Suppose that the consumer expenditure E (in dollars) depends on the market price p per unit (in dollars) according toE = 6,400p − 80p2.a)Because E represents consumer expenditure, only values of E ≥ 0 have meaning. For what p-values is E ≥ 0? (Enter your answer using interval notation.)

Answer:

15[tex]\frac{17}{24}[/tex]

Step-by-step explanation:

5 [tex]\frac{7}{8}[/tex] + 9 [tex]\frac{5}{6}[/tex]  We can write the fractions as equivalent fractions with a common denominator of 24

[tex]\frac{7}{8}[/tex] x[tex]\frac{3}{3}[/tex] = [tex]\frac{21}{24}[/tex]

[tex]\frac{5}{6}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{20}{24}[/tex]

5[tex]\frac{21}{24}[/tex] + 9[tex]\frac{20}{24}[/tex]

5 + 9 + [tex]\frac{21}{24}[/tex] + [tex]\frac{20}{24}[/tex]

14 + [tex]\frac{41}{24}[/tex]

14 + [tex]\frac{24}{24}[/tex] + [tex]\frac{17}{24}[/tex]   I broke up [tex]\frac{41}{24}[/tex] because [tex]\frac{24}{24}[/tex] is another name for 1

14+1 + [tex]\frac{17}{24}[/tex]

15[tex]\frac{17}{24}[/tex]

The graph that represents the solution to the system of inequalities is graph (a).

What is system of inequality?

A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.

The given system of inequalities is,

y < -3x - 2

y ≤ x - 2

y < -3x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a dotted line.

y ≤ x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a closed line.

The above highlights means that the shaded region that represent the solution to the system of inequalities will be at the left-hand side

Hence, graph (a) represents the system of inequalities.

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Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval are additive , linearity , continuity , monotonicity and upper and lowersums.

1. Additivity: The definite integral of a sum is equal to the sum of the definite integrals.

2. Linearity: The definite integral of a linear function is equal to the product of the function's slope and the length of the interval.

3. Continuity: The definite integral of a continuous function is equal to the area under the curve between two points.

4. Monotonicity: If a function is increasing or decreasing on a given interval, then the definite integral of the function is also increasing or decreasing.

5. Upper and Lower Sums: The upper and lower sums of a function are the sums of the areas of rectangles constructed under or over the curve between two points. The definite integral of the function is equal to the difference between the upper and lower sums.

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According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.

A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.

The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.

Given that John paid $485 to build a deck.

And he will pay $25 per hour to his brother for building the deck.

one hour of work costs John $25 + $485 .

Total cost of building deck = $25 × h number of hours + $485

3 hour of work costs $25 × 3 = $75 + $485 = $560

8 hour of work costs = $25 × 8 = $200 + $485 = $685

12 hour of work costs = $25 × 12 = $300 + $485 = $785

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The complete question is-

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?

h c

0 485

3 510

8 535

12 560

h c

0 510

3 535

8 560

12 585

h c

0 485

3 560

8 685

12 785

h c

0 510

3 585

8 710

12 810

Answer:

The new price of the product will be 1.07x, where x is the original price.

The manager has increased the price by 0.07x, which is 7% of the original price. This is equivalent to multiplying the original price by 1 + 0.07, or 1.07.

So, the new price of the product is 1.07 times the original price, or 1.07x.

Answer:

2.5

Step-by-step explanation:

Step-by-step explanation:

Given

Shelf Width = 3ft 9in

Copies = 18

Required

Determine the width of each book

This is calculated by dividing the shelf width by the number of copies.

Width = Shelf Width ÷ Copies

Width = (3 ft 9in) ÷ (18)

[Convert with to inches]

Width = (3 * 12 + 9) ÷ (18)

Width = (36 + 9) ÷ (18)

Width = 45 ÷ 18

Width = 2.5 inches

The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

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The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

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The value for the expression, (f * g)(x) is calculated as: C. 8x³ - 12x² - 6x - 1.

We are given the following functions,

f(x) = 4x² – 4x + 1 and g(x) = 2x – 1.

To find the value of the expression, (f * g)(x), it means we have to multiply the functions together. See the steps explained below.

