solve for x in terms of y: 5y = 3x + 2

Using mathematical operators, the expression [15 + x - 3 7/10 + 9 15/100] ÷ [5x × 3² - 4 7/100] is simplified as [5(20x + 409)] / 4500x - 407

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

In this problem, we have to first of all write out the words and expression in mathematical form. To do this, we have to apply mathematical operators like addition, subtraction, multiplication and division.

This can be rewritten as:-

[15 + x - 3 7/10 + 9 15/100] ÷ [5x × 3² - 4 7/100]

Simplifying this, we have;

[5(20x + 409)] / 4500x - 407

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To obtain precise calculations and solutions, it would be helpful to have the dimensions and geometry of the truss and any other relevant information provided in the problem statement or accompanying diagram.

To determine the magnitude and direction of the force F and the reactions at points A and D in the given loaded truss, we need to analyze the equilibrium of forces. Based on the given information, the resultant force R is directed to the right with a magnitude of 12.4 kN. Here's how we can approach the problem:

Resolve Forces: Resolve the applied forces into their horizontal and vertical components. Let's label the forces as follows:Force at point A: F_A

Force at point B: F_B

Force at point C: F_C

Force at point D: F_D

Equilibrium in the Vertical Direction: Since the truss is in equilibrium, the sum of vertical forces must be zero.

F_A * cos(30°) - F_C = 0 (Vertical equilibrium at point A)

F_B - F_D = 0 (Vertical equilibrium at point D)

Equilibrium in the Horizontal Direction: The sum of horizontal forces must be zero for the truss to be in equilibrium.

F_A * sin(30°) + F_B - F_C * cos(60°) = R (Horizontal equilibrium)

Determine the Reactions: Solving the equations obtained from the equilibrium conditions will allow us to find the values of F_A, F_B, and F_D, which are the reactions at points A and D.

Calculate Force F: Once we know the reactions at A and D, we can calculate the force F using the equation derived from the horizontal equilibrium.

F_A * sin(30°) + F_B - F_C * cos(60°) = R

The size of the structure is necessary to determine the forces accurately. The dimensions and geometry of the truss, along with the loads applied, affect the magnitude and direction of the reactions and the forces within the truss members. Without the size of the structure, it would be challenging to determine the accurate values of the forces and reactions.

To obtain precise calculations and solutions, it would be helpful to have the dimensions and geometry of the truss and any other relevant information provided in the problem statement or accompanying diagram.

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The hydrogen emission spectrum provides strong evidence for energy levels in atoms.

The hydrogen emission spectrum refers to the set of wavelengths of light emitted by hydrogen atoms when excited by energy. These wavelengths are discrete and can be precisely measured. The unique set of wavelengths emitted by hydrogen can be explained by the Bohr model of the atom.

According to the Bohr model, the electrons in an atom occupy specific energy levels or shells. When an electron absorbs energy, it jumps to a higher energy level, or excited state. As it returns to its original energy level, it emits the excess energy in the form of light or radiation. The energy of the emitted light is directly related to the energy difference between the two levels.

The emission spectrum of hydrogen consists of several distinct lines of different wavelengths, each corresponding to the transition of an electron from a higher energy level to a lower energy level. The wavelengths of these lines are given by:

λ = R(1/n₁² - 1/n₂²)

where λ is the wavelength of the emitted light, R is the Rydberg constant (a physical constant), n₁ is the initial energy level, and n₂ is the final energy level.

This equation shows that the wavelengths of the emitted light are directly related to the energy difference between the two energy levels. Therefore, the hydrogen emission spectrum provides strong evidence for the existence of quantized energy levels in atoms.

In conclusion, the discrete wavelengths of light emitted by hydrogen can be explained by the quantized energy levels predicted by the Bohr model. This fundamental concept of quantization has far-reaching implications in modern physics, and its understanding is crucial in many areas of science and technology.

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Answer:

A

Step-by-step explanation:

42+6=48

48/2=24

24-6=18

(2*24)-6=18

The approximate probability of exactly two people in a group of seven having a birthday on April 15 is (C) \(7.4 x 10^-^6\)

To calculate the probability of exactly two people in a group of seven having a birthday on April 15, we can use the binomial distribution formula:

\(P(X = k) = C(n, k) * p^k * (1 - p)^(^n^-^k^)\)

Where:

So, plugging in the values, we get:

\(P(X = 2) = C(7, 2) * (1/365)^2 * (1 - 1/365)^(7 - 2)\)

\(= 21 * (1/365)^2 * (364/365)^5\)

\(= 2.38 x 10^-5\)

The probability of exactly two people in a group of seven having a birthday on April 15 can be calculated using the binomial distribution formula.

The formula takes into account the number of trials, the probability of success in a single trial, and the number of successes desired.

In this case, we want to find the probability that exactly two people in a group of seven have a birthday on April 15, assuming that all days of the year are equally likely for a birthday.

Plugging in the values into the formula gives us an approximate probability of \(7.4 x 10^-^6\), which is the answer (C).

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Answer:

i dont know if you typed this correctly but 59+12=29+18 is false

Step-by-step explanation:

i know if what your looking for but o well  

Answer:

The description of the set is \(A = \{s\in \mathbb{C}|\|s\| = 2\}\).

Step-by-step explanation:

From Complex Analysis, we remember that complex numbers are numbers whose form is:

\(s = a+i\, b\), \(a,b \in \mathbb{R}\) (1)

Where \(i = \sqrt{-1}\).

In addition, the distance from the origin is defined by the following Pythagorean identity:

\(\|s\| = \sqrt{a^{2}+b^{2}}\) (2)

The following condition must be satisfied:

\(\|s\| = 2\)

Then, the set of all complex numbers that are at a distance of 2 units from the origin is described below:

\(A = \{s\in \mathbb{C}|\|s\| = 2\}\) (3)

The set of all complex numbers that are at a distance of 2 units from the origin is \(\{z\in \mathbb{C} :\text{ }|z|=2\}\)

A complex number, written in rectangular form is

\(z=a+ib\\a,b\in \mathbb{R}\)

The distance of a complex number from the origin (the modulus of the complex number, denoted by \(|z|\)) is given by the formula

\(|z|=\sqrt{a^2+b^2}\)

Since we want all the complex numbers to be at the distance of 2 units from the origin, they must satisfy

\(|z|=2\)

thus, the set we are looking for is

\(D=\{z\in \mathbb{C} :\text{ }|z|=2\}\)

where \(\mathbb{C}\) is the set of all complex numbers

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The point- slope form of the line is y-5 = -0.25(x+6).

What is line?

A line is an one-dimensional figure. It has length but no width. A line can be made of a set of points which is extended in opposite directions to infinity. There are straight line, horizontal, vertical lines or may be parallel lines perpendicular lines etc.

A line with a slope of –1/4 passes through the point (–6,5)

Any line in point - slope form can be written as

y - y₁= m(x -x₁) -------(1)

where,

y= y coordinate of second point

y₁ = y coordinate of first point

m= slope of the line

x= x coordinate of second point

x₁ = x coordinate of first point

In the given problem (x₁ , y₁) = (-6,5) and m= -1/4

Putting all these values in equation (1) we get,

y-5= (-1/4) (x- (-6))

⇒ y-5 = -0.25(x+6)

Hence, the point- slope form of the line is y-5 = -0.25(x+6).

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Answer:

D

Step-by-step explanation:

4.8 • 10^3 = 4,800

4,800/200 = 24

To represent a number in scientific notation, there can only be one number before the decimal. Therefore, simply divide 24 by 10 to get 2.4, and multiply it by 10^1 (equivalent to simply 10).

Answer:

5/6

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

-9-(-4)/-4-2

-5/-6

5/6

Best of Luck!

Answer: -2x + 12/5

Step-by-step explanation:

y < -2x - 1

Or it could be some variation of this, like 2x + y < -1

Bill has a total of 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. To find the number of possible outfits he can wear to work, we can use the multiplication principle.

First, we need to determine how many choices Bill has for his top and bottom. He can either wear a jumpsuit or a combination of pants and a shirt. Therefore, he has 3 + (5 x 8) = 43 choices for his top and bottom.

Next, we can use the multiplication principle to determine the total number of possible outfits he can wear. Since he has 43 choices for his top and bottom, and each outfit combination is independent of the others, we can multiply the number of choices for his top and bottom by the number of one-piece jumpsuits he has.

Therefore, Bill has a total of 43 x 3 = 129 possible outfits he can wear to work.

