please help me.... The question no.b and would like to request you all just give me correct answer.
Answers
Answer: see proof below
Step-by-step explanation:
You will need the following identities to prove this:
[tex]\tan\ (\alpha-\beta)=\dfrac{\tan \alpha-\tan \beta}{1+\tan \alpha\cdot \tan \beta}[/tex]
[tex]\cos\ 2\alpha=\cos^2 \alpha-\sin^2\alpha[/tex]
LHS → RHS
[tex]\dfrac{2\tan\ (45^o-A)}{1+\tan^2\ (45^o-A)}\\\\\\=\dfrac{2\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)}{1+\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)}{1+\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{1+\bigg(\dfrac{1-2\tan\A+\tan^2 A}{1+2\tan A+\tan^2A}\bigg)}\\[/tex]
[tex]=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{(1+2\tan A+\tan^2A)+(1-2\tan A+\tan^2 A)}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{2+2\tan^2A}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{2\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}\\\\\\=\dfrac{\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}[/tex]
[tex]=\dfrac{1-\tan A}{1+\tan A}}\times \dfrac{(1+\tan A)^2}{1+\tan^2A}\\\\\\=\dfrac{1-\tan^2 A}{1+\tan^2 A}\\\\\\=\dfrac{1-\dfrac{\sin^2 A}{\cos^2 A}}{1+\dfrac{\sin^2 A}{\cos^2 A}}\\\\\\=\dfrac{\bigg(\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A}\bigg)}{\bigg(\dfrac{\cos^2 A+\sin^2 A}{\cos^2 A}\bigg)}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A+\sin^2 A}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{1}\\\\\\=\cos^2 A-\sin^2 A\\\\\\=\cos 2A[/tex]
cos 2A = cos 2A [tex]\checkmark[/tex]
I hope this helps!
Related Questions
What is the y-intercept of the function f(x) = -2/9x+1/3
Answers
Answer:
The y-intercept is 1/3.
Step-by-step explanation:
The equation given is in slope-intercept form. Recall that in slope-intercept form:
[tex]f(x)=mx+b[/tex]
m is the slope while b is the y-intercept.
Therefore, -2/9 would be the slope while 1/3 would be the y-intercept.
If m(2x−3)+n(x+1)=5x for all real numbers x, where m and n are constants, what is the value of m?
Answers
Answer:
m = 1
Step-by-step explanation:
From the question given,
m(2x − 3) + n(x + 1) = 5x for all real numbers x.
Since x is a real number, we can obtain the value of m as follow:
Let x = 1
m(2x − 3) + n(x + 1) = 5x
m(2×1 − 3) + n(1 + 1) = 5×1
m(2 – 3) + n(2) = 5
m(– 1) + n(2) = 5
– m + 2n = 5 ...... (1)
Let x = 2
m(2x − 3) + n(x + 1) = 5x
m(2×2 − 3) + n(2 + 1) = 5×2
m(4 – 3) + n(3) = 10
m(1) + n(3) = 10
m + 3n = 10 ...... (2)
– m + 2n = 5 ...... (1)
m + 3n = 10 ...... (2)
Solve by elimination method
Add equation 1 and 2
– m + 2n = 5
+ (m + 3n = 10)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
5n = 15
Divide both side by 5
n = 15/5
n = 3
Substitute the value of n into any of the equation to obtain the value of m. Here, we shall substitute n into equation 2.
m + 3n = 10
m + 3(3) = 10
m + 9 = 10
Collect like terms
m = 10 – 9
m = 1
Therefore, the value of m is 1
what is the domain of the function shown in the graph below?
answer type: interval, all real numbers, all values except one, all values except two
interval:
Answers
Answer:
All numbers except 1
Step-by-step explanation:
The graph has an asymptote at 1.
So the function will grow toward but without reaching it.
The equation of the asymptote is x=1
So the domain is all real numbers except 1.
If two 4-sided dice were rolled, what
would be the probability of getting double
2s? Write your answer as a fraction.
Answers
Answer:
It’ll be a 1/8 chance
Step-by-step explanation:
Uh pretty much, if you were to roll one of those 4 sides die it’ll be a 1/4 of being a 2 in which it was. If you were to roll it again it’ll be another 1/4 chance but back to back it’ll be a 1/8 chance
WILL GIVE BRAINLY!!!!!! NEED HELP ASAP!!!!!!!! what is the range of f(x)=3^x+9
Answers
Answer:
y > 9
Step-by-step explanation:
The range of a function is the interval of all possible y-values that make the function true.
Here, one way to figure this out is to look at a graph of the function (see attachment).
From the graph, we can see that y-values approach very closely the value 9 and then the line rises beyond 9 forever. Thus, we can conclude that the range for f(x) is y > 9.
~ an aesthetics lover
A tailor cuts off a 2-meter long section from a 20-meter long piece of cloth every day. After how many days will he cut off the last section?
Answers
Answer: 10 days
Step-by-step explanation:
20/2 = 10
Answer18
Step-by-step explanation:
Name four fractions between 5/6 and 7/8
Answers
Answer:
101/120, 102/120, 103/120, and 104/120.
Step-by-step explanation:
First find the LCM of 6 and 8:24
So the two given fractions are 20/24, and 21/24
Since the the fractions will become decimals with the denominator 24, choose another denominator: 48
So the two given fractions are 40/48 and 42/48.
Even this denominator isn't possible so continue with different denominators.
As I notice, that each multiple increases by 1...
20-21, 40-42, 60-63, 80-84, and 100-105.
100-105 is the only numerator that has 4 numbers in-between so, the four fractions between 5/6 and 7/8 are: 101/120, 102/120, 103/120, and 104/120.
And the 2 given fractions are 100/120 and 105/120.
I hope this helps and plz mark me brainliest!!
The fractions between 5/6 and 7/8 are 6/7, 13/15, 11/13, and 17/20.
What is a fraction?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator, and denominator.
For the given situation,
The fractions are 5/6 and 7/8.
The fractions between any two fractions can be obtained by adding them without considering the denominator.
Fraction 1:
[tex]\frac{5+7}{6+8}=\frac{12}{14}[/tex]
⇒ [tex]\frac{6}{7}\\[/tex]
Fraction 2:
[tex]\frac{6+7}{7+8} = \frac{13}{15}[/tex]
Fraction 3:
[tex]\frac{5+6}{6+7} = \frac{11}{13}[/tex]
Fraction 4:
[tex]\frac{6+11}{7+13}=\frac{17}{20}[/tex]
Hence we can conclude that the fractions between 5/6 and 7/8 are 6/7, 13/15, 11/13, and 17/20.
Learn more about the fractions here
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How many of the positive integer factors of 15552 are perfect squares?
Please show work, will mark brainliest if correct
Answers
Answer: 9 integers factors
Step-by-step explanation:
Let's first find the factor of 15552
15552 / 2 = 7776
7776 / 2 = 3888
3888 / 2 = 1944
1944 / 2 = 972
972 / 2 = 486
486 / 2 = 243
273 / 3 = 81
81 / 3 = 27
27 / 3 = 9
9 / 3 = 3
3 / 3 = 1
Some of the factors of 15552 are:
2×2×2×2×2×2×3×3×3×3×3
4×4×4×9×9×3
4^2 × 9^2 × 4 × 3
The factor that are perfect square are:
4, 9, 16, 36, 64, 81, 144, 576, 1296
Therefore, 9 of the positive integer factors of 15552 are perfect squares.
9 of the positive integer factors of 15552 are perfect squares
how many ways can you order a sandwich if you can order it with or without ham, mustard, mayo, or cheese?
Answers
Hope this helped
Simplify.
sin x cot x
Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function.