(f * g)(x) = f(x) * g(x)

Plug in the values:

(f * g)(x) = f(x) * g(x) = (4x² – 4x + 1)(2x – 1)

(f * g)(x) = 4x²(2x – 1) - 4x(2x – 1) + 1(2x – 1)

Apply the distribution property of equality:

(f * g)(x) = 8x³ – 4x² - 8x² + 4x + 2x – 1

Combine like terms:

(f * g)(x) = 8x³ - 12x² - 6x - 1

Therefore, the answer is: C. 8x³ - 12x² - 6x - 1.

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Answer:

Hi!

The answer would be: 6 + 54t

I hope this helped you! :)

Step-by-step explanation:

Answer:

54t + 6

Step-by-step explanation:

Simplify the expression. Use the distributive property. The distributive property states that an expression which is given in form of a(b + c) can be solved into (ab) + (ac). Distribute and multiply 6 to all terms within the parenthesis. Then, simplify:

[tex]6(1 + 9t)\\\\=(6 * 1) + (6 * 9t)\\= (6) + (54t)\\ = 54t + 6[/tex]

54t + 6 is your answer.

~

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Answer:

[tex]27x^6y^6[/tex]

Step-by-step explanation:

The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex].  So,

[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].

Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex].  So,

[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]

The given expression can be simplified to get the value as 19. The correct option is (A).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

[tex](12b - 2^{c}) /\sqrt[3]{a}[/tex]

Substitute a = 64, b = 9 and c = 5 to obtain the value as below,

⇒ (12 × 9 - 2⁵)/∛64

⇒ (108 - 32)/4

⇒ 76/4

⇒ 19

Hence, the value of the given expression is obtained as 19.

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The image of the complete problem is attached here.

Answer:

4/15

Step-by-step explanation:

To answer this question, we're gonna want to convert the fractions so that they have the same denominator (the number on the bottom of the fraction) and it's easy for us to visualize what's going on. AKA, we need to find the least common denominator (LCD).

We're going to multiply 2/5 and 1/3 by a number so they have the same denominator. In this case, that would mean multiplying them by the other fractions denominator. So multiplying 2/5 by 3 and 1/3 by 5.

2/5x3= 6/15.    1/3x5=5/15.

Now we're viewing the book in 15ths instead of both 5ths and 3rds.

6+5=11, so we know that 11/15 of the book has been read.

15/15-11/15=4/15

4/15 of the book is left to read.

Hope this explanation helped!

Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.

It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.

Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.

Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."

∀xA⇒A(x↔a}

for every formula A and every term a, where A(x↔a}  is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of

∀xA.

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Answer: -2 1/8

Step-by-step explanation:

3 1/2 = 3 4/8

5 5/8 - 3 4/8 = 2 1/8

Add the negative sign back to get -2 1/8

The cosecant of the angle is 0.2

From the question, we have the following parameters that can be used in our computation:

(5,-12)

This means that

(x, y) = (5,-12)

The csc(θ) is calculated as

csc(θ) = 1/x

Substitute the known values in the above equation, so, we have the following representation

csc(θ) = 1/5

Evaluate

csc(θ) = 0.2

Hence, the value of csc(θ) is 0.2

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Step-by-step explanation:

17 of 20

11 of 15

20 of 25

that is in total

17+11+20 = 48

of

20+15+25 = 60

so, he answered 48 of 60 correctly

48/60 = 4/5 = 0.8 = 80%

Answer:

79.44%

Step-by-step explanation:

We are given that there are 3 sections to this test and how the student scored in each of those sections. Let us add all of these fractions together.

[tex]\frac{17}{20} +\frac{11}{15} +\frac{20}{25} =\frac{143}{60} \\[/tex]

We must now divide this amount by 3 to find the average of the three sections. This gives us [tex]\frac{143}{180}[/tex].

These means that the student answered  [tex]\frac{143}{180}[/tex]  of the questions correctly, or 79.44%.

a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.

b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.

c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.

d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.

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As per the given standard deviation, only (i) is true.

The term standard deviation refers the measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Here have given that the Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course.

Here by analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours.

So, let us consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed:

i. For the 5% level, BAOI can infer that the average time to complete exceeds 60 hours.

ii. For the 1% level, BAOI can infer that the average time to complete exceeds 60 hours.

Here we are trying to determine if they should spend at least 480 minutes a day studying.

