which of the following equations are linear?

y=2x - 1/2

y= -1/2x +2

y= -x^2

Answer:

y = (1/8)x

Step-by-step explanation:

The relevant basic formula is y = kx, where k is the constant of proportionality.

We must find k.  To do this, let y = 15/6 and x = 20 in the above formula:

15/6 = k(20)

We solve for k by dividing both sides by 20:  15/(6*20) = k = 1/8

Then the specific formula for this situation is y = (1/8)x

Answer:

k/j

Step-by-step explanation:

i just took the test, good luck!

Answer:

X=25

Step-by-step explanation:

y+2=-7+2=5

\(5^{2} =25\)

Answer:

$65

Step-by-step explanation:

Add 53 and 12 together to see how much it costed.

The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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So, the system of equations representing this situation is: n + d + q = 95; 0.05n + 0.10d + 0.25q = 13.70; q = d + 11.

To represent this situation with a system of equations, we can use the following equations:

The total number of coins: n + d + q = 95

The total value of the coins in dollars: 0.05n + 0.10d + 0.25q = 13.70

The relationship between the number of quarters and dimes: q = d + 11

The first equation represents the total number of coins, which is given as 95.

The second equation represents the total value of the coins in dollars, which is given as $13.70. The values of each coin (nickel, dime, quarter) are multiplied by their respective quantities (n, d, q) and summed up to obtain the total value.

The third equation represents the relationship between the number of quarters (q) and dimes (d), which states that there are 11 more quarters than dimes.

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Answer:

C. strong

Step-by-step explanation:

all the points are close to or on the set line of balance.

Answer:

Step-by-step explanation:

strong

Answer:

The value of x that minimizes the total area of the two squares is x = 5.

Step-by-step explanation:

A wire 10 centimeters long is cut into two pieces, with one piece measuring x centimeters and the other (10 - x) centimeters.

Each piece is bend into the shape of a square, and we want to find the value of x that minimizes the total area of the two squares.

If x is bend into a square with four equivalent sides, then each side measure:

\(\displaystyle A = \frac{x}{4}\)

Likewise, each side of the second square will measure:

\(\displaystyle A = \frac{10-x}{4}\)

The area of a square is its side squared. Hence, the area of both squares will be given by:

\(\displaystyle T = \left( \frac{x}{4}\right) ^2 + \left(\frac{10-x}{4}\right)^2\)

Simplify:

\(\displaystyle \begin{aligned} T &= \frac{x^2}{16} + \frac{x^2 - 20x + 100}{16} \\ \\ &=\frac{2x^2-20x+100}{16}\\ \\ &= \frac{1}{8}x^2-\frac{5}{4}x+\frac{25}{4} \end{aligned}\)

Since this is a quadratic with a positive leading coefficient, the minimum value will occur at the vertex point.

Recall that the x-coordinate of the vertex is given by:

\(\displaystyle x = -\frac{b}{2a}\)

In this case, a = 1/8 and b = - 5/4. Hence:

\(\displaystyle x = -\frac{\left(-\dfrac{5}{4}\right)}{2\left(\dfrac{1}{8}\right)} = 5\)

In conclusion, the value of x that minimizes the total area of the two squares is x = 5.

The height of the tree to the nearest tenth is; 29.66 ft

Similar triangles are defined as the triangles that have the same shape, but their sizes may vary.

Using Pythagoras theorem on the smaller triangle gives the smaller unknown side as;

x = √(9² - 7²)

x = √32

Similarly we will use Pythagoras theorem on the bigger triangle to get;

x' = √(25² - 7²)

x' = √(625 - 49)

x' = √576

x' = 24

Thus, height of tree = x + x'

= 24 + √32

= 29.66 ft

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Answer:

71 inches

Step-by-step explanation:

two feet is 24 inches,

one yard is 36 inches.

11 + 24 + 36 = 71

hope this helped! <3

Tabitha uses 72 inches of trim for her craft project.

Two or more expressions with an Equal sign is called as Equation.

Given,

Tabitha used 3 different decorative trims for a craft project.

She cuts lengths of 11 inches, 2 feet and 1 yard.

We need to find how much trim did Tabitha used for project in inches.

So we have to convert feet to inches and yard to inches

1 feet =12 inches and 1 yard is 36 inches

Total trim used=12 inches+two feet+one yard

=12 inches+2(12 inches)+1(36 inches)

=12 inches+24 inches+36 inches

=72 inches

Hence Tabitha uses 72 inches of trim for her craft project.

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The magnitude of the vector →u is √61 and the angle in which the vector points is approximately 5.06 radians.

The magnitude of a vector →u=⟨5,−6⟩ is given by the formula:

|→u|=√(5^2+(-6)^2)=√(25+36)=√61

The angle θ in which the vector points can be found using the formula:

θ=tan^−1(−6/5)

Since the vector →u is in the fourth quadrant, we need to add 2π to the angle to get the angle in the counterclockwise direction from the positive x-axis:

θ=tan^−1(−6/5)+2π≈5.06

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We need to find the value of x dy - y dx along the line segment connecting the points (x1, y1) and (x2, y2) is (x2y2 - x2y1).

