Answer:
The answer is pi/4
Step-by-step explanation:
You substitute each x for "pi/4", you will see that the equation is incorrect, the two values are no longer equal.
The equation is not an identity. Value of x = nπ, where n∈I , I → set of integers, for which both sides are defined but not equal.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
We have the equation,
cos x - (cos x) (sin x) = cos³x
Simplifying,
cos x [ 1 - (sin x) ] = cos²x (cos x)
1 - sinx = cos²x
1 - sinx = 1 - sin²x
1 - sinx = 1² - sin²x
1 - sinx = (1 - sinx)(1 +sinx)
1 = 1 + sinx
sinx = 0
x = nπ, where n∈I , I → set of integers.
It is not an identity equation.
cos x - (cos x) (sin x) ≠ cos³x
Therefore, both sides are defined but not equal.
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What is the differnce between union and intersection in math
Final answer:
Union and intersection are two operations used in set theory to combine sets or find common elements.
Explanation:
Union and intersection are two operations used in set theory. In mathematics, a set is a collection of distinct objects. The union of two sets A and B, denoted by A ∪ B, is the set that contains all the elements that are in either A or B or in both. The intersection of two sets A and B, denoted by A ∩ B, is the set that contains all the elements that are common to both A and B.
For example, let's consider two sets: A = {1, 2, 3} and B = {2, 3, 4}. The union of A and B is {1, 2, 3, 4}, as it contains all the elements from both sets. The intersection of A and B is {2, 3}, as those are the elements that are common to both sets.
Tan (25pi/2) = ___
A). 1
B). 0
C). -1
D). Undefined
I don't know how to do this
The measure of an angle's supplement is 24 less than twice the measure of the angle. Find the measure of the angle and its supplement
Simplify the expression please
(06.02 MC)
A group of students plotted the number of hours they worked at a cake shop during the holidays and the number of cakes they delivered in a week
Which statement best describes the relationship between the number of hours spent working at the cake shop and the number of cakes delivered?
Greater hours worked, more cakes delivered
Fewer hours worked, more cakes delivered
Greater hours worked, fewer cakes delivered
There is no relationship between hours spent working and number of cakes delivered.
Find (r-s) (t-s) + (s-r) (s-t) for all numbers r, s, and t. (a) 0 (b) 2 (c) 2rt (d) 2(s-r) (t-s) (e) 2(r-s) (t-s)
Answer:
d
Step-by-step explanation:
Use the remainder theorem to determine the remainder when d4 + 2d2 + 5d − 10 is divided by d + 4. A. 42 B. 258 C. 126 D. 106
Answer: The correct option is (B) 258.
Step-by-step explanation: We are give to use the remainder theorem to determine the remainder when
[tex]d^4+2d^2+5d-10[/tex] is divided by [tex]d+4.[/tex]
Remainder Theorem : If p(x) is a polynomial in x and a is any real number, then the remainder when p(x) is divided by (x - a) is p(a).
For the given division, we have
[tex]p(d)=d^4+2d^2+5d-10\\\\d-a=d+4~~~~~\Rightarrow a=-4.[/tex]
Therefore, the remainder when p(d) is divided by (d + 4) is given by
[tex]p(-4)\\\\=(-4)^4+2\times (-4)^2+5\times(-4)-10\\\\=256+32-20-10\\\\=288-30\\\\=258.[/tex]
Thus, the required remainder is 258.
Option (B) is CORRECT.
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
(9x + 7)(4x + 1)(3x + 4) = 0
Answer:
3
Step-by-step explanation:
Name three common measurements that are expressed as a ratio of two units.
Density , Speed and Mileage(Fuel Economy) are the three common measurements which can be expressed as a ratio of two units.
What are Fundamental Units?
A fundamental unit is a tool for measuring a base quantity. Any physical quantity that cannot be expressed in terms of another physical quantity is referred to as a basic quantity. They are
Length - meter (m)Time - second (s)Amount of substance - mole (mole)Electric current - ampere (A)Temperature - kelvin (K)Luminous intensity - candela (cd)Mass - kilogram (kg)Three Common Measurements be Density , Speed and Mileage where
Density = [tex]\frac{kg}{m^{3} }[/tex]
Speed = [tex]\frac{m}{s}[/tex]
Mileage = [tex]\frac{km}{L}[/tex]
Hence , the three common measurements which can be expressed as a ratio of two units are Density , Speed and Mileage
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Sally has 5 red flags, 3 green flags, and 4 white flags. how many 12-flag signals can she run up a flag pole
To solve for the total number of 12 – flag signals Sally can make, we need to make use of the formula:
total flags = d! / (a! b! c!)
Where,
d = is the number of flags to create a signal = 12
a = number of red flags = 5
b = number of green flags = 3
c = number of white flags = 4
We can observe from the equation that the individual number of flags is factored out (or divided from) that is because all the 5 red flags are similar, all the 3 flags are similar and all 4 flags are similar.
Going back into the equation, by substituting and calculating:
total flags = 12! / (5! 3! 4!)
total flags = 27,720
Therefore there are about 27,720 different 12-flags signals.
what is the quotient? x-3 divided into 4x2+3x+2
The quotient of x-3 divided into 4x^2+3x+2 is 4x+9.
Explanation:To find the quotient of x-3 divided into 4x^2+3x+2, we need to perform polynomial long division.
Divide the first term of the numerator (4x^2) by the first term of the denominator (x) to get 4x. Write this as the first term of the quotient.Multiply the entire denominator (x-3) by the quotient term (4x) and subtract it from the numerator (4x^2+3x+2).Bring down the next term from the numerator (-3x).Repeat steps 1 and 2 with the new numerator (-3x) and the denominator (x-3).Continue this process until there are no more terms to bring down and divide.After performing polynomial long division, the quotient is 4x+9.
Final answer:
To find the quotient of x-3 divided into 4x^2+3x+2, you can use long division. The quotient is 4+15 with a remainder of 47.
Explanation:
To find the quotient of x-3 divided into 4x2+3x+2, we can use long division.
First, divide the 4x2 term by the x term, which gives us 4x.Multiply 4x by x-3 to get 4x2-12x.Subtract 4x2-12x from 4x2+3x+2 to get 15x+2.Now, divide 15x by x to get 15.Multiply 15 by x-3 to get 15x-45.Subtract 15x-45 from 15x+2 to get 47.Since there are no more terms to divide, the quotient is 4+15 and the remainder is 47.Therefore, the quotient of x-3 divided into 4x2+3x+2 is 4+15 with a remainder of 47.
The probability of a randomly selected car crashing during a year in a certain country is 0.04770.0477. if a family has threethree cars, find the probability that at least one of them has a car crash during a year. is there any reason why the probability might be wrong?
Negative numbers are less than positive numbers. Does this mean that the absolute value of a negative number must be less than the absolute value of a positive number? Explain.
Are the two functions parallel, perpendicular, the same equation, or none of these choices? -x-3y= -18 9x-3y= -27
Which of the following show the factored equivalent of f(x) = (2x2 +7x + 3)(x - 3) and its zeros?
f(x) = (x + 5)(x + 7)(x - 3); -5, -7, 3
f(x) = (x + 3)(2x + 1)(x - 3); -3, -0.5, 3
f(x) = (x + 5)(x + 7)(x - 3); 5, 7, -3
f(x) = (x + 3)(2x + 1)(x - 3); 3, 0.5, -3
Final answer:
The factored equivalent of [tex]f(x) = (2x^2 +7x + 3)(x - 3)[/tex] is f(x) = (x + 3)(2x + 1)(x - 3), and its zeros are -3, -0.5, and 3.
Explanation:
The factored equivalent of the polynomial f(x) = (2x2 +7x + 3)(x - 3) and its zeros can be determined by factoring [tex]2x^2 + 7x + 3[/tex]. We notice that this quadratic can be factored into (2x + 1)(x + 3). Therefore, when we include the (x - 3) term, we get the fully factored form,
f(x) = (2x + 1)(x + 3)(x - 3). To find the zeros, we set each factor equal to zero:
2x + 1 = 0 gives a zero of -0.5;
x + 3 = 0 gives a zero of -3; and,
x - 3 = 0 gives a zero of 3. Thus, the correct answer is
f(x) = (x + 3)(2x + 1)(x - 3); -3, -0.5, 3.
Melissa is making clothes for her dolls she has 7/8 yard of fabric each doll shirts require 2/7 of a yard of fabric. how many shirts can she make for each dolls.
7/8 / 2/7 =
7/8 * 7/2 = 49/16 = 3 1/16
she can make 3 shirts
In what direction and by how many units is the graph of f(x) = 6 sin(2x + π) − 5 vertically and horizontally shifted?
Down 5, left pi over 2
Up 5, left pi over 2
Down 5, right pi over 2
Up 5, right pi over 2
Answer:
Option 1 is correct.
Step-by-step explanation:
Given graph of f(x)=6 sin(2x + π) - 5
we have to tell in what direction the graph vertically and horizontally shifted.
As, f(x+1) is a change on the inside of function, giving a horizontal shift left by 1, and the subtraction by 3 in f(x+1)-3 is a change to the outside of function, giving a vertical shift down by 3.
Hence, the graph of f(x)=6sin(2x + π) - 5
Here, change on the inside of function, giving a horizontal shift left by [tex]\frac{\pi}{2}[/tex], and subtraction by 5 in function is a change to the outside of function, giving a vertical shift down by 5.
Option 1 is correct.
What is 0.0333333333333333 as a fraction?
The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with a mean of 6.7 minutes and a standard deviation of 2.2 minutes. for a door selected at random, what is the probability the assembly time will be:
a.5 minutes or less?
b.10 minutes or more?
c.between 5 and 10 minutes?
The mean diastolic blood pressure for a random sample of 70 people was 94 millimeters of mercury. if the standard deviation of individual blood pressure readings is known to be 12 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people.
To solve this problem, we make use of the formula for Confidence Interval:
Confidence Interval = X ± z * σ / sqrt (n)
where X is the mean value, z is the z score which is taken from the standard tables, σ is the standard deviation, and n is the number of samples
z = 1.645 (at 90% Confidence Level)
Substituting the values into the equation:
Confidence Interval = 94 ± 1.645 * 12 / sqrt (70)
Confidence Interval = 94 ± 2.36
Confidence Interval = 91.64, 96.36
Therefore at 90% confidence level, the blood pressure reading ranges from 91.64 mmHg to 96.36 mmHg.
Let r=1+2i and s=3+3i find r⋅s
The product of r.s is -3+9i.
r = 1+2i ; s = 3+3i
Product of r and s to be determine.
Any number with representation as a+bi is complex number.
Here,
r.s = (1+2i)(3+3i)
= 3+6i+3i+6i²
= 3+ 9i + 6(-1) (∵ i²=-1)
= 3 - 6 +9i
= -3 + 9i
Thus, the product of r.s is -3+9i.
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Plz help! which expressions are equivalent to 1.06^3t
if g (x)= x^2-5, where does the graph g (x) cross the x-axis?
whitch of the following is (are) the solution(s) to 11x+3=6
Branliest and alot of points who answers first
The chart on a cereal box shows that one serving contains 32% of the rda for dietary fiber the rda for dietary fiber is 25 grams write in the box on the chart the number of grams of dietary fiber in one serving
(05.01 LC)
The graph shows the number of sprays an automatic air freshener dispenses, y, in x minutes
Which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays?
fraction 30 over 2
fraction 2 over 30
fraction 30 over 8
fraction 8 over 30
the first dot is on 2 for number of sprays and 30 for time
so the expression would be number of sprays over time so 2 over 30
2/30 that would reduce to 1/15 meaning each spray happens every 15 minutes
In this exercise we have to interpret the reported graph of an increasing linear function, we find that:
Letter B
Recalling the concepts of an increasing linear function as:
Linear functions happen those whose diagram is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function bear individual independent changing and individual dependent changeable. The independent changeable is x and the helpless changing happen y.With this explanation we have:
Expression would be number of sprays over time so 2 over 30, will be equal to:
[tex]30/2=15[/tex]
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A bag contains 10 marbles: 4 are green, 2 are red, and 4 are blue. Christine chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.
Answer:
The probability that both marbles she chooses are blue is [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
Given : A bag contains 10 marbles: 4 are green, 2 are red, and 4 are blue. Christine chooses a marble at random, and without putting it back, chooses another one at random.
To find : What is the probability that both marbles she chooses are blue?
Solution :
Total number of marbles = 10
Green marbles = 4
Red marbles = 2
Blue marbles = 4
Probability is favorable outcome upon total number of outcomes.
Probability of getting first marble is blue
[tex]\text{P(first blue marble)}=\frac{4}{10}=\frac{2}{5}[/tex].
Without replacement,
i.e. Blue marble left = 3
Total marble left = 9
Probability of getting second marble is blue
[tex]\text{P(second blue marble)}=\frac{3}{9}=\frac{1}{3}[/tex]
The probability that both marbles she chooses are blue is
[tex]\text{P(both blue marble)}=\frac{2}{5}\times\frac{1}{3}[/tex]
[tex]\text{P(both blue marble)}=\frac{2}{15}[/tex]
Therefore, The probability that both marbles she chooses are blue is [tex]\frac{2}{15}[/tex]
Aida is attending a trekking camp. She walks from her tent to a hilltop in 2 hours. She has a picnic with her friends on the hilltop for 6 hours. Aida walks back to her tent in 1 hour. Which graph best represents the distance, y, in miles, traveled by Aida for a certain amount of time, x, in hours? A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 2, 4. The second straight line joins ordered pairs 2, 4 and 8, 4. The third straight line joins ordered pairs 8, 4 and 9, 0. A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 1, 4. The second straight line joins ordered pairs 1, 4 and 8, 4. The third straight line joins ordered pairs 8, 4 and 9, 0. A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 2, 4. The second straight line joins ordered pairs 2, 4 and 7, 4. The third straight line joins ordered pairs 7, 4 and 9, 0. A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 1, 4. The second straight line joins ordered pairs 1, 4 and 7, 4. The third straight line joins ordered pairs 7, 4 and 9, 0.
The correct answer among the given choices is the first one:
“A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 2, 4. The second straight line joins ordered pairs 2, 4 and 8, 4. The third straight line joins ordered pairs 8, 4 and 9, 0.”
The given ordered pairs is in the format of (t, d) where t is time and distance is d. Time will always be on the x-axis since it is always an independent variable.
The first ordered pair should be (2, 4) since it took her 2 hours to trek to the hilltop. From the given choices, only the 1st and 3rd choice has this first ordered pairs so we are down to two choices.
Now the second ordered pair should be (8, 4) since she spent 6 hours at the top but no change in distance. And only the 1st choice has this value therefore it is the answer.
Billy Goats invested some money in stocks and bonds. The total amount he invested was $\$165,\!000$. If he invested 4.5 times as much in stocks as he did in bonds, what was his total investment in stocks?
An equation is formed when two equal expressions. The total investment that Billy made in stocks is $135,000.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount that is invested in stocks be represented by x, while the amount that is been invested in bonds is represented by y.
Given that Bily invested 4.5 times as much in stocks as he did in bonds. Therefore, the equation to represent the given situation can be written as,
x = 4.5y
Also, given that the total amount that Billy invested is $165,000. Therefore, the total invested amount can be written as,
$165,000 = x + y
Substitute the value of x in the equation,
$165,000 = 4.5y + y
$165,000 = 5.5y
y = $165,000 / 5.5
y = $30,000
Now substitute the value of y in the first equation to know Billy's investment in stocks.
x = 4.5y
x = 4.5($30,000)
x = $135,000
Hence, the total investment that Billy made in stocks is $135,000.
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