For each function, determine whether y varies directly with x . If so, identify the constant of variation.

2 y=3

~Shoto Todoroki here~

Answer:

The answer is =−7

Step-by-step explanation:

This is a composition of functions

f(x)=x+8

g(x)=x2−6x−7

f(g(x))=f(x2−6x−7)=x2−6x−7+8=x2−6x+1

Therefore,

f(g(2))=22−6⋅2+1=4−12+1=

−7

hope this helps :D

Answer:

9.25x

Step-by-step explanation:

The area of trapezium with a median of 25 cm and height of 8 cm = 200 cm².

Area of trapezium = 1/2(a + b)h, where a and b are the parallel bases of the trapezium, and h is the height.

Note, median of a trapezium = half of the sum of the length of the two bases of a trapezium = 1/2(a + b). Therefore, the area of a trapezium with a given median would be:

A = median length × height

Given the following:

Area of trapezium = 25 × 8 = 200 cm².

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Answer:

the sale price of the flip flops after tax is $12.87.

Step-by-step explanation:

To calculate the sale price of the flip flops after tax, we need to consider both the discount and the sales tax. Here's how we can calculate it:Calculate the discounted price:

The flip flops cost $15, and there is a 20% discount. To find the discounted price, we subtract the discount amount from the original price:

Discounted price = $15 - (20% of $15)

To calculate the discount amount, we multiply the original price by the discount percentage (expressed as a decimal):

Discount amount = 20% of $15 = 0.20 * $15Discounted price = $15 - (0.20 * $15)Calculate the sale price after tax:

After applying the discount, we need to calculate the sales tax on the discounted price. To do this, we add the sales tax amount to the discounted price:

Sale price after tax = Discounted price + (7.25% of Discounted price)

To calculate the sales tax amount, we multiply the discounted price by the sales tax percentage (expressed as a decimal):

Sales tax amount = 7.25% of Discounted price = 0.0725 * Discounted priceSale price after tax = Discounted price + (0.0725 * Discounted price)Now, let's substitute the values and calculate:Discounted price = $15 - (0.20 * $15) = $15 - ($3) = $12Sale price after tax = $12 + (0.0725 * $12) = $12 + $0.87 = $12.87

Answer:

y=mx+b is the slop formula find the two points on the line or use desmos

Step-by-step explanation:

When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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Constant, variable, operator and terms are four types of expression.

A constant term in mathematics is a term in an algebraic expression whose value is fixed or cannot change since it lacks any variables that may be changed. As the component is not yet included in the new term, a constant term that has a constant applied as a multiplicative coefficient likewise indicates a constant term. The term identify themselves as constants because the phrase has been modified. 5 is a constant term, in the quadratic polynomial 2x^2 + 5.

Yes, negative sign have nothing to do with the definition of constant. -4 is still a constant.

There are four types of expression in mathematics:

1. Constant: any numeric value e.g. 6

2. Variable: any alphabetic/unknow value e.g. x,y etc.

3. Operators: +,-, *, / (addition, subtraction, division, multiplication)

4. Term: it can be constant, variable, constant multiplied by variable. It is separated by an operator.

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The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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Answer:

Mode

Step-by-step explanation:

The median and mean can only have one value for a given data set. The mode can have more than one value

Answer:

Step-by-step explanation:

Answer:

postulates, common notions, and axioms

One reason for Emma's extreme hunger after working for five straight hours on her psychology paper without eating is that her blood glucose level has dropped. Option C.

Our body's supply of glucose is drained when we participate in lengthy mental or physical activity without eating, which lowers blood sugar levels. The brain receives messages from the stomach-dropping that indicate a need for food.

Emma's body sent hunger signals since the prolonged period of intense work had drained her glucose supplies. Several hormones, notably the appetite-stimulating hormone ghrelin, influence this hungry response. Emma's hunger in this situation is mostly caused by the decline in blood glucose levels.

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The complete question is:

Emma worked for five straight hours on her psychology paper and did not stop to eat. After finishing her paper she felt extremely hungry. One reason for her hunger is that her:

A. leptin levels are high

B. blood glucose level has increased

C. blood glucose level has dropped

D. ghrelin production is low

Equation employing the slope-intercept method for two points

The slope-intercept version of the equation may be used to calculate the two-point Y-intercept.

The shape of a point-slope is\(\mathbf{Y-Y_{1} = m(X-X_{1})}.\)

Steps to find the y-intercept with two ordered pairs?

Determine the slope using two points.

\(Slope = \frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{Rise}{Run} = \frac{\bigtriangleup Y}{\bigtriangleup X}\)

As an illustration, two points are (3, 5) and (6, 11)

Slope = \(\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{11 - 5}{6 - 3} = \frac{6}{3} = 2\)

In the slope-intercept form of the equation, substitute the slope(m).

\(\\y = mx+b \\y = 2x+b\)

Either point may be substituted in the equation. You may either use (3,5) or (6,11).

\(\\y = 2x+b \\5 = 2(3)+b\)

Find the answer to the equation for b, the line's y-intercept.

\(\\5 \ \ \ = 2(3) + b \\5 \ \ \ = 6 + b \\\underline{-6\ = -6 \ \ \ \ \ \ \ } \\-1 = b\)

Substitute b,  into the equation.

\(\\y = 2x + b \\y = 2x - 1\)

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Answer:

252 (sorry if im wrong)

Step-by-step explanation:

Answer:

the answer is than u loser for the points :)))) childish kid

Step-by-step explanation:

Answer:

please see the photo above for detailed analysis.

The expected correlation between the supply of a commodity (x) and the price of a commodity (y) depends on the nature of the commodity and market dynamics. However, in general, we would expect a **negative correlation** between the supply of a commodity and its price. Correct option is C.

The law of supply states that as the supply of a commodity increases, assuming demand remains constant, the price tends to decrease. This is because an increase in supply leads to a higher quantity of the commodity available in the market, potentially causing an excess supply or surplus. In such situations, suppliers may lower prices to attract buyers and reduce their inventory.

Conversely, when the supply of a commodity decreases, assuming demand remains constant, the price tends to increase. A decrease in supply results in a lower quantity available in the market, potentially leading to a scarcity or shortage. In such scenarios, suppliers may increase prices to maximize their profits due to the limited availability of the commodity.

It's important to note that real-world markets can be influenced by various factors, including changes in demand, production costs, technological advancements, government policies, and market competition, which can complicate the relationship between supply and price. Nonetheless, the general expectation is that a decrease in supply tends to lead to an increase in price, and an increase in supply tends to lead to a decrease in price, indicating a negative correlation.

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Answer: 2 Hope This Is Right!

Step-by-step explanation:

a) P(x) = 1/600 probability/m .b) The probability is P(x) * 100 m = (1/600) * 100 m = 1/6. c) The constant probability densities are \(P_1\) = 3/1000 probability/m and \(P_2\) = 1/1000 probability/m. d) The probability that Mrs. Reeve's car is in the first 400 m of the lot is 0.8 or 80%.

(a) If the probability density is constant, it means that the probability is equally distributed over the entire length of the lot. Since the lot is 600 m long, the probability density, P(x), would be the reciprocal of the length of the lot. Therefore, P(x) = 1/600 probability/m.

(b) To find the probability that Mr. Vanderbilt's car is in the first 100 m of the lot, we need to calculate the area under the probability density curve over that range. Since the probability density is constant, the probability can be obtained by multiplying the probability density by the length of the range. Thus, the probability is P(x) * 100 m = (1/600) * 100 m = 1/6.

(c) For Mrs. Reeve's car, the probability density is constant in two intervals: \(P_1\) for 0 < x < 200 m and \(P_2\) for 200 m < x < 600 m. We are given that \(P_2 = P_1/3.\) To find the values of \(P_1\) and \(P_2\), we need to ensure that the total probability over the entire range sums to 1.

The total probability can be calculated by integrating the probability density function over the respective ranges and setting it equal to 1:

\(\int\ P(x) dx = \int\limits^{200}_{0}P_1 dx + \int\limits^{600}_{200}P_2 dx = 1\)

Since P(x) is constant within each interval, the integrals simplify to:

\(P_1 * 200 + P_2 * 400 = 1\\Substituting P_2 = P_1/3, we can solve for P_1:\\P_1 * 200 + (P_1/3) * 400 = 1\\200P_1 + 400P_1/3 = 1\\600P_1 + 400P_1 = 3\\1000P_1 = 3\\P_1 = 3/1000\)

\(Since P_2 = P_1/3, we can find P_2:\\P_2 = (3/1000)/3\\P_2 = 1/1000\)

Therefore, the constant probability densities are \(P_1\) = 3/1000 probability/m and \(P_2\) = 1/1000 probability/m.

(d) To find the probability that Mrs. Reeve's car is in the first 400 m of the lot, we need to calculate the area under the probability density curve over that range. Since the probability densities are constant within their respective intervals, the probability is given by the product of the probability density and the length of the range:

\(Probability = (P_1 * 200 m) + (P_2 * 200 m)\\= (3/1000) * 200 m + (1/1000) * 200 m\\= (3/1000 + 1/1000) * 200 m\\= (4/1000) * 200 m\\= 800/1000= 0.8\)

Therefore, the probability that Mrs. Reeve's car is in the first 400 m of the lot is 0.8 or 80%.

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Answer:

Ok I'm not sure but (9 hours)

Step-by-step explanation:

50,000 divided by 25,000 = 7

7 plus 2 equals 9.

Answer: C

Step-by-step explanation:

\(6^2 = 36\)

\(8^2=64\)

\(36+64=100\)

There are several possible reasons why per capita per day water consumption could be higher than the wastewater generated:

Non-domestic water use: Per capita water usage includes not only water used in households but also water used for commercial, industrial, and agricultural purposes. Wastewater, on the other hand, only includes water that has been used in households and is discharged into the sewer system. Therefore, if there is significant non-domestic water use in the area, per capita water usage could be higher than wastewater generated.

Inefficient water use: Even though per capita water usage is high, some of the water used may not end up in the wastewater stream. For example, water may be used for landscaping or irrigation, and much of it could evaporate or soak into the ground before it reaches the sewer system. This would result in higher water usage than wastewater generated.

Water loss: The water distribution system may experience leaks or other losses, resulting in some of the water being lost before it reaches households or other water users. This would result in higher water usage than wastewater generated.

Infiltration and inflow: In some cases, rainwater or groundwater can infiltrate into the sewer system or inflow into wastewater treatment plants, increasing the volume of wastewater generated. This could result in lower wastewater generated than per capita water usage.

Time lag: There may be a time lag between water usage and wastewater generated, especially in areas with septic systems. It is possible that some of the water used today may not be discharged into the sewer system for several days or even weeks, resulting in higher per capita water usage than wastewater generated on any given day.

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Based on the definition of similar triangles, the length of PR is 16 units.

In similar triangles, corresponding sides are in proportion. This means that if two triangles are similar, their corresponding sides will have the same ratio.

Therefore, we will have the proportion:

8/6 = (x + 7 + x - 1) / (x + 7)

4/3 = (2x + 6) / (x + 7)

Cross multiply:

3(2x + 6) = 4(x + 7)

6x + 18 = 4x + 28

6x - 4x = -18 + 28

2x = 10

x = 5

PR = x + 7 + x - 1

PR = 2x + 6 = 2(5) + 6

PR = 16 units

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The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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Answer:

Proof below

Step-by-step explanation:

Trigonometric Identities

We'll prove that:

\(\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\sin A*\cos A\)

Recall:

\(\displaystyle \sec A =\frac{1}{\cos A}\)

\(\displaystyle \csc A =\frac{1}{\sin A}\)

Applying those definitions:

\(\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\frac{\sin A+\cos A}{\frac{1}{\cos A}+\frac{1}{\sin A}}\)

Adding the fractions:

\(\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\frac{\sin A+\cos A}{\frac{\sin A+\cos A}{\cos A*\sin A}}\)

Dividing the fractions:

\(\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=(\sin A+\cos A)*\frac{\cos A*\sin A}{\sin A+\cos A}\)

Simplifying:

\(\displaystyle \frac{\sin A+\cos A}{\sec A+\csc A}=\cos A*\sin A\)

Hence proved

Answer:

112

Step-by-step explanation:

Answer:

One hundred and twelve and two tenths

Step-by-step explanation: