Answers
To prove the identity tan (pi/2-x) = cot x, we can use the identity tan(pi/2-x) = 1/tan x and simplify the expression.
To prove tan (pi/2-x) = cot x, we can use the identity tan(pi/2-x) = 1/tan x. First, rewrite tan(pi/2-x) as 1/tan x. Then, simplify 1/tan x to cot x using the definition of cot x = 1/tan x. Therefore, we have proven that tan (pi/2-x) = cot x.
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To prove tan(π/2 - x) = cot x, we use the co-function identity for tangent and cotangent, showing the relation of these functions in complementary angles. This identity confirms that tan(π/2 - x) equals cot x.
To prove the identity tan (π/2 - x) = cot x, we can use a fundamental trigonometric identity. Here's how:
Recall the co-function identity: tan (π/2 - x) = cot x. This identity is derived from the relationship between tangent and cotangent in complementary angles.
Using the identity tan (π/2 - x) = cot x, we know that the tangent of an angle's complement is equal to the cotangent of the angle.
By definition, tan θ (tangent) is the ratio of the opposite side to the adjacent side in a right triangle. For the complementary angle, the roles of the opposite and adjacent sides switch, which aligns with the definition of cot x (cotangent), i.e., the adjacent side over the opposite side.
This proves that tan (π/2 - x) = cot x.
Related Questions
50x = 100 what does x equal??
Answers
Divide 50 by each side.
X= 2
To find out what x equals, you can divide the numbers 100 and 50 . . .
100 divided by 50 = 2
2 x 50 = 100
x=2 <--------
Hope this helps you.
Have a great day!
The sum of three consecutive odd integers is 153. what is the value of the largest of the integers?
Answers
The value of the largest of the integers will be 53.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of three consecutive odd integers is 153.
Let x be the odd number. Then the other two odd numbers will be x + 2 and x + 4. Then the equation will be
x + x + 2 + x + 4 = 153
3x + 6 = 153
3x = 147
x = 49
Then the other two odd numbers will be
x + 2 = 49 + 2 = 51
x + 4 = 49 + 4 = 53
The value of the largest of the integers will be 53.
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Find the missing lengths of the sides
Answers
Answer:
a) a = 9d, c = 18 yd
Step-by-step explanation:
The given triangle is a 30-60-90 triangle. The ratio of the sides of the triangle is 1x: 2x: √3x.
Here the hypotenuse is 2x, the shorter leg is x and the longer leg is √3x.
In given figure, we are given the longer leg.
√3x = 9√3
From this we can find the value of x, which is the shorter leg.
Dividing both sides by √3, we get
x = 9
The shorter side, a = 9 yd
Now let's find the hypotenuse.
Plug in x = 9, in 2x, we get
= 2*9
= 18 yd
The hypotenuse "c" = 18 yd.
So the answer is a) a = 9d, c = 18 yd
I need to make a matrix in reduced row echelon form
A real estate agency offers three apartments for rent in New Mexico City. The expected total revenue per month from monthly rentals for the three apartments is $1,600. The individual owners of these apartments bear the monthly maintenance costs of 20% of the rent for the first two apartments and 25% of the rent for the third apartment, which is a total amount of $345. The agency charges a monthly fee equal to 10% of the rent for apartments 1 and 3 and a fee equal to 20% of the rent for apartment 2. The monthly rent plus agency fees totals $1,820. Let x, y, and z represent the monthly rental for the first, second, and third apartments, respectively.
Answers
Let the three apartments be A, B & C
The rent of A is $x
The rent of B is $y
The rent of C is $z
So x + y + z = 1600 .......(1)
Now
Maintenance of A is 20% of x = 0.20x
Maintenance of B is 20% of y = 0.20y
Maintenance of C is 25% of z = 0.25z
0.20x + 0.20y + 0.25z = 345
Multiplying by 100 we get
20x + 20y + 25 z = 34500
Dividing by 5 we get
4x + 4y + 5z = 6900 .......(2)
Monthly fee of A is 10% of x = 0.10x
Monthly fee of B is 20% of y = 0.20 y
Monthly Fee of C is 10% of z = 0.10z
Now
0.10x + 0.20y + 0.10 z= 1820 - 1600
0.10x + 0.20y + 0.10z = 220
Multiplying by 100 we get
10x + 20y + 10z = 22000
Dividing by 10
x + 2y + z = 2200 ....(3)
Making a Matrix of equation (1), (2) & (3)
[tex] \left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right] [/tex]
is the required matrix
PLEASE HELP!
You work for a landscaper that has a customer needing to seed an area of land 80 feet by 40 feet in size. The garden center has 5-pound bags of grass seed. Each bag of seed can cover 25 square yards of land.
