Determine the first five terms of the sequence whose nth term is defined as follows. Please enter the five terms in the boxes provided in sequential order.Please simplify your solution an=(n-3(n(n=4)

The answer to the questions C and D are; The angles in a and b cannot be classified as angle D and m∠GDE = 146°

From Answers A and B, we see that;

m∠FDE = 38° and m∠GDF = 108°

C) From the given diagram we see that m∠GDE was divided  by Line F. This means that m∠GDF and m∠FDE are both components of m∠GDE and as such they alone cannot be classified as angle D.

D) From above we see that m∠GDE was divided  by Line F. This means that m∠GDF and m∠FDE are both components of m∠GDE. Thus, this means that;

m∠GDF + m∠FDE = m∠GDE

Plugging in the relevant values gives;

m∠GDE = 108° + 38°

m∠GDE = 146°

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After 19 hours the number of bacteria will be 193.8.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that in a lab experiment, 80 bacteria are placed in a petri dish, and the conditions are such that the number of bacteria is able to double every 19 hours, to determine how many bacteria would there be after 17 hours, to the nearest whole number, the following calculation must be performed:

The number of bacteria will be calculated as,

30 x ((2/6) x 19) = X

30 x (0.34x 19) = X

30 x 6.46= X

193.8= X

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Therefore, y is equal to 12 2/5 and n is equal to 2 2/5 in the equation.

An equation is a mathematical statement that shows that two expressions are equal. An equation is typically written with an equal sign (=) between two expressions. Equations can involve various mathematical operations, such as addition, subtraction, multiplication, division, exponents, and logarithms. Solving an equation typically involves performing mathematical operations on both sides of the equation to isolate the variable (the unknown value) and find its value.

Here,

To solve for y in the equation 2y + 8 1/5 = 33, we can follow these steps:

Subtract 8 1/5 from both sides of the equation:

2y = 33 - 8 1/5

2y = 24 4/5

Divide both sides of the equation by 2:

y = (24 4/5) / 2

y = 12 2/5

Therefore, y is equal to 12 2/5.

To solve for n in the equation 2n + 4 1/5 = 9, we can follow these steps:

Subtract 4 1/5 from both sides of the equation:

2n = 9 - 4 1/5

2n = 4 4/5

Divide both sides of the equation by 2:

n = (4 4/5) / 2

n = 2 2/5

Therefore, n is equal to 2 2/5.

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Answer:

\(LM = MJ = 3\)

\(JK = KL = \sqrt{17\)

Step-by-step explanation:

Given

\(J = (4,5)\)

\(K = (5,1)\)

\(L = (1,2)\)

\(M = (1,5)\)

Required

Prove it's a kite

Start by calculating the length of the sides of the kite using:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2}\)

\(JK = \sqrt{(4 - 5)^2 + (5 -1)^2} = \sqrt{17}\)

\(KL = \sqrt{(5 - 1)^2 + (1 -2)^2} = \sqrt{17}\)

\(LM = \sqrt{(1 - 1)^2 + (2 -5)^2} = \sqrt{9} =3\)

\(MJ = \sqrt{(1 - 4)^2 + (5 -5)^2} =\sqrt{9} = 3\)

Hence:

\(LM = MJ = 3\)

\(JK = KL = \sqrt{17\)

proves that it is a kite

Answer:

B)  LM = JM = 3 and JK = LK = \(\sqrt{17}\)

Step-by-step explanation:

Edge 2021

Good Luck :)

Answer:

The rectangle is 3.5 yd x 4 yd

Step-by-step explanation:

Area = length x width = lw

l = length = 2w - 3

w = width

Area = 14(2w - 3)(w) = 14

2w² - 3w - 14 = 0

Use quadratic equation to find the 2 roots of w:  a = 2, b = -3, c = -14

w = 3.5, -2     disregard the negative root

width = 3.5 yd

length = 2(3.5) - 3 = 4 yd

The dimensions of the rectangle are approximately 2.23 yards by 1.46 yards.

We are assuming the width of rectangle to be "x" yards. Then, the length would be (2x - 3) yards, since it is 3 yards less than double the width. The formula for the area of a rectangle is A = l x w, so we can plug in the values we know:

14 = (2x - 3) x x

Expanding the brackets:

14 = 2x² - 3x

Put this equation=0:

2x² - 3x - 14 = 0

Using the quadratic formula:

x = (3 ± √(3² + 4 x 2 x 14)) / (2 x 2)

x = (3 ± √97) / 4

We can ignore the negative root, since the width cannot be negative. Therefore,

x ≈ 2.23

This is the width of the rectangle. To find the length, we can plug this value back into the expression we derived earlier:

length = 2x - 3

length ≈ 1.46

Therefore, the dimensions of the rectangle are approximately 2.23 yards by 1.46 yards

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To find the correct equations for the missing boxes, we need more information about the relationships between the different activities in Jake's Gems. However, based on the given context, we can make some assumptions and suggest potential equations:

Mining and Cutting activities produce diamonds, rubies, and other gems. Let's assume that the production of each gem type is represented by a variable: D (diamonds), R (rubies), and G (other gems).

Maintenance supports the Mining and Cutting activities. We can assume that the maintenance effort required for each activity is represented by the variable M (maintenance).Since the question mentions five missing boxes, we can suggest additional equations to represent relationships between these variables, such as:

Mining + Cutting = D + R + G (the sum of all gem types produced equals the total production from Mining and Cutting activities).

Maintenance = M (maintenance effort required).

The relationships between these variables might include equations like D = f(M), R = g(M), G = h(M), where f, g, and h represent some functions or formulas that relate gem production to maintenance effort.

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Answer: andy drove  280 miles in 3 hours

Step-by-step explanation:  are you seriousseious right now?  

the correct answer is option D) \(x \neq 1, 3\).

To determine the domain of the function \(f(x) = (x - 1)^2(x - 3)^{\frac{1}{3}}\), we need to identify any values of \(x\) that would make the function undefined.

In this case, there are two potential issues to consider:

1. The expression \((x - 1)^2\) is defined for all real values of \(x\). There are no restrictions or values that would make it undefined.

2. The expression \((x - 3)^{\frac{1}{3}}\) represents the cube root of \((x - 3)\). For the cube root to be defined, the value inside the root \((x - 3)\) must be non-negative. This means that \(x - 3 \geq 0\). Solving this inequality, we find that \(x \geq 3\).

Combining these results, we can conclude that the domain of the function \(f(x)\) is all real numbers greater than or equal to 3, written as \(x \geq 3\).

Now, let's examine the answer choices to determine which one matches this description:

A) \(x \neq 1\), and \(f(0) = \frac{3}{1}\) - This answer choice includes \(x \neq 1\), which is correct, but it does not mention the restriction \(x \geq 3\) for the cube root term. Additionally, the given value of \(f(0)\) does not align with the function \(f(x)\). Therefore, option A) is incorrect.

B) \(x \neq -1, -3\), and \(f(2) = 1\) - This answer choice includes the correct restrictions \(x \neq -1, -3\), but it does not consider the \(x \geq 3\) constraint. Therefore, option B) is incorrect.

C) \(x = 1, 3\) - This option only includes the values \(x = 1\) and \(x = 3\), but the domain of the function is not restricted to just these values. Therefore, option C) is incorrect.

D) \(x \neq 1, 3\) - This option includes the correct restrictions \(x \neq 1, 3\) and encompasses the domain of the function \(f(x)\) defined as \(x \geq 3\). Therefore, option D) is correct.

E) None of these - This option is incorrect since option D) correctly represents the domain of the function \(f(x)\).

In conclusion, the correct answer is option D) \(x \neq 1, 3\).

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The total number of roots of each polynomial function is one.

The roots of a polynomial refer to the values of the variable that make the polynomial equal to zero. The number of roots of a polynomial is dependent on the degree of the polynomial.

The given polynomial functions are already in factored form.

a. f(x) = (x + 1)

The polynomial function f(x) has one root, which is -1.

b. f(x) = (x - 3)

The polynomial function f(x) has one root, which is 3.

c. f(x) = (x - 4)

The polynomial function f(x) has one root, which is 4.

Therefore, the total number of roots of each polynomial function is one.

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In a triangle ABC, we are given the lengths of all three sides as follows:AB=14cm,BC=48cm and AC=50cm. In order to examine whether angle ABC is a right angled triangle, we can make use of the Pythagorean Theorem.

According to the Pythagorean theorem, in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, let us find the square of each side. Squaring both sides,AB^2 = 14^2= 196BC^2 = 48^2= 2304AC^2 = 50^2= 2500Now, we can check whether AB^2+BC^2=AC^2. AB^2+BC^2=196+2304=2500=AC^2As the Pythagorean theorem is satisfied, we can conclude that angle ABC is a right angled triangle. Therefore, angle ABC is equal to 90 degrees.

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Answer:

\(T = 100\)

Step-by-step explanation:

See attachment for parallelogram TRIK

Given

\(T = 5x\)

\(I = 2(x + 30)\)

Required

Determine T

Because T and I are opposite angles of the parallelogram, then they are congruent.

i.e.

\(T = I\)

Substitute values for T and I

\(5x = 2(x + 30)\)

Open bracket

\(5x = 2x + 60\)

Collect Like Terms

\(5x - 2x = 60\)

\(3x = 60\)

Solve for x

\(x = \frac{60}{3}\)

\(x =20\)

Recall that:

\(T = 5x\)

\(T = 5 * 20\)

\(T = 100\)

The variance of the given data set is approximately 0.446.

To calculate the variance of the given data set, we need to follow these steps:

1. Calculate the difference between each temperature and the mean.

  Subtract the mean (4.312) from each temperature in the data set:

  (5.07 - 4.312), (3.57 - 4.312), (5.32 - 4.312), (3.19 - 4.312), (3.49 - 4.312), (4.25 - 4.312), (4.76 - 4.312), (5.19 - 4.312), (3.94 - 4.312), (4.34 - 4.312).

2. Square each of the differences obtained in step 1.

  Square each difference:

  (0.758)^2, (-0.742)^2, (1.008)^2, (-1.122)^2, (-0.822)^2, (0.062)^2, (0.448)^2, (0.878)^2, (-0.372)^2, (0.028)^2.

3. Calculate the sum of the squared differences from step 2.

  Sum all the squared differences: 0.574564 + 0.549364 + 1.016064 + 1.257684 + 0.677284 + 0.003844 + 0.200704 + 0.771684 + 0.138384 + 0.000784.

4. Divide the sum obtained in step 3 by the number of data points minus 1.

  Since we have 10 data points, the variance is calculated as:

  Variance = Sum of squared differences / (Number of data points - 1).

5. Calculate the final result.

  Variance = (0.574564 + 0.549364 + 1.016064 + 1.257684 + 0.677284 + 0.003844 + 0.200704 + 0.771684 + 0.138384 + 0.000784) / (10 - 1).

By performing the calculations, the variance of the given data set is approximately 0.446.

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The variance of the data set is approximately 0.3842.

To find the variance of a data set, we need to calculate the squared differences between each data point and the mean, then take the average of these squared differences.

Given the data set: 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, 4.34, with a mean of 4.312.

Step 1: Calculate the squared differences between each data point and the mean:

\((5.07 - 4.312)^2, (3.57 - 4.312)^2, (5.32 - 4.312)^2, (3.19 - 4.312)^2, (3.49 - 4.312)^2, (4.25 - 4.312)^2, (4.76 - 4.312)^2, (5.19 - 4.312)^2, (3.94 - 4.312)^2, (4.34 - 4.312)^2\)

Step 2: Calculate the average of these squared differences:

Variance = (sum of squared differences) / (number of data points - 1)

Performing the calculations, we get:

Variance = 0.3842

Therefore, the variance of the data set is approximately 0.3842.

