Which of these could be the side lengths of a right triangle? list all possible answers and show your work for full marks.

a) 4-7-10
b) 36-48-60
c) 6-10-14
d) 14-48-50

As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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Answer:

answer is 546

Step-by-step explanation:

To solve the linear programming problem using the simplex method, we first convert the problem into standard form.

The original problem: Maximize z = -x₁ + 3x₂; subject to: x₁ + 3x₂ ≤ 5; -x₁ + x₂ ≤ 1 ; x₁ + x₂ ≤ 4; x₁, x₂ ≥ 0. The problem in standard form: Maximize z = -x₁ + 3x₂, subject to: x₁ + 3x₂ + x₃ = 5; -x₁ + x₂ + x₄ = 1; x₁ + x₂ + x₅ = 4; x₁, x₂, x₃, x₄, x₅ ≥ 0. Using the simplex method, we perform the iterations to find the optimal solution. Starting with the initial basic feasible solution, we pivot until we reach an optimal solution. The optimal solution is found when all coefficients in the objective row are non-negative. The final optimal solution obtained by the simplex method is: x₁ = 0; x₂ = 1; z = 3. To construct the dual linear programming problem, we use the coefficients from the constraints of the primal problem as the objective coefficients in the dual problem.

The variables in the primal problem become the constraints in the dual problem, and the constraints in the primal problem become the variables in the dual problem. The dual problem for the given primal problem is: Minimize w = 5y₁ + y₂ + 4y₃, subject to: y₁ - y₂ + y₃ ≥ -1; 3y₁ + y₂ + y₃ ≥ 3. Using the optimal simplex tableau of the primal problem, we can determine the solution of the dual problem. The optimal tableau will provide us with the values of the primal variables and the dual variables. In this case, the primal variables are x₁ and x₂, and the dual variables are y₁, y₂, and y₃. From the optimal simplex tableau, we find that x₁ = 0, x₂ = 1, y₁ = 1, y₂ = 0, and y₃ = 0. These values give the solution to the dual problem. The minimum value of the dual objective function w is obtained as w = 5(1) + 0 + 4(0) = 5.

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Answer: 65%

Step-by-step explanation:

The organization sent out 640 invitations.

416 out of this 640 attended the fundraiser.

The percentage who attended is:

= 416/ 640

= 0.65

= 65%

By applying the slope of a line and the y-intercept formula, the following are the answer to each table:

Slope of a line (gradient) shows the value or degree of incline on a straight line.

If it is known that two points are passed by a straight line, for example (x₁,y₁) and (x₂,y₂), then the gradient can be obtained by the formula:

m = ∆y/∆x

   = (y₂ - y₁) / (x₂ - x₁)

Y-intercept is the point where the line intersects the y-axis. It is the intersection of the function's graph with the y-axis when x = 0.

For every table, we pick 2 points to calculate the slope and y-intercept:

Table 1:

(x₁,y₁) and (x₂,y₂) = (-5,-4) and (0,-2)

m = (y₂ - y₁) / (x₂ - x₁)

   = (-2 + 4) / (0 + 5)

   = 2/5 (option S)

y-intercept is obtained when x = 0, thus (0,-2) is the y-intercept (option O)

Table 2:

(x₁,y₁) and (x₂,y₂) = (2,0) and (4,3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (3 - 0) / (4 - 2)

   = 3/2 (option N)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (4,3)

 m = (y₂ - y₁) / (x₂ - x₁)

3/2 = (3 - y₁) / (4 - 0)

  6 = 3 - y₁

  y₁ = -3

Thus, (0,-3) is the y-intercept (option K)

Table 3:

(x₁,y₁) and (x₂,y₂) = (1,-5) and (3,-3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (-3 + 5) / (3 - 1)

   = 1 (option M)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (3,-3)

m = (y₂ - y₁) / (x₂ - x₁)

1 = (-3 - y₁) / (3 - 0)

3 = -3 - y₁

 y₁ = -6

Thus, (0,-6) is the y-intercept (option B)

Table 4:

(x₁,y₁) and (x₂,y₂) = (1,3) and (3,1)

m = (y₂ - y₁) / (x₂ - x₁)

   = (1 - 3) / (3 - 1)

   = -1 (option A)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (3,1)

m = (y₂ - y₁) / (x₂ - x₁)

-1 = (1 - y₁) / (3 - 0)

-3 = 1 - y₁

y₁ = 4

Thus, (0,4) is the y-intercept (option Q).

Table 5:

(x₁,y₁) and (x₂,y₂) = (1,3) and (2,6)

m = (y₂ - y₁) / (x₂ - x₁)

   = (6 - 3) / (2 - 1)

   = 3 (option P)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (2,6)

m = (y₂ - y₁) / (x₂ - x₁)

3 = (6 - y₁) / (2 - 0)

6 = 6 - y₁

y₁ = 0

Thus, (0,0) is the y-intercept (option J)

Table 6:

(x₁,y₁) and (x₂,y₂) = (-6,6) and (0,3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (3 - 6) / (0 + 6)

   = -1/2 (option F)

y-intercept is obtained when x = 0, thus, (0,3) is the y-intercept (option G)

Table 7:

(x₁,y₁) and (x₂,y₂) = (0,-5) and (2,0)

m = (y₂ - y₁) / (x₂ - x₁)

   = (0 + 5) / (2 - 0)

   = 5/2 (option E)

y-intercept is obtained when x = 0, thus, (0,-5) is the y-intercept (option L)

Table 8:

(x₁,y₁) and (x₂,y₂) = (0,1) and (3,3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (3 - 1) / (3 - 0)

   = 2/3 (option H)

y-intercept is obtained when x = 0, thus, (0,1) is the y-intercept (option D)

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Answer:

90 beats per minute

Step-by-step explanation:

320 divided by 4 is 90, which would mean that there is 90 beats per minute

Answer: the answer is 64 beats.

Step-by-step explanation:

The least number of socks you need to pick is 10 red socks, 10 blue socks, and 10 white socks to ensure you have a matching pair. The least number of socks that can be taken from the drawer is one.

Follow these steps:
1. Pick one sock from the drawer (it could be any color, let's say red).
2. Pick a second sock from the drawer (if it's red, you have a matching pair; if not, let's say it's blue).
3. If you don't have a matching pair yet, pick a third sock from the drawer (now, it's either red, blue, or white, and you'll have a matching pair for sure).
So, the least number of socks you need to pick to ensure a matching pair is 3.

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The coordinate point (3.5, 3.5), the reflection of the coordinate across the y-axis will form a pre image at (-3.5, 3.5)

If a coordinate (x,y) is reflected across the y-axis, the equivalent coordinate points will be given as (-x, y).

Using the translation for the reflections;

Give the coordinate point (3.5, 3.5), the reflection of the coordinate across the y-axis will form a pre image at (-3.5, 3.5)

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Answer:hahaha

Step-by-step explanation:

nanana

Answer:

0 to 2 minutes - Accelerating

3 to 4 minutes - Constant

6 to 8 minutes - Decelerating

9 to 11 minutes Accelerating

hope i have helped u

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

There are 12 boys and 6 girls, meaning there are 18 students. The girls are 1/3 out of those 18.

To find the g-intercept and x-intercepts of the function g(x) = (x - 7)(x + 3)(x - 1), we set the value of g(x) equal to zero and solve for x. The coordinates of the g-intercept are (0, 21), and the coordinates of the x-intercepts are (7, 0), (-3, 0), and (1, 0).

1. g-intercept:

The g-intercept refers to the point where the function intersects the y-axis. To find it, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3)(0 - 1   = (-7)(3)(-1)   = 21

Therefore, the g-intercept has coordinates (0, 21).

2. x-intercepts:

The x-intercepts are the points where the function intersects the x-axis. To find them, we set g(x) = 0 and solve for x. This means we are looking for the values of x that make each factor of g(x) equal to zero individually:

x - 7 = 0  -->  x = 7

x + 3 = 0  -->  x = -3

x - 1 = 0  -->  x = 1

Therefore, the x-intercepts have coordinates (7, 0), (-3, 0), and (1, 0)

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Answer:

150%

Step-by-step explanation:

Answer:

The equation of the straight line is 4x +y = 1

Step-by-step explanation:

Step(i):-

Given points are (-1,5) and ( 2,-7)

Slope of the line

\(m =\frac{y_{2}-y_{1} }{x_{2} -x_{1} } =\frac{-7-5}{2-(-1)} = \frac{-12}{3} = -4\)

slope of the line m = -4

Step(ii):-

The equation of the straight line passing through the point (-1,5) and having slope 'm' = -4

\(y - y_{1} = m( x-x_{1} )\)

y - 5 = -4 ( x-(-1))

y -5 = -4 x -4

4 x + y -5 +4=0

4x +y -1 =0

Final answer:-

The equation of the straight line is 4x +y = 1

(f)/(g))(x) = (√[(3 + x)(3 - x)]) / (3(x + 2)).

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

To find ((f)/(g))(x), we need to evaluate the function f(x)/g(x) for a given value of x.

We have:

f(x) = √(9 - x^2)

g(x) = 3x + 6

So,

(f/g)(x) = f(x) / g(x) = (√(9 - x^2)) / (3x + 6)

To simplify this expression, we can factor out 3 in the denominator and simplify the square root in the numerator:

(f/g)(x) = (√(9 - x^2)) / (3(x + 2))

= (√[(3^2 - x^2)]) / (3(x + 2))

= (√[(3 + x)(3 - x)]) / (3(x + 2))

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We happen to have

\(\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots\)

which is to say, the base-8 representation of 1/7 is

\(\dfrac17 \equiv 0.111\ldots_8\)

This follows from the well-known result on geometric series,

\(\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}\)

if \(|r|<1\). With \(a=1\) and \(r=\frac18\), we have

\(\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots\)

Uniformly multiplying each term on the right by an appropriate power of 2, we have

\(\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots\)

Now observe that for \(n\ge4\), each numerator on the right side side will contain a factor of 16 that can be eliminated.

\(\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}\)

That is,

\(\dfrac{2^4}{16^4} = \dfrac1{16^3}\)

\(\dfrac{2^5}{16^5} = \dfrac2{16^4}\)

\(\dfrac{2^6}{16^6} = \dfrac4{16^5}\)

etc. so that

\(\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots\)

and thus the base-16 representation of 1/7 is

\(\dfrac17 \equiv 0.249249249\ldots_{16}\)

and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.

the overall speedup in percentage is approximately 22.47%. This means that the system's execution time is improved by approximately 22.47% after the disk upgrade is applied.

Amdahl's Law is used to calculate the overall speedup of a system when only a portion of the system's execution time is improved. The formula for Amdahl's Law is: Speedup = 1 / [(1 - P) + (P / S)], where P represents the proportion of the execution time that is improved and S represents the speedup achieved for that proportion.

In this case, the system spends 55% of its time on I/O, so P = 0.55. The disk upgrade provides for 50% greater throughput, which means S = 1 + 0.5 = 1.5.

Plugging these values into the Amdahl's Law formula, we have Speedup = 1 / [(1 - 0.55) + (0.55 / 1.5)].

Simplifying further, we get Speedup = 1 / [0.45 + 0.3667].

Calculating the expression in the denominator, we find Speedup = 1 / 0.8167 ≈ 1.2247.

Therefore, the overall speedup in percentage is approximately 22.47%. This means that the system's execution time is improved by approximately 22.47% after the disk upgrade is applied.

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The total change to his score as an integer is -115

The total change in Juan score is calculated as follows;

Let Juan's initial score = x

when Juan finished the next level of his video game, he lost 10 points for each of the two targets he missed.

total points deducted = 20 points.

New score = x - 20

He was also penalized 95 points for taking too long.

His final score;

(x - 20) - 95

= x - 115.

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If a raindrop falls to the ground from a raincloud at an altitude of 3000 meters, then it will take 24.74 seconds to fall

A raindrop falls to the ground from a raincloud at an altitude of 3000 meters.

We know the equation of motion

S = ut + 1/2at^2

Where S is the Displacement

u is the initial velocity

a is the acceleration

t is the time of motion

The value of S = -3000

u = 0 m/s

a = g = -9.8 meter per second square

Substitute the values in the equation

-3000 = 0×t + 1/2 ×-9.8 × t^2

-3000 = -4.9t^2

t^2 = -3000 / -4.9

t = 24.74 seconds

Therefore, it will take 24.74 seconds to fall

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0.25  is the probability of rolling a five on the first die and a one on the second die

How do you calculate probability?

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen

Very interesting problem.

1  1

1  2

1  3

1  4

2  1

2  2

2  3

2  4

3  1

3  2

3  3

3  4

4  1

4  2

4  3

4 4

There are 16 possible out comes

1   4

4  1

2  3

3  2

4 out of the 16 outcomes are possible

P(5) = 4/16 = 0.25

The theoretical out come would be 4 times

4/16 = 0.25

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Answer:

Below in bold.

Step-by-step explanation:

The angle in a regular octagon =  180 - (360/8) = 135.

Using trigonometry  sin (135/2) = k/2 / EF

sin 67.5 = k / 2EF

2EF = k / sin 67.5

EF = k / 2 sin 67.5 = k/1.8478

Perimeter of octagon = 8 * k/1.8478

= 4.33k to the nearest hundredth.

Answer: the third and 5th option but I'm not sure if its right

The answer is 23/40

To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.

 
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.

 
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.

 
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.

Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:

2/40 - 25/40 = -23/40.

The absolute value of any number is always positive so it becomes 23/40.

The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.

Answer:

Step-by-step explanation:

P(t) = K / (1 + (K/P0 - 1) * e^(-rt))

In this equation, P(t) is the population at time t, P0 is the initial population at time t=0, K is the carrying capacity, r is the intrinsic growth rate, and e is the base of the natural logarithm ( approximately 2.71828).

To find the carrying capacity, you can set P(t) equal to K and solve for t. This will give you the time at which the population reaches its carrying capacity.

To find the value of k, you can plug in the values for P(t), P0, and r and solve for K.

To write the solution of the equation, you can solve for t by rearranging the equation and taking the natural logarithm of both sides.

To find the population after 10 weeks, you can plug in the values for P0, K, r, and t=10 into the equation and solve for P(t).

I hope this helps! Let me know if you have any further questions.

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

The red shape

Step-by-step explanation:

This is because they are of the same shape and size.

They must look the same in size and shape type.

HOPE THIS HELPED

Answer:

No

Step-by-step explanation:

Linear equations, when graphed, look like straight lines.

Examples include:

y= mx + b

y = 3

x + 2 = 0

y + 6 = 0

y = 7x +2

Answer:

g(x) = x² - 3

Step-by-step explanation:

When doing a, h, and k, there are different stanoints to each of the variables.

in this case, since we are shifting down, we use k

we are moving 3 units down so we subtract 3 with no parentheses

so g(x) = x² -3

The translating function is g(x) = ( x+ 3)².

In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to have the same size as the original shape, and hence the shapes are congruent. They were simply relocated in one or more directions. There is no change in the shape because it is just moved from one location to another.

We have function,

f(x) = x²

and, g(x) = a horizontal translation of 3 units left.

Now, we have to subtract 3 from the x coordinate of g(x).

So, g(x) = f(x-h) where h = -3.

Thus, the translating function is g(x) = ( x+ 3)².

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