1/2x-7=1/3(x-12) Explain or show your reasoning.

Answer:

x = -7

Step-by-step explanation:

Two parallel lines are lines that never intersect each other.

The y-axis can be written as x = 0.

Then if we want a parallel line to this one, it must be something like x = b

such that b ≠ 0.

Now we want that the distance between our line and the line x = 0 is 7 units to the left

(remember that the left is the negatie side of the axis)

then we can write:

b - 0 = -7

b = -7

The parallel line is x = -7

If you are looking for the equation, then it would be y = -x+3

This is the same as y = -1x+3 which is in slope intercept form y = mx+b

m = -1 = slope

b = 3 = y intercept

If you want to graph this, then plot the points (0,3) and (1,2). Then draw a straight line through them both. Extend the line in both directions as much as possible.

Answer:

y = -x + 3

Step-by-step explanation:

If you are asking for the equation of the function in slope-intercept form, this should be your answer.

The slope-intercept for in its general equation is:

y = mx + b

In this equation, "m" is the slope and "b" is the y-intercept.

Since you were given the value of these variables, you can plug them in to get your final equation.

slope = m = -1

y-intercept = b = 3

y = mx + b

y = -1x + 3

y = -x + 3

The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

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

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

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The required value of  P for the given problem is 14 units.

There are six elements of a point usually utilized in  trigonometry.. Their names and shortenings are sine (sin), cosine (cos), digression (tan), cotangent (bed), secant (sec), and cosecant (csc).

We have,

c = 28 units, angle(∅) = 30°

Using sine function to solve the problem.

Sin(∅) = perpendicular/hypothenius

Sin(30°) = P/28

P = 28/2 = 14 units

Thus, required value of P is 14 units.

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The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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Answer:

the answer is 3+h

Step-by-step explanation:

h = hard cover books

3 = how much you get

so the answer is 3+h

We know that function f(x) is given by

where the slope is the coefficient of the variable x, that is, the slope,m, is

Since g(x) is given by

we have that

where the slope is equal to 6, in other words

Therefore, the slope of the graph of g(x) is 6 times the slope of the graph of f(x).

Since the y-intercept of f(x) is zero, then the y-intercept of g(x) is zero too. Then, the answer is: the y-intercept does not change.

Answer: y=-3

Step-by-step explanation:

slope intercept form:y=mx+b

m= slope

b= y-intercept

use the slope formula to get the slope

y2-y1/x2-x1

-3-(-3)/18-3

0/15

0

y=0x+b

plug in values from (3,-3) and solve for b

-3=0(3)+b

-3=b

y=-3

To report the $39.1 million debt on its December 31, 2024, balance sheet, Bahamas Airlines would classify the debt into two categories: current liabilities = $6,200,000 and long-term liabilities =  $32,900,000.

To report the $39.1 million debt on its December 31, 2024, balance sheet, Bahamas Airlines would classify the debt into two categories: current liabilities and long-term liabilities.

Current Liabilities: The portion of the debt that is due within the next year, which is $6.2 million, would be reported as a current liability. This amount represents the short-term portion of the debt that needs to be repaid within the next year.

Long-Term Liabilities: The remaining portion of the debt, which is the difference between the total debt and the current liability, would be reported as a long-term liability. In this case, it would be $39.1 million - $6.2 million = $32.9 million.

Therefore, Bahamas Airlines would report the $39.1 million debt on its December 31, 2024, balance sheet as follows:

Current Liabilities:

Debt due within the next year: $6,200,000

Long-Term Liabilities:

Debt due after one year: $32,900,000

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The total number of leaves that the science display have is 101 leaves.

As per the question, Thomas wants to display leaf specimens for a science fair.  Thomas has 98 leaves.

Total number of leaves Thomas have = 98

Thomas has 98 leaves, which is 3 fewer than the total needed. To calculate the total number of leaves Thomas need in the science display , we need to add 3 leaves in the total number of leaves Thomas have. So, we can write this mathematically as,

Total number of leaves that the science display have = Total number of leaves Thomas have + 3

Total number of leaves that the science display have = 98 + 3 = 101

So, the science display have a total of 101 leaves.

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Solution:

Given:

Question 1:

\(\\ \sf\longmapsto \dfrac{8}{x}=\dfrac{12}{18}\)

\(\\ \sf\longmapsto 12x=18(8)\)

\(\\ \sf\longmapsto 12x=144\)

\(\\ \sf\longmapsto x=\dfrac{144}{12}\)

\(\\ \sf\longmapsto x=12\)

AP / PB = AQ / QC

8 / x = 12 / 18

8 / x = 6 × 2 / 6 × 3

8 / x = 2 / 3

Inverse both sides :

x / 8 = 3 / 2

Multiply both sides by 8

8 × x / 8 = 8 × 3 / 2

x = 2 × 4 × 3 / 2

x = 4 × 3

x = 12

The equation (1 – 2z²)y" – ay = 0 is satisfied by y = arcsin z.


We are given y = arcsin z. Using the chain rule of differentiation, we can show that:y' = 1/√(1 - z²)zy'' = -z/((1 - z²)³/²)

We can use these expressions to find y" in terms of y and z.

To do this, we differentiate the expression for y' with respect to z.

This gives:y" = -1/(1 - z²)³/² + z²/(1 - z²)^(5/2)We can now substitute these expressions into the differential equation (1 – 2z²)y" – ay = 0, and simplify:y" = -1/(1 - z²)³/² + z²/(1 - z²)^(5/2)(1 – 2z²) - ay/(1 - z²)

Now, using the identity 1 - z² = sin² y, we can simplify this expression further:y" = -1/√(1 - z²)² + z²/√(1 - z²)⁴(1 - 2z²) - ay/√(1 - z²)²= -cos y + z²sin²y(1 - 2sin²y) - a

This can be rewritten as:(1 – 2?)y" – ay = 0

Therefore, we have shown that y = arcsin z satisfies the second-order differential equation (1 – 2z²)y" – ay = 0.

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Answer:

4 1/6

Step-by-step explanation:

2 1/2 times 1 2/3 change those numbers into an improper fraction which are 5/2 for 2 1/2 and 5/3 for 1 2/3 multiply 5/2 and 5/3 you get 25/6 change the 25/6 into a mixed number and you get 4 1/6

Answer:

2*(-2)+3*-3+5

=4-9+5

=9-9

=0

Answer:

Equation should be: 15x + 5 = y

Step-by-step explanation:

I do not know the amount of money that he owed

For Example :

15(12) + 5 = y

180 + 5 = y

y = 185

Sorry if I'm incorrect

Answer:

56/40 + 15/40 = 71/40

Step-by-step explanation:

Answer:

15/40

8/40

23/40

Step-by-step explanation:

it's hard to explain

Answer:

55

Step-by-step explanation:

bedcause if you add 50 and 5 then it makes yes

The number of papers checked by both becomes equal in 10 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Teacher Malone is reviewing papers in the educators' parlor. She has previously gotten done with reviewing 20 tasks and is evaluating 5 additional tasks each hour. Her showing colleague just came in to help her. He can grade at a pace of 7 tasks consistently.

Let 'x' be the number of hours and 'y' be the number of assignments. Then the equations are given as,

y = 5x + 20        ...1

y = 7x                ...2

At some point, they will be finished and will have graded the same number of papers. Then from equations 1 and 2, we have

7x = 5x + 20

7x - 5x = 20

2x = 20

x = 20 / 2

x = 10

The number of papers checked by both becomes equal in 10 hours.

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The number of bears living in the area after 17 years is; 22555

We are given the function;

f(t) = 103/(1 + 26e^(-0.31t))

Where f(t) is a function that models the number of bears living in the area after t period of years.

Thus, to find the number of bears living in the area after 17 years, we will just substitute 17 for t in the given function to get;

f(17) = 103/(1 + 26e^(-0.31*17))

f(17) = 103/0.00456653759

f(17) ≈ 22555 bears

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Answers:

==================================================

Explanation:

For problems 1 and 2, we just multiply the base and height. This is the same as multiplying the length and width.

So in problem 1 we have 10*12 = 120 square feet. In problem 2 we have 6*10 = 60 square inches.

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

Problem 3 follows the same idea, but we do a bit more work. The area of the garden is 5*12 = 60 square feet.

Let's say x is the number of bags needed.

1 bag covers 6 square feet

2 bags cover 12 square feet

and so on

x of those bags cover 6x square feet. The x is just a placeholder for a number. Specifically, a positive whole number.

The expression 6x represents how much area that can be covered by x bags. We want to cover 60 square feet.

The equation we need to solve is 6x = 60. Doing so leads to x = 10 after dividing both sides by 6.

So this means Travis needs 10 bags.

Part A: It can be written as y = sin(x - c), where c represents the amount of phase shift. Part B: We can use the equation y = sin(x - a), where a represents the amount of rightward shift. Part C: The period is the distance between corresponding points on the graph, such as two peaks or two troughs. Part D: There are infinitely many equations that can be written to map the parent sine function onto itself.

1. Part A: To introduce a phase shift to the parent sine function y = sin(x), we subtract a constant value c from the input variable x. The equation y = sin(x - c) has an identical graph to the parent sine function, but it is shifted horizontally by an amount of c units to the right or left. The value of c determines the amount of phase shift, where a positive value shifts the graph to the right, and a negative value shifts it to the left.

2. Part B: To map the parent sine function onto itself by shifting it to the right, we can use the equation y = sin(x - a), where a represents the amount of rightward shift. By subtracting a constant value a from the input variable x, the graph is shifted a units to the right while maintaining the same shape.

3. Part C: The equations in parts A and B indicate that the period of the sine function remains the same. The period of the sine function is the distance between corresponding points on the graph, such as two peaks or two troughs. Introducing a phase shift or rightward shift does not alter the period; it only changes the starting point or position of the graph.

4. Part D: There are infinitely many equations that can be written to map the parent sine function onto itself. By combining different values of phase shifts and rightward shifts, we can obtain various equations. The sine function is periodic, meaning it repeats itself indefinitely. Any combination of phase shift and rightward shift will result in the same graph repeating after a specific interval, which is the period of the sine function. Therefore, there is no limit to the number of equations that can be written to achieve this mapping.

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CI = 6.76 ± 1.96 × (2.67/√50)
CI = 6.76 ± 0.96
Therefore, the 95% confidence interval for the population means rating for Miami is: (5.80, 7.72)

We can be 95% confident that the true mean rating for Miami International Airport falls within this interval.
To develop a 95% confidence interval for the population means rating for Miami International Airport, we need to follow these steps:

1. Calculate the sample mean (x) by adding up all the ratings and dividing by the sample size (n=50).
2. Calculate the sample standard deviation (s).
3. Use a t-distribution to find the t-score for a 95% confidence interval with (n-1) degrees of freedom.
4. Calculate the margin of error (ME) using the t-score, standard deviation, and sample size.
5. Add and subtract the margin of error from the sample mean to find the lower and upper limits of the confidence interval.

To calculate the 95% confidence interval, we need to use the formula:
CI = x ± Z' (s/√n)
Where:
x = sample mean
Z' = z-score for the desired confidence level (in this case, 95%, so

Z' = 1.96)
s = sample standard deviation
n = sample size

Step 1: Calculate the sample mean (x)
Sum of ratings = 346
Sample size (n) = 50
x = 346/50 = 6.92

Step 2: Calculate the sample standard deviation (s)
Variance = [(Sum of (rating - x)^2) / (n-1)] = 88.48
Standard deviation (s) = √(88.48) = 9.41

Step 3: Find the t-score
For a 95% confidence interval with 49 (n-1) degrees of freedom, the t-score is approximately 2.01.

Step 4: Calculate the margin of error (ME)
ME = t-score × (s / √n) = 2.01 × (9.41 / √50) = 2.01 × 1.33 = 2.67

Step 5: Find the confidence interval
Lower limit: x - ME = 6.92 - 2.67 = 5.80
Upper limit: x + ME = 6.92 + 2.67 = 7.72

Thus, the 95% confidence interval for the population mean rating for Miami International Airport is approximately

(5.80, 7.72)

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Answer:

x = 38.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opposite/ adjacent

tan x = 8/10

Take the inverse tan of each side

tan ^-1 ( tan x) = tan ^-1 (8/10)

x = tan ^-1 (8/10)

x =38.65980825

To the nearest tenth

x = 38.7

(not my answer, cr wegnerkolmp2741o on brainly. i just saw that this wasn't answered properly and saw that a diff post with the same question was already answered)

1 Ampere = 1 Coulomb of charge per second

2.5 A  =  2.5 C of charge per second

Time to deliver 3.5 C of charge = (3.5 C) / (2.5 C / sec)

Time = (3.5 / 2.5) (C / C-sec)

Time = 1.4 sec

A current of 2.5 A delivers 3.5 C of charge in 1.4 seconds.

Answer:

$4.34

Step-by-step explanation:

Given the information:

We can find out the actual price that Diane bought a bunch of balloons that was marked down 20% is:

= the original price (100% - discount rate)

= 5(100% -20%)

= $4

= The actual price*tax rate

= $4*8.5%

= $0.34

=> the total cost of the bunch of balloons :

The actual price + tax price

= $4 + $0.34

= $4.34

Hope it will find you well.

Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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