Sarah was explaining her first step factoring, but made an error in her explanation.
Factor: 5x^2-4x-9
Sarah said, “I know that a=5, b=-4, and c=-9. Now, I need to find factors of -9 that add to -4.”
Explain the error in Sarah’s thought process.

The equation in slope intercept form for a line that passes through (10,-1) and a y intercept of -6 is y = -1/10x - 6.

Equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions that are separated by an equals sign (=), and the equation is true if and only if both expressions have the same value.
Slope intercept form is a way to express a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y intercept. In this equation, m is equal to -1/10 (the slope of the line between the two given points) and b is equal to -6 (the given y intercept). This equation can be used to describe the line that passes through (10,-1) and has a y intercept of -6.

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To write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5, you can use the following code:

This program will print a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. The table will display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places, with all numbers being right justified. The columns of the table will have appropriate headings.

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Answer:

To find out how many books each member read, we can divide the total number of books by the number of members in the reading group:

168 books ÷ 6 members = 28 books per member

Therefore, each member of Dan's reading group read 28 books this year.

168/6 = 28

28 books per member

16. The expression of the product as a sum: 7 cos(6x)cos(7x) = 7/2 * (cos(13x) + cos(x))
17. The expression of the sum as a product: sin(2x) - sin(7x) = -2 cos(9x/2) sin(5x/2)

The product as a sum can be written using the formula for the product of two cosines:

cos a * cos b = 1/2 * (cos(a + b) + cos(a - b))

Using this formula, we can write the product 7 cos(6x)cos(7x) as a sum:

7 cos(6x)cos(7x) = 7/2 * (cos(6x + 7x) + cos(6x - 7x))
= 7/2 * (cos(13x) + cos(-x))
= 7/2 * (cos(13x) + cos(x))


The sum as a product can be written using the formula for the difference of two sines:

sin a - sin b = 2 cos((a + b)/2) sin((a - b)/2)

Using this formula, we can write the sum sin(2x) - sin(7x) as a product:

sin(2x) - sin(7x) = 2 cos((2x + 7x)/2) sin((2x - 7x)/2)
= 2 cos(9x/2) sin(-5x/2)
= 2 cos(9x/2) (-sin(5x/2))
= -2 cos(9x/2) sin(5x/2)

So the final answers are:
7 cos(6x)cos(7x) = 7/2 * (cos(13x) + cos(x))
sin(2x) - sin(7x) = -2 cos(9x/2) sin(5x/2)

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The addition of the two supplementary angles will be equal to 180 degrees,

The tilt is the partition caught between lines, surfaces, or vectors that intersect. Degrees are another mode to reveal the slant. For a full rotation, the arc is 360°.

A tilt is a figure in Geometric shapes created by two rays, called the flanks of the arc, that share a common termination, called the apex of the angle.

Two slants are said to be supplementary tilts if their totality is 180 degrees.

Let ∠1 and ∠2 be the supplementary angles. Then the equation is written as,

∠1 + ∠2 = 180°

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Answer:

See below.

Step-by-step explanation:

We are asked to find the result of the expression.

We have 3 proper fractions, and they don't have a common denominator.

Meaning, that in order to simply subtract the Numerators, we should have the same Denominator for each.

We can find the Denominator simplify by finding the LCM.

The LCM is the smallest multiple that 2 or more numbers share.

We can easily find the LCM by making a list of numbers that adds the number to itself. The previous explanation is simpler, but what really is happening is we're multiplying the number with a number that grows by 1 each time; A common multiple.

The list should look like;

[tex]4; 4 \times 1 ,\ 4 \times 2, \ 4 \times 3, \ 4 \times 4, \ 4 \times 5, \ 4 \times 6, \ 4 \times 7.\\4; 4, 8, 12, 16, 20, 24, 28.[/tex]

Let's find the LCM of 5, 3, and 15:

[tex]5; 5, 10, [15], 20, 25\\3; 3, 6, 9, 12, [15]\\15; [15], 30, 45, 60, 75[/tex]

These numbers share a LCM of 15.