In summary, Bill has 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. He can wear either a jumpsuit or pants and a shirt to work. Using the multiplication principle, we determined that he has a total of 129 possible outfits he can wear.

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1. Three examples of situations where consistency is important:

Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.

Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.

Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.

2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.

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Answer:

\(\begin{array}{|c|c|}\cline{1-2} \sf I\:\!nput & \sf Ou\:\!tput\\\cline{1-2} \sf Muffins & \sf Cost\\\cline{1-2} 1 & 2.25\\\cline{1-2} 3 & 6.75\\\cline{1-2} 6 & 13.50\\\cline{1-2} x & 2.25x\\\cline{1-2} 12 & 27\\\cline{1-2} \end{array}\)

Step-by-step explanation:

Definitions:

To determine if the relationship is linear, calculate the rate of change between the ordered pairs given in the table:

\(\implies \sf rate\;of\;change=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{13.50-6.75}{6-3}=\dfrac{6.75}{3}=2.25\)

\(\implies \sf rate\;of\;change=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{6.75-2.25}{3-1}=\dfrac{4.5}{2}=2.25\)

As the rate of change is the same, the relationship is linear.

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

The rate of change is the slope of a linear equation.

Therefore, to create an equation, substitute the found slope (2.25) and one of the ordered pairs (1, 2.25) into the formula:

\(\implies y-2.25=2.25(x-1)\)

\(\implies y-2.25=2.25x-2.25\)

\(\implies y=2.25x\)

Therefore, the output is 2.25 times the input.

If the input is x, then the output is 2.25x.

If the input is 12, then the output is 2.25 × 12 = 27.

\(\begin{array}{|c|c|}\cline{1-2} \sf I\:\!nput & \sf Ou\:\!tput\\\cline{1-2} \sf Muffins & \sf Cost\\\cline{1-2} 1 & 2.25\\\cline{1-2} 3 & 6.75\\\cline{1-2} 6 & 13.50\\\cline{1-2} x & 2.25x\\\cline{1-2} 12 & 27\\\cline{1-2} \end{array}\)

Answer:

-----------------------------------

Number of hours is h.

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

The distance that she runs from one corner of the field to another is:

147.1 yards.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:

d² = 85² + 120²

d = \(\sqrt{(85)^2+(120)^2}\)

d = 147.1 yards.

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Answer:If p and q vary inversely, it means that their product remains constant. So we can set up the equation:

p * q = k

where k is the constant of variation.

Given that p is 29 when q is 25, we can substitute these values into the equation:

29 * 25 = k

725 = k

Now, let's determine the value of q when p is equal to 5:

p * q = k

5 * q = 725

Dividing both sides of the equation by 5:

q = 725 / 5

q = 145

Therefore, when p is equal to 5, q is equal to 145.

Step-by-step explanation:

Answer:p1q1=p2q2

q1=25,p1=29;

p2=5,q2=?;

q2=p1q1/p2;

q2=25*29/5;

q2=29*5;

q2=145.

Step-by-step explanation:

Therefore, the resulting error in the volume of the sphere is approximately 1.13 cubic inches.

To estimate the resulting error in the volume of the sphere, we can use linear approximation. The formula for the volume of a sphere is given by:

V = (4/3)πr³

where V is the volume and r is the radius.

The linear approximation formula is given by:

ΔV ≈ dV/dr × Δr

where ΔV is the resulting error in the volume, dV/dr is the derivative of the volume with respect to the radius, and Δr is the error in the radius.

Taking the derivative of the volume formula with respect to the radius, we have:

dV/dr = 4πr²

Given that the radius is claimed to be 3.0 inches, correct to within 0.01 inch, we can consider the error (Δr) to be 0.01 inch.

Now we can substitute the values into the linear approximation formula:

ΔV ≈ dV/dr × Δr

ΔV ≈ (4π(3.0)²) × 0.01

ΔV ≈ (4π(9.0)) × 0.01

ΔV ≈ (36π) × 0.01

ΔV ≈ 0.36π

Approximating π to be 3.14, we can calculate the resulting error:

ΔV ≈ 0.36π

ΔV ≈ 0.36 × 3.14

ΔV ≈ 1.13 cubic inches

Therefore, the resulting error in the volume of the sphere is approximately 1.13 cubic inches.