(please help, no idea how to solve this problem)
Answers
Answer:
cos x
Step-by-step explanation:
sin x = (sin x) / (1) and cot x = (cos x) / (sin x)
Put those fractions next to each other and multiply them out (numerator times numerator, denominator times denominator).
Cancel out the (sin x) in the numerator and denominator
You should be left with just (cos x) / (1), whoch equals just (cos x).
Hope this helps!
My brother said that’s it
A teacher has 1,425 marbles to divide equally among 9 groups of students to use in an experiment. What is the least number of marbles he could have left after the marbles are distributed?
Answers
Answer:
3
Step-by-step explanation:
Basically we need to find out whats the remainder of 1425 when you divide by 9.
1425/9 = 158 R3
R3 is 3 marbles left, so the answer is 3.
A fortnight is 1/26 of a year. What part of a year is 8 fortnights?
Answers
Answer:
Isn’t it just 8/26
Step-by-step explanation:
Since 1 is 1/26 so 8 is just 8/26?
The part of a year is 8 fortnights is ( 8 / 26 ).
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics.
It is given that a fortnight is 1/26 of a year. The part of the year for 8 fortnights is calculated as:-
⇒ 8 x ( 1 / 26 )
⇒( 8 / 26 )
Therefore, the part of a year is 8 fortnights is ( 8 / 26 ).
To know more about multiplication follow
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Cathy is paid at a rate of $7 20 per hour for a basic hour-week of 70 hours. She is paid time-and-a-half for over-time during the week and double-time on weekends. In a fortnight she worked 160 hours, and 4 hours on Saturday and 2 hours on Sunday. What is Cathy's hours in a fortnight
Answers
Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.
So the answer is 166
Here is the calculation:
Cathy's basic pay for the fortnight is 7.2 × 70 = $504.
Her overtime pay for the week is (1.5 × 7.2) × 9 = $97.2.
Her weekend pay is (2 × 7.2) × 6 = $86.4.
Her total pay for the fortnight is 504 + 97.2 + 86.4 = $687.6.
Therefore, Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.
So the answer is 166
Learn more about fortnight here: brainly.com/question/26709960
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can someone turn this into slope intercept form please ?? thank you .
Answers
Answer:
1) -1 - 0 fraction on top of -4 -3
Step-by-step explanation:
(x1,y1) and the second (x2,y2)
and the formula is x2- minus x1 over as ina fraction over y2- minus y1,,,, apply this to the other questions
Answer:
Hi there!!!
just use double point formula for the equation of st.line.
(i.e (y-y1 )= y2-y1/x2-x1 times (y-y1)
I hope the answers in the pictures will help you....
Sue's ice cream has 6 more scoopsthan Tessa's ice cream cone.
Sue's ice cream cone has 9 scoops.
How many scoops are on Tessa's ice cream cone?
Answers
Answer:
Tessa has 3 ice-cream scoops
Step-by-step explanation:
Find the area of the shape shown below.
Answers
Answer
72-30=42. The answer is 42
Step-by-step explanation:
to find the area of this, we first need to add are to the missing space, so we can make a rectangle. If we multiply the dimension of this new shape, we get 72. Now we need to find the are of the triangle-shaped space I added. To do this I must multiply the base by the height, and then divide it by 2, after multiplying the base with the height, which gave me 60, I divided it by 2 which gave me 30. Then I subtracted 30 from 72, therefore giving me 42
Answer:
42cm2
Step-by-step explanation:
You can divide the shape into two parts from the length at the top and the length at the bottom. Which means you have two shapes A and B.
Area of A which is a triangle= 1/2bh
= 1/2*5(THIS IS THE BASE OF THE TRIANGLE)12
= 30CM2
Area of b which is a rectangle= L*W
= 1(LENGTH) * 12(WIDTH)
= 12CM2
So to get the total area of the shape you add the area of shape a and b
THE ANSWER IS 42cm2
I am confused on this: "Find the area of a square with a perimeter of 20 inches"
Answers
Answer:
25 square inches
Step-by-step explanation:
A square has 4 congruent sides.
By knowing the perimeter of a square, you can find the length of a side.
perimeter = 4 * side
20 in. = 4s
s = 20 in./4
s = 5 in.
A side of this square measures 5 in.
Now we use the area formula to find the area of the square.
area = (side)^2
area = (5 in.)^2
area = 25 in.^2
Answer:
The area will be 25 inches.
Step-by-step explanation:
Hi! So, this might be a pretty easy question for some people, but I can see how it might be confusing.
If you want to find the area of a square, which has four equal sides, it's pretty easy. You just need to know the length of one side instead of two different lengths, because both are equal!
The question gives you the perimeter, which is 20 inches. To get the perimeter of something, like this square, you add up all the sides. All you have to do to find the length of one side is divide the total sum of the sides, 20 (perimeter!) by the number of sides you have, four!
Note: This won't work with things like rectangles. You can only do things like this with squares, because you know ahead of time that all of the sides will be equal.
So! 20 divided by the number of sides, 4, is five!
Know we know all we need to be able to find the area of the square. To find the area, all you have to do is multiply the length of the square (5) by the width of the square (also 5!) That's 25, which is the area of your mystery square.
Hope you understand and this helps!
Mr. Brust tried to simplify the following but made a really common mistake in the problem. Identify the mistake, then show the correct solution. 8 + 2(3p + 1) = 10(3 p +1) = 30p +10
Answers
Answer:
The correct answer is 10+6p
Step-by-step explanation:
The mistake is that for the first step instead of distributing 2 to 3p and 1 they added 8+2 first. your actually supposed to distribute and get, 8+6p+2, then combine like terms and get 10+6p
Answer:
Mistake: He added 8 to the 2 that you needed to multiply to the 3p and 1 inside the parentheses.
Correct solution: 10 + 6p
Step-by-step explanation:
8 + 2(3p + 1) =
8 + 6p + 2 =
10 + 6p
Hope that helps and maybe earns a brainliest!
Have a fantastic day! :)
The graph shows the first 5 terms of the arithmetic sequence, an.
Which is the 6th term of the sequence?
A.)3
B.)6
C.)9
D.)12
E.)18
Answers
Answer:
D) 12
Step-by-step explanation:
the graphs slope is 3 using the rise over run method we have found this
now since we know the fifth x value gives a y value of 9 we can add 3 and have 12
5.
A leaky faucet is losing water and is filling a 7-gallon bucket every 21 hours. At that rate, how many
gallons of water will the faucet leak in 30 hours?
(2-Point Holistic Rubric)
Show your work.
Answers
Answer:
10 gallons.
Step-by-step explanation:
A leaky faucet is losing water and;
filling a 7-gallon bucket every 21 hrs.
So 7 gallons of water are leaked in 21 hrs
We are to find the number of gallons that will be leaked in 30 hrs.
Cross-multiplying this gives;
[tex]\frac{30 * 7}{21}[/tex] = 10 gallons.
Use the clues in the sentences to determine the best meaning for each bolded word
"He was a tenacious worker, and by sticking firmly to his plan, he succeeded."
"Students planning to become scientists must select a science major, such as biology, chemistry, or physics."
"I want to take a class in calligraphy, or artistic writing, at the community center."
Done
Answers
Answer:
1. Determined
2. area of study
3. artistic writing
Step-by-step explanation:
Hope this helps! <3
Answer:
✔ determined
✔ area of study
✔ artistic writing
Explanation:
a grandfather purchased a brand new car in 1958 for $2500.the car depreciated $325 a year. what would the car be worth 4 years after it was bought?
Answers
Answer:
The car would be worth 1200.
Step-by-step explanation:
Okay, the way to solve this type of question is quite simple,
you would start with the amount is lost per year being $325 a year, then multiply that by the 4 years grandpa waited and then subtract the overall amount lost in worth of the car from the original price and you got your answer.
The math: 2500-(325*4)=1200
so basically, we have $325 depreciated per year. We have 4 years of that, which means $325 yearly x 4 years = 1300. So the car lost 1300 dollars in value meaning that the car is now worth 1200.
Hope this helped!
If you're good at bearings pls help meeeeee
Pls show full working out ty
Answers
Answer:
201
Step-by-step explanation:
use the law of sines
sine B / b = sine C / c
sine 75 / 19.6 = sine C / 12.5
inv sine C = ( sine 75 * 12.5 ) / 19.6
C = 38
the bearing C = 180 + 59 - 38 = 201
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
Answers
Answer:
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at negative 0.5 and is pointing to the left.
Step-by-step explanation:
Required
[tex]2x - 6 \geq 6(x - 2) + 8[/tex]
Required
Determine the number line
[tex]2x - 6 \geq 6(x - 2) + 8[/tex]
Open the bracket
[tex]2x - 6 \geq 6*x - 6*2 + 8[/tex]
[tex]2x - 6 \geq 6x - 12 + 8[/tex]
[tex]2x - 6 \geq 6x - 4[/tex]
Collect Like Terms
[tex]2x - 6x \geq 6 - 4[/tex]
[tex]- 4x \geq 2[/tex]
Divide both sides by -4
[tex]\frac{- 4x}{-4} \geq \frac{2}{-4}[/tex]
[tex]x \leq -0.5[/tex]
From the list of given options, the correct answer is option C
Answer:
b
Step-by-step explanation:
The area of a regular hexagon is 40 in^2. What is the length of a side to the nearest tenth? A. 15.4 in. B. 9.6 in. C. 6.7 in. D. 3.9 in.
Answers
Answer:
The answer is D
Step-by-step explanation:
pls help!! Consider the sequence below.
-34, -21, -8, 5...
Complete the recursively defined function to describe this sequence.
Answers
Answer:
a₁= -34
aₙ = 13n - 47
Step-by-step explanation:
This is an AP with the first term of -34 and the common difference of 13.
The nth term is:
aₙ= a₁ + (n-1)daₙ= -34 + (n-1)*13aₙ = 13n - 47This is the required formula.
find the total surface area of this square based pyramid
Answers
Answer:
300 ft²
Step-by-step explanation:
Surface area= area of base + 4*area of triangle
a= 10 ft
h= 10 ft
Surface area:
10*10+ 4*1/2*10*10= 300 ft²A line plot has a range of 4, from 1 to 5, with 5 modes. How would you describe the graph?
The graph has an outlier.
The data is clustered around 3.
Each column will be the same height.
There is not enough information.
will give brainliest
Answers
Answer:
Each column will be the same height.
Step-by-step explanation:
Mode refers to the most occurring number, and there are five within a data set that is 4 wide, so there will be 5 columns of equal length.
w is greater than -1 and less than or equal to 4
Use a only once in your inequality.
Answers
Answer:
-1 + w ≤ 4
Step-by-step explanation:
w is greater than -1 = -1 + w
Less than or equal to 4 = (anything less than or equal to 4)≤4
Answer:
[tex]-1<w\leq 4[/tex]
This shows that w is greater than -1 and less than or equal to 4
, through an inequality.
This is the greater than symbol: <
This is the less than or equal to symbol: [tex]\leq[/tex]
Hope that helped!!!
Marlye posted a story on her blog. On the first day there were 80 responses and on the second day there were 180 responses. What percent is the increase, 100, of the original number of responses, 80?
Answers
Hey there! I'm happy to help!
In our problem, 100 is a certain percent of 80. When talking about percents, the word "is" means equals. Let's represent our certain percent with p and solve for it.
100=80p
Let's flip the equation around so p is on the left side.
80p=100
We divide both sides by 80.
p=1.25
As a percent, the increase is 125%.
Have a wonderful day!