Multiply the fractions by setting up a proportion:

[tex]\frac{4}{5} -\frac{1}{3} -\frac{1}{15} \\\frac{4 \times 3}{5 \times 3} = \frac{12}{15} \checkmark \\\frac{1 \times 5}{3 \times 5} = \frac{5}{15} \checkmark\\\frac{1}{15} \ stays \frac{1}{15} \checkmark[/tex]

Subtract:

[tex]\frac{12}{15} - \frac{5}{15} - \frac{1}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5} .[/tex]

Your final answer is [tex]\frac{2}{5} .[/tex]

The correct answer is c. 7/15.

To find the result of 4/5 - 1/3 - 1/15, you need to first find a common denominator for all three fractions. The smallest common denominator for these fractions is 15.

Next, you need to convert each fraction to an equivalent fraction with a denominator of 15.

4/5 = 12/15
1/3 = 5/15
1/15 = 1/15

Now you can subtract the numerators of each fraction and keep the common denominator of 15.

12/15 - 5/15 - 1/15 = 6/15 - 1/15 = 5/15

Finally, you can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.

5/15 = 1/3

So the result of 4/5 - 1/3 - 1/15 is 7/15, which is answer choice c.

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The required inequality expression is 2 + w ≥ 360.

In mathematics, an inequality is a statement that compares two quantities or expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

An inequality states that one quantity is either less than or greater than the other, but not necessarily equal to it.

Here we have

You get 100 points for playing the game. In addition, you get 50 points for each seven-letter word you make with the ten letters you receive.

Sal wants to break the record, and he needs 18,000 or more points.

Let's assume Sal does 'w' number of seven-letter words

Then total points that Sal will gain = 100 + 50(w)

To break the record Sal wants 18000 points or more

=> 100 + 50w ≥ 18000    

=> 2 + w ≥ 360

Therefore,

The required inequality expression is 2 + w ≥ 360.

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Shawn’s science class takes 1 and half hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Shawn’s science class starts at 11:25 a. M.

It ends at 12:45 p. M.

Now, to find the How long is Shawn’s science class we have to find the time difference as

= 12: 45 pm - 11: 25 am

So, From 11:25 am to 12:25 pm it is one hour and additional of 30 minutes or half an hour.

This, the class is 1 and half hour long.

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Answer: $21.60

Step-by-step explanation: This is a similar way I solve this problem..

You take 20%, notice is it 20% of 100%, our 100% in this case is $27.00, our 20% is missing.. so.. divide 27.00 by 5, because 5 20%'s is 100%, after you divide by 5 you will end up with $5.40, so we know that 20% of $27.00 is $5.40..

Take $27.00 and take $5.40 away, and you will be left with 21.60

20%x5=100%

27.00/5=5.40

27.00-5.40=21.60

Coretta's pair of jeans is $21.60 when it is on sale for 20% off.

The polynomial function is f(x) = (x + 1)³(x - 1)²(x - 3). A polynomial function is a mathematical expression that consists of variables, constants, and exponents that are combined using the operations of addition, subtraction, multiplication, and division.

The zeros of a polynomial function are the values of x that make the function equal to zero. The given polynomial function has a triple zero at x = -1,

double zero at x = 1, and zero at x = 3.

This means that the factors of the polynomial function are (x + 1)³, (x - 1)², and (x - 3).

Multiplying these factors together gives us the polynomial function:f(x) = (x + 1)³(x - 1)²(x - 3).

To find the value of the constant term, we can use the given point (2, 27). Substituting x = 2 and f(x) = 27 into the polynomial function gives us:

27 = (2 + 1)³(2 - 1)²(2 - 3)27

3³(1)²(-1)27 = 27(-1)27

= -27

To make the function pass through the point (2, 27), we need to multiply the polynomial function by -1:

f(x) = -1(x + 1)³(x - 1)²(x - 3)f(x)

= -(x + 1)³(x - 1)²(x - 3)

Therefore, the polynomial function is f(x) = -(x + 1)³(x - 1)²(x - 3).

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The maturity value of the loan is $13487.58 and the interest paid on the loan is $5487.58.

The maturity value of a loan is the amount that will be due at the end of the loan period. To calculate the maturity value of the loan, we will use the formula:
Maturity Value = Principal x (1 + Interest Rate/Compounding Periods)^(Compounding Periods x Number of Years)
(a) Maturity value of the loan
Maturity Value = 8000 x (1 + 0.11/12)^(12 x 5)
Maturity Value = 8000 x (1 + 0.0091666667)^60
Maturity Value = 8000 x 1.685947578
Maturity Value = $13487.58
The maturity value of the loan is $13487.58.
(b) Interest are you paying on the loan
To calculate the interest paid on the loan, we will subtract the principal from the maturity value.
Interest = Maturity Value - Principal
Interest = 13487.58 - 8000
Interest = $5487.58
The interest paid on the loan is $5487.58.