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The inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

The given parameters are:

Budget = $700

New bicycle = $296.71

Three bicycle reflectors = $12.34 each

Pair of a bike gloves = $33.66.

New biking outfits = $68.49 each.

Let the number of new biking outfits be x

So, we have the inequality;

New bicycle + 3 times price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget

This gives;

296.71 + 3( 12.34) + 33.66+ 68.49x ≤ 700

296.71 + 68.49x ≤ 700

Solve the inequality

367.39 + 68.49x ≤ 700

Hence, the inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700

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overflow in two's complement arithmetic causes the wrap-around of the most significant bit, resulting in the representation of positive numbers as negative numbers.

In two's complement representation, numbers are represented using a fixed number of bits. The most significant bit (MSB) is reserved to indicate the sign of the number, where 0 represents a positive number and 1 represents a negative number.

Overflow occurs in two's complement arithmetic when the result of an operation exceeds the range that can be represented with the available number of bits.

When overflow occurs, the result is truncated or wrapped around to fit within the bit representation. This wrapping around effectively causes the MSB to flip its value, changing the sign of the number. As a result, the number that was intended to be positive becomes negative in the two's complement representation.

For example, consider an 8-bit two's complement representation. The range for a signed 8-bit number is -128 to +127. If we add 1 to the maximum positive value of 127, overflow occurs because the result exceeds the range. The binary representation of 127 is 01111111, and adding 1 results in 10000000. Since the MSB changed from 0 to 1, the number is interpreted as -128 in two's complement representation.

In summary, overflow in two's complement arithmetic causes the wrap-around of the most significant bit, resulting in the representation of positive numbers as negative numbers.

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Answer:

$198

Step-by-step explanation:

To find how much the tax was, we multiply 10% by 220. We do this in decimal form, so we write it as 0.1*220. 0.1*220 is 22. Although, we don't stop there. Now that we know how much tax is, we must subtract the tax from the price with tax to find the OG price. 220-22 is 198. That means our answer is $198. Hope this helps!

The value of US$4.50 in Eastern Caribbean currency is 12.15 dollars.

The exchange rate for one United States dollar (US $1.00) is two dollars and seventy cents in Eastern Caribbean currency (EC$2.70) .

Therefore, the value of US$4.50 in EC currency can be computed as follows:

Using the conversion rate,

1 US dollars = 2.70 Eastern Caribbean dollars

4.50 US dollars = ?

cross multiply

Therefore,

value of 4.5 US dollars to EC dollars = 2.7 × 4.50

value of 4.5 US dollars to EC dollars = 12.15 dollars

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Answer:

22

Step-by-step explanation:

gcf 56, 120 = 8, 56/8=7, 120/8=15, 7+15=22. 22

Answer:

1. $3.60

2. $8.40

3. $42

Step-by-step explanation:

Hope this helps.

Out of 52 cards, there is only one Queen of Hearts. Hence, then, the probability = 47/52

5 cards can be chosen from a deck of 52 cards in ⁵²C₅

In order to avoid choosing a queen of hearts, we must choose 5 cards. There is only one queen of hearts in a deck of 52 cards. There are still 51 cards left, and 5 of them can be chosen in ⁵²C₅.

Therefore, the likelihood that a five-card poker hand does not include the queen of hearts is equal to ⁵¹C₅/⁵²C₅

47/52

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The full question

What is the probability that a five-card poker hand does not contain the queen of hearts?

According to the Pythagorean theorem, the length of the other leg of the right triangle is 12.

To find the length of the other leg of the right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given that the hypotenuse is 13 and one of the legs is 5.

Let's denote the other leg as 'x'. ,

According to the Pythagorean theorem, we have the equation:

\(13^{2} = 5^{2}+x^{2}\)

Simplifying the equation, we get:

169 = 25 +\(x^{2}\)

Subtracting 25 from both sides, we have:

144 = \(x^{2}\)

To solve for 'x', we take the square root of both sides:

x = √144

x = 12

Therefore, the length of the other leg of the right triangle is 12.

In conclusion, the other leg of the triangle is 12 units long.

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The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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Answer:

width = 6 feet

length = 19 feet

Step-by-step explanation:

'w' = width

'2w+7' = length

50 = 2w + 2(2w+7)

50 = 2w + 4w + 14

36 = 6w

6 = w

length = 2(6)+7 = 19

To find dy/dx using implicit differentiation for the equation tan(2x) = x^3 / (2y + ln(y)), we'll differentiate both sides of the equation with respect to x.

Let's start by differentiating the left side of the equation:

d/dx[tan(2x)] = d/dx[x^3 / (2y + ln(y))]

To differentiate tan(2x), we'll use the chain rule, which states that d/dx[tan(u)] = sec^2(u) * du/dx:

sec^2(2x) * d/dx[2x] = d/dx[x^3 / (2y + ln(y))]

Simplifying:

4sec^2(2x) = d/dx[x^3 / (2y + ln(y))]

Now, let's differentiate the right side of the equation:

d/dx[x^3 / (2y + ln(y))] = d/dx[x^3] / (2y + ln(y)) + x^3 * d/dx[(2y + ln(y))] / (2y + ln(y))^2

Simplifying:

3x^2 / (2y + ln(y)) + x^3 * (2 * dy/dx + (1/y)) / (2y + ln(y))^2

Now, we can equate the derivatives of the left and right sides of the equation:

4sec^2(2x) = 3x^2 / (2y + ln(y)) + x^3 * (2 * dy/dx + (1/y)) / (2y + ln(y))^2

To solve for dy/dx, we can isolate the term containing dy/dx:

4sec^2(2x) - x^3 * (2 * dy/dx + (1/y)) / (2y + ln(y))^2 = 3x^2 / (2y + ln(y))

Multiplying both sides by (2y + ln(y))^2 to eliminate the denominator:

4sec^2(2x) * (2y + ln(y))^2 - x^3 * (2 * dy/dx + (1/y)) = 3x^2 * (2y + ln(y))

Expanding and rearranging:

4sec^2(2x) * (2y + ln(y))^2 - x^3 * (2 * dy/dx + (1/y)) = 6x^2y + 3x^2ln(y)

Now, we can solve for dy/dx:

4sec^2(2x) * (2y + ln(y))^2 - x^3 * (2 * dy/dx + (1/y)) = 6x^2y + 3x^2ln(y)

4sec^2(2x) * (2y + ln(y))^2 = x^3 * (2 * dy/dx + (1/y)) + 6x^2y + 3x^2ln(y)

Finally, we can isolate dy/dx:

4sec^2(2x) * (2y + ln(y))^2 - x^3 * (1/y) = x^3 * 2 * dy/dx + 6x^2y + 3x^2ln(y)

dy/dx = (4sec^2(2x) * (2y + ln(y))^2 - x^3 * (1/y) - 6x^2y - 3x^2ln(y)) / (2 * x^3)

This is the expression for dy/dx = (4sec^2(2x) * (2y + ln(y))^2 - x^3 * (1/y) - 6x^2y - 3x^2ln(y)) / (2 * x^3)

This is the expression for dy/dx using implicit differentiation for the equation tan(2x) = x^3 / (2y + ln(y)).

Please note that simplification of the expression may be possible depending on the specific values and relationships involved in the equation.

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Answer: A shirt costs $8 and the pants cost $ 12.

Step-by-step explanation:

Let x = Cost of each shirt, y = Cost of each pant.

As per given, we have

\(y-x=4 \ \ \ (i)\\\\ 10x-5y = 20\ \ \ (ii)\)

Multiply 5 on both sides of (i), we get

\(5y-5x=20 \ \ \ (iii)\)

Add (ii) and (iii), we get

\(5x=40\\\\\Rightarrow\ x=8\)

From (i), y=4+8=12

Hence, a shirt costs $8 and the pants cost $ 12.

Both sets have the same cardinality as the set of real numbers. The sets (0,1) and [0.1] are not equivalent to the set of real numbers.

Real numbers are a broad and fundamental concept in mathematics. They include all the numbers that can be represented on the number line, including both rational and irrational numbers.

The following sets have the same cardinality as the set of real numbers:

The set (0,1) on the real line

The set [0,1] on the real line

Real numbers have the same cardinality as the set (0,1) on the real line and the set [0,1] on the real line.

The reason is that there are as many real numbers as there are points on the unit interval (0,1).

And, in general, there are as many real numbers between two distinct real numbers as there are real numbers on the entire real line.

Therefore, both sets have the same cardinality as the set of real numbers. The sets (0,1) and [0.1] are not equivalent to the set of real numbers.

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Answer:

(8 * x) -14 = -11

Step-by-step explanation:

* = multiply sign (i didnt want to put "x" as the multiply sign since "x" is already being used) ( mightve confused you with 2 "x"s in the parenthesis.

x = the number that is missing being multiplied by 8

I put "8" multiplied by "x" in parenthesis since you do parenthesis first in an equation.

Answer:

\(a_{n}\) = 8n - 11

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence, that is

5 - (- 3) = 13 - 5 = 21 - 13 = 8

This indicates the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 8 , thus

\(a_{n}\) = - 3 + 8(n - 1) = - 3 + 8n - 8 = 8n - 11 ← note this is the second option, that is

f(n) = - 3 + 8(n - 1)

Answer:

\(l = 28\)

Step-by-step explanation:

Given

\(S = \sum (2k - 3); k = 4\ to\ l\)

Required

What is l when S = 725

This can be solved using Sum of n terms of an AP;

\(S_n = \frac{n}{2}(T_1 + T_n)\)

Where

\(S_n = 725\)

\(T_1 = first\ term\)

To get T1; we substitute 4 for k in 2k - 3

\(T_1 = 2 * 4 - 3\)

\(T_1 = 8 - 3\)

\(T_1 = 5\)

\(T_n = last\ term\)

To get Tn; we substitute l for k in 2k - 3

\(T_n = 2 * l - 3\)

\(T_n = 2l - 3\)

n = the number of terms;

Since k = 4 to l, then

\(n = l - 4 +1\)

\(n = l - 3\)

Substitute these values in \(S_n = \frac{n}{2}(T_1 + T_n)\)

\(725 = \frac{l-3}{2}(5 + 2l - 3)\)

Collect Like Terms

\(725 = \frac{l-3}{2}(2l + 5- 3)\)

\(725 = \frac{l-3}{2}(2l + 2)\)

Open the bracket

\(725 = \frac{l-3}{2} * 2l + \frac{l-3}{2} * 2\)

\(725 = (l-3) * l + (l-3)\)

\(725 = l^2-3l + l-3\)

\(725 = l^2-2l -3\)

Subtract 725 from both sides

\(725 - 725 = l^2-2l -3 - 725\)

\(l^2-2l -3 - 725 = 0\)

\(l^2-2l - 728 = 0\)

\(l^2 + 26l - 28l - 728 = 0\)

\(l(l + 26) - 28(l + 26) = 0\)

\((l - 28)(l + 26) = 0\)

\(l - 28 = 0\) or \(l + 26 = 0\)

\(l = 28\) or \(l = -26\)

But l must be positive;

Hence, \(l = 28\)

Answer:

He needs to answer at least 20 questions correctly.

Step-by-step explanation: