Use the cosine double-angle identity cos(2θ) = 1 − 2sin2θ to derive an identity for 2sin2θ
To derive an identity for 2sin2θ using the cosine double-angle identity cos(2θ) = 1 − 2sin²θ, we can rearrange the equation and substitute the value of sin²θ to obtain the identity 2sin²θ = 1 - cos(2θ).
Explanation:To derive an identity for 2sin2θ using the cosine double-angle identity cos(2θ) = 1 − 2sin²θ, we can start by rearranging the equation to solve for sin²θ. This gives us sin²θ = (1 - cos(2θ))/2.
Next, we can substitute this value into the expression for 2sin²θ. This gives us 2sin²θ = 2(1 - cos(2θ))/2 = 1 - cos(2θ).
Therefore, the identity for 2sin²θ is 1 - cos(2θ).
Find the value of x and the value of y.
A.
x = 10, y = 130
B.
x = 65, y = 10
C.
x = 65, y = 130
D.
x = 130, y = 10
the 2 angls need to equal 180 degrees
so 2x-y + 60 = 180
and 2x+y + 40 = 180
using the choices you have
answer is B x = 65, y = 10
when you use those values they both equal 180
At an automobile factory, 1849 parts are made in 4 hours. What is the average rate at which parts are made per hour?
Answer:
462.25
Step-by-step explanation:
At an automobile factory, the number of parts are made in 4 hours = 1849.
We have to calculate the average rate of production per hour.
We will divide the production of parts in 4 hours by 4 to get the number of parts made per hour.
The average rate of production in one hour = [tex]\frac{1849}{4}[/tex]
= 462.25/hour
462.25 parts are made per hour.
kalen's truck has a 60 gallon fuel tank The fuel gauge points to 1/4 how much fuel does he need to buy to fill the tank show Your work
Chris answered 61/66 questions correctly. What is his test average to the nearest thousandth?
Find the point of intersection of the tangent lines to the curve r(t) = 5 sin(πt), 6 sin(πt), 3 cos(πt) at the points where t = 0 and t = 0.5.
A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.
Based on the dispersion of the scatterplot, we can infer that there is no relationship between the variables.
Relationships in scatterplots Data points are used to predict relationships. If a line can be drawn based on these data points, then a relationship exists.The fact that these data points are dispersed however and offer no form of grouping, means that the variables are not related and show no correlational trend.
Find out more on scatterplots at https://brainly.com/question/2749543.
What is the value of x?
Line IJ has an equation of a line y = −3x − 8. Which of the following could be an equation for a line that is parallel to line IJ?
A) y=3x+7
B) y=1/3x+7
C) y= -3x+7
D) y= -1/3x+7
C) y = -3x +7
Step-by-step explanation:It's all about recognizing patterns.
The form of the equation is ...
... y = mx + b
In this form, the coefficient of x, which we called "m" in the above, is the slope of the line. When two lines have the same slope, they are parallel. So, we're looking for an equation that has an x-coefficient of -3, the same as in the given equation.
The coefficient of x in selection C is -3, so that is our answer choice.
... C) y = -3x +7
Answer:
y = -3x +7 which is option C
got it right on my test.
What produces a graph in a straight line
Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores.
88%, 73%, 97%, 76%, 90%, 80%
Answer: The Mean
The mean is when you add up all of those grades and divide by the amount of exams.
what is the sum of 2 3/8 and 3 3/7
What is the total rounded to the nearest tenth of 94.23
Car A began a journey from a point at 9 am, traveling at 30 mph. At 10 am car B started traveling from the same point at 40 mph in the same direction as car A. At what time will car B pass car A
Car a 30(t+1)
Car b 40t
30(t+1) =40t
30t+30 =40t
30=10t
T = 30/10 = 3hours
9 +3 = 12 noon
Find the integer a such that
a.a ≡ 43 (mod 23) and −22 ≤ a ≤ 0.
The integer a such that a ≡ 43 (mod 23) and −22 ≤ a ≤ 0 is -3. A zero, a positive natural number, or a negative integer with a minus sign is an integer.
What do we mean when we say that integers are congruent to modulo?When two positive integers a and b are divided by a positive integer n, they are said to be congruent modulo n (or an is congruent to b modulo n), or if a b is divisible by n. It can be expressed as a b mod n, where n is the modulus.If n is a positive integer, then the integers a and b are said to be congruent modulo n, as denoted by the expression a b (modn).Division algorithm Allow dd and aa to be both positive integers. Following that, there are two distinct integers, qq and rr, where rd0 and rd are equal, resulting in a = dq + ra = dq + rTherefore,
-3 is in between -22 and 0 so a =-3
a ≡ 43 (mod 23) and −22 ≤ a ≤ 0.
a ≡ 43 (mod 23)
≡ 43-22 (mod 23)
Simplifying,
≡ 20 (mod 23)
≡ 20-23 (mod 23)
Then we get,
≡ -3 (mod 23)
-3 is in between -22 and 0 so a =-3
To learn more about congruent modulo refer to:
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208,000,478 in expanded form
how many fossil kits with 10 samples each have the same number of fossils as 30 fossil kits with 8 samples each?
Answer:
24 fossil kits.
Step-by-step explanation:
Given,
The number of fossil kits = 30,
the number of samples each has = 8,
So, the total samples = number of fossil kits × the number of samples contained by each kit
= 30 × 8
= 240,
Let x be the number fossil kits with 10 samples each,
Total samples = 10x
According to the question,
10x = 240
[tex]\implies x =\frac{240}{10}=24[/tex]
Hence, there would be 24 fossil kits with 10 samples each.
Select all numbers that are irrational. 1049−−√ 3.14 π 0.5
The answer would be 10/49 and π which are irrational numbers from the definition of the irrational number.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
It is given that:
The numbers are:
10/49, 3.14, π, 0.5
As we know, from the definition of the irrational, the numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
The numbers 10/49 and π are irrational numbers.
Thus, the answer would be 10/49 and π which are irrational numbers from the definition of the irrational number.
Learn more about the irrational number here:
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write the equation of the line MN, which is formed by the points M(-3,5) and N(2,0)
Step 1
Find the slope of the given line
Let
[tex]M(-3,5)\ N(2,0)[/tex]
we know that
the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{0-5}{2+3}[/tex]
[tex]m=\frac{-5}{5}[/tex]
[tex]m=-1[/tex]
Step 2
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-1[/tex]
point N [tex](2,0)[/tex]
substitute the values
[tex]y-0=-1(x-2)[/tex]
[tex]y=-x+2[/tex]
therefore
the answer is
[tex]y=-x+2[/tex]
How is adding 4.56 + 2.31 similar to adding $2.31 + $4.56?
Mark earns $135 for selling a $1500 refrigerator. Which sale listed has the same commission rate? $36 commission on a $400 dryer or B) $40 commission on a $500 dryer sale C) $210 commission on $1400 oven sale d) $30 commission on a $600 freezer sale?
salelisted has the same commssion rate. ?
Answer:
Option A is the correct choice.
Step-by-step explanation:
We have been given that Mark earns $135 for selling a $1500 refrigerator.
Since proportions states that two fractions are equal , so we will use proportions to find the same commission rate with the listed price from our given choices.
We can set proportion for commission and listed price as:
[tex]\frac{\text{Commission}}{\text{Listed price}}=\frac{135}{1500}[/tex]
Let us compare our given choices one by one.
A. $36 commission on a $400 dryer.
[tex]\frac{36}{400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{9}{100}=\frac{9}{100}[/tex]
[tex]0.09=0.09[/tex]
We can see that commission rates for both items are equal, therefore, option A is the correct choice.
B. $40 commission on a $500 dryer sale.
[tex]\frac{40}{500}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{2}{25}=\frac{9}{100}[/tex]
[tex]0.08\neq 0.09[/tex]
We can see that both commission rates are different, therefore, option B is not a correct choice.
C. $210 commission on $1400 oven sale.
[tex]\frac{210}{1400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{3}{20}=\frac{9}{100}[/tex]
[tex]0.15\neq 0.09[/tex]
Since the commission rates are different, therefore, option C is not a correct choice.
D. $30 commission on a $600 freezer sale.
[tex]\frac{30}{1400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{3}{140}=\frac{9}{100}[/tex]
[tex]0.0214\neq 0.09[/tex]
Since the commission rates are different, therefore, option D is not a correct choice.
Jemma has 24 balls. Out of the 24 balls,
12 are yellow, 4 are pink, and the rest
are red. What is the ratio of the number
of red balls to the number of balls that
are either yellow or pink?
I thought of a number, then divided it by another number, and got a result of 7. Think of the possible values for my number and the number I divided it by. What number is impossible to divide by? What number can my original number not be?
My number is a multiple of ?
The number I divided my number by can be any number but ?
My number cannot be a number which we cannot divide by ?
Evaluate 3(y-5) for y=7
Please help
differentiate please..
y= √x +6 ÷ √x-6
write a word problem that can be solved by ordering three decimals to thousandths.
A)- -17
B)- -8
C)- -2
D)- 2
E)- 5
F)- 8
G)- 15
SELECT ALL THAT APPLY
put these in order from the smallest
6² 3 to the power of 4 2 to the power of 5 5³
solve the following system of equations 3x+4y=17 -4x-3y=-18
A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all ?