You calculate that the area you need to seed is 3200 square feet. You divide by 25 to find that you need 128 bags to seed the area. Is this correct?
A) Yes.
B) No, you need to convert the 3200 square feet to yards by dividing by 3. Then calculate the number of bags.
C) No, you need to convert the 3200 square feet to yards by dividing by 9. Then calculate the number of bags.
D) No, you need to convert the 3200 square feet to yards by multiplying by 9. Then calculate the number of bags.
Answers
(1 yard)^2 = (3 feet)^2 ... square both sides
1 yard^2 = 9 feet^2
which means 1 square yard is equal to 9 square feet
think of a square yard as a 3x3 square where each smaller square is 1 square foot.
To convert from square feet to square yards, we multiply by the conversion factor (1 yard^2/9 feet^2). Or put simply we multiply by 1/9 which is the same as dividing by 9
This is why the answer is choice C.
Answer:
Since the mulch is measured in yards you need to either convert the area to be seeded to yards or the bag to feet. No, you need to convert the 3200 square feet to yards by dividing by 9. Then calculate the number of bags.
write the equation of the line that passes throughout (-1,5) and has a slope of 3 in point-slope form
Answers
[tex]y - k = m(x-h)[/tex]
So, here, you just plug in values:
[tex]y - 5 = 3(x+1)[/tex]
It would be + 1 because remember, the '-' sign just means the opposite of, not subtraction in this case. Also, m = slope.
Help why did I get this wrong? Corrections!!! Janie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?
Answers
The line is g(x) = 2x
Use www.cymath.com and enter the following line and press enter.
graph y = 2x^2 + 1; y = 2x
You will see that the line passes through the origin (0, 0), and goes up to the right and stays to the right of the parabola, so the two graphs do not intersect.
Please help asap! 44 pts (:
Answers
Answer choice A is wrong because y-y^1=m(x-x^1) remember, you cannot subtract a negative so it becomes posotive which means that answer choice C is your best bet
Have a nice day!
x - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? (1, -1) (-1, 1) (0, 3/2)
Answers
hope it helps!!
Answer: The correct answer is (1,-1).
Explanation:
The given equations are,
[tex]x-2y=3[/tex] ..... (1)
[tex]5x+3y=2[/tex] ..... (2)
Use elimination method to solve the equations.
Multiply equation (1) by 5.
[tex]5(x-2y)=5(3)[/tex]
[tex]5x-10y=15[/tex] ..... (3)
Subtract equation (3) from equation (2).
[tex]5x+3y-(5x-10y)=2-15[/tex]
[tex]5x+3y-5x+10y=-13[/tex]
[tex]13y=-13[/tex]
[tex]y=-1[/tex]
The y-coordinate is -1.
Put y=-1 in equation (1).
[tex]x-2(-1)=3[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
The x-coordinate is 1.
Therefore the intersection point is (1,-1).
The second step in the process for factoring the trinomial x2-5x-36 is to
Answers
Write -5x as a sum or difference.
x²+4x-9x-36
Factor out x from the expression.
x(x+4)-9(x+4)
Factor out x+4 from the expression.
(x+4)(x-9)
Answer: The second step is to factor out x.
Answer:
Find the sum of the factors of 36
Step-by-step explanation:
Tim’s bank requires its customers to have a 4-digit personal identification number (PIN) to access their accounts. If each digit can be a value from 0 to 9, and a 4-digit number is randomly generated, what is the probability that the number 1234 will be Tim’s PIN? A. 1 6,561 B. 1 5,040 C. 10,000 D.1 10,000
Answers
Answer:
1/10000
Step-by-step explanation:
There are 10 choices for each of the 4 digits. This means the total number of choices for the PIN are
10(10)(10)(10) = 10000
The number 1234 will only appear 1 time in this list; this makes the probability it is Tim's PIN 1/10000.
Hence, the probability that the number [tex]1234[/tex] will be Tim’s PIN is
What are digits?
A numerical digit is a single symbol used alone or in combinations, to represent numbers in a positional numeral system.
The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base [tex]10[/tex] numeral system, i.e. the decimal digits.
From the given information,
We have [tex]10[/tex] choices for each of the four digits.
This means that the total number of choices for the PIN is:-
[tex]10(10)(10)(10) = 10000[/tex]
The number [tex]1234[/tex] will only appear one time in this list which makes the probability of the form Tim's PIN [tex]\frac{1}{10000}[/tex].
Hence, the probability that the number [tex]1234[/tex] will be Tim’s PIN is [tex]\frac{1}{10000}[/tex].
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A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. What is the rectangle’s width and length?