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The annual payment for the loan is $48,867.89.

To find how much is the annual payment for the loan, we must first find the total cost of the land and the loan amount.

The total cost of the land is $4,100 × 215 = $881,500.

The down payment is 25% of the total cost, so the down payment is $881,500 × 0.25 = $220,375.

The loan amount is the total cost minus the down payment, so the loan amount is $881,500 - $220,375 = $661,125.

To find the annual payment, we can use the formula A = P(1 + r)^n / [(1 + r)^n - 1], where A is the annual payment, P is the loan amount, r is the annual interest rate (APR), and n is the number of years.

Plugging in the values, we get:

A = $661,125(1 + 0.0675)^20 / [(1 + 0.0675)^20 - 1]

A = $661,125(1.0675)^20 / [(1.0675)^20 - 1]

A = $661,125(3.0878) / (3.0878 - 1)

A = $2,040,756.55 / 2.0878

A = $977,357.72

So the annual payment is $977,357.72 / 20 = $48,867.89.

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From the diagram of a Regular hexagon ABCDEFG in inscribed into circle O, we can state that the radius of circle O is 8/√3 cm

1. (a) The radius of circle O is equal to the length of OB, which is also equal to the length of OA.

Since OA = OB = OC, and OC is the perpendicular bisector of AB, triangle OAB is equilateral.

Thus, using the formula for the length of the side of a regular hexagon, we get:

AB = 8cm

OA = OB = OC = AB/√3

OA = OB = OC = 8/√3 cm

Radius of circle O = OA = OB = OC = 8/√3 cm

We only need to focus on triangle AOB to calculate the radius of the circle.

Since OA, OB, and AB are all known (OA and OB being equal to each other, and AB being given as 8 cm), we can use the Pythagorean theorem to solve for the length of AO (which is the same as the length of BO), and hence the radius of the circle.

b. The area of circle O can be calculated using the formula:

Area = πr²

Area = π(8/√3)²

Area = 64π/3 square cm.

The measure of arc AB is equal to twice the measure of angle BOC, since arc AB subtends angle BOC:

m(arc AB) = 2m∠BOC

m(arc AB) = 2(60°)

m(arc AB) = 120°f.

The measure of arc ACE is equal to the sum of the measures of angles BOC and COE, since arc ACE subtends both of these angles:

m(arc ACE) = m∠BOC + m∠COE

m(arc ACE) = 60° + 60°

m(arc ACE) = 120°g.  

The length of arc AB is equal to the circumference of circle O times the fraction of the circle subtended by arc AB:

Length of arc AB = (m(arc AB)/360°) x 2πr

Length of arc AB = (120°/360°) x 2π(8/√3) cm

Length of arc AB = (1/3) x (16π/√3) cm

Length of arc AB = (16π)/(3√3) cm.

The area of sector AOB is equal to the fraction of the circle subtended by arc AB times the area of circle O:

Area of sector AOB = (m(arc AB)/360°) x πr²

Area of sector AOB = (120°/360°) x π(8/√3)^2 cm²

Area of sector AOB = (1/3) x (64π/3) cm²

Area of sector AOB = 64π/9 square cm

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The frequency of a repeated event is its number of instances for every unit of time. In below given way frequency table can be constructed.

The frequency of a repeated event is its number of instances for every unit of time. It differs from angular frequency and is sometimes made reference to as temporal resolution for clarification. The unit of frequency is hertz (Hz), or one occurrence per second.

The time elapsed between events is measured by the period, which is the opposite of the frequency. For instance, the period, T—the time between beats—is equal to half a second if a heart beats 120 times per minute. Frequency tables to represent the morning and afternoon dogs as two sets of data are:

range        frequency

0- 9             2

10- 19           3

20-29         1

30-39         2

40-49         1

50-59         1

Therefore, in above given way frequency table can be constructed.

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a) B = -8/3.

b) B = 3.

c) B = √(13 - 8) = √5.

a), u and v are orthogonal if and only if their dot product is 0. To calculate the dot product, multiply the corresponding components of u and v and then add them together. Therefore, u · v = 2i · 4i + 3j · Bj = 8 + 3B = 0, so B = -8/3.

b), u and v are parallel if and only if all components are equal. Therefore, 2i = 4i and 3j = Bj. To solve for B, we have B = 3.

c), the angle between u and v is π/6 if and only if their dot product is equal to the product of their magnitudes. The magnitude of u is |u| = √(2^2 + 3^2) = √13 and the magnitude of v is |v| = √(4^2 + B^2) = √(16 + B^2). To solve for B, we have u · v = √13 · √(16 + B^2) = 2cos(π/6), so B = √(13 - 8) = √5.

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Question 1
a) The density function of X is given by f(x)= 3x^2/64 for 0 ≤ x ≤ 4 and f(x) = 0 otherwise.
b) The expected value of X is E(X)= 3/2 and the variance of X is Var(X)= 3/8.
c) The mean of the net profit Y is given by E(Y) = 0.1E(X) - 1000 = -950 and the standard deviation is given by σY = 0.1σX = 0.1(√3/2) = 0.1825.

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The revised mean is thus 20.8, which is consistent with choice (B).

How can you calculate the mean?

Simply dividing the total number of values in a data collection by the aggregate of all of the values yields it. The computation can be performed on unprocessed data or data that has been combined into a frequency chart.

We must first compute the average of the dataset such as the new number, then split by the overall number of data points in order to determine the innovative mean within a week of adding a count to the dataset.

Let's call the four original numbers in the dataset A, B, C, and D. We know that their mean is 19, so we can write:

(A + B + C + D)/4 = 19

Multiplying both sides by 4 gives us:

A + B + C + D = 76

Now, if we add the number 28 to the dataset, we get a new sum:

A + B + C + D + 28

To find the new mean, we need to divide this sum by the total number of values in the dataset, which is 5 now:

(A + B + C + D + 28)/5

Substituting in our earlier expression for A + B + C + D, we get:

(76 + 28)/5 = 104/5 = 20.8

Therefore, the new mean is 20.8, which corresponds to option (B).

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The correct answer is c: Initial value: 1, rate of change 5 over 3. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5).

A linear equation is an equation that describes a straight line when it is graphed. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. Linear equations are used to describe many real-world situations, such as the height of a ball thrown in the air, the distance traveled by a car, or the height of a person over time.

This question is asking for the initial value and rate of change for a linear equation. The initial value is the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is 1, so the initial value is 1. The rate of change is the slope of the line, which can be found by calculating the change in y over the change in x. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5). Therefore, the rate of change is 5 over 3, so the correct answer is c: Initial value: 1, rate of change 5 over 3.

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The quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

To find the quotient and remainder, use long division. First, divide the leading terms of both polynomials. 3x^4 divided by x^3 gives x.

Next, multiply the quotient by the divisor and subtract from the dividend. x(x^3-x^2+1) subtract from 3x^4-x^2 gives x+1.

Finally, divide the remainder by the divisor to get the remainder. x+1 divided by x^3-x^2+1 gives 2x^2-3. Therefore, the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

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The equation of the parabola can be written as

y=-0.16(x+2.0)(x-4.6)

A parabola is a curve made from the conic section whose eccentricity is 1 and is defined by the linear equation,

y=a(x-h)²+k, where a is an arbitrary constant and (h,k) denotes the vertex of the parabola.

According to the Intercept form of a parabola, if two x-intercepts (h1, 0), (h2, 0) are given, then the equation of parabola can be written as,

y=a(x+h1)(x-h2)

In this question,

h1 = 2.0

h2 = 4.6

So, the equation of the parabola would be,

y=a(x+2.0)(x-4.6)

Now, to find the value of the arbitrary constant "a", we can plug the point (0, 1.5) in this equation,

1.5 = a(0+2.0)(0-4.6)

1.5 =  a(-9.2)

a = -0.16

So, the equation of the parabola can be written as,

y=-0.16(x+2.0)(x-4.6)

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I chose the Quadratic Formula and Graphing because they are both straightforward methods that can give us the exact solutions.

A quadratic equation in the form ax^2 + bx + c = 0 where a > 1 is 2x^2 + 5x + 3 = 0.

To find the number of solutions based on the discriminant, we can use the formula D = b^2 - 4ac. In this case, D = (5)^2 - 4(2)(3) = 25 - 24 = 1. Since D > 0, the quadratic equation has two distinct real solutions.

Two ways to find the specific solutions or show that there is no solution are the Quadratic Formula and Graphing.

The Quadratic Formula is x = (-b ± √D)/2a. Plugging in the values from the equation, we get x = (-5 ± √1)/4 = (-5 ± 1)/4. This gives us the two solutions x = -1 and x = -2.

Graphing is another way to find the solutions. We can graph the equation y = 2x^2 + 5x + 3 and find the x-intercepts, which are the solutions to the equation. The graph shows that the x-intercepts are -1 and -2, which are the same solutions we found using the Quadratic Formula.

I chose the Quadratic Formula and Graphing because they are both straightforward methods that can give us the exact solutions. The Quadratic Formula is a formula that can be applied to any quadratic equation, and Graphing allows us to visually see the solutions. The other methods, such as Factoring, Square Root Property, and Completing the Square, may not always be applicable or may require more steps to find the solutions.

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The simplified form of the expression ( 1/10 ) - 30 is -299/10 or -29 9/10.

Given the expression in the question;

( 1/10 ) - 30

To solve the expression (1/10) - 30, we need to first find a common denominator for the two terms in the expression.

The common denominator between 1/10 and 30 is 300, so we can rewrite the expression as:

(1/10) - 300/10

Now we can combine the two terms by subtracting the second term from the first:

(1/10) - 300/10 =

(1 - 300 )/10

-299/10

Convert -299/10 to mixed fraction

-29 9/10

Therefore, the solution to (1/10) - 30 is -299/10 or -29 9/10.

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Answer:

358.65

Step-by-step explanation:

sin27 = x/790

so x = sin27 × 790 = 358.65

Answer:

  see attached

Step-by-step explanation:

Given some of the angles in a parallelogram with diagonals shown, you want the measures of missing angles.

The measures of missing angles are found by making use of triangle and parallelogram angle relations:

In the attached diagram, the given angles are shown in red. The requested angles are shown in blue.

  ∠BDC = 40°, congruent to alternate interior angle ABD

  ∠DEA = 78°, supplementary to adjacent angle AEB

  ∠BDA = 70°, congruent to alternate interior angle DBC

  ∠BCD = 70°, supplementary to adjacent angle ABC = 40°+70°.

We can see here that solving the parallelogram, we have:

A parallelogram is a quadrilateral (a polygon with four sides) in which opposite sides are parallel to each other. This means that the opposite sides of a parallelogram have the same slope and will never intersect, even if extended infinitely.

A parallelogram has four sides, four angles, and two pairs of opposite sides that are equal in length. The opposite angles of a parallelogram are also equal in measure.

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The shape with a series of parallel cross sections that are congruent circles is a cylinder.

The cross-section that results from cutting a cylinder parallel to its base is a circle that is congruent to all other parallel cross-sections. This is true for any plane that is perpendicular to the cylinder's base. The only shape that has parallel cross-sections that are congruent circles is a cylinder, for this reason.

Two parallel, congruent circular bases that lay on the same plane make up the three-dimensional shape of a cylinder. A curved rectangle connecting the bases makes up the cylinder's lateral surface. Congruent circles are produced when a cylinder is cut in half parallel to its base.

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1. There are 4896 possible ways for the 18 members of a Boy Scout troop to elect a president, a vice-president, and a secretary, assuming that no member can hold more than one office.

2. The probability that two of the three children are girls is 3/8.

3. There are 144 possible ways to seat 7 people at a round table with a certain 3 people side by side.

4. The probability that fewer than 4 out of the 15 printers tested fail to pass the test print is 0.8539.

1. The number of ways to elect a president, vice-president, and secretary from 18 members is 18 * 17 * 16 = 4896. This is because there are 18 choices for president, 17 choices for vice-president (since one person has already been chosen for president), and 16 choices for secretary (since two people have already been chosen for the other offices).

2. The probability of having two girls out of three children is 3/8. This is because there are eight possible outcomes for the genders of three children (BBB, BBG, BGB, GBB, GGB, GBG, BGG, GGG), and three of these outcomes have two girls (BBG, BGG, GBG).

3. The number of ways to seat 7 people at a round table with a certain 3 people side by side is 4! * 3! = 144. This is because there are 4! ways to arrange the other 4 people around the table, and 3! ways to arrange the 3 people who are side by side.

4. The probability that fewer than 4 out of 15 printers fail to pass the test print is 0.8539. This can be found using the binomial probability formula: P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (15 choose 0)(0.25^0)(0.75^15) + (15 choose 1)(0.25^1)(0.75^14) + (15 choose 2)(0.25^2)(0.75^13) + (15 choose 3)(0.25^3)(0.75^12) = 0.8539.

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The  percent decrease in student's weight is 15%.

To calculate this, take the difference between his starting and ending weight and divide it by his starting weight. Multiply the result by 100 to express it as a percent.

To find the percent decrease in his weight, we can use the formula:
percent decrease = (original weight - new weight) / original weight * 100

First, let's plug in the given values:
percent decrease = (280 - 238) / 280 * 100

Next, we can simplify the numerator:
percent decrease = 42 / 280 * 100

Then, we can divide 42 by 280 to get 0.15:
percent decrease = 0.15 * 100

Finally, we can multiply 0.15 by 100 to get the percent decrease:
percent decrease = 15%

Therefore, his weight decreased by 15%.

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The polynomial 7x^(7)-9x^(5)+3x^(4)+12x+1 has four roots. Roots are the values of x that make the polynomial equal to zero. To find these values, one can use a variety of methods, such as factoring, graphing, and the quadratic formula.

Factoring is the simplest method to use, and it involves breaking the polynomial down into simpler terms. In this case, the polynomial can be broken down into the product of two linear polynomials (7x^(7)-9x^(5) and 3x^(4)+12x+1). By setting each factor equal to zero and solving for x, you can find the roots.

Graphing is also a useful tool for finding the roots of a polynomial. By graphing the polynomial, you can see the x-intercepts, which are the values at which the graph crosses the x-axis. These are the roots.

Finally, the quadratic formula can be used to find the roots of this polynomial. This formula is a general solution for any quadratic equation, and it can be applied to the polynomial by replacing the coefficients of x^2 with those of x^7 and solving for x.

In conclusion, the polynomial 7x^(7)-9x^(5)+3x^(4)+12x+1 has four roots. These can be found using factoring, graphing, or the quadratic formula.

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the complete question in the attached figure

Part 1) find sec (theta)

we know that

sec (theta)=1/ cos (theta)

cos (theta)=adjacent side angle theta/hypotenuse

adjacent side angle theta=5

hypotenuse=13

so

cos (theta)=5/13

sec (theta)=1/(5/13)-------> sec (theta)=13/5

the answer Part 1) is

sec (theta) = 13/5

Part 2)simplify sec(theta)*cos (theta)

sec (theta)=13/5

cos (theta)=5/13

so

sec(theta)*cos (theta)=(13/5)*(5/13)----> 1

the answer part 2) is 1

Part 3)simplify cot(theta)/cos(theta)

cot (theta)=5/12

cos (theta)=5/13

so

cot(theta)/cos(theta)=(5/12)/(5/13)----> 13/12

we know that

sin (theta)=opposite angle theta/hypotenuse

opposite side angle theta=12

hypotenuse=13

sin (theta)=12/13

csc (theta)=1/sin (theta)------> csc (theta)=1/(12/13)----> csc (theta)=13/12

therefore

cot(theta)/cos(theta)=csc (theta)

the answer Part 3) is

csc (theta)

Part 4)simplify cot(theta)*sin(theta)

cot (theta)=5/12

sin (theta)=12/13

so

cot(theta)*sin(theta)=(5/12)*(12/13)----> 5/13

cos (theta) =5/13

therefore

cot(theta)*sin(theta)=cos (theta)

the answer part 4) is

cos (theta)

The total number of codes possible is 9 × 10 × 10 × 8.

To find the total number of codes possible, we need to multiply the number of choices for each digit.

For the first digit, there are 9 choices (0 is not allowed).

For the second and third digits, there are 10 choices each (0-9).

For the last digit, there are 8 choices (0 and 1 are not allowed).

So the total number of codes possible is 9 × 10 × 10 × 8 = 7200.

Therefore, there are 7200 different codes possible for the lock.

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