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Answer:

Step-by-step explanation:

y - 1 = -9/2 (x + 7)

Distribute -9/2:

y - 1 = -9/2x - 63/2

Add 1 on both sides to isolate y:

(y - 1) + 1 = (-9/2x - 63/2) + 1

y = -9/2x -61/2

A line parallel to another has the same slope as that line so both slopes are -9/2.

M = -9/2

According to the question this equation represents a single point in the xy-plane, and does not have a constant rate of change. It doesn't have a linear function as a result.

When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.

Equation representing a linear function:

Y is equivalent to x plus 5 times the negative one-fourth.

Linear functions have a constant rate of change, which means that as x increases or decreases by a certain amount, y also changes by a constant amount. The equation y equals negative one fourth times x plus 5 has a constant slope of negative one fourth, which means that for every increase of one in x, y will decrease by one fourth. This is a characteristic of a linear function.

The equation y equals two thirds times x squared represents a quadratic function, which has a curved graph.

The equation x = 5 is a linear equation, but it only represents a vertical line passing through x = 5. It does not have a slope or a y-intercept, which are necessary for a linear function.

The equation 2x + 7 = 12 can be simplified to a linear equation of the form y = mx + b by solving for y:

2x + 7 = 12

2x = 5

x = 5/2

Substituting x = 5/2 back into the equation gives:

y = 2(5/2) + 7 = 12

This equation represents a single point in the xy-plane, and does not have a constant rate of change. Therefore, it is not a linear function.

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Answer:

20 slices

Step-by-step explanation:

2 3/5 = 13/5

13/5 / 1/8

(13/5)(8/1) = 20.8

about 20 slices

If radius of sphere B is 5times radius of sphere A, then ratio of volume of sphere B to volume of sphere A is 125 , the correct answer is (c) .

Let the radius of the sphere B = r₁ , and

Let the radius of the sphere A = r₂ ;

So , The ratio of the volume of sphere B to the volume of sphere A is written as :

⇒ (Volume of sphere B)/(Volume of sphere A) = (4/3)πr₁³/ (4/3)πr₂³ ;

Simplifying the expression,

We get ,

⇒ (Volume of sphere B)/(Volume of sphere A) = (r₁/r₂)³ ,

It is given that the radius of sphere B is 5 times the radius of sphere A, which means that , r₁ = 5r₂ ,

Substituting the radius in the expression above,

We get ,

⇒ (Volume of sphere B)/(Volume of sphere A) = (5r₂/r₂)³ = (5)³ = 125 ;

Therefore, the ratio of volume of sphere B to sphere A is (c) 125.

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The given question is incomplete , the complete question is

If the radius of sphere B is 5times the radius of sphere A, then the ratio of the volume of sphere B to the volume of sphere A is

Select one:

(a) 0.008

(b) 25

(c) 125

(d) 5

(e) 0.2

Answer: no

Step-by-step explanation:

The quetion provides two functions, that is f(x) and g(x).

For what value of x is f(x) = g(x)

We can solve this by simply equating both functions, as shown below;

The answer is, when x = 3

**Note**

Thi can also be solved graphically and at the point where the graph of both function intersect, we'll have our answer. The graphs of f(x) and g(x) is shown below;

Note that the blue line represents

The green line represents

Observe carefully that both graphs intersect at the point -3.

Therefore, the value of x that makes f(x) = g(x) is -3

Answer:

Answer: A- 1.50$ for (1 lb) make sure you pick the graph with the coat that go to 7 not 12!

Step-by-step explanation:

but maybe its 1.25

Answer:

1.25

Step-by-step explanation:

The solution to the inequality is:

x ∈ (-∞, -21].

The correct option is F.

To solve the given inequality, we'll first simplify the expression:

23 < 3x - 3 ≤ -66

To simplify the inequality,

23 < 3x - 3 ≤ -66

Adding 3 to all parts of the inequality:

23 + 3 < 3x - 3 + 3 ≤ -66 + 3

Simplifying:

26 < 3x ≤ -63

Next, divide all parts of the inequality by 3:

26/3 < 3x/3 ≤ -63/3

Simplifying:

8.67 < x ≤ -21

Therefore, the solution to the inequality is:

x ∈ (-∞, -21]

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