The total amount paid during the lease period is £45,665.64.
To find the total amount paid during the lease period, we need to add the initial payment of £10,000 to the present value of the four equal payments, which can be calculated using the present value formula:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. In this case, the present value of the four equal payments is £26,496, the discount rate is 8%, and the number of periods is 4. We can solve for the future value by rearranging the formula:
FV = PV × (1 + r)^n
Plugging in the given values, we get:
FV = £26,496 × (1 + 0.08)^4
FV = £26,496 × 1.34
FV = £35,664.64
This is the total future value of the four payments. To find the total amount paid during the lease period, we need to add this to the initial payment of £10,000. Therefore, the total amount paid during the lease period is:
£35,664.64 + £10,000 = £45,665.64
Therefore the total amount paid during the lease period is £45,665.64.
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A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A(0, 0), B(3, 8), and C(6,0).
One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
The triangle ABC is an isosceles triangle because AB = BC = √73
How to prove that the triangle is an isosceles triangle?From the question, we have the following parameters that can be used in our computation:
A(0, 0), B(3, 8), and C(6,0).
An isosceles triangle is any triangle that has two of its sides to be equal
So, we start by calculating the lengths of the sides using the distance equation represented as follows
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
AB = √[(0 - 3)² + (0 - 8)²]
AB = √73
AC = √[(0 - 6)² + (0 - 0)²]
AC = 6
BC = √[(3 - 6)² + (8 - 0)²]
BC = √73
Because AB = BC = √73, then the triangle is an isosceles triangle
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What is the root of the polynomial equation x(x-2)(x+3)= 18? Use a graphing calculator and a system of equations.
-3
0
2
3
Answer:
3
Step-by-step explanation:
on edge
Answer:
x = 3
Step-by-step explanation:
You want the root of the polynomial equation x(x -2)(x +3) = 18.
GraphA graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.
System of equationsThere are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.
Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...
x = 18/((x -2)(x +3))
This can be graphed as two equations:
y = x
y = 18/((x -2)(x +3))
This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)
__
Additional comment
Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.
Solve: StartFraction 20 Over x EndFraction = 2 a. x = 40 c. x = 20 b. x = 10 d. x = 15
The value of 'x' in the expression 20/x = 2 is 10.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A numerical expression in the form of fraction 20/x = 2.
Now, To make 'x' in the numerator we'll move it to the other side which is,
2x = 20.
x = 20/2.
x = 10
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Graph the solution to this inequality on the number line. −18≤−3p
100 points pls help me
Answer:
Look at the image
Step-by-step explanation:
You can solve the problem like in the image
Select all the points that are on the graph of the line Y=2x+5
Answer:
Some points that are on this line are:
(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)
Decide which of the two given prices is the better deal. You can buy laundry product in a 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08 .
A) not enough information
B) 24-ounce bottle for $4.08
C) equal value
D) 30-ounce bottle for $6.00
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.
We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08. The unit price for each bottle will be: The bottle having the lower price will be:-
30-ounce bottle = $6.00
One ounce bottle = 30 / 6.00 = $5.00
and
24-ounce bottle = $4.08
One ounce bottle = $24/ 4.08 = $5.88
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
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Question 17
Suppose that the given statement is true.
If Stacie likes pizza, then Amir likes soda.
Which statement must also be true?
O If Amir likes soda, then Stacie likes pizza.
O If Stacie likes pizza, then Amir does not like soda.
If Stacie does not like pizza, then Amir does not like soda.
O If Amir does not like soda, then Stacie does not like pizza.
The conditional statement that must also be true is given as follows:
If Stacie does not like pizza, then Amir does not like soda.
What is a conditional statement?A conditional statement has the format defined as follows:
p -> q.
It is read as follows:
If p then q.
In which:
p is the hypothesis.q is the conclusion.The statement in this problem is given as follows:
If Stacie likes pizza, then Amir likes soda.
Then the parameters are given as follows:
p: Stacie likes pizza.q: Amir likes soda.When the conditional statement is true, the inverse statement must also be true, that is:
~p -> ~q.
The symbol ~ represents negation.
Thus the inverse statement is given as follows:
If Stacie does not like pizza, then Amir does not like soda.
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A rectangular floor tile is shown.
Its dimensions are given to the nearest 0.1 metres.
1.6m
The tile is only able to sustain a maximum pressure
of 200 Newtons per square metre (N/mf),
correct to the nearest 5 N/mf.
2.3m
Given that Pressure =
Force
Area
work out the maximum force, in Newtons, that can safely be applied to the tile.
The maximum force on the rectangular floor tile is 32 N.
What is force?Force is the product of mass and acceleration.
To calculate the maximum force, we use the formula below
Formual:
F = Plw..................... Equation 1Where:
F = ForceP = Pressurel = Length of the tilew = Width of the tileFrom the question,
Given:
P = 200 N/m²l = 1.6 mw = 0.1 mSubstitute these values into equation 1
F = 200×1.6×0.1F = 32 NHence, the maximum force is 32 N.
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In the current year, Bonnie, who is single, sells stock valued at $60,000 to Linda for $15,000. Later that year, Bonnie gives Linda $25,000 in cash. Bonnie's taxable gifts from these transfers totalO $55,000.
O $70,000.
O $59,000.
O $25,000.
In the current year, Bonnie sells stock valued at $60,000 to Linda for $15,000. Later that year, Bonnie gives Linda $25,000 in cash. Bonnie's taxable gifts from these transfers total a) $55,000.
Shares, also known as stocks, are securities that represent partial ownership of the issuing company. A unit of stock is called a "share" and allows the holder to receive a portion of the company's assets and profits equal to the number of shares held.
shares are traded primarily on stock exchanges and form the basis of many individual investor portfolios. Stock trading must comply with government regulations designed to protect investors from fraud.
Taxable Gifts:
Gifts valued at $75 or more are taxable.
Non-cash gifts of small value (less than $75 annually) to employees. Holiday turkeys are tax exempt.
tax-free value is capped at $1,600 for all her awards for one year.
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Brian sped up from 68 mph to 80 mph. What was his percent change?
The percent change in the speed of Brian is found as 15%.
Describe the term percent change?The percentage difference between such a final and starting value is known as percent change. Divide the value differences by the starting value to calculate the percent change.The outcome is known as the rate of change, sometimes known as the percentage change, and is expressed in percent (with absolute numbers, it's merely a difference).For the stated question-
Initial speed = 68 mph
Final speed = 80 mph.
Difference = Final speed - Initial speed
Difference = 80 - 68
Difference = 12 mph
Percent change = Difference/Initial speed x 100
Percent change = 12/80 x 100
Percent change = 15%
Thus, the percent change in the speed of Brian is found as 15%.
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Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even.
In order for mn to be even, m must be even or n must be an even number.
What is Contraposition ?The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.
Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:
Let n and m be equal to 2a +1 and 2b + 1 respectively, then their product is:
(2a +1) (2b + 1) = 4ab + 2a + 2b + 1
= 2(2ab +a + b) + 1
This shows that the expression 2(2ab +a + b) + 1 is of the form 2n +1, thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.
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Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students. You may use your calculator to solve.
Confidence interval for the mean score of all students is (91.679, 98.321)
Given:
Sample mean = 95
Standard deviation = 6.6
The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
We have to construct a 99% confidence interval for the mean score of all the students.
Sample Standard Error =
[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]
= 1.205
t-value for the 99% confidence interval = 2.756
(use the t-tables for this)
Margin of error = 2.756 x 1.205 = 3.321
If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.
So, for the 99% confidence interval:
(95 - 3.321, 95 + 3.321) = (91.679, 98.321)
This is the final confidence interval.
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Choose ALL solutions of the following system of linear inequalities listed below.
A (0, -1)
B (6, 2)
C (9, 9)
D (8, 2)
E (-2, 4)
F (2, 6)
All solutions of the following system of linear inequalities are given-
B (6, 2), C (9, 9), D (8, 2)
Explain the term linear inequalities?Mathematical expressions known as linear inequalities compare two expressions using the inequality sign. The expression may be either a numerical or an algebraic expression, or it may be both.The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilized in this inequality, the LHS is clearly greater than the RHS.For the stated question,
The solution for the blue line given in graph will be the region under the line including the values on the line.Similarly, the solution for the red line given in graph will be the region above the line excluding the values on the line.Thus, the total solution becomes, the common shaded region of containing both lines.Therefore, the solutions of the following system of linear inequalities are-
B (6, 2), C (9, 9), D (8, 2).
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The current population of a small city is 48500 people. Due to a loss of jobs, the population is decreasing by an average of 325 people per year. How many years (from now) will it take for the population to decrease to 46875 people?
It takes 5 years for the population to decrease to 46785 from the current population of 48500 of a small city whose population is decreasing by an average of 325 people per year.
What is the equation for the given statement?It is given that,
Current population = 48500 people
Rate of decrease = 325 per year
Number of years = x
decreased population after x years = 46785
Then, the equation is
46785 = 48500 - 325x
Calculation:On simplifying the obtained equation, we get
46785 = 48500 - 325x
⇒ 325x = 48500 - 46785 = 1625
⇒ x = 1625/325 = 5 years
So, the people become 46785 after 5 years.
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Determine the solution/s to the following quadratic equation. Type "NONE" in any unused blank.
y = x² + 14x + 49
Answer:
Step-by-step explanation:i'm pretty sure that y=x^2+14x+49=625.
consider the value of t such that 0.05 of the area under the curve is to the right of t. step 2 of 2: assuming the degrees of freedom equals 18, select the t value from the t table.
Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306
Degree of freedom {df}=18
We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t
It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]
As we know, t distribution provides the cumulative probability
As the value of the total area under the t distribution will 1
So, we can write it as:
[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]
Now, using excel, we can easily calculate the t-critical value as follows
=T. INV ( Probability, DF)
Where Probability is the area and DF is the degree of freedom,
Now we will enter these values in excel:
=T. INV (0.95,18)
t-critical value can also be found using t table
Look up for df = 18, in very first column
Now look up for 0.05 in one tail row
Now intersect both of them to get the t-critical value
We will get it as: 2.306
So t-critical value will be =2.306
[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]
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A square name tag has sides that are 10 centimeters long. What is the name tag's area?
The area of square is 100 square centimeter.
What is square?
A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.
Given:
A square has sides 10 centimeters long.
We have to find the area of square.
Since,
Area of square = (side)^2
Here side of square is 10cm
So,
Area of square = (10 cm)^2
Area of square = 100 cm^2
Hence, the area of square is 100 square centimeter.
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Angle 0 is in standard position and (5, -6) is a point on the terminal
side of 0. If 0° 0 < 360°, what is the measure of 0, to the nearest
tenth of a degree (if necessary)?
The corresponding trigonometric ratios are -6/√61, 5/√61, -6/5, -5/6, √61/5, -√61/6
What are trigonometric ratios?Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec) are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.
First of all we need to find the distance between the point (5,-6) and origin (0,0)
Distance (r) = √(5-0)²+(-6-0)²
= √25+36
= √61
Now, P(5,-6) is compared with (x,y)
Now, sin Ф = y/r = -6/√61
cos Ф = x/r = 5/√61
tan Ф = y/x = -6/5
cot Ф = 1/tan Ф = -5/6
sec Ф = 1/cos Ф = √61/5
cosec Ф = 1/sin Ф = -√61/6
The corresponding trigonometric ratios are -6/√61, 5/√61, -6/5, -5/6, √61/5, -√61/6
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Solve x²-3x + 7 = 0.
OA. 3+√-37
2
OB. 3+√-19
2
and 3-√-37
2
and ³-v-19
3-√-19
2
O C. 3+√19 and 3-√/19
2
2
O D. 3+√37 and 3-√37
2
2
Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.
Define quadratic formula.The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.
Given
Equation
x²-3x + 7 = 0
Using quadratic formula,
x = -b±√b² - 4ac/2a
x = -(-3) ± √((-3)² - 4×1×7/2×1
x = 3/2± √19 1/2i
x = 3 + √19/2 and 3 - √19/2
Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.
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If the radio program plays 40 minutes of music, how many minutes will be used for commercials?
The number of minutes that will be used for commercials will be 20 minutes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
If the radio program plays 40 minutes of music.
Suppose the radio program is of one hour which is 60 minutes. Then the number of minutes will be used for commercials will be given as,
⇒ 60 - 40
⇒ 20 minutes
The number of minutes that will be utilized for plugs will be 20 minutes.
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DUE IN AN HOUR HELP!!!!
Answer:
D. x=4
Step-by-step explanation:
32. m<1=m<2 ==> angle bisectors divide an angle into two equal angles
m<2=m<RQP
m<1=m<SQP
m<RQP+m<SQP=m<SQR
m<2+m<1=m<SQR
m<2+m<2=m<SQR
(2+7x)+(2+7x)=16x-4
2+7x+2+7x=16x-4
2+2+7x+7x=16x-4
4+14x=16x-4
4-4+14x=16x-4+4
4+4+14x=16x-4+4
14x+8=16x
14x-14x+8=16x-14x
8=2x
x=8/2
x=4 ==> D
I took a number, wrote a 9 to the right of it, and added the new number to double the original number. The sum is 633. What is the original number?
The original number is, if The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number is 52.
What is the number?An arithmetic value used to indicate an amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers.
Given:
The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number,
Assume the original number is x then, according to the condition,
10x + 9 + 2x = 633
12x = 633 - 9
x = 624 / 12
x = 52
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9. In the diagram below, a Il b. Use the following information to find the missin
measures.
m21 =
m22 =
m23 =
d
(8.x-8)
2
1
m24=
m25 =
m26=
CT
(4y+44)
(3x + 17)
9
3
7
a
8
6
4
5
m27 =
m28 =
m29=
b
10
11 12
(6y+46)
m210=
m211=
m212=
The measurement of all the angles in the given geometrical image are mentioned below.
What are angles? What is a mathematical function, equation and expression?angle : In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the anglefunction : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is a figure as shown in the image.
We can write the following equations -
∠1 + ∠2 + (8x - 8)° + (3x + 17)° = 360°
and
(8x - 8)° = (3x + 17)° {Vertically opposite angles}
8x - 3x = 17 + 8
5x = 25
x = 5
So -
8x - 8 = 8 x 5 - 8 = 32°
3x + 17 = 3 x 5 + 17 = 32°
So -
∠1 + ∠2 + (2 x 32) = 360°
2∠1 + 64 = 360
2∠1 = 296
∠1 = 148° = ∠2 {Vertically opposite angles}
∠6 = ∠1 = 148°
∠3 = 32°
∠5 = (180 - 148) = 32°
∠4 = 148°
∠6 = 148°
∠5 = 32°
Now -
(4y + 44) + (6y + 46) = 180°
10y + 90 = 180
10y = 90
y = 9
So -
(4y + 44) = 4 x 9 + 44 = 36 + 44 = 80
∠8 = 80°
Now -
6y + 46 = 6 x 9 + 46 = 100°
∠10 = 100°
∠11 = 80°
∠7 = ∠10 = 100°
∠7 = 100°
∠11 = ∠12 = 80°
∠12 = 80°
Therefore, the measurement of all the angles in the given geometrical image are mentioned above.
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plified and labeled.
4) Mindy bought a new painting. It was
8 feet wide. The wall she wants to
place it on is 12 1/4feet wide. About how
far from each side will she have to place
the painting for it to be centered?
Mindy needs to place the painting at 2.125 feet away from each side of the wall.
what do we mean by wall dimension?The horizontal distance of two side of a wall is defined as width and the vertical distance is called length of wall.
How do we place a paint at the center of a wall?We need to place the paint at an equal distance from each side of wall (horizontal distance).
suppose Mindy will place the paint at x feet away from each side of wall.
for both side she counts 2x feet
width of wall =12.25 feet
width of painting= 8 feet
now, 8+ 2x = 12.25
2x= 4.25
x=2.125 feet
hence, Mindy will place the paint at 2.125 feet away from each side horizontally.
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Type your answers into the boxes.
What are the next two numbers in this sequence?
45.7
46.2
46.7
47.2
Answer:
Step-by-step explanation:
Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7
The sum of three numbers is 96. The first number is 6 less than the second. The third number is 4 times the second. What are the numbers?
Step-by-step explanation:
x = second number
first number = x - 6
third number = 4x
x - 6 + x + 4x = 96
6x - 6 = 96
6x = 102
x = 102/6 = 17
first number = x - 6 = 17 - 6 = 11
second number = x = 17
third number = 4x = 4×17 = 68
k x 20 = 1.07 what is k
Erin has a balance of $1,123.72 in her check register. On her statement, the balance of her account is $879.87.
Not reported on the bank statement are deposits of $62.42, $21, and $61.14. There are outstanding checks in the
amount of $60.24 and $50.24 and an ATM withdrawal of $40. After Erin reconciles her check register with her
statement, what entry does she need to make in her register?
Answer: After reconciling her check register with her statement, Erin needs to make the following entry in her register: $1123.72 - $879.87 + $62.42 + $21 + $61.14 - $60.24 - $50.24 - $40 = $226.23. This is the updated balance in Erin's account after accounting for all the transactions that were not reflected on her bank statement.
Lines DE and AB intersect at point C.
What is the value of x?
A.12
B.25
C.38
D.05
Answer:
B
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25°
Express tan P as a fraction in simplest terms.
Q
15
R
29
P
Tan P expressed as a fraction in simplest terms is 15/29
What are trigonometric identities?Trigonometric Identities are defined as equalities involving trigonometry functions and also holds true for all the values of variables given in the equation.
There are five types of trigonometric identities;
sinecosinetangentcosecantsecantFrom the information given, we have that;
Opposite side = 15
Adjacent side = 29
But the tangent trigonometric identity is;
Tan P = opposite/adjacent
Substitute the value
Tan P = 15/29
Hence, the value is 15/29
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