The vertex of the parabola is at (1, -9). The x-intercepts are (-2, 0) and (4, 0), which are the points where the parabola crosses the x-axis. The y-intercept is (0, -8), which is the point where the parabola crosses the y-axis.
What is vertex ?
To find the vertex and the x- and y-intercepts of the equation y = x² - 2x - 8, we can start by completing the square to put the equation in vertex form:
y = x² - 2x - 8
y + 8 = x² - 2x
y + 8 + 1 = x² - 2x + 1
y + 9 = (x - 1)²
So, the vertex of the parabola is at (1, -9). The x-coordinate of the vertex is found by taking the opposite of the coefficient of x in the equation (which is -2) and dividing by two times the coefficient of x (which is 1), giving x = -(-2) / (2*1) = 1. The y-coordinate is found by substituting x = 1 into the equation.
What are the intercepts?
To find the x-intercepts, we set y = 0 and solve for x:
0 = x² - 2x - 8
0 = (x - 4)(x + 2)
So, the x-intercepts are at (-2, 0) and (4, 0).
To find the y-intercept, we set x = 0 and solve for y:
y = 0² - 2(0) - 8
y = -8
So, the y-intercept is at (0, -8).
To graph the parabola, we can use the vertex and intercepts we found.
The vertex is (1, -9), which is the lowest point on the parabola. The x-intercepts are (-2, 0) and (4, 0), which are the points where the parabola crosses the x-axis. The y-intercept is (0, -8), which is the point where the parabola crosses the y-axis.
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Pat listed all the numbers that have 15 as a multiple. What’s the numbers in Pats list
Answer:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735...
Step-by-step explanation:
Find the value of z such that 0.5762
0.5762
of the area lies between −z
−
z
and z. Round your answer to two decimal places.
Answer:
z = 0.80
Step-by-step explanation:
You want the value of z such that p(-z < X < z) = 0.5762 for a normal distribution.
TailsThe area outside the region of interest will be split evenly between the two tails. That is, the lower tail will hold (1 -0.5762)/2 = 0.2119 of the area of the distribution. The required value of z will be the magnitude of the Inverse CDF function for this value.
Inverse CDFThe attached calculator shows the required value of z is about 0.80.
Rewrite the following in scientific notation and calculate the answer in scientific notation. If necessary, convert your answer to scientific notation. 2,520,000/14,000
The given expression can be written in scientific notation as 1.8 x 10² To obtain this, we first divide 2,520,000 by 14,000 to get 180. Then, we express this as 1.8 x 10² by moving the decimal point two places to the left and adding an exponent of 2.
What is scientific notation?For expressing very big or very small numbers in scientific notation, the number is written as the product of a number between 1 and 10 and a power of 10
How do you convert a number to scientific notation?To convert a number to scientific notation, first express it in the form a x 10^b, where a is a number between 1 and 10, and b is an integer.
Then, move the decimal point in a to obtain a number between 1 and 10, and add an exponent to 10 that corresponds to the number of places you moved the decimal point.
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PLEASE HELP ASAP PLEASE!!
Answer: a/ c/ d and e
Step-by-step explanation:
PLSSSSSSSSSSSSSSSSS HURRRYYYYYYYYYYYYYYYYYYYYYYY
A triangle with an area of 360 square meters was created from a triangle with an area of 2.5 square meters using a scale factor. What is the scale factor?
900:1
72:1
30:1
12:1
Answer:
Step-by-step explanation: Multiply all numbers and add all then divided by the lowest
Let x be the scale factor.
Then, the ratio of the areas of the two triangles is x².
We are given that the larger triangle has an area of 360 square meters and the smaller triangle has an area of 2.5 square meters. So we can set up the equation:
x²(2.5) = 360
Solving for x, we get:
x = sqrt(360/2.5)
x = sqrt(144)
x = 12
Therefore, the scale factor is 12:1. Answer: 12:1.
Using the table, what is the average daily balance of the credit card for the October 1 - October 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00. Day 1112131 Activity − Payment Purchase Purchase Adjustment −−2000+1500+1000 Closing Balance 100008000950010500
The balance based on the.data given in the table is shown below.
Balance from day 1 to 10 = 11000
Balance from day 11 to 21= 8000
Balance from day 21 to 30- 5500
Balance on day 31 7500
How to explain the balanceBalance from day 1 to 10= 11000
Balance from day 11 to 21= 8000 Balance from day 21 to 30 5500
Balance on day 31- 7500
The average daily balance of the credit card for the month of december is:
Average daily balance The ratio of total balance from each day in cycle to the total number of days in cycle.
Total balance from each day in cycle=
(11000 x 10)+(8000 × 10)+(5500 x 10) + (7500 x 1) = 104000
Average daily balance=104000 / 31
= 8145
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I need help asap!!!!!
Answer:
B
Step-by-step explanation:
Courtney has a headache, and takes 250mg of Tylenol. The amount, A of Tylenol remaining in her body after n hours is given by the formula A=250(.73)^n. How much of the Tylenol remains in her body after 4 hours?
Approximately 106.79 mg of Tylenol remain in Courtney's body after 4 hours.
What is the capacity of taking medication?
When someone takes medication, it is important to understand how long the medication remains in their system. This can help ensure that the medication is effective and prevent unwanted side effects. In this case, Courtney has taken 250mg of Tylenol to relieve a headache. We are asked to find out how much of the Tylenol remains in her body after 4 hours.
To answer this question, we can use the formula A=250(.73)ⁿ, where A represents the amount of Tylenol remaining in the body after n hours. The value 250 represents the initial amount of Tylenol Courtney took, and 0.73 represents the percentage of Tylenol that is eliminated from the body per hour.
When we substitute n=4 into the formula, we get A= 250(.73)⁴. This means that after 4 hours, approximately 106.79 mg of Tylenol remain in Courtney's body. This calculation assumes that Courtney has not taken any additional Tylenol during this time period.
It is worth noting that individual factors such as age, weight, and metabolism can affect how long a medication remains in someone's system. Additionally, taking medications with other substances, such as alcohol or other medications, can also impact the body's ability to eliminate the medication. Therefore, it is always important to follow the advice of a medical professional and carefully read medication labels and instructions.
A = 250(.73)ⁿ
A = 250(.73)⁴ (substituting n=4)
A ≈ 106.79
In conclusion, we can calculate that after 4 hours, approximately 106.79 mg of Tylenol remains in Courtney's body. It is important to remember that medication elimination can vary based on individual factors, and it is always best to consult a healthcare professional if you have any concerns about medication use or potential side effects.
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I need help for number 12
Evaluating the function f(x) = [x - 1] at different values of x, f(-1.30)=-3, f(-3)=-4, f(2.3)=1, f(4)=3, and f(7.1)=6
What is the evaluation of the functionGiven the function f(x) = [[x - 1]], we are asked to evaluate f at several values of x.
For x=-1.30, we have:
[tex]$f(-1.30) = [[-1.30 - 1]] = [[-2.30]] = -3$[/tex]
For x=-3, we have:
[tex]f(-3) = [[-3 - 1]] = [[-4]] = -4[/tex]
For x=2.3, we have:
[tex]$f(2.3) = [[2.3 - 1]] = [[1.3]] = 1$[/tex]
For x=4, we have:
[tex]$f(4) = [[4 - 1]] = [[3]] = 3$[/tex]
For x=7.1, we have:
[tex]$f(7.1) = [[7.1 - 1]] = [[6.1]] = 6$[/tex]
Therefore, f(-1.30)=-3, f(-3)=-4, f(2.3)=1, f(4)=3, and f(7.1)=6
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Which series has a sum of 20?
a) [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex] series has sum of 20.
What is sum?
In mathematics, the sum of a series is the result obtained by adding together all the terms in a sequence of numbers.
The series that has a sum of 20 is [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex].
To see why, we can use the formula for the sum of an infinite geometric series:
[tex]S = \frac{a}{(1-r)}[/tex]
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, the first term is:
[tex]a = 5(\frac{3}{4} )^0 = 5[/tex]
And the common ratio is:
[tex]r = \frac{3}{4}[/tex]
So, the formula becomes:
[tex]S = \frac{5}{(1-\frac{3}{4} )}[/tex]
Simplifying the denominator, we get:
[tex]S = \frac{5}{\frac{1}{4}}[/tex]
Multiplying by the reciprocal, we get:
S = 20
Therefore, the sum of the series is 20, which means that the series [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex]
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A house is advertised for sale. If the sale price
is $140,000. Calculate the mortgage of the deposit is 25% of the cash price
Answer: $105,000
Step-by-step explanation:
$140,000-25%deposit =$105,000
w/ solution please thanks
Answer:
x=-5, y=-2
Step-by-step explanation:
2x+4y=-18 (1)
5x-10y=-5 (2)
apply 5×(1)+2×(2)
10x+20y=-90 (3)
10x-20y=-10 (4)
by adding (3) and (4)
20x=-100
x=-5
put the value of x in (1)
we get 2×(-5)+4y=-18
⇒y=-2
After solving the given equations, the value of x and y are -5 and -2 respectively.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
So, we have the equations:
2x+4y=-18 (1)
5x-10y=-5 (2)
Apply as follows: 5×(1)+2×(2)
10x+20y=-90 (3)
10x-20y=-10 (4)
After adding (3) and (4):
20x=-100
x=-5
Insert the value of x in (1) as follows:
We obtain: 2×(-5)+4y=-18
⇒y=-2
Therefore, after solving the given equations, the value of x and y are -5 and -2 respectively.
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You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x-3y=12 Equation 1 -2x+y=8 Equation 2 A. Add equation 2 to equation 1. B. Multiply equation 2 by 3. Then subtract the result from equation 1. C. Add the left side of equation 2 to the left side of equation 1.
Multiply equation 2 by 3. Then subtract the result from equation 1.
Explanation:
The 2nd equation given to us is -2x+y = 8
Triple both sides to get -6x+3y = 24
This means the original system
[tex]\begin{cases}2x-3y = 12\\-2x+y = 8\end{cases}[/tex]
is equivalent to
[tex]\begin{cases}2x-3y = 12\\-6x+3y = 24\end{cases}[/tex]
If we were to add the equations, then the y terms would cancel out because -3y+3y = 0y = 0.
Subtracting the equations will not cancel out the y terms.
-3y minus 3y = -3y -3y = -6y
Therefore the portion saying "Then subtract the result from equation 1." in answer choice B is not correct. It should be "add the equations" or "add the result to equation 1" after tripling both sides of the 2nd equation.
Answer choices A and C say the same thing more or less. Adding the original equations straight down will cancel out the x terms. Therefore, choices A and C are valid approaches to using elimination. We can cross choices A and C off the list.
Which of the following statements regarding local extrema is/are correct?
*A local extremum of a function is a maximum or minumum value of the function over some
open interval.
*A local extremum is an x-value.
*A local extremum of a function is a maximum or minimum value of the function over a given
closed interval.
*When a function is defined over a closed interval, a local extremum may occur at the endpoint
of the interval.
*The location of a local extremum is a y-value.
*A local extremum is a y-value.
*When a function is defined over a closed interval, a local extremum never occurs at the
endpoint of the interval.
*The location of a local extremum is an x-value.
The correct statements regarding local extrema are:
A local extremum of a function is a maximum or minimum value of the function over some open interval.What are local extrema?The point at which the function's highest or minimum value is reached in some open interval containing the point is known as the local extremum (or relative extremum) of the function.
The correct statements regarding local extrema are:
A local extremum of a function is a maximum or minimum value of the function over some open interval.When a function is defined over a closed interval, a local extremum may occur at the endpoint of the interval.The location of a local extremum is an x-value.Thus, the correct options are explained above.
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An airplane flies 55" east of north from City A to City B, a distance of 470 miles. Another airplane flies 7" north of east from City A to City C, a distance of 890 miles. What is the
distance between Cities B and C? Round to the nearest tenth of a mile.
The distance between City B and City C is about miles
Answer:
d = 523.8 miles
Step-by-step explanation:
law of cosines
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Step-by-step explanation:
The drawing attached represents the question. We create a triangle with the distances from each pair of cities, and we call the distance from B to C by 'd'.