To find the value of x dy - y dx along the line segment c, we need to parameterize the line segment and then compute the integral. Let's parameterize the line segment c as follows:

x = x1 + t(x2 - x1)

y = y1 + t(y2 - y1)

where t is a parameter ranging from 0 to 1.

Now, we can express dx and dy in terms of dt:

dx = (x2 - x1) dt

dy = (y2 - y1) dt

Substituting these expressions into x dy - y dx, we have:

x dy - y dx = (x1 + t(x2 - x1))(y2 - y1) dt - (y1 + t(y2 - y1))(x2 - x1) dt

Expanding and simplifying this expression, we get:

x dy - y dx = (x1y2 - x1y1 + t(x2y2 - x2y1) - x2y1 + x1y1 + t(y2x1 - y1x1)) dt

Canceling out the common terms, we are left with:

x dy - y dx = (x2y2 - x1y1 - x2y1 + x1y1) dt

Simplifying further, we obtain:

x dy - y dx = (x2y2 - x2y1) dt

Therefore, the value of x dy - y dx along the line segment c connecting the points (x1, y1) and (x2, y2) is (x2y2 - x2y1).

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Describe four common ways in which individuals respond to perceived inequity are -

Equity, also known as shareholders' equity (or shareholders' equity for private companies), is the sum of money which would be handed back to a company ’s creditors if each of its assets have been liquidated and all of its debt was paid off in the event of liquidation.

Some key features regarding the equity are-

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Answer:

The points which are reflections across both axis are;

1) (1.5, -2) and  \(\left (-1\dfrac{1}{2} , \ 2\right )\)

2) (1.75, -4) and \(\left (-1\dfrac{3}{4} , \ 4\right )\)

Step-by-step explanation:

The coordinate of the image of a point after a reflection across the 'x' and 'y' axis are given as follows;

\(\begin{array}{ccc}& Preimage&Image\\Reflection \ about \ the \ x-axis&(x, \ y)&(x, \, -y)\\Reflection \ about \ the \ y-axis&(x, \ y)&(-x, \, y)\end{array}\)

Therefore, a reflection across both axis changes (only) the 'x' and 'y' value signs

The given points which are reflections across both axis are;

(1.5, -2) and  \(\left (-1\dfrac{1}{2} , \ 2\right )\)

We note that \(\left (-1\dfrac{1}{2} , \ 2\right )\) = (-1.5, 2)

The reflection of (1.5, -2) across the x-axis gives the image (1.5, 2)

The reflection of the image (1.5, 2) across the y-axis gives the image (-1.5, 2)

Similarly, we have;

(1.75, -4) and \(\left (-1\dfrac{3}{4} , \ 4\right )\)

We note that \(\left (-1\dfrac{3}{4} , \ 4\right )\) = (-1.75, 4)

The reflection of (1.75, -4) across the x-axis gives the image (1.75, 4)

The reflection of the image (1.75, 4) across the y-axis gives the image (-1.75, 4).

The other points have changes in the values of the 'x' and 'y' between the given pair and are therefore not reflections across both axis

Answer:

495

Step-by-step explanation:

Si desea saber de cuántas maneras puede elegir a 4 estudiantes de 12 para formar un comité, debe usar algunas matemáticas sofisticadas llamadas combinaciones. Esta matemática te dice cuántos grupos diferentes puedes hacer con un montón de cosas, sin importar quién va primero o último.

Las combinaciones matemáticas se ven así:

n C r = n! / (r! · (n - r)!)

donde n es el número de cosas que tienes, r es el número de cosas que quieres elegir, y ! significa factorial, que es una forma elegante de decir multiplicar todos los números de 1 a ese número.

En su caso, n es 12 (el número total de niños en la clase) y r es 4 (el número de niños en el comité). Entonces, poniendo estos números en las matemáticas, obtenemos:

12 C 4 = 12! / (4! · (12 - 4)!)

      = 12! / (4! · 8!)

      = (12 · 11 · 10 · 9 · 8!) / (4! · 8!)

      = (12 · 11 · 10 · 9) / (4 · 3 · 2 · 1)

      = 495

Entonces, hay 495 maneras de elegir un comité de 4 de una clase de 9 niños y 3 niñas.

¡Eso es un montón de comités! Me pregunto qué hacen todo el día.

In triangle JKL the measurement of line segment KJ is obtained as 22 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

Two triangles - ΔJKL and ΔPQR is given.

It is given that both the triangles are similar.

In ΔJKL, the ∠LJK = 35° and in ΔPQR, the ∠RPQ = 35°.

In ΔJKL, the measurement of line segment LJ is = 28 units

In ΔJKL, the measurement of line segment KJ is = x units

In ΔPQR, the measurement of line segment RP is = 42 units

In ΔPQR, the measurement of line segment QP is = 33 units

To find the value of x use the method of indirect measurement.

According to the rule of indirect measurement -

LJ/RP = KJ/33

Substituting the values into the equation -

28 / 42 = x / 33

28 × 33 = 42x

x = (28 × 33) / 42

x = 924 / 42

x = 22 units

Therefore, the measurement of x is 22 units.

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To determine the distance traveled by Katie at different marks, we can use the formula Distance = Rate × Time.

To determine how far Katie has traveled at each mark, we can use the formula:
Distance = Rate × Time

So, the elements in the range of the function that would be used to determine how far Katie has traveled at each mark are 384 miles, 416 miles, and 448 miles.

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The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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The probability of a sample proportion of non-vaccinated children in a sample of 800 children more than 185/800 is approximately 0.7937, or 0.7936 when rounded to four decimal places.

The sample proportion is given by: p-hat = 185/800 = 0.23125So, the probability of a sample proportion of non-vaccinated children in a sample of 800 children more than 185/800 is to be determined.

To determine this probability, we need to find the z-score associated with the given sample proportion. z = (p-hat - p) / √[p(1-p)/n]where n = 800, p = 0.25, and p-hat = 0.23125Substituting these values, we get z = (0.23125 - 0.25) / √[(0.25 x 0.75) / 800]= -0.014559 / 0.017789= -0.81796Using a standard normal distribution table, we can find that the area to the left of this z-score is 0.2063.

Therefore, the probability of a sample proportion of non-vaccinated children in a sample of 800 children more than 185/800 is approximately 0.7937, or 0.7936 when rounded to four decimal places.

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Answer: The area is 6.5

The correct answer for the first question is B.

Only statement 2 is accurate. Statement 1 is incorrect because an entire set of data is typically referred to as a population, not a distribution. A distribution refers to the pattern or spread of data within a population or sample.

For the second question, Ibrahim, as a planner in the Quality Assurance Department of Free Free plc, would belong to the operating core building block. Mintzberg's organizational structure theory defines the operating core as the individuals directly involved in producing the organization's products or services. Since Ibrahim is part of the Quality Assurance Department, which is responsible for ensuring the quality of the products, he falls under the operating core category. The support staff typically includes administrative or auxiliary personnel, the middle line refers to managers responsible for coordinating and overseeing different departments, and the technostructure consists of individuals who specialize in analytical and support functions related to the organization's operations.

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The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

In the Social Exchange Theory of interpersonal relationship satisfaction, you would feel happiest in relationships when you feel that the rewards of the relationship equal or exceed its costs.

The Social Exchange Theory states that people evaluate their relationships in economic terms, with rewards being the benefits of the relationship and costs being the negatives. Rewards can include affection, attention, emotional support, sex, and companionship. Costs can include time, effort, money, and negative emotions such as stress, anxiety, and sadness.

According to the theory, individuals will be motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

The opposite is also true; if individuals feel that the costs of the relationship are greater than the rewards, they will be motivated to leave the relationship.

Therefore, people are constantly evaluating their relationships to determine whether they are getting what they need from the relationship and whether it is worth continuing.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

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You like to watch movies at the local theater. You have two payment options. Your first option is to buy a discount card which will cost you $160, and then $20 for m movies, 20m + 160. Your second option will cost you $100, and then pay $40 for m movies, 40m + 100. After how many movies will the total costs of the two options be the same?

the answers is 3

Answer:

X. y

10. $7

24. $14

38. $ 21

If a storage tank holds 50,000 gallons of water then its volume is 189.25 cubic meters.

The volume of the storage tank in cubic meters can be calculated by first converting the volume from gallons to liters and then converting from liters to cubic meters.

Step 1: Convert the volume from gallons to liters:
50,000 gallons * 3.785 liters/gallon = 189,250 liters

Step 2: Convert the volume from liters to cubic meters:
189,250 liters * (1 cubic meter/1000 liters) = 189.25 cubic meters

Therefore, the volume of the storage tank is 189.25 cubic meters.

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

56 tests

Step-by-step explanation:

first find the amount of test he took each week. if we divide 12 by 6 (12 ÷ 6 = 2) we find out that he took 2 tests per week.

So if he continues with the same rate for the next 28 weeks of school, in order to find out how many tests he would have taken, we just need to  multiply 28 by 2 (28 × 2 = 56), which will be equal to 56

hope this helps! if you have any questions, let me know!

Using the concepts of domain and range of functions, we have that:

10. The range is y ≥ 2.

11. The domain is all real numbers, the range is y ≤ 3, and it is a function.

12. The domain is (-4,3], and the range is (-5,5).

Hence, for these problems:

10. The range is y ≥ 2.

11. The domain is all real numbers, the range is y ≤ 3, and it is a function.

12. The domain is (-4,3], and the range is (-5,5).

In item 11, we have that it is a function because it has no vertically aligned points, that is, each value of x is associated with only one value of y.

In item 12, the open intervals are due to the open circles at the extremes of the domain and the range on the graph.

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