The triangle with vertices at l space open parentheses minus 2 comma space 5 close parentheses comma e space open parentheses 1 comma space 4 close parentheses comma and d space open parentheses 2 comma space minus 2 close parentheses is translated 4 units left, 3 units up, and then reflected over the line y equal 4 to form the image triangle l apostrophe e apostrophe d apostrophe. Which vertex of the image is the greatest distance from the origin?.

Answers

Answer 1

The greatest distance from the origin is 10, which corresponds to vertex L'' (6, 8) of the image triangle.

To determine the vertex of the image triangle that is the greatest distance from the origin, we need to follow the given transformations step by step and find the coordinates of the image vertices.

1. Translation: The given triangle is translated 4 units left and 3 units up.

  - Vertex L' is located at (-2 - 4, 5 + 3) = (-6, 8).

  - Vertex E' is located at (1 - 4, 4 + 3) = (-3, 7).

  - Vertex D' is located at (2 - 4, -2 + 3) = (-2, 1).

2. Reflection: The translated triangle is reflected over the line y = 4.

  - The line y = 4 acts as a mirror. The y-coordinate of each vertex remains the same, but the x-coordinate is reflected.

  - Vertex L'' is located at (-(-6), 8) = (6, 8).

  - Vertex E'' is located at (-(-3), 7) = (3, 7).

  - Vertex D'' is located at (-(-2), 1) = (2, 1).

Now, we have the coordinates of the image triangle vertices: L'' (6, 8), E'' (3, 7), and D'' (2, 1).

To determine which vertex is the greatest distance from the origin (0, 0), we can calculate the distances using the distance formula:

- Distance from the origin to L'': √[(6 - 0)² + (8 - 0)²] = √(36 + 64) = √100 = 10.

- Distance from the origin to E'': √[(3 - 0)² + (7 - 0)²] = √(9 + 49) = √58.

- Distance from the origin to D'': √[(2 - 0)² + (1 - 0)²] = √(4 + 1) = √5.

Therefore, the greatest distance from the origin is 10, which corresponds to vertex L'' (6, 8) of the image triangle.

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Related Questions

The library sponsors a chess club for members of all ages and skill levels. Currently, the ages of the members are 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, and 22. The librarian uses a histogram to track the number of members in different age groups. For this situation, which is the appropriate way to label the age intervals on the x-axis?

Answers

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Which would cause a shift in the supply curve?

Answers

The supply curve shifts as a result of every factor but a change in market price. The movement along the supply curve and the change in price are correlated.

What is meant by supply curve?

The supply curve can change depending on a number of variables, such as shifts in production costs (such as raw material and labor prices), advancements in technology, the level of competition and the number of sellers/producers, as well as the regulatory and tax environment.

Although a shift in the quantity supplied or along the supply curve for a given commodity or service is frequently brought about by a change in price, the supply curve itself does not alter as a result.

Input prices, weather conditions, technological advancements, as well as governmental taxes, regulations, and subsidies, can all modify the supply curve for goods and services, resulting in a different quantity being delivered for a given price.

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The blue points follow a pattern. Drag the black point to show your prediction for what come next then explain your thinking​

The blue points follow a pattern. Drag the black point to show your prediction for what come next then

Answers

The new point will be located at the coordinate (7,8)

What are patterns?

Patterns are simply the procedures and the rules that are followed to create a sequence.

Determining the pattern on the graph

From the graph, we have the following highlights

A point is translated 2 units upThe same point is then translated 3 units right, to form the next point

The position of the new point

Using the above pattern, the new point will be located at the coordinate (7,8)

See attachment for the next position

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The blue points follow a pattern. Drag the black point to show your prediction for what come next then

A triangle has angle measurements of 108°, 30°, and 42°. What kind of triangle is it?
Equilateral
Isosceles not Equilateral
Scalene

Answers

it is a scalene triangle

Step-by-step explanation:

equilateral triangle has 3 equal sides, isosceles triangle has two equal sides and scalene has 3 three different angle measurement