Now, our knoll is that the mean is 480 and then we are looking for evidence that they are studying less than 480.

Here we don't know the population standard deviation so we're going to use a distribution.

In the given, critical values are going to be a distribution with degrees of freedom.

So, if we look at a chart 11 of freedom, we can see our critical value. I'm going to center to zero if I draw our T.

Therefore, the tail probability of.05 and the rest of it is.95%.

Based on these value we have conform that option (1) is correct.

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The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

The population propose will match the pattern mean's proposal. The population trendy deviation divided by the rectangle root of the sample length yields the same results as the standard deviation of the distribution of the sample means, also known as the same old mistakes of the proposed (n).

The general sample recommends factors to be included in the pattern mean calculation.

The population suggest is calculated using the sum of all values within the population denoted with the aid of the summation of X divided by the number of values in the population that is denoted with the aid of N. The population suggest is the mean or average of all values within the given population.

Therefore,

The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

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The length of the Zambezi river is 838 × 10⁵ or 83.8 × 10⁶ or 8.38 × 10

What is scientific notation?

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

For example, 750,000,000 can be written in scientific notation as 7.5 ✕ 10⁸.

The length of the Zambezi river 83,800,000 feet.

Rewrite 83,800,000:

83,800,000 = 838 × 100000

83,800,000 = 838 × 10⁵ [Since the number of zeros is 5]

Multiply and divide 10:

83,800,000 = 838 × 10⁵ × (10/10)

83,800,000 = (838/10) × 10⁵ × 10

83,800,000 = 83.8 × 10⁵ × 10

83,800,000 = 83.8 × 10⁶

Multiply and divide 10:

83,800,000 = 83.8 × 10⁶ × (10/10)

83,800,000 = (83.8/10) × 10⁶ × 10

83,800,000 = 8.38 × 10⁷

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For the given diagram 1. d) all of them are correct, 2. d)none of them are correct and Total Revenue is 3. b. $90,125

1.

Marginal Revenue is

the change in Total Revenue/Change in units of output produced

In the given question the price of the output is fixed at $125.

Hence no matter what the quantity of output sold, every additional output produced will generate an additional revenue of $125.

hence option d) all of them are correct has to be chosen.

2.

Now we already know that if the price has been fixed at $125, the marginal revenue generated cannot be anything but $125.

Hence, option d) None of them are correct.

3.

Total Revenue = Price X Quantity

Here it is given that the Price is $175

Output is 515 units

Hence, the Total Revenue will be $(175  X  515)

= $90125

Hence, option b. $90125 is correct.

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Complete Question

(Image Attached)

 For recording the angular velocity we will use

     angular velocity, ω = dθ /dt

Angular velocity:

Angular velocity is a vector quantity, expressed as the angular velocity or rotational speed of an object and the rate of change of angular displacement that specifies the axis about which the object rotates. The amount of change in a particle's angular displacement over time is called its angular velocity. The trajectory of the angular velocity vector is usually perpendicular to the plane of rotation in the direction given by the right-hand rule.

Total Moment of Inertia:

The total moment of inertia is the sum of the moments of inertia of the mass elements in the body.

Unlike mass, which is a constant for a given body, the moment of inertia depends on the location of the center of rotation. In general, the moment of inertia is calculated by using integral calculus.

Thin cylindrical shell open at both ends, radius r, mass m.

This formula assumes that the thickness of the shell is negligible. This is a special case of a thick-walled cylindrical tube with r1=r2. A point mass m at the end of a rod of length r has the same moment of inertia and the value r is called the radius of gyration.

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The characteristics of polynomial graphs' intercepts reveal the multiplicity's characteristics. The function is a potential representation of the graph; f(x) = x²·(x - a) (x - a) , ²·(x - b) (x - b),⁴·(x - c) (x - c).

The alternative provides a function that can represent a graph;

f(x) = x²·(x - a) (x - a)

²·(x - b) (x - b)

⁴·(x - c) (x - c)

Reason:

The graph's description is as follows:

Three points on the graph deviate from the x-axis.

Therefore;

The first equation is satisfied by the graph's even multiplicity at three places, such as x2, (x - a)2, and (x - b)4.

The graph once almost linearly crosses the x-axis.

Therefore;

The first equation's function contains a single zero or component, such as (x - c), so;

The function is a potential representation of the graph;

f(x) = x²·(x - a) (x - a)

²·(x - b) (x - b)

⁴·(x - c) (x - c).

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The value of missing x = 5

The value of missing y = 17 / 3

The standard line equation, y = mx + b, or the slope formula, m = (y2 - y1)/(x2 - x1), can both be used to find the slope, m.

According to the given information

Let two points be [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] are ( 3 , 8 ) and ( 6 , 15 )

Slope of the two points = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

                                       = [tex]\frac{15-8}{6-3}[/tex]

                                       = 7 / 3

Let the equation passing through points  ( 3 , 8 ) be

[tex]( y - y_{1}) = m(x - x_{1})[/tex]

y - 8 = 7/3( x - 3 )

3y - 24 = 7x - 21

3y = 7x - 21 + 24

3y = 7x + 3

When x = 2

3y = 14 + 3

y = 17 / 3

When y = 38/5

114/3 = 7x + 3

7x = 114/3 - 3

21x = 114 - 9

x = 5

So

The value of missing x = 5

The value of missing y = 17 / 3

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The  interval containing the middle-most 86% of sample mean in the interval notation is  is (196.4, 203.5)

The 50 +/- 86/2 percentile will make up the center 86% of the sample means' distribution.

The 86th percentile's z-score is 1.08

sample mean population mean = 200

standard deviation from mean = 19

sample size = 33.

Standard error (SE) is equal to 19 / sqrt(33) = 3.3077.

86th percentile x can be located using the formula z = (x - population mean)/sample error.

1.08 = (x - 200)/3.3077

x = 3.3077* 1.08 + 200 = 203.57

that is the interval's upper bound.

it is 3.5721 over the population mean (203.57 - 200).

Due to the symmetry of the normal distribution, the interval's bottom bound will be 1.66 standard deviations below the population mean (200 - 3.572 = 196.428).

then the interval is (196.4, 203.5).

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Answer:

x=5

Step-by-step explanation:

If p and q are parallel, then the two angles in question should be equal to one another.

So,

(3x+15)°=(8x-10)°

(3x+15)°+10°=(8x-10)°+10°

(3x+25)°=(8x)°

(3x+25)°-(3x)°=(8x)°-(3x)°

25°=5x°

5=x

So, the two angles should be (8(5)-10)° and (3(5)+15)°.  Both of these expressions equal 30°.  This makes sense, as the illustration shows that the two angles are acute.

If Caleb's school is five blocks due north of his home,  the figure that is  closest to the straight-line distance from Caleb's s  is (D) 1,481 ft.

Distance can be defined as how far an object is from another object.

Using Pythagoreans theorem

Hypotenuse =√Perpendicular² + Base²

Where:

Perpendicular = 275 feet ×5 = 1375ft

Base = 275 feet × 2 = 550ft

Let plug in the formula

Hypotenuse =√ 1375 ft² + 550ft

Hypotenuse =√1,890,625 + 302,500

Hypotenuse =√2,193,128

Hypotenuse = 1,480.9ft

Hypotenuse = 1,481ft (Approximately)

Therefore the correct option is D.

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The standard deviation of Y is 432.

                (Y = 75X - 100)

The formula of the standard deviation is :

                           SD(Y) = SD(75X - 100)

Substituting the value of SD(X) and SD(100) in the above expression.

SD(Y) = 75SD(X) - SD(100)

SD(Y) = 75 SD(X) - 0

SD(Y) = 75 × 5.76

SD(Y) = 432

Hence, the standard deviation of Y is 432.

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The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Now, According to the question:

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Let's know:

What is Confidence Interval?

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.

The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.

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The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.

When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.

This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.

Given that triangle AXY is similar to triangle ABC, it means that:

m<A = m<A

m<X = m<B

m<Y = m<C

AX/AB = AY/AC = XY/BC

To find the length of AB, we could use the following expression derived from the ratios stated above:

AX/AB = AY/AC

Cross multiply:

(AB) * (AY) = (AX) * (AC)

Divide both sides by AY

(AB) * (AY) / AY = (AX) * (AC) / AY

AB = AX * AC/AY

The expression to use is: A. AB = AX * AC/AY

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