Select a composite number to break into factors. Continue
factoring until all factors are prime.
56

The answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:

3 cupcakes + 1 tea = £9

3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5

1 cupcake = £7.5 ÷ 3 = £2.5

So 2 cupcakes would cost:

2 cupcakes = 2 × £2.5 = £5

Therefore, the answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

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Answer:

Hm

Step-by-step explanation:

The bacteria population is observed to double after five days, which means that its growth rate is 100% over a period of five days. This corresponds to a daily growth rate of r = 100%/5 = 20%.

If the initial population is 10,000, then the bacteria population after d days can be modeled by the exponential function:

f(d) = 10,000 * (1 + r/100)^d

Substituting r = 20% and simplifying, we get:

f(d) = 10,000 * (1.2)^d

Therefore, the correct option is:

D. f(d) = 10,000 * (1.2)^d

When a rectangle is dilated by a scale factor of , the area of the rectangle will be multiplied by. This is because the width and the height of the rectangle are both multiplied by, therefore the area of the rectangle is multiplied by .

A rectangle is a two-dimensional shape with four sides and four right angles. It is one of the most common shapes found in nature and in the world. A rectangle has two pairs of equal-length sides and each angle is 90°. All four sides of a rectangle are straight, and the opposite sides are parallel. Rectangles are a special type of parallelogram and quadrilateral, which has two pairs of parallel sides. Rectangles can be used to make various structures, including buildings, furniture, and artwork. They are also used in mathematics to calculate area and perimeter.

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Complete Question:

The equation of the circle is x² + y² - 4x - 6y - 60 = 0

The equation of a circle is generally given by the formula:

=> (x - a)²+ (y - b)² = r²

Where (a, b) is the center of the circle, and r is its radius. The equation describes all the points (x, y) in the xy-plane that are a fixed distance r from the center point (a, b).

Here we have

A circle with centre O(2, 3) contains the point A(5, 11).  

Since point A(5, 11) is located on the circle with center O(2, 3), use the distance formula to determine whether A is actually on the circle.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

=> d = √(x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, the distance between O(2, 3) and A(5, 11) is:

d = √(5 - 2)² + (11 - 3)²)

= √(3² + 8²)

= √(9 + 64)

=√(73)

This distance is the radius of the circle with center O.

Therefore, the equation of the circle is:

(x - 2)² + (y - 3)² = (√(73))²

x² - 4x + 4 + y² - 6y + 9 = 73

x² + y² - 4x - 6y - 60 = 0

Therefore,

The equation of the circle is x² + y² - 4x - 6y - 60 = 0

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If we consider a mountain number with its middle digit is larger than any other digit, then there are possible three-digit mountain numbers are equals the 240.

A number is called a 'mountain' if its decimal digits insitiate with 1, i.e. 'base camp', increase continuously to one largest digit, then decrease continuously back to one i.e. back to base camp. We have a number is called a mountain number. Now, there are 100 to 999 total 3-digit numbers. Now, with 2 in the middle, we have = 2 numbers[1 x 2] - 120 = 121

So, we have a total of Total Number = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "mountain numbers". Hence, the required number , value is 240.

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The approximate volume of the small truck is 577.5 cubic feet.

A truck that would be best for them to rent is the 3-Bedroom Moving Truck.

The volume of the Mega Moving Truck is about 641.25 cubic feet greater than the 2-bedroom moving truck.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

For the approximate volume of the small truck, we have;

Volume of small truck = 11 1/3 × 7 5/12 × 7

Volume of small truck = 577.5 cubic feet.

The approximate volume of each moving truck can be calculated as follows;

2-Bedroom Moving Truck = 14.5 × 7.5 × 7 = 761.25 cubic feet.

3-Bedroom Moving Truck = 21 × 7.5 × 8 = 1,260 cubic feet.

Mega Moving Truck = 22 × 7.5 × 8.5 = 1,402.5 cubic feet.

Difference = 1,402.5 cubic feet - 761.25 cubic feet

Difference = 641.25 cubic feet.

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The second one both fractions have the same answer so there equal two first is right tho

The equation that represents the volume of water in cubic meters after T minutes of water being pumped out is V = -1.5T + 30.

The given data shows that the volume of water is decreasing as time goes on. Therefore, we need to use a function that is decreasing with respect to time. One such function is a linear function.

Let V be the volume of water in cubic meters after T minutes of water being pumped out. Then, we can use the two points (0, 30) and (15, 7.5) to find the equation of the line that represents the volume of water in terms of time.

The slope of the line is

slope = (change in volume) / (change in time) = (7.5 - 30) / (15 - 0) = -1.5 cubic meters per minute

The y-intercept of the line is the volume of water when time is zero, which is 30 cubic meters.

Therefore, the equation that represents the volume of water in cubic meters after T minutes of water being pumped out is

V = -1.5T + 30

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The given question is incomplete, the complete question is:
The table shows the volume of water in cubic meters, V, in a tank after water has been pumped out after water has been pumpee out for a certain number of minutes. Which equation could represent the volume of water in cubif meters after T minutes of water being pumped out . Time after pumping begin 0 5 10 15 Volume of water (cubic meters) 30 27.5 20 7.5

Answer: 9m

Step-by-step explanation:

there is one “m” in each and there is a 9 in both number. (9*2=18), (9*3=27)

The probability of selecting such a permutation is very low, only about 0.31%.

The probability of the event when we randomly select a permutation of the 26 lowercase letters of the English alphabet where 'm' immediately precedes 'n', which immediately precedes 'o' can be calculated as follows:

Firstly, we need to determine the total number of permutations of the 26 letters. Since there are 26 letters in the alphabet, there are 26! ways to arrange them.

Next, we need to determine the number of permutations where 'm' immediately precedes 'n', which immediately precedes 'o'. To do this, we can consider 'mno' as a single unit and then there are 24! ways to arrange the 24 units (23 individual letters and 1 unit of 'mno').

However, there are 3! ways to arrange 'mno' within the unit, so we need to multiply by 3!. Therefore, the total number of permutations where 'm' immediately precedes 'n', which immediately precedes 'o' is 24! x 3!.

Thus, the probability of randomly selecting a permutation where 'm' immediately precedes 'n', which immediately precedes 'o' is:

P = (24! x 3!) / 26!

P ≈ 0.0031 or 0.31%

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Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

If the amount of £15837.77 is to be increased by 18.5%, then the resulting amount after the increase is £18764.75.

A percentage is a number or ratio expressed as a fraction of 100. It represents a portion of something relative to the whole, and is commonly used to express changes or comparisons between two values

To increase a number by a percentage, you can use the following formula

New value = Original value + (Percentage increase / 100) × Original value

Using this formula, we can find the new value of £15837.77 after an 18.5% increase

New value = 15837.77 + (18.5 / 100) × 15837.77

= 15837.77 + 2926.98

= 18764.75

Therefore, an 18.5% increase on £15837.77 is £18764.75, rounded to 2 decimal places.

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The total surface area of the composite shapes are 69 square cm, 63 square cm and 108 square yd

The surface area of composite shapes can be found by breaking the composite shape down into simpler shapes and then finding the surface area of each individual shape.

Once the surface areas of all the individual shapes are found, they can be added together to find the total surface area of the composite shape.

Figure 1

Here, we have

Area = Area of rectangle + square

So, we have

Area = 5 * 5 + 4 * 11

Area = 69 square cm

Figure 2

Here, we have

Area = Area of  square + triangle

So, we have

Area = 7 * 7 + 1/2 * 7 * 4

Area = 63 square cm

Figure 3

Here, we have

Area = Area of rectangle + square

So, we have

Area = 12 * 6 + 6 * 6

Area = 108 square yd

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We need the specific amounts of milk in each recipe in order to determine the difference between the recipe with the most milk and the recipe with the least milk.

In order to calculate the difference in milk between the recipes, we need to know the amount of milk in each recipe. Without this information, we cannot determine which recipe has the most milk or the least milk, or how much more milk is in one recipe compared to another. It's important to have specific information about each recipe to accurately determine the difference in milk. Once we have the specific amounts of milk for each recipe, we can calculate the difference between the two and give a definitive answer.

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--The complete question is, What information do you need in order to determine the difference in the amount of milk between the recipe with the most milk and the recipe with the least milk?--

Choose the 3rd table .

Exactly one output value from a different set, known as the range, is what a function in mathematics does for each input value from the set known as the domain.

A function can be compared to a device that processes an input to create a particular output.

Given that the output value depends on the value of the input variable, the input value is sometimes referred to as the independent variable.

For instance, if a function is defined as

f(x) = 2x + 1, x

is the input variable and f is the output variable.(x).

A variable in mathematics is a symbol that designates a value or quantity that is subject to variation or change.

In order to solve equations and describe relationships between different quantities, variables are needed.

Variables in algebra are frequently denoted by letters like x, y, and z. They are used to express a relationship between two or more quantities or to represent undiscovered quantities that we are trying to locate.

For instance, x is the independent variable and y is the dependent variable in the equation y = 3x + 2.

According to question  

Substitute X=14 into f(x) =  4/3  |x+2 |  - 5

f (-14） = 4/3  |-14+2 |  - 5

           = 4/3  |-12 |  - 5

           = 4/3 X12 -5

           = 16 - 5

            = 11

hence when x=-14 fix=11

the first table is false

substitute x= -10 into  f(x) =  4/3  |x+2 |  - 5

                                          =  4/3  |-10+2 |  - 5

                                          =  4/3 X 8 -5

                                          = 32-15 =17/3 ≠ 11

hence the second table is false

HENCE , Choose the 3rd table .

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Answer:

Step-by-step explanation:

You want to know the number of cubic meters in a cube that is 10^3 meters on each side, and whether that volume amounts to a pond, lake, or ocean.

The volume of a cube is given by ...

  V = s³

where s is the edge length.

The volume of interest is ...

  V = (10³ m)³ = 10⁹ m³

The volume of oil is 10⁹ cubic meters.

The sizes of ponds and lakes vary, but we might consider a pond to be a body of water larger than about 150 square meters and less than 6 meters in depth. On the other hand, a lake will generally be larger than about 4000 square meters. An average size lake may be about 10 meters in depth.

If we put the given amount of volume in a space with a depth of 40 meters, it would cover an area of about 25 million square meters, roughly 6000 acres. That is the area of a circle about 7 km in diameter. This might be considered a medium-sized lake.

The oil would fill a medium-sized lake.

__

Additional comment

A "lake" is generally a body of water upwards of an acre in area. While an average lake in some areas is about 10 m deep, worldwide, the average is just over 40 m in depth. Some lakes are well over 20,000 acres in area.

A "pond" may be larger than a "lake", but will generally be smaller than 500 acres.

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The amount of money less per hour which Melanie earn than Olivia is equal to $268.

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

y = mx + c

Where:

Based on the information provided about Melanie's earnings, we have the following:

y = 22.2x

When x = 40 hours, the y-value is given by;

y = 22.2(40)

y = $888.

Difference in earnings can be calculated as follows;

Difference = $1156 - $888

Difference = $268.

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Answer:

square, quadrilateral, rhombus, parallelogram, rectangle



Answer:

Quadrilateral, rectangle, parallelogram, rhombus, square

Step-by-step explanation:

It is a quadrilateral bc it has four sides.

It is a rectangle bc it has four right angles.

It is a parallelogram bc it has two pairs of parallel sides.

It is a rhombus bc all four sides are congruent.

It is a square bc it is both a rectangle and a rhombus.

Answer:

We can use the trigonometric function of sine to find the measure of angle ACB.

First, we note that sin(ACB) = opposite/hypotenuse = BC/AB.

To find BC, we use the Pythagorean theorem:

BC^2 = AB^2 - AC^2

BC^2 = (10.6 m)^2 - (5.8 m)^2

BC^2 = 67.24 m^2 - 33.64 m^2

BC^2 = 33.6 m^2

BC = sqrt(33.6) m

BC = 5.8 m (rounded to 1 decimal place)

Therefore, sin(ACB) = BC/AB = 5.8/10.6 = 0.5472

Using the inverse sine function on a calculator, we find:

ACB = sin^-1(0.5472)

ACB = 33.11°

Therefore, the measure of angle ACB is 33.11 degrees, rounded to 3 significant figures.

The total number of students surveyed (170 in this case) as the full height of the bar, with each vacation category represented as a different color within the bar.

The term "data range" refers to the range or set of values that a particular data set or variable can take. It represents the minimum and maximum values that can be observed in a given data set.

Enter the data into a worksheet, with the vacation categories in column A and the number of students in column B.

Select the data range, including both columns.

In the Excel ribbon, click on the "Insert" tab.

Click on the "Stacked Bar" chart type in the "Charts" section.

The stacked bar chart will be created in the worksheet. You may want to adjust the chart title, axes titles, and legend to make the chart easier to read.

The resulting chart will show the total number of students surveyed (170 in this case) as the full height of the bar, with each vacation category represented as a different color within the bar. The height of each section of the bar will correspond to the number of students who chose that vacation category. This will allow you to compare the popularity of each vacation category to the whole.

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This means that if the average weight of the men in the elevator is more than 180 lbs, the elevator would be overloaded.

To determine the average weight beyond which the elevator would be considered overloaded, we can follow these steps:
Find the total weight limit for 33 occupants: 5940 lbs.

Divide the total weight limit by the number of occupants to find the average weight per person: 5940 / 33 = 180 lbs.
Now, we need to find the difference between the average weight per person (180 lbs) and the mean weight of the population (166 lbs): 180 - 166 = 14 lbs.
Since we have the difference and the standard deviation (26 lbs), we can now calculate the Z-score:

Z = (difference) / (standard deviation) = 14 / 26 ≈ 0.54.
The average weight beyond which the elevator would be considered overloaded is 180 lbs.

The corresponding Z-score for this weight is approximately 0.54.

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From a "standard-deck" of "playing-cards", the number of ways which are required to form a "5-card" hand with "2-pairs" is 123,552 ways.

A "Standard-Deck" of playing cards generally consists of 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 ranks: Ace, 2 through 10, and three face cards.

To form a 5-card hand with 2 pairs from a standard deck of playing cards, we break it down into two steps:

Step(1) : Select the values for the two pairs.

There are 13-ranks in a standard deck of playing cards, ranging from 2 to 10, and then Jack, Queen, King, and Ace, for a total of 13 possible values.

We need to select 2 of these values to form the two pairs. The number of ways to do this is "C(13, 2)" which is : 78,

So, there are 78 ways to select the values for the two pairs.

Step(2) : Select the specific-cards for each pair and the fifth card.

For each pair, we need to select 2 cards of that value from the 4 cards of each rank in the deck.

The number of ways to do this is "C(4, 2)" which is : 6,

So, there are 6 ways to select the specific cards for each pair.

Finally, for the fifth-card, we can choose any of the remaining "44-cards" in the deck (after selecting the 8 cards for the two pairs).

So, total number of ways to form a "5-card" hand with "2-pairs" from a standard deck of playing cards is,

⇒ 78 × 6 × 6 × 44 = 123,552 ways,

Therefore, the required number of ways are 123,552 ways.

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The given question is incomplete, the complete question is

Using a standard deck of playing cards, how many ways are to form a 5-card hand with 2 pairs?

The expression that is the difference of two squares is [tex]9a^2 - 4b^6[/tex]

The difference of two squares is an algebraic expression of the form a² - b², which can be factored as (a + b)(a - b).

Using this rule, we can determine which of the given expressions is the difference of two squares.

[tex]9a^2 - 4b^6[/tex] is the difference of two squares because [tex]9a^2[/tex] is a perfect square [tex](3a)^2[/tex]and [tex]4b^6[/tex] is a perfect square[tex](2b^3)^2[/tex]. Therefore, we can write:

[tex]9a^2 - 4b^6 = (3a + 2b^3)(3a - 2b^3)[/tex]

So, the expressions that are the difference of two squares is [tex]9a^2 - 4b^6[/tex]

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Answer:

189

Step-by-step explanation:

27,006 / 42

= [tex]\frac{27}{6/42}[/tex]

= [tex]\frac{27}{\frac{1}{7} }[/tex]

= 27 x 7

= 189

So, the answer is 189

1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students. 2) The correct circle graph is option 2. 3) Option 4: Paddleboarding.

The frequency or relative frequency of the data points falling within each interval is depicted by the height of the bars in a histogram, which is a graphical representation of the distribution of continuous data. Histograms are frequently used in data analysis to show how a single variable is distributed and to spot any patterns or trends. Additionally, they can be used to compare the distributions of two or more variables or to spot anomalies or outliers in the data.

1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students.

2) Given the type of transportation we have he total number of visitors as:

(120+24+45+30+81=300)

Now, for walk we have:

120/300 = 40/100 = 40%

For Bicycle we have:

24/300 = 8%

Thus, the correct circle graph is option 2: circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent

3) For the central angle to be 54 the number of campers needs to correspond to this number. The activity that corresponds to 54 degrees is Paddleboarding.

4) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

5) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

6) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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The distance between the ladder's bottom and the wall is around 7.5 feet (rounded to the nearest tenth).

The Pythagorean theorem is a basic mathematical theorem that describes the connection between the sides of a right triangle. It asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the other two sides.

The Pythagorean theorem can be stated mathematically as:

[tex]C^2 = A^2 + B^2[/tex]

where "C" indicates the length of the hypotenuse and "A" and "B" represent the lengths of the other two sides of the right triangle.

In this scenario, the ladder is the hypotenuse of a right-angled triangle, with the wall constituting one side and the distance between the bottom of the ladder and the wall forming the other.

Given,

Length of the ladder (hypotenuse) = 15 feet

Height of the ladder on the wall (one side) = 13 feet

Let's call the distance between the bottom of the ladder and the wall "x" feet.

Using Pythagorean theorem ,

[tex]15^2 = 13^2 + x^2[/tex]

225 = 169 + [tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 225 - 169

[tex]x^{2}[/tex] = 56

x = [tex]\sqrt{56}[/tex]   (taking the square root of both sides)

x [tex]$\approx$[/tex] 7.5 feet

As a result, the distance between the bottom of the ladder and the wall is around 7.5 feet (rounded to the nearest tenth).

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The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.

Hence, OC bisects AB, as congruent parts of congruent triangles are equal.

When two or more geometric figures are similar in size, form, and orientation, this is referred to as congruency in geometry. Two figures can be overlaid on one another by translation, rotation, and/or reflection when they are congruent because they are almost similar to one another and do not alter in size, form, or orientation.

For the given problem, the complete steps of proof with reasoning are:

(a) OC is perpendicular to AB in circle O (given). i.e ∠OCA and ∠OCB are right angles.

Reason: This is given in the problem statement. It establishes that OC forms a right angle with AB at point C in circle O. i

(b) Draw OA and OB (construction).

Reason: This is a construction step that introduces radii OA and OB from the center O of the circle to points A and B on the circle. This sets up the framework for the subsequent steps and establishes the positions of A and B in relation to the circle and the perpendicular OC.

(c) OA = OB (radii of the same circle are equal).

Reason: Radii of the same circle are always equal in length. This is a basic property of circles, where all radii have the same length, which can be stated as OA = OB based on the definition of a circle.

(d) OC = OC (Reflexive Property of Equality)

Reason: It is a property of line segments that they are equal to themselves. This is known as the Reflexive Property of Equality, which states that any quantity is equal to itself.

(f) AC = BC (common side of congruent triangles).

Reason: AC and BC are line segments that are both radii of the same circle, and OA = OB (Step c). Therefore, by the definition of congruent segments, AC = BC.

(e) Triangle ACO is congruent to triangle BCO (HL congruence criterion for right triangles).

Reason: Angle ACO and angle BCO are both right angles based on the given information that OC is perpendicular to AB (Step a). Also, AC = BC (Step d) and OA = OB (Step c). Therefore, by the Hypotenuse-Leg congruence criterion for right triangles, triangle ACO is congruent to triangle BCO.

(g) OC bisects AB (congruent parts of congruent triangles are equal).

Reason: Since triangle ACO is congruent to triangle BCO (Step e), the corresponding parts of congruent triangles are equal. In this case, OC is a common side (hypotenuse) of both triangles, and AB is a side of both triangles. Therefore, by the definition of a segment bisector, OC bisects AB.

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