Can you help my sister with fractions while I'm studying. I need to review on my exams

Can you help my sister with fractions while I'm studying. I need to review on my exams

Answers

Answer:

4 + \(\frac{1}{2}\) = 4 \(\frac{1}{2}\)

Step-by-step explanation:

We have 4 whole circles and half a circle so 4 + \(\frac{1}{2}\) = 4 \(\frac{1}{2}\)

1. Carly bought 7 folders that cost $0.15 cents each and 2 packages of pens
that cost $1.50 each. What is the total cost in dollars and cents of the folders
and pens, not including tax?

Answers

the correct answer is 4.05

Find the largest six digits number which is divisible by 120 exactly.​

Answers

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

HELP DUE IN 15 MINS!
Solve for x in the parallelogram below:

X=??

HELP DUE IN 15 MINS! Solve for x in the parallelogram below:X=??

Answers

Answer:

x = 4

Step-by-step explanation:

Consecutive angles in a parallelogram are supplementary, sum to 180°, so

14x + 6 + 118 = 180

14x + 124 = 180 ( subtract 124 from both sides )

14x = 56 ( divide both sides by 14 )

x = 4

Answer:

x = 4

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary

14x + 6 + 118 = 18014x + 124 = 18014x = 180 - 12414x = 56x = 56/4x = 4

You deposit $2500 in a bank account. Find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly. Round to the nearest dollar.
pls help test today!!

Answers

After 3 years, the balance in the account would be approximately $2,708.

To find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final balance

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case:

P = $2500

r = 2.5% = 0.025 (as a decimal)

n = 12 (monthly compounding)

t = 3 years

Plugging in these values into the formula, we get:

A = $2500(1 + 0.025/12)^(12*3)

A = $2500(1.00208333333)^(36)

Using a calculator, we can evaluate the expression inside the parentheses and calculate the final balance:

A ≈ $2500(1.083282498) ≈ $2708.21

Therefore, after 3 years, the balance in the account would be approximately $2,708.

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Line l and m are parallel lines cut by transversals p and q as shown in the diagram.

What is the value of X?

A.135
B.45
C.23
D.68

Line l and m are parallel lines cut by transversals p and q as shown in the diagram.What is the value

Answers

Answer:

D

Step-by-step explanation:

∠1 = 2x - 1   {Vertically opposite angles}

2x - 1 + 45 = 180     {Co interior angles}

2x + 44 = 180

       2x = 180 - 44

      2x = 136

        x = 136/2

x = 68

suppose you take a sample of 50 students from your school and measure their height. which one of the following is a random variable?

Answers

If we take a sample of 50 students from your school and measure their height , then (c) The mean of the sample data. will be a Random Variable .

A Random Variable is a defined as a variable whose value depends on the outcome of a random event.

Option (c) : the random event is the selection of 50 students from the school to measure their height. The mean height of this sample of 50 students is a random variable because it can vary depending on the specific students who are selected.

Option (a) : The true mean height of all students from your school is a population parameter and is a fixed value, so it cannot be called as a random variable.

Option (b) : The mean of the sampling distribution of mean heights for samples of size 50 is a population parameter as well, and it represents the average of all possible sample means of size 50 taken from the population. So,  it is a fixed value and not a random variable.

Therefore , The mean of the sample data will be a random variable .

The given question is incomplete , the complete question is

Suppose you take a sample of 50 students from your school and measure their height.  Which one of the following is a random variable?

(a) The true mean height of all students from your school.

(b) The mean of the sampling distribution of mean heights for samples of size 50.

(c) The mean of the sample data.

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Suppose that the rational preference relation is continuous and monotone. Then there is a continuous utility function that represents the rational preference relation. Prove it with the help of a diagram for 2 commodity framework.

Answers

Yes, there is a continuous utility function that represents a rational preference relation when it is both continuous and monotone.

In a two-commodity framework, let's assume the two commodities are represented by X and Y. We can construct a diagram with the axes representing the quantities of X and Y. The indifference curves, which represent the bundles of X and Y that yield the same level of utility, can be plotted on this diagram.

Since the preference relation is continuous and monotone, we can draw the indifference curves as smooth, upward-sloping curves without any gaps or jumps. The upward slope reflects the monotonicity, indicating that more of either X or Y is preferred to less.

To represent this preference relation with a continuous utility function, we can assign utility levels to different bundles of X and Y. For example, we can assign a utility level of 1 to a specific bundle (X₁, Y₁), and higher utility levels to bundles that are preferred to (X₁, Y₁).

By assigning utility levels in a continuous manner across the diagram, we can construct a continuous utility function that represents the rational preference relation. This function will map each bundle of X and Y to a corresponding level of utility.

In conclusion, for a rational preference relation that is continuous and monotone in a two-commodity framework, there exists a continuous utility function that represents this preference relation. The utility function can be constructed by assigning utility levels to different bundles of commodities, and the resulting indifference curves on a diagram will be smooth, upward-sloping curves. This relationship between the utility function and the preference relation allows us to mathematically model and analyze the choices and preferences of individuals in economics.

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Pls help, I will give brainlist!

Pls help, I will give brainlist!

Answers

Answer:

Step-by-step explanation:

2.)A=\(\frac{bh}{2}\)

\(\frac{15*10}{2}\)=75.

3.) years to month

6 years is 72 month+2 month=74 month

month to days

74 month=2250.84days.

Suppose the volume of timber in a forest at a certain time ( t ) is given by the function: V(t)=10t−0.2t
2
. Determine the number of years that would be associated with the maximum volume of timber. Answer: Suppose the volume of timber in a forest was given by the function: V(t)=20t. Determine the profit-maximizing number of years ( t ) that a forester would wait before harvesting the timber when the interest rate was 20%. Answer:

Answers

The profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.

Given the volume of timber in a forest at a certain time (t) as: V(t) = 10t - 0.2t^2

Let's differentiate the given volume function w.r.t 't' to find the maximum value of timber as follows:

           dV(t)/dt = 10 - 0.4t

Now, equate dV(t)/dt = 0 to find the value of 't' for which V(t) is maximum.0

                                   = 10 - 0.4t0.4t = 10t

                                   = 10/0.4t = 25years

Therefore, the number of years that would be associated with the maximum volume of timber is 25 years.

Let's suppose the volume of timber in a forest is given by the function: V(t) = 20t

We need to find the profit-maximizing number of years (t) that a forester would wait before harvesting the timber when the interest rate is 20%.

It is given that, the interest rate (i) = 20%

                                                        =0.2

The cost of harvesting the timber is given by the formula:

                                           C = K +r*W where K is the fixed cost,

r is the interest rate,

and W is the amount of timber harvested.

Let's suppose the fixed cost (K) = $50 and the price of timber (p)

                                                    = $10 per unit.

Therefore, the profit function can be written as:

P(t) = p*V(t) - C

     = $10*20t - (50 + 0.2*10t)

     = $200t - 50 - 2t= 198t - 50

Now, differentiate P(t) w.r.t t to find the value of t for which P(t) is maximum.

dP(t)/dt = 198Equating dP(t)/dt  

= 0, we get,0

= 198t

= 198/20t

= 9.9

Therefore, the profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.

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How do you find the mean of 20?

Answers

10.5 is the mean of 20 .

What are the mean, median, and example?

A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

 x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + ................. + 20/20

  x = 210/20

  x = 10.5

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The complete question is -

How do you find the mean of 20 natural numbers?

Question 2: If I increase the price of a dress by 15%, what would
the multiplier be ?

Answers

If the price was $1 and it increased by 15% it would now be $1.15 therefore the multiplier is 1.15 as that increases a number by 15%

marla earns an annual salary of $28,000 at her new job. She received a 3% salary increase every year. Find Marla’s total earnings over the course of her first five years working at her job.

Answers

ANSWER:

$148,655.8

STEP-BY-STEP EXPLANATION:

Given:

Original salary = $28,000

Increase per year = 3%

The sum of all the earnings would be the sum of the original salary, the salary after 1 year, the salary after 2 years, the salary after 3 years and the salary after 4 years.

The salary in each year is calculated by multiplying the original salary by the increase raised after n years, just like this:

\(\begin{gathered} s_n=28000\cdot(1+3\%)^n_{} \\ s_n=28000\cdot(1+0.03)^n_{} \\ s_n=28000\cdot(1.03)^n_{} \end{gathered}\)

Therefore, the total earnings would be as follows:

\(\begin{gathered} t=28000+28000\cdot(1.03)^1+28000\cdot(1.03)^2+28000\cdot(1.03)^3+28000\cdot(1.03)^4 \\ t=28000+28840+29705.2+30596.4+31514.2 \\ t=148655.8 \end{gathered}\)

Therefore, the earnings in the first 5 years of MARla is $148,655.8

In a Survey of a group of students, it was found that 35% of the student likes mathematics, 30% of student Like account and 600 student like both of them and 5%. Like none of them.​

Answers

Answer:

Explanation: The idea is to draw a Venn Diagram and find the intersection. We have one circle of 70 and another with 40. When we add the two circles plus the 10 students who joined neither, we should get 100 students.

Step-by-step explanation:

A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high.
(a) How much work is done in pulling the rope to the top of the building?
(b) How much work is done in pulling half the rope to the top of the building?

Answers

A is what I believe to be the answer

What is the inequality shown

What is the inequality shown

Answers

Answer:

it shows that the answer is (-2,8(

the brackets are the symbols of inequality

Question 12 (Multiple Choice Worth 10 points)
(08.01 MC) For time t > 0, the velocity of a particle moving along the x-axis is given by v(t) = sin(e0.3). The initial position of the particle at time t = 0 is x = 1.25. What is the displacement of the particle from time t = 0 to time t = 10?
A. 2.020
B. 3.270
C. 6.903
D. 8.153

Answers

The displacement of the particle from time t=0 to time t=10 is given by the definite integral of the velocity function v(t) with respect to time from t=0 to t=10, as follows:

Δx = ∫(v(t) dt) from 0 to 10

We have v(t) = sin(e^(0.3)), so we can evaluate the integral as follows:

Δx = ∫(sin(e^(0.3)) dt) from 0 to 10

Using u-substitution with u = e^(0.3), we get:

Δx = ∫(sin(u) / 0.3 u dt) from e^(0.3) to e^(3)

Using integration by parts with u = sin(u) and dv = 1 / (0.3 u) dt, we get:

Δx = [-cos(u) / 0.3] from e^(0.3) to e^(3)

Δx = [-cos(e^(3)) / 0.3] + [cos(e^(0.3)) / 0.3]

Δx ≈ 3.270

Therefore, the answer is (B) 3.270.

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25 points please help!

25 points please help!

Answers

Answer:

x= 10

Step-by-step explanation:

If line m is parallel to line n,

(8x +50)°= 130° (corr. ∠s, m//n)

8x +50= 130

Bring constants to one side:

8x= 130 -50

8x= 80

Divide both sides by 8:

x= 80 ÷8

x= 10

round off 86 625 mm to the nearest significant figure​

Answers

answer.

86 630

explanation.

86 62|586 630

which inequality is represented?



A 1 < x < 6


B 1 < x ≤ 6


C x ≤ 1 or x ≤ 6


D x < 1 or x =6

Answers

The inequality that is represented by the inequality

x < 1 or x = 6 is D.

x < 1 or x = 6. What is an inequality? An inequality is a statement of the form x > y or x < y, which states that one quantity is not equal to another. For instance, the inequality x < 5 states that x is a number less than five.

The correct option is D.

An inequality can also include symbols such as ≤, ≥, and ≠, which indicate less than or equal to, greater than or equal to, and not equal to, respectively. What is x < 1 or x = 6 ? This implies that x can take on any value that is less than one, as well as the value of 6.  

