Decide whether or not the relation is a function.

[(0,1), (-5,4), (0,2), (5,-4)]

Answer:

Parallelogram

Step-by-step explanation:

is a polygon that has exactly four sides. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.)

Answer:

Here is the answer......

Answer:

2x² - 7x - 15

Step-by-step explanation:

Given

(2x + 3)(x - 5)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x - 5) + 3(x - 5) ← distribute parenthesis

= 2x² - 10x + 3x - 15 ← collect like terms

= 2x² - 7x - 15

The equation that expresses the relationship between the two branches is\(x + (1/4)x = 1,650\), where x represents the number of students at Branch B.

The number of students taking classes at RSM Branch A is 1/4 more than the number of students taking classes at RSM Branch B. If Branch A has 1,650 students, Branch B has 1,320 students. The equation that shows the relationship between the two branches is\(x + (1/4)x = 1,650\). Solving for x, we get x = 1,320, meaning there are 1,320 students at Branch B.

To summarize, if Branch A has 1,650 students, the number of students at Branch B is 1,320.

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After w weeks, the expression for the total cost of games is 250 + 4000w.

What is Expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1.

As an illustration, while x is a variable raised to the first power, x2 is a variable raised to the second power. An illustration of a constant is 5.

Linear expressions are what the two expressions are. One variable raised to the power of one makes up a linear expression.

250 + 1000g.

Where: g(w) = 4w.

250 + 1000(4w).

250 + 4000w.

Therefore, number of games produced in w weeks is 250 + 4000w.

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Answer:

x = -6 or 6

Step-by-step explanation:

=> x² - 36

=> x² - 6²

=>(x + 6 ) (x - 6)

=> x = -6 or x = 6

\(x^2-36\\\\=x^2-6^2\\\\=(x+6)(x-6)\)

Answer:

30 pounds in 480 ounces.

Step-by-step explanation:

16 ounces = 1 pound.

480 ounces divided by 16 = 30 pounds

Answer:

30 pounds. 480 ounces

30 pounds

divide the mass value by 16

Answer:

C

Step-by-step explanation:

The constant of proportionality 'k' is 90.

Therefore, the answer is option c. 90.

To find the constant of proportionality in this indirect variation problem, we can set up a proportion using the given information.

Let's denote the constant of proportionality as 'k'. We know that when Bartolo runs at an average speed of 15 feet/second, he finishes the race in 6 seconds. We can write this as:

15 feet/second x 6 seconds = k

Similarly, when Bartolo runs at an average speed of 18 feet/second, he finishes the race in 5 seconds:

18 feet/second x 5 seconds = k

Now we can solve for 'k' by setting the two expressions equal to each other:

15 feet/second x 6 seconds = 18 feet/second x 5 seconds

90 feet = 90 feet

This shows that the constant of proportionality 'k' is 90.

Therefore, the answer is option c. 90.

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If we have that y varies directly with x by a constant of 3/2, we can pose this as follows:

Thus, if the value for y = 14, then we can use the previous relation to find the value of x:

Then, the value for x = 9.33333... or 91/3:

Answer:

D

Step-by-step explanation:

\(\dfrac{\sqrt{4}}{\sqrt{25}}= \\\\\\\dfrac{2}{5}= \\\\\\0.4\)

Hope this helps!

Answer:

Hi! The answer to your question is \(-1/12\)

Step-by-step explanation:

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Hope this helps!!

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- Brooklynn Deka

Answer: -\(\frac{1}{12}\)

Step-by-step explanation:

Lets make the demonater both equal \(\frac{4}{6}\)=\(\frac{16}{24}\),  \(\frac{6}{8}\)=\(\frac{18}{24}\)

\(\frac{16}{24}\)-\(\frac{18}{24}\)=-\(\frac{2}{24}\)

Simplify it and it's -\(\frac{1}{12}\)

Hope this helped! :)

Kepler's third law of planetary motion states that the square of the orbital period of a planet or moon is directly proportional to the cube of its mean orbital radius.

Let's denote the orbital period of Hyperion as T_h and its mean orbital radius as R_h. Similarly, let T_t and R_t represent the orbital period and mean orbital radius of Titan, respectively.

According to Kepler's third law, we have the following relationship:

(T_h)^2 / (T_t)^2 = (R_h)^3 / (R_t)^3

Plugging in the given values, we have:

(T_h)^2 / (15.95)^2 = (1.48 x 10^9)^3 / (1.22 x 10^9)^3

Simplifying the equation, we can solve for T_h:

(T_h)^2 = (15.95)^2 * (1.48 x 10^9)^3 / (1.22 x 10^9)^3

Taking the square root of both sides, we find:

T_h = 15.95 * (1.48 / 1.22)^(3/2)

Calculating this expression, we can determine the orbital period of Hyperion in days.

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12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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The equation of the tangent line to the function \(f(x) = -2x^3 - 4x^2 - 3x + 2\) at the point where x = -1 is y = -x + 6. The slope of the tangent line is -1, and the point of tangency is (-1, 7).

To find the equation of the tangent line to the function\(f(x) = -2x^3 - 4x^2 - 3x + 2\) at the point where x = -1, we need to determine both the slope of the tangent line and the point of tangency.

First, we find the derivative of the function f(x) to obtain the slope of the tangent line. The derivative of \(-2x^3 - 4x^2 - 3x + 2 is f'(x) = -6x^2 - 8x - 3\).

Next, we substitute x = -1 into the derivative to find the slope of the tangent line at x = -1: \(f'(-1) = -6(-1)^2 - 8(-1) - 3 = -6 + 8 - 3 = -1\).

Now, we have the slope of the tangent line, which is -1. To find the point of tangency, we substitute x = -1 into the original function f(x): \(f(-1) = -2(-1)^3 - 4(-1)^2 - 3(-1) + 2 = -2 + 4 + 3 + 2 = 7\).

Therefore, the point of tangency is (-1, 7), and the equation of the tangent line can be written in a point-slope form as y - 7 = -1(x - (-1)) or y - 7 = -1(x + 1).

In slope-intercept form, the equation simplifies to y = -x + 6.

Therefore, the equation of the tangent line to the function \(f(x) = -2x^3 - 4x^2 - 3x + 2\) at the point where x = -1 is y = -x + 6. The slope of the tangent line is -1, and the point of tangency is (-1, 7).

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Let's write the likelihood of a promotion as P(promotion) and the likelihood of a rise as P(raise). The following details are sent to us:

P (promotion) = 0,40 P (promotion or raise) 0,72 P (promotion and raise) 0,25The inclusion-exclusion concept can be used to calculate the likelihood of receiving a rise. This rule states that the probability of two events (A or B) coming together is equal to the sum of each event's individual probabilities less the likelihood that A and B will come together.

P(promotion or raise) equals P(promotion) + P(raise) – P(promotion andraise).

By substituting the specified values, we obtain:

0.7 = 0.40 + P (b) - 0.25

We can rewrite the equation to isolate P(raise) as follows:P(raise) = 0.72-0.40+0.25

P(rise) = 0.57

The likelihood of receiving a rise is therefore 0.57, or 57%.

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Answer:

3x³ + 17x² + 33x + 27

Explanation:

(x + 3)(3x² + 8x + 9)

= (x + 3)(3x² + 8x + 9)

= (x)(3x²) + (x)(8x) + (x)(9) + (3)(3x²) + (3)(8x) + (3)(9)

= 3x³ + 8x² + 9x + 9x² + 24x + 27

= 3x³ + 17x² + 33x + 27

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

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Answer:

The Snowplow needs to turn 44 times.

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

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Answer:

k = 37/8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

-29 = 9 - 6k - 2k - 1

Step 2: Solve for k

Step 3: Check

Plug in k into the original equation to verify it's a solution.

Here we see that -29 does indeed equal -29.

∴ k = 37/8 is the solution to the equation.

The exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

Let's consider that three charges are placed in a straight line along the z-axis, and the charges are +Q on z=+D, -Q on z=-D, and -2Q at z=0.

To find the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole, let's proceed with the following steps:

To find the electrostatic potential at a point P in the x-axis, we need to consider that the distance from the charges that are on the axis is r, and the distance from the charges that are on the axis and are at +D and -D is d.

The distance from the charges on the axis and at 0 is x. Now we can write,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D].

Now, we can substitute the values in the above expression and obtain,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D] .

Now, we need to use symmetry to argue that we can switch from x to r, which is given by r2 = x2 + y2.

Thus, the exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

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Answer: Triangles a used for those types of things because they have flat bottoms making it easy to put on structures and also the have sides going downwards causing things like rain and leaves to fall off unlike flat roof which would keep the rain and leaves on until you went up there to clean it yourself

Step-by-step explanation: I don't know if this is the best answer, but it will probably help for writing that response

Step-by-step explanation:

Function A Linear

Function A LinearFunction B (on the graph) nonlinear (exponential function)

The length of the third side of ALMN is 20 units.

If AGHI and ALMN are similar, then their corresponding sides are proportional.

Let's call the length of the third side of ALMN "x". We can set up the proportion using the two sides of AGHI and ALMN that we know:

10/8 = 15/12 = x/16

To find x, we can cross-multiply and simplify:

15 × 16 = 12x

240 = 12x

x = 240/12

x = 20

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The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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The equilibrium quantity is q = 24 at price p = $7,200

To find the equilibrium quantity and price, we need to set the supply equal to demand:

q^2 + 30q = -4q^2 + 10q + 19,200

Simplifying and rearranging, we get:

5q^2 - 20q + 19,200 = 0

Using the quadratic formula, we can solve for q:

q = [20 ± sqrt(20^2 - 4(5)(19,200))]/(2(5))

q = [20 ± 220]/10

Since a negative quantity of the commodity doesn't make sense in this context, we can reject the negative solution, leaving us with:

q = (20 + 220)/10 = 24

Now, we can use either the supply or demand function to find the equilibrium price. We'll use the demand function:

p = -4(24)^2 + 10(24) + 19,200

p = $7,200

Therefore, the equilibrium quantity is 24 units and the equilibrium price is $7,200 per unit.

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Step-by-step explanation:

The sum of the measures of the interior angles of any quadrilateral can be found by breaking the quadrilateral into 2 triangles.

Since, the measure of the interior angles of any triangle equals 180 degrees,

a+b+c=180

p+q+r=180

Each of the two triangles will contribute 180 degrees to the total for the quadrilateral.

Sum of angles of quadrilateral

= b+(a+p)+q+(r+c)=a+b+c+p+q+r=180+180

=360=4×90

=4 right angles

Answer: