Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.
What are Trigonometric Identities?Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.
Given that the value of tan(x) = -4/3 and x is in quadrant 2.
In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,
[tex]\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}[/tex]
Since the value of tan(x) is known, substitute the value in the identity,
[tex]\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\[/tex]
cos(2x) = (-7/9) × (9/25)
Cancelling 9 from the numerator and the denominator,
cos(2x) = -7/25
Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.
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The correct answer is c. [tex]$\cos(2x) = -\frac{7}{25}$[/tex].
First, we find [tex]$\sin(x)$[/tex] and [tex]$\cos(x)$[/tex] using the given value of [tex]$\tan(x)$[/tex]:
[tex]$\tan(x) = \frac{\sin(x)}{\cos(x)} = -\frac{4}{3}$.[/tex]
We can use the Pythagorean identity [tex]$\sin^2(x) + \cos^2(x) = 1$[/tex] to find [tex]$\sin(x)$[/tex] and [tex]$\cos(x)$[/tex]. Let's assume [tex]$\sin(x) = \frac{4}{5}$[/tex] (since [tex]$\tan(x) = -\frac{4}{3}$[/tex], and we are looking for a positive value of [tex]$\sin(x)$[/tex] in quadrant 2). Using the Pythagorean identity:
[tex]$\left(\frac{4}{5}\right)^2 + \cos^2(x) = 1$ \\ $\frac{16}{25} + \cos^2(x) = 1$ \\ $\cos^2(x) = 1 - \frac{16}{25}$ \\ $\cos^2(x) = \frac{25}{25} - \frac{16}{25}$ \\ $\cos^2(x) = \frac{9}{25}$. \\[/tex]
Since [tex]$\cos(x)$[/tex] is negative in quadrant 2, we have [tex]$\cos(x) = -\frac{3}{5}$[/tex].
Now, we can use the double-angle formula for cosine:
[tex]$\cos(2x) = 2\cos^2(x) - 1$ \\ $\cos(2x) = 2\left(-\frac{3}{5}\right)^2 - 1$ \\ $\cos(2x) = 2\left(\frac{9}{25}\right) - 1$ \\ $\cos(2x) = \frac{18}{25} - 1$ \\ $\cos(2x) = \frac{18}{25} - \frac{25}{25}$ \\ $\cos(2x) = -\frac{7}{25}$.[/tex]
Therefore, the value of [tex]$\cos(2x)$[/tex] = [tex]$ -\frac{7}{25}$[/tex].
Help with #30 Please!
Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the northeast?
The probability is 0.187 or 18.7% that the restaurant chosen at random is in the north east and is located in a city with a population over 500,000.
To find the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east, we really want to know the quantity of cafés that meet these two rules and are situated in the north east.
Let's look for this information using the table:
Northeast Midwest South West More than 500,000 Over 500,000 110 95 178 66 Less than 500,000 53 39 38 9 The table indicates that 110 restaurants are located in the north east of the United States in cities with more than 500,000 residents. In this manner, the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east is:
P(Northeast and North of 500,000) = 110/588 = 0.187
Thus, the likelihood is 0.187 or 18.7% that the café picked aimlessly is in the north east and is situated in a city with a populace more than 500,000.
you earn $70 per week mowing lawns one week you work 10 hours during the week and spend $20 on gasoline for your mower how much do you earn each hour
An airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 276 tickets.
a. what is the expected number of ticket holders that will fail to show for the flight?
The expected number of ticket holders that will fail to show for the flight is 11.
Given that,
There is a fail percentage of 4%.There are 267 seats.And, the 276 airline tickets are sold.Based on the above information,
= 276%
= 2.76
Now the number of ticket holders who fail for presenting the flight should be
[tex]= 2.76\times 4[/tex]
= 11
Therefore we can conclude that the expected number of ticket holders that will fail to show for the flight is 11.
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how do you factor 30n^2b-87nb+30b?
The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t2 − 70t + 300, where t is the temperature of the food in degrees Fahrenheit. The function t(h) = 2h + 3 gives the temperature of the food h hours after it is removed from refrigeration. Which expression correctly represents the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated?
what percent of 176 is 17.6
Lydia purchased a 15 cup bag of pasta. the suggested serving is 3/4 cup per person. how many servings are in a 15 cup bag of pasta
To find out how many servings are in a 15 cup bag of pasta when serving size is 3/4 cup per person, divide 15 by 3/4, which equals 20 servings.
Firstly, convert the mixed fraction into an improper fraction for easier division: 3/4 remains the same since it is already a proper fraction.
Now, carry out the division: 15 ÷ (3/4)
= 15 × (4/3) (You multiply by the reciprocal of 3/4)
Then, multiply the numbers:
= 15 × 4 ÷ 3
= 60 ÷ 3
= 20
Therefore, there are 20 servings in a 15 cup bag of pasta when the serving size is 3/4 cup per person.
Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?
6 rolls of dimes = $30.
6 rolls of quarters = $60.
Answer:
7 roll of quarter and 4 roll of dimes.
Step-by-step explanation:
Let x be the number of rolls of quarters and y be the number of rolls of dimes,
Given,
Total rolls = 11
⇒ x + y = 11 ------(1),
Also, the total value of $ 90 in which Each roll of quarters has a value of $10 and each roll of dimes has a value of $5.
⇒ 10x + 5y = 90 ------(2),
Equation (2) - 5 × Equation (1),
We get,
5x = 90 - 55
⇒ 5x = 35 ⇒ x = 7
From equation (1),
7 + y = 11 ⇒ y = 4
Hence, the number of roll of quarters = 7,
And, the number of roll of dimes = 4
After a discount of 10%, the price of a pair of jeans, including tax, was $69.62. The following equation can be used to find x, the price of the pair of jeans without the discount:
x - 0.1x + 0.07(x - 0.1x) = 69.62
What is the price of the pair of jeans without the discount?
A-$70.58
b-$72.29
c-$74.86
d-
22 less than 5 times a number f into a algebraic expression
The sum of three consecutive integers is 90. Find the integers
The sum of three consecutive integers is 90. So you know that 3 numbers that are next to each other in numerical order equals 90.
First step: Make an equation:
Let's take x as the smallest of the three numbers.
[tex]x +(x+1)+(x+2)=90[/tex]
2nd step: Open the brackets:
[tex]x+x+1+x+2=90[/tex]
3rd step: Simplify:
[tex]3x+3=90[/tex]
4th step: Keep similar integers on one side of the equation
[tex]3x+3-3=90-3[/tex]
5th step: Solve for x:
[tex]3x=87[/tex]
[tex]\frac{3x}{3} =\frac{87}{3}[/tex]
[tex]x=29[/tex]
So if the numbers are consecutive, they have to be next to each other.
Answer: 29, 30, 31
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What is the answer to 5(6*5)
One number is 4 less than a second number. Twice the second number is 16 less than 5 times the first. Find the two numbers.
The two numbers are 8 and 12.
What is Algebraic expression ?
Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables.
Let us assume first number be = x
and, let the second number be = y
the,
One number is 4 less than a second number means :
x = y - 4........(1)
Twice the second number is 16 less than 5 times the first means :
2y = 5x - 16.......(2)
Substitute x equals from the first equation in the second equation.
2y = 5(y - 4) - 16
2y = 5y - 20 - 16
-3y = -36
y = 12
Now use the first equation for find x.
x = y - 4
x = 12 - 4
x = 8
Thus, The numbers are 8 and 12.
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Write 0.0004571 in scientific notation.
The sum of any two consecutive prime numbers is also prime
there are 182 seats in a theater. The seats are evenly divided into 13 rows. How many seats are in each row
During the 2008-2009 season,there were 801,372 people who attended the home hockey games in Philadelphia.There were 609,907 people who attended the home hockey games in Phoenix. How much greater was the home attendance in Philadelphia than in Philadelphia than in Phoenix that season?
Which second-degree polynomial function has a leading coefficient of 3 and roots –4 and 6?
What is 2r+7+r=? I'm not sure
What is factor out the coefficient of the variable of 4h-3
What is the general term equation, an, for the arithmetic sequence 5, 1, −3, −7, . . . , and what is the 21st term of this sequence?
Suppose you are trying to estimate the number of field mice in a small field. one day you capture 100 mice, mark them and release them. the next day you capture 150 mice of which 15 are marked. what is the estimate for the population size?
The perimeter of a rectangular house is 122 ft. the width is 5 ft less than the length. find the length and the width.
A black-tailed jackrabbit hops about 7 feet in a single hop how far can a hop in 5 seconds
Answer:
A black-tailed jackrabbit can hopes 36 in 5 seconds.
Step-by-step explanation:
Consider the provided information.
Black tailed jackrabbit hopes 51 feet in one second.
Therefore, in 5 second Black tailed jackrabbit covers a distance of:
51×5=255 feet
So, in 5 seconds a black-tailed jackrabbit will travel 255 feet.
In one hops Black tailed jackrabbit covers 7 feet.
Now find the number of hops, we need to divide the distance by the length of one hop:
[tex]255\div 7=\frac{255}{7}\approx36[/tex]
Hence, A black-tailed jackrabbit can hopes 36 in 5 seconds.
What point in the feasible region maximizes the objective function constraints: x>=0 y>=0 -x+3>=y y<=1/3 x+1 Objective function: C=5x-4y Please explain!
Answer:
So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)
Step-by-step explanation:
When you graph all of the constraint functions, the vertices of the shape that is made are at the points above. Now you plug those points into the function equation C=5x-4y and see where you get a max or min.
(0,1)
(1.5,1.5)
(0,0)
(3,0)
(1,1)=C=1
(1.5,1.5)=C=1.5
(0,0)=C=0
(3,0)=C=15
So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)
The surface area of an open-top box with length L, width W, and height H can be found using the formula: A= 2LH + 2WH + LW Find the surface area of an open-top box with length of 7 cm, width 6 cm, and height 3 cm.
Final answer:
The surface area of an open-top box with a length of 7 cm, width of 6 cm, and height of 3 cm is calculated using the formula and comes out to be 120 cm².
Explanation:
To find the surface area of an open-top box with given dimensions, we use the formula: A= 2LH + 2WH + LW. Substituting in the provided lengths for length (L), width (W), and height (H):
A = 2(7 cm)(3 cm) + 2(6 cm)(3 cm) + (7 cm)(6 cm)
A = 2(21 cm²) + 2(18 cm²) + 42 cm²
A = 42 cm² + 36 cm² + 42 cm²
A = 120 cm²
This gives us the total surface area of the open-top box which is 120 cm².
69.5 is What precent of 85?
if the sin 30 degrees is 1/2 then the cos ____=____.
We have that if the sin 30 degrees is 1/2 then the cos __60=1/2.__
Option C
TrigonometryQuestion Parameters:
The sin 30 degrees is 1/2
Generally, the Trigonometry of a right angle triangle gives values for sin, cos, tan.
Using the triangle we have that
if the sin 30 degrees is 1/2 then the cos60=1/2
Therefore, if the sin 30 degrees is 1/2 then the cos __60=1/2__.
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Birth weights of babies born to full-term pregnancies followed roughly a normal distribution. at meadowbrook hospital, the mean weight of babies born to full-term pregnancies is 7 pounds with a standard deviation of 14 ounces (1 pound = 16 ounces). what is the probability that the average weight of the four babies will be more than 7.5 pounds
To find the probability that the average weight of four babies will be more than 7.5 pounds, we calculate the z-score and look it up in the standard normal distribution table. The probability is approximately 0.2843, or 28.43%.
Explanation:To find the probability that the average weight of four babies will be more than 7.5 pounds, we need to calculate the z-score and look it up in the standard normal distribution table.
First, we convert the weight of 7.5 pounds to ounces: 7.5 pounds * 16 ounces = 120 ounces.
Next, we calculate the z-score using the formula: z = (x - &μ) / &σ, where x is the given weight, &μ is the mean weight, and &σ is the standard deviation. In this case, z = (120 - 112) / 14 = 0.571.
Finally, we can look up the probability using the z-score in the standard normal distribution table. The probability of the average weight of four babies being more than 7.5 pounds is approximately 0.2843, or 28.43%.
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