The inequality x < 1 or x = 6 represents a set of numbers that are either less than 1 or equal to 6. The statement "x < 1 or x = 6" is true for any value of x that is less than 1 or equal to 6. n inequality can also include symbols such as ≤, ≥, and ≠, which indicate less than or equal to, greater than or equal to, and not equal to, respectively. What is x < 1 or x = 6?This implies that x can take on any value that is less than one, as well as the value of 6.

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3. Find \( y^{\prime} \) for the following implicit function \( y^{2}-x^{2} y=-2 \)

Answers

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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One factor of f (x ) = 4 x cubed minus 4 x squared minus 16 x + 16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.

Answers

\(f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16\)

\(divide \: by \: x - 2\)

\(4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} \)

\(g(x) = 4x {}^{2} - 16x + 16\)

\(4x \: into \: (x - 2) = 4x {}^{2} - 8x\)

\(z(x) = - 8x + 16\)

\( - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder\)

\(f(x) = (x - 2)(4x {}^{2} + 4x - 8)\)

\(f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ \)

\(x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1\)

\(x = 2\)

\(x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2\)

Answer: B

Step-by-step explanation:

Edge 2023

Find the directional derivative of the function at the given point in the direction of the vector v.

f(x, y) = 7 e^(x) sin y, (0, π/3), v = <-5,12>

Duf(0, π/3) = ??

Answers

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half, complete the statements to show that △abc ~ △def by the sas similarity theorem. horizontal and vertical lines are . so, angles are right angles by definition of perpendicular lines. all right angles are . therefore, △abc ~ △def by the sas similarity theorem.

Answers

Lines running horizontally and vertically are parallel. So, angles A, B, and C are right angles by definition of perpendicular lines. All right angles are equal. Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

Step 1: Multiply both sides of the equation by de:

a/b * de = bc/ef * de

Step 2: Simplify the left side of the equation:

ade = bcde

Step 3: Divide both sides of the equation by ad:

a/d = b/e

Step 4: Multiply both sides of the equation by be:

ab/d = be/e

Step 5: Simplify the left side of the equation:

ab = be

Step 6: Divide both sides of the equation by be:

a/b = 1/e

Step 7: Multiply both sides of the equation by ef:

a/b * ef = 1/e * ef

Step 8: Simplify the left side of the equation:

aef = ef

Step 9: Divide both sides of the equation by ef:

a/b = 1/e

Conclusion: startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half

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Answer:

perpendicular

b and e

congruent

Isabella is going to an amusement park. The price of admission into the park
is $20, and once she is inside the park, she will have to pay $2 for every ride
she rides on. How much money would Isabella have to pay in total if she goes
on 13 rides? How much would she have to pay if she goes on r rides?
Cost with 13 rides:
Cost with r rides:

Answers

Answer:

46$ in total

y=2r+20

Final answer:

If Isabella goes on 13 rides, she would have to pay a total of $46. If she rides 'r' times, the total cost would be expressed by the mathematical equation 20 + 2r.

Explanation:

This question relates to a linear relationship involving a fixed cost and a variable cost. In Isabella's case, the fixed cost is the admission fee, which is $20. The variable cost is the rides, where each ride costs $2.

So, if she goes on 13 rides, she will have to pay: $20 (for admission) + ($2 * 13 (rides)) = $20 + $26 = $46.

For r rides, the total cost would be: $20 (for admission) + ($2 * r (rides)). So the total cost for r rides can be expressed in a mathematical equation as: 20 + 2r.

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If f(x)=3x-7, find f(x)=2

Answers

Answer:

f(3) = 2 or (3, 2)

The y-value we solved for is 2.

Step-by-step explanation:

The equation they give you, all you need to do is plug in the x-value they give you.

f(x) the y-value in (x, y)

it will be on that bold, vertical line on the graph

2=3x-7

add 7 to both sides

9=3x

divide both sides by 3

x=3

y=2

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