First, we need to find the angle BAC:
55° + BAC + 7° = 90°
BAC = 28°
Then, we can use the law of cosines to find the value of d:
d^2 = 470^2 + 890^2 - 2*470*890*cos(BAC)
d^2 = 470^2 + 890^2 - 2*470*890*0.8829
d^2 = 274365.86
d = 523.8 miles
A 4 m ladder leans against a
building. If the bottom of the
ladder is 1.3 m from the bottom of
the building, how far up the wall
will the ladder reach? Round your
answer to one decimal place.
Miguel’s coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $5.95 per pound, and type B coffee costs $4.65 per pound. This month’s blend used three times as many pounds of type B coffee as type A, for a total cost of $796.00. How many pounds of typeA coffee were used?
Answer:
Step-by-step explanation:
Let's start by setting up two variables to represent the number of pounds of type A and type B coffee used in the blend. Let:
x be the number of pounds of type A coffee used
3x be the number of pounds of type B coffee used (since there were three times as many pounds of type B used as type A)
The total cost of the blend is given as $796.00, so we can set up an equation based on the cost of each type of coffee and their respective amounts:
5.95x + 4.65(3x) = 796
Simplifying and solving for x, we get:
5.95x + 13.95x = 796
19.90x = 796
x = 40
Therefore, 40 pounds of type A coffee were used in the blend. To find the number of pounds of type B coffee, we can substitute x = 40 into our expression for the number of pounds of type B:
3x = 3(40) = 120
Therefore, 120 pounds of type B coffee were used in the blend.
I js need help with this question
Answer: D. y=-x+7
Step-by-step explanation: For example,
(-1,8)
x= -1
y=8
-(-1) = 1
1 + 7 = 8
help pls show ur work
So, any positive value of x is 3for this triangle. correct answer is (A)
What is Triangle?A triangle is a three-sided polygon that is formed by connecting three straight lines or line segments. It is a basic geometric shape that is commonly studied in mathematics, geometry, and trigonometry. Triangles have a wide range of properties and characteristics that are important in various fields of study, including their angles, sides, and area. Triangles can be classified based on their angles (as acute, right, or obtuse triangles) or based on their sides (as equilateral, isosceles, or scalene triangles). The study of triangles is fundamental in many areas of mathematics and physics and is also important in practical applications such as engineering, architecture, and surveying.
by the question.
PC =7 and PQ= 14
PB = 9 and PR = 6X
Thel's theorem
[tex]PC/PQ =PB/PR\\7/14 = 9/6X\\42X = 126\\ X = 126/42\\ X= 3[/tex]
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solve using substitution method y = -3x 4x+y = 2
[tex]\Large\textbf{Please give complete questions}[/tex]
if you have an 84% in a class and you get 100% on an assignment that’s worth 20% of your overall grade, what is your new grade?
Step-by-step explanation:
The 84 represents 80% of your grade and the 100 is 20 percent :
84 * 80% + 100 * 20% =
84 (.8) + 100(.2) = 87.2 %
PLSSS HELPPP QUICK
What is the product of the monomial x and the
trinomial 2x² -5x+1?
(X+Y)(X-1) if x=-3 and y=-5
Answer: 16
Step-by-step explanation: Solve the parentheses inside first, which should be (3 + 5) (3 - 1). Solve the inside which the answer would be (8) (2). Multiply after (2x8) to get the answer 16
hope it helps!!
Hi i need help with this question
The measures of the numbered angles in the rhombus include the following:
m∠1 = 31°m∠2 = 90°m∠3 = 59°m∠4 = 59°m∠5 = 31°m∠6 = 59°What is a rhombus?In Mathematics and Geometry, a rhombus can be defined as a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal). Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees).
This ultimately implies that, the opposite sides of a rhombus are parallel and the sum of all the four (4) interior angles is equal to 360 degrees.
m∠3 + 90° + 31° = 180°
m∠3 + 121° = 180°
m∠3 = 180° - 121°
m∠3 = 59°
m∠3 ≅ m∠6 ≅ m∠4 = 59°
Since opposite angles are equal, we have:
m∠1 ≅ m∠5 = 31°
Since the two (2) diagonals bisect each other at right angles (90 degrees), we have:
m∠2 = 90°
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what is the length of tr?
Answer:
12
Step-by-step explanation:
Solving Systems of Quadratic Equations
5. Solve this nonlinear system of equations. Show your work.
a. Use substitution to combine equations. Rewrite so that one side is equal to 0. (1 point)
b. Factor your equation from Part a. (1 point)
c. Identify the x-values of the solutions. (1 point)
d. Identify the solutions to the system. (1 point)
Using equations,
A: y=-x²+6x-5
y=3
3=-x²+6x-5
y=0
B: (x-2) (x-4) =0
C: x-2=0 OR x-4=0
D: x=2 OR x=4
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, etc.
Y=-x²+6x-5
Y=3
Using substitution:
3 = - x²+6x- 5
x²- 6x+8 = 0
Now factor your equation:
x²- 6x+8 = 0
⇒ x² -2x - 4x + 8 = 0
⇒ x (x-2) -4(x-2) = 0
⇒ (x- 2) (x-4) =0
Identify the x-values of the solutions:
x-2=0 or x-4 =0
x=2 or x=4
Identify the solution to the system:
x=2 y=3 and
x=4 y=3
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The graph of a proportional relationship contains the point (-12, 3).
What is the corresponding equation?
(A) y = 1/4x
(B) y = - 1/4x
(C) y = - 4/1x
(D) y = 4/1x
____
The variables x and y have a proportional relationship, and y=3 when x=4
Which equation represents this relationship?
(A) y = −12x
(B) y = 4/3x
(C) y = 7x
(D) y = 3/4x
____
correct answers gets brainliest
on a separate sheet of paper, sketch the rectangle for each problem using any method round and estimate to check your answer problem 1 5 x 4,751
The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.
The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.
2. 7 x 6000 = 42,000.
To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.
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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.
In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.
Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.
2. 7 x 6000 = 42,000.
We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.
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Why is it important to understand an index before deciding whether to trust it?
An index provides a simple way to
▼
made at different times or in different places based on
▼
an index value.
a reference value.
a rounding value.
a percentage value.
Understanding this value provides context to the index which can help determine if the index is trustworthy.
Also, we can contrast many indices and select the most pertinent and reliable one for our individual requirements.
A percentage is what?A percentage, which is denoted by the number 100, is a proportion, fraction, or piece of a whole. The Roman phrase per centum, which meaning "by the 100" or "per one hundred," is where the term "percent" originates. A numerical value and the percentage symbol (%) can be used to express percentages.
When deciding whether to believe an index, it's crucial to grasp it because it gives the data being provided context. A statistical measure known as an index reflects changes in a certain set of data across time, across several regions, or among various populations. However, the techniques, calculations, or underlying assumptions used by various indices might vary, which may have an impact on their validity and dependability.
An index, for instance, can be based on a tiny sample size, use biassed data sources, or employ an antiquated methodology that doesn't adequately reflect contemporary trends or circumstances. In certain situations, the index might not accurately represent the phenomenon being assessed, which could result in inaccurate judgements or decisions.
Hence, by comprehending the underlying information, methods, and constraints of an index, we may more accurately evaluate its validity and trustworthiness and make defensible choices according to the data it offers. Also, by contrasting many indices, we can select the one that best suits our unique requirements and is the most reliable.
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Question
Prove the trigonometric identity.
csc x cos x / tan x + cot x =cos^2 x
Drag an expression to each box to correctly complete the proof.
Drag the following expressions accordingly to complete the proof:
1/sinx· cos x)/ (sinx/cosx + cosx/sinx) = cos²x
(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x
(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x
(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x
(cos x/sinx) · (sinx·cosx) = cos²x
How to prove the trigonometric identity?Given: (csc x cos x)/ (tan x + cot x) = cos²x
We want to prove the trigonometric identity.
We have:
(csc x· cos x)/ (tan x + cot x) = cos²x
Recall the following trig. expressions and substitute for them:
csc x = 1/sinx
tan x = sinx/cosx
cot x = cosx/sinx
(1/sinx· cos x)/ (sinx/cosx + cosx/sinx) = cos²x
(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x
(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x
Recall sin²x+cos²x = 1. Subsitiute for it to get:
(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x
(cos x/sinx) · (sinx·cosx) = cos²x
cosx · cos x = cos²x
cos²x = cos²x
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