Answers
l = 2x - 1
wl = 100
(5x+2)(2x-1) = 100
10x^2 - x - 2 = 100
10x^2 - x - 102 = 0 <--this is a quadratic equation so use the quadratic formula
x = 3.24144...
w = 5(3.24) + 2 l = 2(3.24) - 1
width = 18.2 ft length = 5.48 ft
Final answer:
To find the width and length of the rectangle, set the equation (5x + 2)(2x - 1) = 100, simplify to 10x² - x - 102 = 0, factor to find x = 6, then substitute back to find the dimensions: 32 feet by 11 feet.
Explanation:
A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. To find the rectangle’s width and length, we need to solve for x using the area of a rectangle, which is the product of its length and width. The equation is:
(5x + 2)(2x - 1) = 100
First, expand the left side of the equation:
10x²- 5x + 4x - 2 = 100
Combine like terms:
10x² - x - 2 = 100
Subtract 100 from both sides to set the equation to zero:
10x² - x - 102 = 0
Now, we can use the quadratic formula, factorization, or a graphing utility to find the values of x that satisfy the equation. For simplicity, we are looking for integer solutions because the setup of the problem suggests that such solutions are likely.
Factoring the quadratic equation, we get:
(10x + 17)(x - 6) = 0
Setting each factor to zero gives us two potential solutions for x:
10x + 17 = 0 or x - 6 = 0
Solving these, we find:
x = -17/10 or x = 6
Since a negative width does not make practical sense for a rectangle, we discard the negative solution and keep x = 6.
Inserting x = 6 into the original expressions for width and length, we find:
Width = 5(6) + 2 = 32 feet
Length = 2(6) - 1 = 11 feet
Therefore, the rectangle's dimensions are 32 feet by 11 feet.
The Jensen family took a road trip in September.the dad fills up the tank,he records the miles on the SUV as 24,033.he pays $83.58 to fill up the tank. what is the size of the SUV's tank in gallons, rounded to the nearest whole number. One gallon of gas cost $3.79,
Answers
A triangle has an area of 1102 m², and two of the sides of the triangle have lengths 60 m and 56 m. find the angle included by these two sides.
Answers
1102 m^2 = (1/2)*(60 m)*(56 m)*sin(C)
2*1102/(60*56) = 551/840 = sin(C)
C = arcsin(551/840) ≈ 41°
What is the ratio of pennies to dimes in a dollar
Answers
You need 10 dimes to make a dollar
ratio of pennies to dimes is 100:10, or 10:1 simplified
hope this helps
You are a lab technician and it takes you 1 hour 30 minutes to complete a lab test. At this rate, how many hours would it take you to complete 5 of the lab tests?
Answers
For this question, any non-integer answers should be entered as decimals, rounded to the hundredths place. Consider this data set. 25.5 26 18.2 15.3 28.5 27 20.7 20.2 26.1 18.2 21.4 17.9 24.3 22.6 19.6 The mean of the data set is , and the sample proportion of numbers less than the mean is .
Answers
The mean of the data set is 22.1 , and the sample proportion of numbers less than the mean is 0.53
Explanation:
.
1) Mean
Formula: mean = sum of values / number of data
sum of values = 25.5 + 26 + 18.2 + 15.3 + 28.5 + 27 + 20.7 + 20.2 + 26.1 + 18.2 + 21.4 + 17.9 + 24.3 + 22.6 + 19.6 = 331.5
number of data = 15
mean = 331.5 / 15 = 22.10
2) proportion of numbers less than the mean
This is easier if you order the data. These are the data in growing order:
15.3
17.9
18.2
18.2
19.6
20.2
20.7
21.4
---------
22.6
24.3
25.5
26
26.1
27
28.5
The discontinues line shows the split of the data that are less than the mean.
Those are 8 numbers less than 22.1 and the proportion is:
8 / 15 = 0.53
Answer:
Step-by-step explanation:
this is it
25 points need help ASAP!!!
Answers
in 56 years, kevin will be 9 times as old as he is right now. how old is he right now?
Answers
This is because
m + 56 = 9m
9m – m = 56
56/8
7
56+9A
A=7
he will be 7 years old he is pretty old
Find the second of 3 consecutive integers if the sum of the first and the third is 26
Answers
x+1= 2nd integer
x+2= 3rd integer
Add the 1st and 3rd set equal to 26.
x + (x+2)= 26
combine like terms
2x + 2= 26
subtract 2 from both sides
2x= 26
divide both sides by 2
x= 13
Substitute x=13 to find 2nd integer.
= x+1
= 13 + 1
= 14 second integer
ANSWER: The second integer is 14.
