There are 32 students in the class, 3/4 of the class play sport. How many students played sport.

The difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure is ΔU ≈ 0.2511J/K * T

To calculate the difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure, we need to consider the ideal gas law and the difference in pressure.

The ideal gas law states:

PV = nRT

Where:

P = pressure

V = volume

n = number of moles of gas

R = ideal gas constant

T = temperature

Since we are comparing the same volume of air, we can assume V1 = V2, and the equation becomes:

P1 = n1RT

P2 = n2RT

The internal energy (U) of an ideal gas depends only on its temperature. Therefore, the internal energy of the air in the bicycle tire and the equivalent volume of air at atmospheric pressure will be the same if they have the same temperature.

To calculate the difference in internal energy, we need to consider the difference in pressure. The change in internal energy (ΔU) can be expressed as:

ΔU = n1RT - n2RT

To calculate the moles of each gas (nitrogen and oxygen) in the given composition, we need to consider their percentages.

Composition: 78% nitrogen (N2) and 21% oxygen (O2)

Volume: 1.2 liters

Pressure: 5.4×10^5 Pa

We can assume that the temperature is constant.

Let's calculate the moles of each gas:

For nitrogen (N2):

n1 = 78% * V / Vm

= 0.78 * 1.2 L / 22.4 L/mol

≈ 0.0415 mol (rounded to four decimal places)

For oxygen (O2):

n2 = 21% * V / Vm

= 0.21 * 1.2 L / 22.4 L/mol

≈ 0.0113 mol (rounded to four decimal places)

Now, we can calculate the difference in internal energy:

ΔU = n1RT - n2RT

= (0.0415 mol) * R * T - (0.0113 mol) * R * T

= (0.0415 - 0.0113) mol * R * T

= 0.0302 mol * R * T

Since the temperature (T) is the same for both scenarios, we can simplify the equation to:

ΔU = 0.0302 mol * R * T

The value of the ideal gas constant (R) is approximately 8.314 J/(mol·K).

Therefore, the difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure is:

ΔU ≈ 0.0302 mol * 8.314 J/(mol·K) * T ≈ 0.2511J/K * T

Please note that we need the temperature (T) in order to calculate the exact value of the difference in internal energy.

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Value of r is different for every series

let

a , b , c , d ..... be geometric series then

r = b/a or d/c and so on

where r is common ratio

Answer:

Your expression would be 150(11)=x

The answer to this expression would be 1,650. Producing the equation 150(11)= 1,650

Step-by-step explanation:

Your equation is 150(11)=x because; the hot air balloon owner charges $150 per ride. And there are 11 rides. So our equation is solely saying $150 charged per ride for 11 rides.

Let's solve this equation

150(11)= 1,650

So, we would multiply 150 by 11 to get 1,650.

And if your professor asks a statement for your equation you would say; The total income for the balloon owner that weekend is $1,650. $900 made on Saturday plus $750 made on Sunday.

, Hope this helps :)

Have a great day!!

The best graphical tool to display the relative frequency of a Philippineal variable is a histogram.

A histogram is a graphical representation that organizes data into intervals or bins and displays the frequency or relative frequency of each interval. It is particularly useful when dealing with numerical or continuous data, such as Philippine variable data. By dividing the data into intervals and representing the relative frequency of each interval using bar heights, a histogram provides a visual representation of the distribution and patterns within the data.

When displaying the relative frequency of Philippine variables, a histogram allows for easy comparison between different intervals and provides insights into the overall distribution of the data. It helps identify the central tendency, shape, and spread of the Philippine variables, making it an effective tool for data analysis and visualization. Additionally, a histogram can be customized to suit specific requirements, such as adjusting the number of bins or adding labels and titles, enhancing its usefulness in displaying Philippine variable data accurately and meaningfully.

