geometry worksheet find the measure of the arc or angle indicated

Answer:

13)  4.9 m

14)  0.9 m

Step-by-step explanation:

The given diagram shows the height of the same cactus plant a year apart:

We are told that the cactus continues to grow at the same percentage rate. To calculate the growth rate per year (percentage increase), use the percentage increase formula:

[tex]\begin{aligned}\sf Percentage \; increase &= \dfrac{\sf Final\; value - Initial \;value}{\sf Initial \;value}\\\\&=\dfrac{ 2-1.6}{1.6}\\\\&=\dfrac{0.4}{1.6}\\\\&=0.25\end{aligned}[/tex]

Therefore, the growth rate of the height of the cactus is 25% per year.

As the cactus grows at a constant rate, we can use the exponential growth formula to calculate its height in Year 6.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Exponential Growth Formula}\\\\$y=a(1+r)^t$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value. \\ \phantom{ww}$\bullet$ $r$ is the growth factor (in decimal form).\\ \phantom{ww}$\bullet$ $t$ is the number of time periods.\\\end{minipage}}[/tex]

The initial value is the height in Year 1, so a = 1.6.

The growth factor is 25%, so r = 0.25.

As we wish to calculate its height in Year 6, the value of t is t = 5 (since there are 5 years between year 1 and year 6).

Substitute these values into the formula and solve for y (the height of the cactus):

[tex]\begin{aligned}y&=a(1+r)^t\\&=1.6(1+0.25)^5\\&=1.6(1.25)^5\\&=1.6(3.0517578125)\\&=4.8828125\\&=4.9\; \sf m\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, if the cactus continues to grow at the same rate, its height in Year 6 will be 4.9 meters (to the nearest tenth).

Check by multiplying the height each year by 1.25:

[tex]\hrulefill[/tex]

The given diagram shows the height of the same snowman an hour apart:

We are told that the snowman continues to melt at the same percentage rate. To calculate the decay rate per hour (percentage decrease), use the percentage decrease formula:

[tex]\begin{aligned}\sf Percentage \; decrease&= \dfrac{\sf Initial\; value - Final\;value}{\sf Initial \;value}\\\\&=\dfrac{1.8-1.53}{1.8}\\\\&=\dfrac{0.27}{1.8}\\\\&=0.15\end{aligned}[/tex]

Therefore, the decay rate of the snowman's height is 15% per hour.

As the snowman melts at a constant rate, we can use the exponential decay formula to calculate its height after another 3 hours.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Exponential Decay Formula}\\\\$y=a(1-r)^t$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value. \\ \phantom{ww}$\bullet$ $r$ is the decay factor (in decimal form).\\ \phantom{ww}$\bullet$ $t$ is the number of time periods.\\\end{minipage}}[/tex]

The initial value is the snowman's initial height, so a = 1.8.

The decay factor is 15%, so r = 0.15.

As we wish to calculate the snowman's height after another 3 hours, the value of t is t = 4 (i.e. the first hour plus a further 3 hours).

Substitute these values into the formula and solve for y (the height of the snowman):

[tex]\begin{aligned}y&=a(1-r)^t\\&=1.8(1-0.15)^4\\&=1.8(0.85)^4\\&=1.8(0.5220065)\\&=0.93961125\\&=0.9\; \sf m\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, if the snowman continues to melt at the same rate, its height after another 3 hours will be 0.9 meters (to the nearest tenth).

Check by multiplying the height each hour by 0.85:

The figures are similar because the ratio of segment BC to segment EF is equal to the of segment AB to segment DE.

The scale factor is equal to 3/2.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following:

Scale factor = BC/EF = AB/DE

Scale factor = 9/6 = 6/4

Scale factor = 3/2 = 3/2 (similar)

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Answer:

Step-by-step explanation:

z=6

Considering the definition of an equation and the way to solve it, there are 84 green counters in the box.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Knowing that:

the equation in this case is:

2/9 × total counters on the box =24

Solving:

total counters on the box =24÷ 2/9

The first step in dividing by a fraction is to find the reciprocal (reverse the numerator and denominator) of the second fraction.

Then, the two numerators and the two denominators must be multiplied and, if necessary, the fractions are simplified.

total mountain bikes =24× 9/2= 24/1× 9/2

total mountain bikes =(24×9)/ (1×2)

total mountain bikes =216/2

total mountain bikes =108

Then, there are 108 green and yellow counters in the box.

So, the amount of green counters in the box is calculated as:

Amount of green counters= 7/9× 108

Amount of green counters= 7/9× 108

Amount of green counters= 84

Finally, there are 84 green counters in the box.

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The solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

Given the inequalities that include 3 in the following inequalities

x > 1.4, x < 2.6, x > 4.2, x < 5.1 and x < 8.2.

To find the solution set which include 3, write the solution set which consists of integer.

The solution set of x > 1.4 is { 2, 3, 4, 5, 6,     ........}

The solution set of x < 2.4 is { 2, 1. 0, -1, ...............}

The solution set of x > 4.2 is { 5, 6. 7, 8, ...............}

The solution set of x < 5.1 is { 5, 4, 3, 2, 1, ...............}

The solution set of x < 8.2 is { 8, 7, 6, 5, 4, 3, ...............}

Hence, the solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

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The road trip will take approximately 5 hours.

Two one-step equations:

a) 2x + 5 = 13

In this equation, the variable 'x' represents an unknown number. By performing one step of subtraction, we can find the value of 'x' that makes the equation true.

The solution is x = 4.  

b) 3y - 7 = 16

Similar to the first equation, 'y' represents an unknown number.

By adding 7 to both sides of the equation, we can isolate the variable and solve for 'y.'  

The solution is y = 7.

Two equations with fractions:

a) (1/3)x + 2 = 5

Here, the variable 'x' is multiplied by a fraction.

To isolate 'x,' we can subtract 2 from both sides and then multiply both sides by the reciprocal of 1/3, which is 3/1.

The solution is x = 9.

b) (2/5)y - 3 = 1

In this equation, 'y' is multiplied by a fraction.

We can isolate 'y' by adding 3 to both sides and then multiplying both sides by the reciprocal of 2/5, which is 5/2.

The solution is y = 4.

One equation with the distributive property:

a) 2(x + 3) = 10

This equation demonstrates the distributive property.

By applying it, we multiply 2 by both x and 3, resulting in 2x + 6 = 10.

We can then solve for 'x' by subtracting 6 from both sides.

The solution is x = 2.

One equation with decimals:

a) 0.4x + 0.8 = 1.6

In this equation, 'x' is multiplied by a decimal.

To isolate 'x,' we subtract 0.8 from both sides and then divide both sides by 0.4.

The solution is x = 2.

Real-world problem:

Imagine you're planning a road trip.

The distance you'll be traveling is 250 miles, and your car's average speed is 50 miles per hour.

You want to determine how long the trip will take.

Let 't' represent the time in hours it will take to complete the trip.

The equation that represents this situation is:

50t = 250

By dividing both sides of the equation by 50, we find that t = 5.

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The number of bags of rice that would be needed to make 80 recipes is 48.664 bags.

1 recipe = 3.5 Cups of rice

If

1 cup of rice = 158 grams

1 bag of rice = 2 pounds

2.2 lbs. = 1 kg,

1kg = 1000 g

80 recipes = 3.5 cups 80

= 280 cups

1 cup of rice = 158 grams

280 cups = 158 × 280

= 44,240 grams

1kg = 1000 g

44,240 grams = 44.24 kg

2.2 lbs. = 1 kg; x lbs = 44.24

2.2/1 = x/44.24

x = 2.2 × 44.24

x = 97.328 pounds

1 bag of rice = 2 pounds ; x bags = 97.328 pounds

1/2 = x/97.328

97.328 = 2x

x = 48.664 bags

Hence, 48.664 bags of rice is needed for 80 recipes.

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The exponential regression equation that best fits the data is y = 2^x.

To determine which exponential regression equation best fits the given data points (2, 4), (3, 8), (4, 16), and (5, 32), let's analyze the options for regression equations:

Option 1: y = 2^x

Option 2: y = 3^x

Option 3: y = 4^x

Option 4: y = 5^x

To find the best fit, we need to compare the predicted y-values from each equation with the actual y-values of the given data points.

The equation that produces the least amount of error or the closest predicted y-values to the actual ones will be the best fit.

Let's calculate the predicted y-values for each option using the given x-values:

Option 1: [tex]y = 2^2, 2^3, 2^4, 2^5 = 4, 8, 16, 32[/tex]

Option 2:[tex]y = 3^2, 3^3, 3^4, 3^5 = 9, 27, 81, 243[/tex]

Option 3:[tex]y = 4^2, 4^3, 4^4, 4^5 = 16, 64, 256, 1024[/tex]

Option 4:[tex]y = 5^2, 5^3, 5^4, 5^5 = 25, 125, 625, 3125[/tex]

By comparing the predicted y-values with the actual y-values of the data points, we can determine which option provides the closest fit.

Based on the given data points, we can observe that the predicted y-values from Option [tex]1 (y = 2^x)[/tex] match the actual y-values most closely.

The predicted values for Option 1 are 4, 8, 16, and 32, which exactly match the given data points.

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The complete question may be like: Consider the following data points: (2, 4), (3, 8), (4, 16), (5, 32). We need to determine which exponential regression equation best fits this data. Please provide the options for the regression equations so that I can assist you in finding the best fit.

The ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.

The idea of combinations can be used.

The number of ways to select k items from a set of n items is given by the formula for combinations:

C(n, k) = n! / (k! * (n - k)!)

In this case, n = 8 (the total number of routines they have learned) and k = 6 (the number of routines they will perform).

Using the formula, we can calculate:

C(8, 6) = 8! / (6! * (8 - 6)!)

= 8! / (6! * 2!)

The factorial function is represented in this case by the exclamation symbol (!).

The sum of all positive integers from 1 to n is the factorial of the number n.

Calculating the factorials involved:

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

2! = 2 * 1 = 2

Plugging in these values:

C(8, 6) = 40,320 / (720 * 2)

= 40,320 / 1,440

= 28

Therefore, the ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.

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The required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex].

Given that, the astronomer is finding the distance(d) of star to the sun in astronomical unit (AU) and tan [tex]\theta[/tex] = 0.000001389.

To find the equation by using the trigonometric function that is

tan a = perpendicular / base.

By using the data and the tangent trigonometric function, the equation is

tan [tex]\theta[/tex] = 1/d.

On simplifying gives,

Thus, d = 1/tan [tex]\theta[/tex].

Hence, the required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex]

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The correct answer is 86.08, as the octagon is given and the apothem given here is 13 units. The calculation after putting the value in formula is  86.08.

An octagon is a polygon with eight sides and eight angles. It is a two-dimensional geometric shape.  Each angle in a regular octagon measures 135 degrees, and all sides of a regular octagon are of equal length.

The formula is given below,

P= side length ×n

Apothem of octagon =13 units,

side length is = tan (360° / (2 × 8)) = (n/2) ÷ 13

= tan (360° / (2 × 8)) = n/26

tan 22.5°= n/26

n/26 =  0.4142

n = 10.76

perimeter of octagon = 8 ×  10.76 = 86.08

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Answer:

The missing variable θ is equal to (11π)/8.

Step-by-step explanation:

Given:

ω = π/8 radian per min

t = 11 min

Step 1: Identify the formula and the missing variable.

The formula is ω = (θ/t), and we are trying to find the value of θ.

Step 2: Rearrange the formula to solve for the missing variable.

To isolate θ, we can multiply both sides of the equation by t:

ω * t = θ

Step 3: Substitute the given values.

Substituting the given values into the rearranged formula, we have:

θ = (π/8) * 11

Step 4: Simplify the expression.

To multiply fractions, we multiply the numerators and multiply the denominators:

θ = (π * 11) / (8 * 1)

θ = (11π) / 8

Step 5: Finalize the answer.

The value of the missing variable θ is (11π)/8. This is the exact answer unless otherwise indicated.

Therefore, the step-by-step process shows that the missing variable θ is equal to (11π)/8.

In 6 years Juan will have the double of Carlos age.

The ages of each one are:

Carlos = 18 years old.

Juan = 42 years old.

In x years, they will have:

C = 18 + x

J = 42 + x

Carlos will have the double of Juan's age when:

J = 2*C

Replacing the equations we will get the linear equation:

42 + x = 2*(18  + x)

Solving for x we will get:

42 +x = 36 + 2x

Solving for x:

42 - 36 = 2x - x

6 = x

So Juan will have the double of Carlos age in 6 years.

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The coefficient h in the expression means the time taken for the job to be completed in hours.

The custom cake baker charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h where h is the hours it takes for the job.

Therefore, the coefficient h in the expression can be interpreted as follows:
total amount of bills = 40 + 25h

where

40 dollars is the flat fee for each job

Then the coefficient h means the hourly rate for the time taken for the job to be completed.

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When dividing the polynomial[tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2), the quotient is [tex]5x^2 + 10x + 20.[/tex]

To find the quotient when dividing the polynomial [tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2), we can use synthetic division. Synthetic division is a method used to divide polynomials quickly and efficiently.

First, we set up the synthetic division table by writing the coefficients of the polynomial in descending order:

    2  |   5   -3   4

        |___________

Next, we bring down the first coefficient, which is 5:

    2  |   5   -3   4

        |___________

        |   5

To calculate the next row, we multiply the divisor (2) by the value in the previous row (5) and write the result below the next coefficient:

    2  |   5   -3   4

        |___________

        |   5

        |___________

             10

We add the values in the second and third rows:

    2  |   5   -3   4

        |___________

        |   5

        |___________

            10    7

We repeat this process until we reach the last coefficient:

    2  |   5   -3   4

        |___________

        |   5

        |___________

             10    7

             20  34

The quotient is given by the numbers in the bottom row: [tex]5x^2 + 10x + 20.[/tex]

Therefore, when dividing the polynomial[tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2), the quotient is [tex]5x^2 + 10x + 20.[/tex]

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The complete question may be like:

Using synthetic division, what is the quotient when dividing the polynomial [tex]P(x) = 2x^3 + 5x^2 - 3x + 4[/tex] by the binomial (x - 2)? human generated answer without plagiarism. 200 words.

The meaure of m∠KJL in the circle is:

m∠KJL = 25°

Since ΔJKL is inscribed in circle P with diameter JK and mJL = 130°. Thus, m∠JLK is an inscribed angle.

Since an angle inscribed in a semicircle is a right angle.

Thus, m∠DFE = 90°

Since the measure of inscribed angle is half the measure of its intercepted arc. Thus:

m∠JKL = 1/2 * mJL

m∠JKL = 1/2 * 130

m∠JKL = 65°

Therefore:

m∠KJL = 180 - 90 - 65 = 25° (sum of angles in a triangle)

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Two equivalent expressions for the given expression 14(8 - 16x) + 3x are 112 - 221x and 112 - 221x.

Equivalent expression 1:

Expanding the expression 14(8 - 16x) and combining like terms, we get:

112 - 224x + 3x

Simplifying further, we have:

112 - 221x

Equivalent expression 2:

Distributing the coefficient 14 to both terms inside the parentheses, we have:

112 - 224x + 3x

Combining the terms with the same variable, we get:

112 - 221x

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Answer:

(a) - [tex]y=-2x+18[/tex]

(b) - [tex]y=\frac{1}{2} x-\frac{9}{2}[/tex]

Step-by-step explanation:

Given the equation of a line, which we'll call line 1, find the following.

(a) - The equation of a line, which we'll call line 2, that is parallel to line 1 and travels through the point (9,0)

(b) - The equation of a line, which we'll call line 3, that is perpendicular to line 1 and travels through the point (9,0)

Given:

[tex]3y+6x=-6[/tex]

(1) - Write the equation of line 1 in slope-intercept form

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Slope-Intercept Form:}}\\y=mx+b\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ b \ \text{is the y-intercept of the line}\end{array}\right}[/tex]

[tex]3y+6x=-6\\\\\Longrightarrow 3y=-6-6x\\\\\Longrightarrow y=-\frac{6}{3} -\frac{6}{3}x \\\\\therefore \boxed{y=-2x-2}[/tex]

Thus, we can conclude the slope of line 1 is -2.

(2) - Answering part (a)

To find a line that is parallel to line 1, the slopes must be the same, -2. Use the point-slope form for a line to find the equation for line 2.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Point-Slope Form:}}\\y-y_1=m(x-x_1)\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ (x_1,y_1) \ \text{is a point the line passes through}\end{array}\right}[/tex]

[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=-2 \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=-2(x-9)\\\\\therefore \boxed{\boxed{ y=-2x+18}}[/tex]

Thus, the equation for line 2 is found.

(2) - Answering part (b)

To find a line that is perpendicular to line 1, the slope of line 3 must be the opposite-reciprocal of line 1's. Once again, use the point-slope form of a line to find the equation of line 3.

[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=\frac{1}{2} \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=\frac{1}{2}(x-9)\\\\\therefore \boxed{\boxed{ y=\frac{1}{2} x-\frac{9}{2} }}[/tex]

Thus, the equation of line 3 is found.

Answer:

Naomi will need to score at least 89% on her fourth test to have an average of 90% in her math class.

Step-by-step explanation:

To find out what score Naomi needs to earn on her fourth test in order to have an average of 90%, we can set up an equation.

Let's denote the score on the fourth test as "x". Naomi has taken three tests, and their scores are 87%, 98%, and 86%. To find the average, we sum up all the scores and divide by the number of tests:

(87 + 98 + 86 + x) / 4 = 90

Now we can solve for x:

(87 + 98 + 86 + x) = 4 * 90

271 + x = 360

x = 360 - 271

x = 89

Naomi will need to score at least 89% on her fourth test to have an average of 90% in her math class.

1. The area of composed figure is 52.26 cm².

2. The area of composed figure is 74 ft².

1. Area if Triangle

= 1/2 x b x h

= 1/2 x 6 x 8

= 24 cm²

Area of semicircle

= πr²/2

= 3.14 x 3 x 3

= 28.26 cm²

So, area of composed figure

= 28.26 + 24

= 52.26 cm²

2. Area of Trapezium

= 1/2 (7 + 13) x 5

= 1/2 x 20 x 5

= 50 ft²

Area of Triangle

= 1/2 x b x h

= 1/2 x 8 x 6

= 24 ft²

So, area of composed figure

= 24 + 50

= 74 ft²

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Based on the figure, if I and K are parallel lines, the value of x+y in degrees is 62°.

The correct answer choice is option A.

From the diagram

x + 149° = 180° (Sum of angle on a straight line)

x = 180° - 149°

x = 31°

Also,

y = 31° (alternate angles are equal)

Therefore,

x + y = 31° + 31°

= 62°

Hence, the sum of angle x and angle y is 62°.

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| P | Q | ~Q | ~Q → P | ~P | (~Q → P) ⋀ ~P |

|---|---|----|--------|----|----------------|

| T | T | F  | T      | F  | F              |

| T | F | T  | T      | F  | F              |

| F | T | F  | T      | T  | T              |

| F | F | T  | F      | T  | F              |

To construct a truth table for the logical statement (~Q → P) ⋀ ~P, we need to consider all possible truth values for the variables Q and P. The symbol "~" represents negation or "not" in logic, so ~Q denotes "not Q" and ~P denotes "not P".

In the above table, we first list all possible truth values for P and Q and then determine the truth values for ~Q, ~Q → P, and ~P based on these values. Finally, we evaluate the logical statement (~Q → P) ⋀ ~P based on the truth values for (~Q → P) and ~P to determine the overall truth value of the statement for each combination of P and Q.

The output of the above truth table shows that the statement (~Q → P) ⋀ ~P is true only in one case when P is false and Q is true. In all other cases, the statement is false. Therefore, we can infer that the statement is not always true and hence it is not a tautology. The statement is only true in one specific case where P is false and Q is true.

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Answer:

A.  19.8

B.  15.9

Step-by-step explanation:

A.  

To find the geometric mean between two numbers, you multiply them together and then take the square root of the product.

28 × 14 = 392

[tex]\sqrt{392}[/tex] = 19.799 ≈ 19.8

B.

7 x 36 = 252

[tex]\sqrt{252}[/tex] = 15.8745 ≈ 15.9

The measure of angle AEC is 225 degree.

Given ABCD square then all sides are equal and all angles are of 90°

AB=BC=CD=DA

and also CDE is an equilateral triangle

CD=DE=EC and all angles are of 60°

Now, In ΔADE, ∵AD=AE ⇒ ∠DAE=∠AED

∠ADE=∠ADC-∠EDC=90°-60°=30°

By angle sum property of triangle

∠ADE+∠DAE+∠AED=180°

30°+2∠AED=180°

2∠AED=150°

∠AED=75°

and, ∠EAB = ∠DAB-∠DAE = 90°-75° = 15°

Reflex angle ∠AEC= 360°-∠AED-∠DEC

=360° - 75° -60°

=225°

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The complete and correct question is attached below:

a) We can factor out a common factor of two from the denominator and a half from the numerator: (6p - 7q)/(12p - 14q) = (3p - 7q/2)/(6p - 7q)

b) The numerator and denominator can be factored to provide a common factor of2x²: (6x⁵ - 8x²)/(2x) = 2x³ - 4

c) A common factor of 5 may be extracted from the numerator: (10a + 15b)/5 = 2a + 3b

d) By grouping factors, we may factor the numerator: p² - 6q + 8/3p - 6 = [(p² - 6q) + 8]/[3(p - 2)] = (p - 2)(p - 4)/(p - 2) = p - 4 (where p ≠ 2)

Factorising is the process of employing brackets to represent an expression as the product of its components. We do this by eliminating any elements that are shared by all of the expression's terms. Maths. Algebra. We must eliminate any factors that are shared by each word in an expression before we can factorize it. Expanding brackets is the process's reverse.

Finding an expression's highest common factor (HCF), or the largest number or letter that each term can be split by, is necessary to ensure that it has been properly factorized. Otherwise, there will still be common factors inside the bracket, preventing the expression from being properly factorized.

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The total amount of money shared by Lee and Olivia is £132 and  Lee and Olivia shared £84 and £48, respectively.

Lee has 7/11 of the total money, which means Lee has (7/11) × x amount of money.

When Lee gives Olivia £18, they have the same amount of money.

So Olivia's share becomes equal to Lee's share.

Therefore, we can set up the following equation:

(7/11) × x - £18 = (1/2)×x

To solve this equation, we can simplify it:

7x/11 - £18 = x/2

Multiplying both sides of the equation by 22 (the least common multiple of 11 and 2) to eliminate the denominators:

14x - 22 × £18 = 11x

14x - 396 = 11x

Subtracting 11x from both sides:

14x - 11x - 396 = 0

3x - 396 = 0

Adding 396 to both sides:

3x = 396

Dividing both sides by 3:

x = 396/3

x = 132

To find Lee and Olivia's individual shares, we can substitute this value back into the initial conditions:

Lee's share = (7/11)× £132 = £84

Olivia's share = £132 - £84 = £48

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The value of angle BCD is determined as 108⁰.

option B is the correct answer.

The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc AB =  m∠ACB

m∠ACB =  72⁰

The value of angle BCD is calculated as follows;

angle BCD = 180 - 72⁰ (sum of angles in a circle)

angle BCD = 108⁰

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