Transversals of Parallel lines: corresponding angles

A statement which is true include the following: C. The functions have opposite slopes.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models one of the function is given by;

y = 4x

mx = 4x

Slope, m = 4.

For the other function, the slope can be calculated as follows;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 4)/(1 - 0)

Slope (m) = -4/1

Slope (m) = -4.

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The expression for the marginal revenue function is MR(q) = 600r - 7.

The given product's revenue function is R(q) = - 7q + 600qr.

To find an expression for the marginal revenue function, we can use the following steps:

Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).

Step 2: Simplify the expression for MR(q) to record the final result.

In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.

So, we have to differentiate R(q) with respect to q to get MR(q).

The derivative of - 7q with respect to q is - 7.

The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.

MR(q) = dR(q) / dq

= (d/dq)(- 7q + 600r)

= (- 7) + (600r)

= 600r - 7

The equation that represents the marginal revenue function is MR(q) = 600r - 7.

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Answer:

Step-by-step explanation:

Hi there! Just multiply by x and find the value of f=p. Good luck!

Answer:

x + y = 12

Step-by-step explanation:

We are given the following system of equations:

2x + 2y =24

x = 3y

We want to find the value of x + y.

We first need to find the values of x and y, which we will do by solving the system.

We can solve this system by substitution.

We know that x = 3y, so we can substitute 3y as x in 2x+2y=24.

This gives us:

2(3y) + 2y = 24

Multiply.

6y + 2y = 24

Add the terms together.

8y = 24

Divide both sides by 8.

y = 3

We found the y value, now let's find the value of x.

The second equation is x=3y, so if we plug the value of y in there, we can find the value of x.

Substitute 3 as y.

x = 3(3) = 9

The value of x is 9.

So, to find x+y, we substitute the values we found.

x + y = 3 + 9 = 12

Jada overtakes Elena after 7.5 seconds.

The set of equations that best captures the scenario is =y=15+20x.

Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x

y1 = 15 + 20x

Jada's distance from the origin at time x is determined similarly by:

y2 = 22x

Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.

y1 = y2

With the formulas for y1 and y2 substituted, we obtain:

15 + 20x = 22x

When we simplify this equation, we obtain:

2x = 15

x = 7.5

Jada therefore overtakes Elena after 7.5 seconds.

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A zero balance in Armando's account can be achieved by subtracting $250 from the account balance. This can be done through a combination of withdrawals and/or transfers out of the account.

Subtracting is a mathematical operation that involves taking one number away from another. It is the inverse of addition, and is represented by the minus sign (-). Subtracting is used to determine the difference between two numbers, or to reduce a number by a given amount. In algebraic terms, subtracting is represented by the equation: a - b = c, where a is the starting number, b is the number to be subtracted, and c is the resulting difference. Subtracting can also be used on fractions, decimals, and other forms of numbers.

For example, Armando could make a $250 withdrawal from the account or transfer $250 to another bank account.

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The probability that a student selected randomly owns either a laptop or a car is 85%.

Given a survey with a total of 1000 students, the following data was obtained: 750 students own laptops450 students own cars350 students own laptops and cars a university student is selected at random, what is the (empirical) probability that the student owns either a laptop or a car?

For two events A and B, the union of A and B is the probability that event A or event B occurs. It is the addition of the probabilities of each event minus the intersection of the two events. So in this case, the probability of a student owning either a laptop or a car is P(A∪B) = P(A) + P(B) - P(A∩B) where:

P(A) = probability of owning a laptop = 750/1000 = 0.75

P(B) = probability of owning a car = 450/1000 = 0.45

P(A∩B) = probability of owning both a laptop and a car = 350/1000 = 0.35

Now, substituting values into the formula:

P(A∪B) = 0.75 + 0.45 - 0.35= 0.85

Therefore, the probability that a university student selected randomly owns either a laptop or a car is 85%.

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The answers are a) ASA congruence rule b) SSS congruence rule c) it is not necessary congruent.

