Find tn for the geometric sequence where t3 = 24 and t9 = 1536. Why are there 2 answers? (4 marks)

Answers

Answer 1
To find tn for a geometric sequence, we need to know the first term t1 and the common ratio r. We can use the given terms t3 and t9 to set up two equations and solve for t1 and r.

From the formula for the nth term of a geometric sequence, we have:

t3 = t1 * r^2 (equation 1)
t9 = t1 * r^8 (equation 2)

We can divide equation 2 by equation 1 to eliminate t1:

t9/t3 = (t1 * r^8)/(t1 * r^2)
t9/t3 = r^6

Now we can solve for r:

r = (t9/t3)^(1/6)
r = (1536/24)^(1/6)
r = 2

Substituting r = 2 into equation 1, we have:

24 = t1 * 2^2

Solving for t1, we get:

t1 = 6

So the first term of the sequence is t1 = 6, and the common ratio is r = 2.

Now we can use the formula for the nth term of a geometric sequence to find tn:

tn = t1 * r^(n-1)

Substituting t1 = 6 and r = 2, we have:

tn = 6 * 2^(n-1)

To find tn, we need to know the value of n. We know that t3 = 24, so we can substitute n = 3 to find:

t3 = 6 * 2^(3-1) = 6 * 2^2 = 24

This confirms that our values for t1 and r are correct.

We can also use t9 = 1536 to find another value of n:

t9 = 6 * 2^(9-1) = 6 * 2^8 = 1536

So, tn can be 6 * 2^(n-1) for n = 3 or n = 9.

The reason there are two answers is because a geometric sequence has an infinite number of terms, and any power of the common ratio r will give us a valid value of tn. In this case, since r = 2, we can find tn for any value of n using the formula tn = 6 * 2^(n-1). However, since we only

Related Questions

I BEG U FOR HELP WILL GIVE BRAINLIEST PLLSSSS

Answers

Answer:

3,4,5 is the answer

Step-by-step explanation:

for the explanation using pythagoras theoem

[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]

may you give me branliest as you promised

The answer is 25 hope it helps

Write a fraction that has a value greater than 3/8 using 3 as the numerator

Answers

Answer: 3/4

Step-by-step explanation:

Any number as the denominator of the fraction that is less than 8 (the denominator) will give you a fraction greater than 3/8.

Another different answer could be 3/5 or 3/6.

A fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.

What is the fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

The given fraction is 3/8.

Here, 3/8 = 0.375

We need write the fraction which is greater than 3/8 using 3 as the numerator is 3/6 = 0.5

Therefore, a fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.

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Use the slip and y-intercept to identify the equation of this line

Answers

Answer:

y=2x

Step-by-step explanation:

equation formula is y=mx+b

m is slope

b is y-intercept

you know that slope is 2

y intercept is 0

so plug it into the equation

y=2x+0 or just y=2x

Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5 if-2.5 if-1.5 if -0.5 if 0.5 ≤x≤1.5

Answers

Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)

What is a Graph?

A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.

In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.

For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.

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The owner of a sports complex wants to carpet a hallway connecting to buildings. The carpet costs $1.50 per square foot. How much does it cost to carpet the hallway?

Answers

Answer:

$526.75 i believe

Step-by-step explanation:

Evaluate the expression for the given value.

–a – 7 for a = –4

A11
B–11
C3
D–3

Answers

The answer for -a - 7 for a =-4 is -3

Need help with is question

Answers

Answer:

27.78%

Step-by-step explanation:

To calculate the percentage of the total spending that is on rent, we need to divide the amount spent on rent by the total amount spent, and then multiply by 100 to get the percentage.

Total spending = food + rent + other + fun

Total spending = $400 + $500 + $600 + $300

Total spending = $1800

So, the percentage of the total spending that is on rent is:

($500 / $1800) x 100% = 27.78%

Therefore, approximately 27.78% of the total spending is on rent.

Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if Y′(−6, −1).

y-axis
x-axis
y = −1
x = 6

Answers

Answer:

To determine the line of reflection if the image of Y, Y′, is at (-6, -1), we need to find the perpendicular bisector of the line segment connecting Y and Y′. This perpendicular bisector will be the line of reflection.

The midpoint of the line segment YY′ is:

[(6 + (-6))/2, (-1 + (-1))/2] = (0, -1)

The slope of the line segment YY′ is:

(-1 - (-1))/(-6 - 6) = 0/(-12) = 0

Since the slope of YY′ is 0, the perpendicular bisector of YY′ is a vertical line passing through its midpoint (0, -1), which is the y-axis. Therefore, the line of reflection is the y-axis.

Which is the closest to the area of the shaded region in the given square containing a circle? (Use ≈ 3.14.)
10 m
21.5 square meters
50 square meters
O 78.5 square meters
O 100 square meters
5m

Answers

The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option

21.5 square meters

What is a square?

A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.

The figure is a composite figure comprising of a square and a circle

The radius of the circle, r = 5 meters

The side length of the square = 10 meters

The value of π = 3.14

The area of the square = 10 m × 10 m = 100 m²

The area of the circle = π × (5 m)² = 25·π m²

The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;

The area of the shaded region = (100 - 25·π) m²

The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²

The area of the shaded region is 21.5 square meters

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A local department store can sell 100 gaming systems at a price of $180 each. Research
shows that for each $18 price increase, the store will sell 4 fewer systems, and vice versa.
a. Find a linear price equation for the gaming system. That is, express the price, p, as a
function of the quantity, q. (2 points)
b. Use your answer from (a) to find the revenue equation.
c. Use your knowledge of quadratic functions to find the price and quantity sold that will maximize revenue.

Answers

Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.

What is the unit price?

In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the number of items bought.

According to given information

a. Let x be the number of $18 price increases from the original price of $180, and let y be the corresponding decrease in the number of gaming systems sold. Then we have the data point (x, y) = (0, 0) and the slope of the line is -4/18 = -2/9. Using the point-slope form of a linear equation, we have:

y - 0 = (-2/9)x

y = (-2/9)x

Substituting x = 18n, where n is the number of $18 price increases, we have:

y = (-2/9)(18n) = -4n

Let q be the quantity of gaming systems sold at a price of $180. Then the equation for the price of the gaming system as a function of the quantity sold is:

p(q) = 180 + 18n = 180 + 18(q - q0)/4 = 180 + (9/2)(q - q0),

where q0 is the quantity of gaming systems sold at the original price of $180.

b. The revenue equation is given by R(q) = q*p(q). Substituting the expression for p(q) found in part (a), we have:

R(q) = q*(180 + (9/2)(q - q0)) = (9/2)q^2 + (180 - 9q0/2)q

c. To find the price and quantity sold that will maximize revenue, we can differentiate the revenue equation with respect to q, set the derivative equal to zero, and solve for q:

R'(q) = 9q - 9q0/2 = 0

q = q0/2

Substituting q = q0/2 into the revenue equation, we have:

R(q0/2) = (9/2)(q0/2)^2 + (180 - 9q0/2)(q0/2)

R(q0/2) = (9/8)*q0^2 + (45/2)*q0

To find the corresponding price, we can use the expression for p(q) found in part (a):

p(q0/2) = 180 + (9/2)(q0/2 - q0)

p(q0/2) = 135

Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.

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The width of the set of the shelves needs to be 5 times the height of the set of shelves and the set of shelves must have three shelves If there are 80 feet of wood to use to build the set of shelves what should the dimensions the set of shelves be?​

Answers

The dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.

What is a linear equation?

When plotted on a coordinate plane, an algebraic equation known as a linear equation looks like a straight line. The variable (or variables) in this equation always have a greatest power of 1, making it a constant. In other words, a linear equation simply makes use of the fundamental operations of addition, subtraction, and multiplication of variables to the first power, as well as constants.

Given:

Width of the set of shelves = 5 times the height of the set of shelves

Number of shelves = 3

Total amount of wood available = 80 feet

Let's denote the height of the set of shelves as "h" and the width of the set of shelves as "w".

Using the first given information, we can write the equation:

Width (w) = 5 times the height (h) ==> w = 5h

Next, we know that the set of shelves has 3 shelves, so the number of shelves is fixed at 3.

Finally, we are given that we have 80 feet of wood available to build the shelves.

Using these equations, we can substitute w = 5h into the equation for the total amount of wood:

3w + 4h = 80

Substituting w = 5h, we get:

3(5h) + 4h = 80

15h + 4h = 80

19h = 80

h = 80/19

So, the height of the set of shelves is approximately 4.21 feet.

Now, substituting this value of h back into w = 5h, we get:

w = 5(4.21)

w = 21.05

So, the width of the set of shelves is approximately 21.05 feet.

Therefore, the dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.

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4. Tamara claims that Sweet Grove apple juice tastes better than Bushels apple juice. Isaac claims that there is no difference between the 2 types of apple juice. Tamara and Isaac would like to find the answer to the following question: Do more 6th graders prefer Sweet Grove apple juice or Bushels apple juice? a. Is this a statistical question? Explain your reasoning. 5. Explain how this question can be answered with an experiment​

Answers

Answer: a. Yes, this is a statistical question since it includes collecting information from a test of 6th graders and utilizing factual strategies to analyze the comes about and draw a conclusion approximately the inclinations for Sweet Grove and Bushels apple juice.

b. Draw a conclusion based on the results of the experiment, and report any limitations or assumptions made during the experiment.

Step-by-step explanation:

12. Higher Order Thinking If a clock face
reads 1:00, how many hours must pass for
the hands to form a straight angle?
own

Answers

Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.

Explain about the hand of clock:

To read the time on an analogue clock, look in the direction its hands are pointing. The current hour is indicated by the smallest hand, the current minute by the largest hand, and the current second by the thinnest hand.

There are 24 hours in a day, and the hour hand completes two full rotations of the clock because the numbers on the dial only go up to 12. once, from noon to midnight, and once, from midnight to noon.

Given data:

Current time on clock = 1:00

Hour hand at 1 .

Minute hand at 12.

Number of hours must pass for the hands to form a straight angle:

When

minute hand is at 12 and hour hand will be at 6.

Number of hours = 6: 00 - 1: 00

Number of hours = 5 hours

Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.

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rewrite the equation in Ax +By = C. y -5 = 2(x - 1)

Answers



-2X + y = 3

y-5=2(x-1)
y=2x-2+5
-2x+y=3

A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?

A$24
B$13
C$15
D$16

Answers

Answer:

24

Step-by-step explanation:

Answer:

A. $24

Step-by-step explanation:

Given:

total of $288number of values is 12 tables

Solve for average tip:

Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24

Answer:

Thus, the waiter's average tip per table is $24.

The answer is A.

Alberto gets a fish tank

Answers

Jackson is on point. Of all fish, catfish make up one-third of the total.

How much gravel does Alberto add to the tank in pounds?

The United States of America, Great Britain, and other English-speaking countries predominately utilise the pound as a unit of weight.

Any quantity associated with something is assumed to contain one pound if it does. The pound is the most widely used weight unit in the English-speaking world, including Britain, America, and other nations.

Zebra danios make up half of all the fish.

More fancy guppies than catfish, by a factor of two.

x = guppies

2x = catfish

x + 2x = 1/2 of the fish population

3x = 1/2 of the fish population

3x * 2 = 6x

x = 1/6 number of fancy guppies

catfish:

2x = 2(1/6) = 2/6 = 1/3 catfish.

Jackson is on point. Of all fish, catfish make up one-third of the total.

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The complete question is,

Alberto puts 3 kinds of fish in his fish tank: zebra danios, fancy guppies, and cat fish. Half of Alberto's fish are zebra danios. He has 2 times as many catfish as he has fancy guppies. Alberto's friend Jackson says 1/3 of Alberto's fish are catfish. Is Jackson correct?

An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.

to close the expansionary gap, the government would need to increase or decrease spending by $ billion.

Answers

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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A car, van, truck and bike are all travelling in the same direction on the road. Each travels at a constant speed, but the speeds of the 4 vehicles may be different. At 10 am the car overtakes the van. At noon it overtakes the truck. At 2 pm it overtakes the bike. At 4 pm the truck overtakes the bike. At 6 pm the van overtakes the truck. When does the van overtake the bike?

Answers

Answer:

at 6 pm

Step-by-step explanation:

I'm 99.9% sure that it's correct, please tell me if I'm wrong

What is the range of the relation whose graph is shown?

Answers

The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.

What is a domain?

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-4, 4} or -4 ≤ x ≤ 4.

Range = {-1, 1} or -1 ≤ y ≤ 1.

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Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?

Answers

None of the given numbers make the equation 8/y² + 2 true.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.

Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.

Substituting y=1 would give us:

8/1² + 2 = 8 + 2 = 10

So, 1 is not the answer.

Substituting y=2 would give us:

8/2² + 2 = 8/4 + 2 = 2 + 2 = 4

So, 2 is not the answer.

Substituting y=3 would give us:

8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888

So, 3 is not the answer.

Substituting y=4 would give us:

8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5

So, 4 is not the answer.

Therefore, none of the given numbers make the equation 8/y² + 2 true.

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a right triangle has a hypotenuse of length 7 inches. If one angle is 38 degrees, find the length of each leg.

Answers

Check the picture below.

[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]

Make sure your calculator is in Degree mode.

Answer:

4.31 in5.52 in

Step-by-step explanation:

You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.

Trig functions

The mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:

  Sin = Opposite/Hypotenuse   ⇒   Opposite = Hypotenuse×Sin

  Cos = Adjacent/Hypotenuse   ⇒   Adjacent = Hypotenuse×Cos

Application

The given triangle will have opposite and adjacent sides of ...

  opposite = (7 in)sin(38°) ≈ 4.31 in

  adjacent = (7 in)cos(38°) = 5.52 in

The leg lengths of the triangle are 4.31 inches and 5.52 inches.


2. A non-Jewish woman meets with a Jewish counselor to seek guidance on dealing with he
future Jewish in-laws. The Jewish counselor has strong personal beliefs against interfaith
marriages. At the end of the third session, the counselor recommends that the client
reconsider marrying her fiancé.
Harmful use of bias?
Unharmful use of bias?

Answers

As the counselor recommends that the client reconsider marrying her fiancé based on his belief discretion, this is an example of harmful use of bias.

Why is the Scenario an example of harmful Bias?

The counselor's personal beliefs against interfaith marriages are influencing their professional advice, which can be harmful to the client's well-being and may even violate ethical guidelines for mental health professionals.

The counselor should provide unbiased and objective guidance to the client based on their specific needs and circumstances, rather than imposing their own beliefs or values onto the client's decision-making process.

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7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm​

Answers

Answer:

B

Step-by-step explanation:

THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE

Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used. 2 one half 4 one fourth

Answers

Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)

Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

 A' = 2A

 A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).

Answer: 1/2

Step-by-step explanation:

I took the quiz!

Can someone please help me with this problem? I'm really struggling and the assignment is already late :(

Answers

The simplified exponential expression is given as follows:

[tex]21^6[/tex]

How to simplify the exponential expression?

The exponential expression in the context of this problem is defined as follows:

[tex]\frac{21^3 \times 21^5}{21^2}[/tex]

First we look at the numerator, when we have two terms with the same base and different exponents multiplying, we keep the base and add the exponents, hence:

21^3 x 21^5 = 21^8

Now we have the following division operation:

21^8/21^2.

When we have two terms with the same base and different exponents dividing themselves, we keep the base and subtract the exponents, hence:

21^(8 - 2) = 21^6.

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Calculate the value for each determinant:

Answers

Answer:

step by step explanation:

1. 9 4. -12

2. -48 5. 0

3. 17 6. 1

At a train station in the morning rush hour, the Westbound train arrives every 9 minutes, and the Eastbound train arrives every 15 minutes. If both trains were just in the station, after how many minutes will both trains again be in the station at the same time?

Answers

Step-by-step explanation:

Find the LCM of 9 and 15

West   9    18     27    36     45  

East       15             30         45                   In 45 minutes

So I tried solving this problem with the population growth formula,
· Population Growth: =^; a=initial amount, r=growth rate as a decimal; t=time in years; y=resulting population

My equation looked like this but I got this question wrong so any help will be appreciated
9667=11211e^(.418)(t)

Answers

The number of years it would take is approximately equal to 53 years.

How to determine the population after a number of year?

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

P(t ) represent the population.t represent the time or number of years.I represent the initial number of persons.r represent the exponential growth rate.

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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A machine in a factory makes chairs at rate of two chairs every 10 minutes how much time does the machine take to make five chairs how many minutes would it take for the factory to fulfill an order for 32 chairs show your work or explain how you determine your answers

Answers

If the machine makes 2 chairs every 10 minutes, then it makes 1 chair in 5 minutes (since 10/2 = 5).

To make 5 chairs, the machine will need 5 times as much time, which is 5 x 5 = 25 minutes.

To fulfill an order for 32 chairs, the machine will need to make 32/2 = 16 sets of 2 chairs.

This means the machine will take 16 x 10 = 160 minutes to make 32 chairs.

I obtained these answers by using basic math. First, I found out how many chairs the machine makes in one minute by dividing the rate of production (2 chairs every 10 minutes) by the number of minutes (10). That gave me the production rate of 1 chair every 5 minutes.

Using that production rate, I could then multiply it by the number of chairs I needed to find out how many minutes it would take for the machine to produce them.

For the order of 32 chairs, I used the production rate to figure out how many sets of two chairs the machine would need to make to reach the total amount. And then I multiplied that number by the time it takes to make two chairs (10 minutes) to get the total time it would take to produce 32 chairs.

if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?

Answers

the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.

How to solve the question?

To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:

AB' = AB x 3

where AB' is the length of AB after the dilation, and AB is the original length of AB.

However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:

AB²= AC²+ BC²

Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.

Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:

AB' = AB x 3

For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:

AB' = 5 x 3 = 15 units

Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.

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