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The average accelerations for the four pairs are approximately:

(a) 1.1 m/s²

(b) -1.3 m/s²

(c) 0.8 m/s²

(d) -2.6 m/s²

To calculate the average acceleration for each pair, we can use the formula:

average acceleration = (change in velocity) / (elapsed time)

(a) For pair (a):

Change in velocity = final velocity - initial velocity = 4.9 m/s - 1.6 m/s = 3.3 m/s

Average acceleration = 3.3 m/s / 3.0 s ≈ 1.1 m/s²

(b) For pair (b):

Change in velocity = final velocity - initial velocity = 1.6 m/s - 5.5 m/s = -3.9 m/s

Average acceleration = -3.9 m/s / 3.0 s ≈ -1.3 m/s²

(c) For pair (c):

Change in velocity = final velocity - initial velocity = -3.4 m/s - (-5.9 m/s) = 2.5 m/s

Average acceleration = 2.5 m/s / 3.0 s ≈ 0.8 m/s²

(d) For pair (d):

Change in velocity = final velocity - initial velocity = -3.5 m/s - 4.4 m/s = -7.9 m/s

Average acceleration = -7.9 m/s / 3.0 s ≈ -2.6 m/s²

Therefore, the average accelerations for the four pairs are approximately:

(a) 1.1 m/s²

(b) -1.3 m/s²

(c) 0.8 m/s²

(d) -2.6 m/s²

The negative sign indicates acceleration in the opposite direction of the positive x-axis.

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Based on the given quadrilaterals and their angles, the following are true:

The first shape given is a square which means that all the angles have the equal number of 90°. The value of x is therefore:

x = 90 - 45

= 45°

The second quadrilateral is a Trapezium and adjacent angles will add up to 180°. The value of y is:

= 180 - 60

= 120°

The third shape is a parallelogram and the lengths of sides that are opposite each other are the same. This means that a will have the same value as the opposite side of 15 cm.

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Answer: 39 students.

Step-by-step explanation: 1/5 of 75 is 60. Now we need to find out what 3/5 of 60 is. 3/5 times 60 = 39. 39 students need to give their speeches.

Answer:

y=3x-12

Step-by-step explanation:

to find slope we use y2-y1/x2-x1 by using any 2 points on the graph

(0,-12) (4,0)

0-(-12)/4-0)

12/4

3

The slope is 3

The y intercept is -12 since it crosses the y axis when y=-12

So we write those is y=Mx+b format where m is the slope and b is the y intercept

y=3x-12

Hopes this helps please mark brainliest

Answer:

id-k. scars run too deep

Step-by-step explanation:

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

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Answer: 15kg is equivalent to 33.0693 or 33, for short.

Step-by-step explanation:

33.0693 kilograms, or 33, are equal to 15 kilograms.

A pound is about equivalent to 0.45359237 kilograms. By dividing the specified pound value by 0.45359237, one can convert a pound to kilograms. Remember that 1 kg equals 2.2046 lbs when converting weights.

The weight of a kilogram (kg) is said to be 2.2 times that of a pound. Thus, 2.26 pounds are equal to one kilogram of mass. In light of this, we shall now examine some of the primary variations between the pound and the kilogram. A pound is an imperial unit used to measure bulk or weight.

A weight of 500 pounds exceeds a weight of 200 kilograms because 227 kilograms is greater than 200 kilograms.

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1)

8. ∠ABC, 5. \(\overrightarrow{BA}\), 9. Point C, 3. Plane W, 6. \(\overline{AB}\), 2. \(\overrightarrow{BC}\) and \(\overrightarrow{BA}\), 1. \(\overleftrightarrow{AB}\), 7. Plane ABC, 4. line m.

2)

a) The output of the rule is (-6,9)

b) The output of the rule is (-3,0)

c) No.

3) The image is attached below.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.

1)

Angle: An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Therefore first image is ∠ABC.

In mathematics, a ray is a segment of a line with a fixed starting point but no ending.

The fixed point is B. Then second image represents \(\overrightarrow{BA}\). The sixth image represents two rays that are \(\overrightarrow{BC}\) and \(\overrightarrow{BA}\),

A point is a basic concept in traditional Euclidean geometry that represents an exact place in space and has no length, breadth, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.

The image represent point C.

A plane is an infinitely long, Euclidean, two-dimensional surface in mathematics. A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.

The fourth image represent Plane W. The eighth image represents Plane ABC.

The seventh image represents  \(\overleftrightarrow{AB}\) and the ninth image represents line m.

2)

The translation rule is

(x,y) → (x-3, y+4)

(a) The translation of the point (-3,5) is (-3 -3, 5 + 4) = (-6,9).

(b) The translation of the point (0,-4) is (0 -3, -4 + 4) = (-3,0)

(c) No, since a function consists of one variable. But in the translation, there is two variables.

3)

The vertices of △PQR are P(1,-1), Q(3,-2), R(3,-4).

The rule of 180° rotation about origin is (x,y) → (-x,-y)

After rotation, P'(-1,1), Q'(-3,2), R(-3,4).

The rule reflection about x-axis is (x,y) → (x,-y)

After reflection,  P''(1,1), Q''(3,2), R''(3,4).

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Answer:

7 Days

Step-by-step explanation:

Miles cost:

$0.10 * 200 = $20

Daily Cost

Her budget at this point is $330 because $350 - $20 (the miles)

$330 / 42.72  = Roughly 7.72

Therefore Zoey can drive for 7 days before her budget runs out.

Answer:

but what to do in do I have to find the area of the particular Region or a length of that

Answer:

24/9

Step-by-step explanation:

-20-4=-24

-8-1=-9

1. The percentage of people surveyed in East Harlem is 58.5%

2. The percentage of people surveyed in Upper East Side is 41.5%

From the question given above, the following data were obtained:

1. Determination of the percentage of people surveyed in East Harlem.

Percentage of East Harlem = (people surveyed in East Harlem / Total) × 100

Percentage of East Harlem = (183/313) × 100

Percentage of East Harlem = 58.5%

2. Determination of the percentage of people surveyed in Upper East Side.

Percentage of Upper East Side = (Total percentage) – (Percentage of East Harlem)

Percentage of Upper East Side = 100 – 58.5

Percentage of Upper East Side = 41.5%

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The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.

This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.

x²+4x=1

as, the x has coefficient 4.

so,

half the coefficient of x and add and subtract the square of the remaining.

x²+4x + 2 ² - 2² =1

Now,

make the whole square term

x²+4x + 2 ² - 4 - 1=0

( x + 2)² -5= 0

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Answer: Option B, i.e., \(h=\dfrac{V}{\pi r^2}\)

Option C, i.e., \(h=4\text{ cm}\).

Step-by-step explanation:

It is given that formula for the volume V of a cylinder is

\(V=\pi r^2h\)

We need to find the formula for h.

Divide both sides by \(\pi r^2\).

\(\dfrac{V}{\pi r^2}=h\)

\(h=\dfrac{V}{\pi r^2}\)

Therefore, the required formula for height is \(h=\dfrac{V}{\pi r^2}\). Hence option B is correct.

If volume is 36π cm³ and base with a radius of 3 cm, then height of the cylinder is

\(h=\dfrac{36\pi}{\pi (3)^2}\)

\(h=\dfrac{36}{9}\)

\(h=4\text{ cm}\)

Therefore, the height of a cylinder is 4 cm. Hence option C is correct.

1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

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No, the assertion made by your buddy is false. It is impossible to utilize the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate itself. You must employ known facts and theorems rather than the theorem you are attempting to show in order to prove a theorem.

If your buddy is utilizing the SSS congruence theorem (Thm. 5.8) and the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate the theorem, they are not offering a proper proof since they are employing the theorem they are attempting to demonstrate as part of the proof itself. This results in a circular argument and is invalid as evidence

The parallelogram opposing sides theorem has to be proven using other well-known facts and theorems, like the definition of a parallelogram, the definition of congruent figures, and other relevant theorems and postulates from geometry.

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The value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n

The expression is given as

(n+8)(n-4) - (n+3)(n-2) + 27

Open the brackets

So, we have

n^2 + 8n - 4n - 32 - n^2 - 3n + 2n - 6 + 27

Collect the like terms

So, we have

n^2 - n^2 - 3n + 8n - 4n  + 2n - 32  - 6 + 27

Evaluate the like terms

So, we have

3n - 11

The above expression cannot be expressed as a factor of 3

Hence, the value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n

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Answer:

130

Step-by-step explanation:

120 - (-10)

120 + 10

change it to add then remove the negative

Answer:

For a random sample of 4 players, the sampling distribution of the sample mean age would have:

the mean wouldn't be close to 26.8 years, as a sample mean will be an unbiased estimator of the population mean but the sample here is far smaller than a sample of 50.

A larger standard deviation compared to the standard deviation of individual player ages (4.2 years), as the standard deviation of the sample mean decreases with larger sample sizes (i.e., the Central Limit Theorem). The standard deviation of the sample mean for a sample of 4 players can be calculated using the formula:

s_mean = s / sqrt(n)

where s is the population standard deviation (4.2 years) and n is the sample size (4).

For a random sample of 50 players, the sampling distribution of the sample mean age would have:

A mean close to 26.8 years, as the sample mean will be an unbiased sample mean for a sample of 4 players, as the standard deviation of the estimator of the population mean.

A smaller standard deviation compared to the standard deviation of the sample mean decreases with larger sample sizes (i.e., the Central Limit Theorem). The standard deviation of the sample mean for a sample of 50 players can be calculated using the formula:

s_mean = s / sqrt(n)

where s is the population standard deviation (4.2 years) and n is the sample size (50).

After cutting each of the four 1-meter ropes into fifths, Drew would have a total of 5 * 4 = 20 pieces of rope, each measuring 0.2 meters in length.

If Drew has four pieces of rope, each measuring 1 meter long, and he cuts each of them into fifths, we can calculate the length of each resulting piece.

Since each rope is cut into fifths, each fifth would have a length of 1 meter divided by 5, which is 0.2 meters (or 20 centimeters).

As Drew cuts each rope into fifths, he would obtain 5 pieces from each rope, with each piece measuring 0.2 meters in length.

Therefore, after cutting each of the four 1-meter ropes into fifths, Drew would have a total of 5 * 4 = 20 pieces of rope, each measuring 0.2 meters in length.

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Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.

According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.

To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.

Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.

Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.

Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.

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Answer:

The answer is 24

Step-by-step explanation:

Simplify using distributive property.

2*9+2*3=18+6

Add

18+6=24

I hope this has helped you, have a wonderful day.

Answer:

24

Step-by-step explanation:

First we add the 2 numbers in the parentheses.

9 + 3 = 12

Then we multiply the result by 2.

2(12) = 24

Step-by-step explanation:

=

−

±

2

−

4

√

2

x=2a−b±b2−4ac​​

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

9

2

−

8

1

=

0

9x^{2}-81=0

9x2−81=0

=

9

a=

a=9

=

0

b={\color{#e8710a}{0}}

b=0

=

−

8

1

c={\color{#129eaf}{-81}}

c=−81

=

−

0

±

0

2

−

4

⋅

9

(

−

8

1

)

√

2

⋅

9

x=2⋅9−0±02−4⋅9(−81)​​

Answer:

see explanation

Step-by-step explanation:

4x + 10 = 2y - 4x ( add 4x to both sides )

8x + 10 = 2y , that is

2y = 8x + 10 ( divide through by 2 )

y = 4x + 5

then

x = 2 : y = 4(2) + 5 = 8 + 5 = 13

x = 4 : y = 4(4) + 5 = 16 + 5 = 21

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

so table is

 x      y

-----------

 2      13

  4      21

 - 1        1

Answer:

21

Step-by-step explanation:

i rest my case

Answer:

3

Step-by-step explanation:

2+1=3 trust me