Congruent refers to having the same height and shape. Congruent therefore involves comparing two numbers, and equivalent denotes the equality of two expressions. Therefore, to state two line segments are congruent implies that the two lines have equal measures.

a) ∠GIH is corresponding to ∠LJK

GH = KL

∠IHG = ∠KLJ

By ASA congruence rule

ΔGIH ≅ ΔJKL

b) AB  = DF

AC = DE

BC = EF

By SSS congruence rule

ΔABC ≅ ΔDEF

c) Two Corresponding sides are congruent, which is not enough to make them congruent.

So, it is not necessary congruent.

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The required time is mathematically given as

t-150 minutes.

This is further explained below.

We know that the volume of the prism is given by.

[tex]\text{Volume}=\text{(Base Area)}\times\text{height}[/tex]

[tex]\text{Base Area}=\dfrac{1}{2}\times(1.4+0.6)\times2[/tex]

[tex]\text{Base Area}=2\ \text{m}^2[/tex]

Now,

[tex]\text{Volume}=2\times1=2\ \text{m}^3[/tex]

Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.

Because of this, the volume increases.

[tex]\text{Volume}=2\times0.8=1.6\ \text{m}^3[/tex]

Now, the rate of emptying the tank is,

[tex]=\dfrac{2-1.6}{30} =\dfrac{1}{75} \ \text{m}^3/ \text{min}[/tex]

In conclusion, We also know that,

$$

[tex]\text{time}=\dfrac{\text{volume}}{\text{rate}}[/tex]

[tex]\text{time}=\dfrac{2}{\frac{1}{75} } =150 \ \text{min}[/tex]

Therefore, Colin must wait for the pond to drain for a total of 150 minutes.

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The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).

To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.

f(t) = t, 0 ≤ t ≤ 3

f(t) = 2t - 3, 3 < t ≤ 4

f(t) = 5, 4 < t

Using the Heaviside function uc for the jump at c, we can represent each interval as follows:

f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3

f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4

f(t) = 5uc(t-4), 4 < t

Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)

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The line [tex]12x + 6y = 432[/tex] is represented by the red line, and the line equation [tex]9x + 3y = 270[/tex]is represented by the blue line. The point where these two lines intersect is (36,0).

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex]states that the word "2x + 3" corresponds to the number "9". The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components. For example, in the equations" [tex]x^2 + 2x - 3 = 0[/tex]," the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.

To plot these lines on a graph, we first need to solve for y in terms of x for each equation.

can plot these lines

[tex]12x+6y 4326y=-12x+432y = -2x+729x+3y=2703y=9x+270y=-3x+90[/tex]

[tex]|100|_ | . | . 90|_ . | . | .80|_ . | . | .70|_ . | . | .60 |___________________________________________ 0 30 60 90 120 150 180 210 240 270 300[/tex]

The line[tex]12x + 6y = 432[/tex]is represented by the red line, and the line 9x + 3y = 270 is represented by the blue line. The point where these two lines intersect is (36,0).

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Answer:

y = -5x - 3

Step-by-step explanation:

A linear equation is y = mx + b

m = the slope

b = y-intercept

We know

Points (-2,7) (0,-3)

Slope = rise/run or (y2 - y1) / (x2 - x1)

We see the y decrease by 10 and the x increase by 2, so the slope is

m = -10/2 = -5

Y-intercept is located at (0, -3)

So, the equation is y = -5x - 3

Answer:

Step-by-step explanation:

Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]

                        [tex]= 17.70 \times \frac{3}{2}[/tex]

                       [tex]=\frac{53.10}{2}[/tex]

                      [tex]=\pounds26.55[/tex]

Pay [tex]=11*26.55=\pounds 292.05[/tex]    (I assume you can use a calculator for this)

Solution: [tex]\pounds 292[/tex]

Answer:

Step-by-step explanation:

you are going to give more info ?????

The method used to collect data will depend on the specific research question being asked and the resources available to the researcher.

One common method for collecting data is through experimentation. This involves designing a controlled experiment that allows researchers to manipulate one or more variables while keeping all other factors constant.

Observational data can be particularly useful when it is not possible or ethical to manipulate variables in an experiment.

Surveys and questionnaires are another way to collect data. These methods involve asking people to provide information about their attitudes, beliefs, and behaviors.

Other methods for collecting data include case studies, in which researchers closely examine a single individual or group, and archival research, in which data is collected from existing records, such as census data or medical records.

By carefully selecting the right method for their research, scientists can gather accurate and reliable data that can help to advance our understanding of the world around us.

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Answer:

6 29 25

Step-by-step explanation:

those are the prime numbers on the 2023 feb calendar

(x-11, y+14) = (-4-7, 7+7) = (-11,14) which matches the new coordinates T(-11,14).

In this sense, coordinates are the points where a grid system intersects. GPS coordinates are typically created by combining latitude and longitude. The distance of north and the south from the equator, which is 0 degrees iof north and south, is measured by lines of latitude.

8. T (-4,7)             7 units right, 7 units up                      (x-11, y+14)    

9. U (3,-4)               7 units left, 7 units up                         (x+7, y+7)      

10. V (-2,-10)           7 units right, 7 units down                  (x+7, y-7)  

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The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer.  If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:

Number of students traveling = 30 x 1/3 = 10  

Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:

Number of students traveling out of the country = 10 x 1/5 = 2

Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.

It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.

In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.

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The rate of oil flowing from the site of the accident is 47123.74 cubic feet per minute.

To find the rate at which oil is flowing from the site of the accident, we need to determine the rate of change of the volume of oil in the slick with respect to time.

We know that the slick is circular with a thickness of 0.08 feet and a radius that is increasing at a rate of 0.5 feet per minute. Let's call the radius of the slick at time t "r" and the volume of oil in the slick at time t "V".

The volume of a cylinder (which the slick approximates) is given by the formula V = πr^2h, where π is the constant pi and h is the height or thickness of the cylinder.

Differentiating both sides with respect to time, we get:

dV/dt = 2πrh(dr/dt) + πr^2(dh/dt)

We know that the thickness of the slick is constant at 0.08 feet, so dh/dt = 0. We also know that the radius is increasing at a rate of 0.5 feet per minute, so dr/dt = 0.5. Finally, we know that the radius of the slick is currently 150 feet, so r = 150.

Substituting these values into the formula, we get:

dV/dt = 2π(150)(0.5) + π(150)^2(0)

dV/dt = 47123.74 cubic feet per minute

Therefore, the rate at which oil is flowing from the site of the accident is approximately 47123.74 cubic feet per minute.

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To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.

The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.

We start with 10 and 20 as our starting numbers.

10 = 2 * 5

20 = 2 * 2 * 5

We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.

Therefore, the greatest number of portions of trail mix Stanley can make is 10.

The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.

The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.

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Answer: Below :)

Step-by-step explanation:

A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.

The markup is 25% of the cost, which is 0.25 * 500 = €125.

So the total cost of the produce plus markup is €500 + €125 = €625.

Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.

125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.

Therefore, the profit is the markup, which is €125.

B) To find the total income, we add the profit to the total cost:

Total income = €500 + €125 = €625

Answer:

A)  €125

B)  €625

1. The breakeven in units equals 31 units.

2. The dollar amount to breakeven is

The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:

= $16.50 + $0.50

= $17.00

The contribution margin per unit is:

= 22.00 - $17.00

= $5.00

The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:

= $45 + $60 + $50

= $155

Using the breakeven formula, we can calculate the number of units required to break even:

= Fixed costs / Contribution margin per unit

= $155 / $5.00

= 31 units

To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:

The breakeven in dollars equals to:

= Breakeven in units x Selling price per unit

= 31 x $22.00

= $682.00

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To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.

The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.

The volume of the box can be calculated by multiplying the width, height, and length:

16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.

Two-thirds of this volume can be found by multiplying the total volume by 2/3:

5,376 cubic inches x 2/3 = 3,584 cubic inches.

Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.

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Answer:

D

Step-by-step explanation:

First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.

Hope this helps.

Answer:

9.5 decimal

espero y te ayude

Answer:

In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.

ASA Postulate:

ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.

SSS Postulate:

SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.

SAS Postulate:

SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.

Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.

Answer:

They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent

Step-by-step explanation:

and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.