function. It is a simple linear equation in one variable, but it has no independent variable to define a function. It is just an equation that states a relationship between two constants, 56.01 and 5, which sum up to 61.01.

3.The function d = (g-28)7/11 is a linear function because it can be written in the form y = mx + b, where m and b are constants and y and x are variables.

In this case, if we let d = y and g = x, we get:

y = (x-28)7/11

This can be simplified as:

y = 7/11 * x - 196/11

So we can see that the function has a constant slope of 7/11, and a constant intercept of -196/11. Therefore, it is a linear function.

4. This is a non-linear function since it includes a variable raised to a power (r³).

5.The function e=124² is a non-linear function as it involves squaring the value of 124, which produces a curved graph instead of a straight line.

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Answer:

The product of two numbers is 21.

Step-by-step explanation:

If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21.

Answer: When there are n teams in a league and each team plays every other team twice, then each team will play a total of n-1 games (since they don't play against themselves). Therefore, the total number of games played in the league is the sum of all the games played by each team, which is:

Total number of games = (number of teams) × (number of games played by each team) / 2

The division by 2 is necessary since each game involves two teams, so counting each game twice would result in double counting.

For the given basketball league with 11 teams, the total number of games played would be:

Total number of games = 11 × (11-1) / 2

= 11 × 10 / 2

= 55 × 2

= 110

Therefore, 110 games would be played in the league.

Step-by-step explanation:

Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.

Here,

The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where P is the principal amount (initial investment).

To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.

Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).

Then, we have:

[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]

Dividing both sides by P, we get:

[tex]2= (1 +\frac{r}{n})^{nt}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]

Using the properties of logarithms, we can simplify this expression as:

[tex]ln(2) = n*t * ln(1 + r/n)[/tex]

Dividing both sides by n*ln(1 + r/n), we get:

[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]

Plugging in the values for r and n, we get:

[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]

Solving this expression on a calculator, we get:

t ≈ 13.47 years

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Answer: Da der Graph punktsymmetrisch zum Ursprung ist, können wir annehmen, dass er die Form f(x) = ax^3 hat.

Step-by-step explanation:

Da der Graph einen Tiefpunkt an der Stelle x = 1 hat, gilt f'(1) = 0 und f''(1) < 0.

Also gilt:

f(x) = ax^3 + bx^2 + cx + d

f'(x) = 3ax^2 + 2bx + c

f''(x) = 6ax + 2b

Da f'(1) = 0, haben wir:

3a + 2b + c = 0

Da f''(1) < 0, haben wir:

6a + 2b < 0

3a + b < 0

b < -3a

Da der Graph punktsymmetrisch zum Ursprung ist, haben wir:

f(-x) = -f(x)

Also haben wir:

-a x^3 + bx^2 - cx + d = -ax^3 - bx^2 - cx - d

oder

2bx^2 + 2d = 0

b = -d

Da der Graph durch A(2|2) geht, haben wir:

8a + 4b + 2c + d = 2

Und da der Graph einen Tiefpunkt bei x = 1 hat, haben wir:

f(1) = a + b + c + d = 0

Jetzt können wir die Gleichungen lösen, um die Koeffizienten der Funktion zu finden. Zunächst setzen wir b = -d ein und erhalten:

3a + 2b + c = 0

6a - 2d < 0

b < -3a

a + b + c + d = 0

8a - 2b + 2c - d = 2

Lösen dieser Gleichungssysteme liefert a = -1

Answer:

18,739

Step-by-step explanation:

14 thousands = 14,000. 46 hundreds = 4,600. 13 tens = 130. 9 = 9. You add them all up and get 18,739.

Solving the system of equations:

B = 9 + 3*H

Area  27 = B*H/2

We can see that the height is 3 inches and the base is 18 inches.

For a triangle of base B and height H the area is given by the equation:

Area = Base*height/2 = B*H/2

here we know two relations so we can write a system of equations which is:

B = 9 + 3*H

Area  27 = B*H/2

Replace the first equation into the second to get:

27 = (9 + 3*H)*H/2

2*27 = 9H + 3H²

H² + 3H - 18 = 0

The quadratic formula gives the solutions:

[tex]H = \frac{-3 \pm \sqrt{3^2 - 4*1*-18} }{2}[/tex]

So the positive solution is H = (-3 + 9)/2 = 3

And the base is.

B = 9 + 3*3 = 18

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Answer:

For the first 40 hours that Mr. Ed works, he earns his regular rate of pay, which is $15.50 per hour. So, his regular pay for the week is:

40 hours x $15.50 per hour = $620

For the additional 5 hours he works, he earns overtime pay at a rate of time-and-a-half, which is 1.5 times his regular pay rate. So, his overtime pay for the week is:

5 hours x $15.50 per hour x 1.5 = $116.25

Therefore, Mr. Ed's total pay for the week in which he works 45 hours is:

$620 (regular pay) + $116.25 (overtime pay) = $736.25.

The product of the expressions are;

Step 1: (x + 2)(x + 3) and 3(x + 3)/4(x + 5)

Step 3: 4(x + 3) × 3(x + 3)/4(x + 5)

Step 4: 3/x + 5

It is important to note that algebraic expressions are described as expressions that are composed of variables, terms, coefficients, constants and factors.

From the information given, we have the fraction;

4x + 8/x² + 5x + 6 × 3x + 9/4x + 20

To determine the product, let us reduce the expressions to their lowest forms, we have;

4x + 8 = 4(x + 2)

x² + 5x + 6 = (x + 2)(x + 3)

3x + 9 = 3(x +3)

4x + 20 = 4(x + 5)

Substitute the expressions

4(x + 2)/(x + 2)(x + 3)  × 3(x +3)/4(x + 5)

divide the common terms

4(x + 3) × 3(x + 3)/4(x + 5)

Divide further, we have.

3/x + 5

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Answer:

volume = 290m

Step-by-step explanation:

box 1

[tex]vol= lwh\\=3*5*6\\=90m[/tex]

box 2

[tex]vol=lwh\\=8*5*5\\=200m[/tex]

total volume = 90+200 =290m

Answer:

Step-by-step explanation:

We can solve this question by applying the Pythagorean theorem to the triangle (a^2+b^2=c^2). The Pythagorean theorem states that if the two shorter lengths are both squared and added the sum of those two numbers should be equal to the longest side squared. So 6 and 8 are the shorter sides of this triangle so we can plug either one in for either a or b, 6^2+8^2=9^2. Once you do that you have to square each individual number. You should get 36+64=81

36+64 is 100 and 100 does not equal 81 therefore this triangle is not a right triangle.

Answer:

Step-by-step explanation:

If a² + b² > c² , the triangle is acute,  

If a² + b² = c² , the triangle is a right triangle,

If a² + b² > c² , the triangle is obtuse,  

where "a" and "b" are the lengths of the 2 shorter sides of the triangle and "c" is the length of the longest side.

~~~~~~~~~~~~~

6² + 8² > 9² ⇒ given triangle is acute

To describe the transformation of the graph of function f(x) onto the graph of function g(x), we can compare the two functions and identify the changes that have been made.

First, note that f(x) and g(x) have different denominators: x-1 for f(x) and x+2 for g(x). This means that the graphs of f(x) and g(x) will have vertical asymptotes at x=1 and x=-2, respectively.

Next, we can see that g(x) is a transformation of f(x) because it is obtained by applying one or more transformations to f(x). Specifically, we can identify the following transformations:

Horizontal shift to the left by 3 units: f(x) is shifted 3 units to the right to get g(x). This is because g(x) has x+2 in the denominator, which is equivalent to f(x) with x-(-2) = x+2 in the denominator. So g(x) is equivalent to f(x) shifted 3 units to the left.

Vertical shift upwards by 4 units: The entire graph of f(x) is shifted 4 units upwards to get the graph of g(x). This is because the constant term 4 is added to g(x) but not present in f(x).

Vertical compression: The vertical scale of the graph of g(x) is compressed compared to the graph of f(x). This is because the size of the denominator is increasing for g(x) relative to f(x), so the graph will appear "squeezed" vertically.

Therefore, the transformation of the graph of function f(x) onto the graph of function g(x) involves a horizontal shift to the left by 3 units, a vertical shift upwards by 4 units, and a vertical compression.

Answer: 6

2 possibilities for each student if they are first and 3 students so 3*2=6.