Hope this helps! :)
Tabitha defines a sphere as the set of all points equidistant from a single point. Is Tabitha's definition valid?
Answers
YES it is VALID.
Explanation.
In 3 dimension, it can be seen that a sphere is a round solid. It is a round object where the distance from the centre to every point on the surface is equal.
Tabitha says that a sphere is a set of all points equidistant from a single point. This single point must be the centre of the sphere for that definition to be true. This definition is correct.
Answer: Yes, Talid's definition is valid.
Step-by-step explanation:
Definition of sphere:- In geometry , a sphere is a perfectly round three-dimensional shape . It is defined as the set of points that are all at the same distance which is known as radius from a given point in a 3-dimensional space. Talid's definition:- A sphere as the set of all points equidistant from a single point.
Hence, Talid's definition is valid.
Mark has a bag containing a mixture of 30 green and white marbles. Without looking, he guesses that half of the marbles in the bag are green. He randomly selected 1 marble from the bag, recorded the color, and returned the marble to the bag. After 15 trials, Mark has drawn 10 green marbles and 5 white marbles. Which of the conclusions below is BEST supported by his data?
The bag contains more white than green marbles.
The bag contains 10 green marbles and 20 white marbles.
The bag contains an equal amount of each color.
The bag contains more green than white marbles.
Answers
The pentagons JKLMN and PQRST are similar find the length x of TP
Answers
Answer:
the answer is 2.8 assuming you had the same messurments and questions as me
Step-by-step explanation:
what is (-5.62x - 0.8) + (1.12+ 1.4x)
Answers
Which expression is a factor of 4ab + 4a − 3b − 3?
b − 1
4a − 3
3b + 1
4a + 3b
Answers
=4a(b + 1) - 3(b+1)
= (b+1)(4a - 3)
(b+1) and (4a - 3) are factors
answer
4a − 3
(4a − 3) is a factor of 4ab + 4a − 3b − 3. Option B is correct. It is obtained by solving the given expression and taking the common terms.
What is the factored form of an expression?When an expression is written as the result of multiplication of some terms, then that multiplication form is called the factored form of that expression.
From the given expression;
[tex]= \rm 4ab + 4a - 3b - 3\\\\ =4a(b + 1) - 3(b+1) \\\\ = (b+1)(4a - 3)[/tex]
From the expression, (b+1) and (4a—3) are factors.
Hence, option B is correct.
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y = 2x2 - 3x - 20?
A) x = -5 and 2
B) x = 5 and -2
C) x = -2.5 and 4
D) x = 2.5 and -4
Answers
40
2 20
4 10
5 8
2x² - 8x 5x - 20
2x(x - 4) 5(x - 4)
(2x + 5) (x - 4)
2x + 5 = 0 x - 4 = 0
2x = -5 x = 4
x = -5/2
C) x = -2.5 and 4
George Orwell based his novel, 1984, on the idea of
capitalism
totalitarianism
fascism
constitutional monarchy
Answers
totalitarianism
The following expression models the total money earned by setting up a food stall at a funfair, where x represents the number of cheeseburgers sold.
Answers
Answer:
C is correct option.
The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
Step-by-step explanation:
We are given expression [tex]\dfrac{6x}{x+3}+10[/tex]
Let us suppose f(x) is total money earned by setting up a food stall at a funfair.
where, x represents the total number of cheeseburger were sold.
Therefore, [tex]f(x)=\dfrac{6x}{x+3}+10[/tex]
We need to collect the information about constant 10.
If we put x=0 into f(x)
f(0)=10
10 is a money earn when no cheeseburger sold.
It means 10 would be initial cost of setting up of Food stall.
Thus, The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answers
Use a graphing calculator to solve the equation in the interval from 0 to 2π Round your answers to the nearest hundredth. 1.21, 2.26, 3.31, 4.35, 5.40 3.64 1.21, 4.35 0.404, 1,452.5, 3.55, 4.59, 5.64
Answers
The solution to the equation at the given interval is x = 3.64
Using a graphing calculator to solve the equation
From the question, we have the following parameters that can be used in our computation:
[tex]3\tan(\dfrac 13\theta) = 8[/tex]
This can be expressed as
[tex]y = 3\tan(\dfrac 13\theta)[/tex]
y = 8
Next, we plot the graph of the system of the equations
See attachment for the graph
From the graph, we have solution to the system to be the point of intersection of the lines
This point is located at x = 3.64
Hence, the solution to the equation at the inverval is x = 3.64
Question
Use a graphing calculator to solve the equation
[tex]3\tan(\dfrac 13\theta) = 8[/tex]
in the interval from 0 to 2π Round your answers to the nearest hundredth.