Final answer:
The identity sin x cos x tan x cot x = 1 is false. By using the definitions of tan and cot, we can show that sin x cos x tan x cot x simplifies to sin x cos x.
Explanation:
The student has asked to prove or disprove the identity sin x cos x tan x cot x = 1. To verify this identity, we need to remember the definitions of the trigonometric functions. The tangent (tan) of an angle is the ratio of the sine (sin) to the cosine (cos) of that angle, and the cotangent (cot) is the reciprocal of the tangent.
Therefore, tan x = sin x / cos x, and cot x = cos x / sin x. When we multiply tan x by cot x, we get:
tan x × cot x = (sin x / cos x) × (cos x / sin x) = 1
Now, multiplying this result by sin x cos x gives:
sin x cos x tan x cot x = sin x cos x × 1 = sin x cos x
Therefore, the correct equation is sin x cos x tan x cot x = sin x cos x, which means the correct answer is:
(C) the identity is false. sin x cos x tan x cot x = sin x cos x
Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy
1/2(6x-4)=2/3x How do i solve this?
Suppose a rectangular garden has a length of 3c + 15 feet and a width of 4c feet. write an expression for the area of the garden in square feet.
The area of the rectangle is given by the equation A = 12c² + 60c
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the equation will be
Let the length of the rectangle L = ( 3c + 15 ) feet
Let the width of the rectangle W = 4c feet
Now , the area of the rectangle A = length of the rectangle L x width of the rectangle W
Substituting the values in the equation , we get
Area of Rectangle A = ( 3c + 15 ) ( 4c )
On simplifying the equation , we get
Area of Rectangle A = ( 3c ) ( 4c ) + 15 ( 4c )
Area of Rectangle A = 12c² + 60c
Therefore , the value of A is 12c² + 60c
Hence , the area of the rectangle is A = 12c² + 60c
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D: region D helppppppppp
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
A quadratic equation is shown below:
25x2 + 10x + 1 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
hello :
help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
how many solutions does this system have -3x+6y=10 -3x+6y= -4
Find the sum of the geometric sequence. (1 point) 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen
Answer:
31/16
Step-by-step explanation:
A triangle has measurements of 39, 52, and 65 units. Is it a right triangle?
Yes
No
Not enough information to tell
Solve 2x2 + 5x + 5 = 0. Round solutions to the nearest hundredth.
Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
To solve the quadratic equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex], we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 2\), \(b = 5\)[/tex], and [tex]\(c = 5\)[/tex].
Substituting the values into the quadratic formula:
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 5}}}}{{2 \cdot 2}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 40}}}}{{4}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{-15}}}}{{4}}\][/tex]
Since the discriminant [tex](\(b^2 - 4ac\))[/tex] is negative, the solutions will involve imaginary numbers.
Using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\),[/tex] we can rewrite [tex]\(\sqrt{{-15}}\)[/tex] as [tex]\(i\sqrt{{15}}\):[/tex]
[tex]\[x = \frac{{-5 \pm i\sqrt{{15}}}}{{4}}\][/tex]
So, the solutions to the equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex] are complex numbers. Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
These solutions represent the points where the graph of the quadratic equation intersects the x-axis. They lie on the complex plane.
Find the surface area of each figure to the nearest tenth. Show your work, please
Two pools are being filled with water. To start, the first pool contains 2200
liters of water and the second pool contains 1840
liters of water. Water is being added to the first pool at a rate of 21.25
liters per minute. Water is being added to the second pool at a rate of 32.5
liters per minute.
(PLEASE ANSWER QUICK)
2200 + 21.25X = 1840 +32.50X
subtract 1840 from each side
360+ 21.25X= 32.50X
subtract 21.25x from each side
360=11.25X
x= 360/11.25 = 32 minutes pool will have the same amount
21.25*32 = 680+2200 = 2880 liters
32.5*32 = 1040 + 1840=2880 liters
it will take 32 minutes and they will have 2880 liters each
Shyla used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
16 blue
20 green
14 yellow
heads 18
tails 32
Using Shyla's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
Answer:
512/2500
Step-by-step explanation:
The base of the parallelogram, b, can be found by dividing the area by the height. If the area of the parallelogram is represented by 6x2 + x + 3 and the height is 3x, which represents b, the length of the base
Answer:
[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
Step-by-step explanation:
Given: The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
To find: The base of the given parallelogram.
Solution: It is given that The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
Now, area of parallelogram is given as:
[tex]A=b{\times}h[/tex] where b is the base and h is the height of teh gievn parallelogram.
Substituting the given values, we have
[tex]6x^2+x+3=b{\times}3x[/tex]
⇒[tex]\frac{6x^2+x+3}{3x}=Base[/tex]
⇒[tex]\frac{6x^2}{3x}+\frac{x}{3x}+\frac{3}{3x}=Base[/tex]
⇒[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
which is the required expression for the base of the given parallelogram.
Which side has an equal measure to BC?
A.DE
B.AB
C.EF
D.DF
PLEASE HELP
In the given diagram, we are given two triangles, triangle ABC and triangle DEF.
And we are given a line or reflection l.
Triangle DEF is the mirror image of triangle ABC.
Therefore, all sides of the triangle ABC would be congruent to sides of triangle DEF.
AB = DF
AC = DE and
BC = EF.
We can see than BC is the smallest side of triangle ABC and EF is the smallest side of triangle DEF.
Therefore, correct option is C option.C.EFWhat is the length of diagonal ac in parallelogram ABCD if the diagonal BD = 10cm which is twice the diagonal AC?
The length of the diagonal AC in parallelogram ABCD is 5 cm.
Explanation:Given that the diagonal BD is twice the length of diagonal AC, we can represent the length of diagonal AC as x. So, the length of diagonal BD would be 2x. From the given information, we know that BD = 10 cm. Therefore, we can write the equation 2x = 10 to solve for x. Dividing both sides of the equation by 2 gives x = 5. So, the length of diagonal AC is 5 cm.
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In the given parallelogram, the length of the diagonal AC is 5 cm, given that the length of the diagonal BD is twice that of AC.
Explanation:The question pertains to the properties of a parallelogram. In this case, it has been provided that diagonal BD (10 cm) is twice the length of the other diagonal AC. This implies that the length of diagonal AC is half the length of BD. Therefore, to find the length of AC, take the length of BD and divide by 2:
AC = BD / 2 = 10 cm / 2 = 5 cm
So, the length of diagonal AC is 5 cm.
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The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
.help me with this please thanks
Thank you very much for your help!
Half of the population of cool town owns a bicycle, and 25% of the population owns a car. if 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from cool town owns either a car or a bicycle or both?
Solve the following equation by transforming it into a perfect square trinomial. x2 – 4x = 5 will mark as brilliant
The solution of the given equation is -1 or 5
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given is an equation, x²-4x = 5,
we need to transform it into a perfect square,
The equation is =
x²-4x = 5
Add 4 to each side,
x²-4x+4 = 5+4
x²-4x+4 = 9
(x-2)² = 9
Solving for x,
x-2 = √9
x-2 = ±3
x = -1 or x = 5
Hence, the solution of the given equation is -1 or 5
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The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is
Answer:
$180,997.50.
Step-by-step explanation:
1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.
2. Select the rate-per-period column corresponding to the period interest rate.
3. Locate the value in the cell where the periods row intersects the rate-per-period column.
4. Multiply the annuity payment by the table value from step 3.
Future value = annuity payment × table value
FV = $7500.00 * 24.133 = $180,997.50
HELP PLEASE! Which of these shows the following expression factored completely? 6x^2-13x=5
a (3x-1)(2x+5)
b (3x-5)(2x-1)
c (3x-1)(2x-5)
d (3x-5)(2x+1)
The solution is: the following expression factored completely,
6x^2-13x=5 is: c (3x-1)(2x-5)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, we have,
we have,
6x² - 13x = +5
6x² - 13x - 5 = 0
6x² - 15x + 2x - 5 =0
so, we get,
(3x-1)(2x-5) = 0
The sign of the constant term is the product of the signs of the constants in the binomial factors: (+1)·(+5). We want a positive sign for the constant, so both binomial factor constants must have the same sign.
When the signs of the binomial factor constants are the same, the x-term constant will match them. Thus, for a positive x-term constant, both binomial factor constants must be positive.
The signs of the x-term and the constant term are both positive, so the signs of the constants in the binomial factors must be the same and must both be positive. The only offering that meets that requirement is
... C (3x-1)(2x-5)
Hence, The solution is: the following expression factored completely, 6x^2-13x=5 is: c (3x-1)(2x-5)
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at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 when gas cost $2.20 per gallon on average
Ue can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?
I need help with all of these
Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula V=4/3 pi r^2
ROUND 3.05947821031 TO THE NEAREST WHOLE NUMBER HELP
Y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. what is the value of y when x = 5 m and z = 12 m?
a. 90 m
b. 4 m
c. 40 m
d. 9 m
a 23 gram sample of a substance thats a by-product of fireworks has a K-value of .13. whats the substances half life in days
Answer:
5.3 is the right answer.
Step-by-step explanation: