cos^4x - sin^4x +1 = 2cos^2x
prove
Proved [tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x
We will use the Pythagorean Theorem:
Sin²x + Cos²x = 1
from which we can get:
Sin²x = 1 - Cos²x
Also, note that the difference in the similarity of squares can be written:
A² - B² = (A - B)
We can use this with A = Sin²x and B = Cos²x as follows:
[tex]Sin^{4}x - Cos^{4}x[/tex]
= (Sin²x)² - (Cos²x)²
= (Sin²x - Cos²x) (Sin²x + Cos²x)
= Sin²x - Cos²x
= (1 - Cos²x) - Cos²x
= 1 - 2Cos²x
Now move the 1 and negative symbols to the left.
[tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x
The trigonometric ratios are related to each other by equations called trigonometric identities.
Learn more about the Trigonometry problem at
https://brainly.com/question/13971311?referrer=searchResults
A man's taxable income is $3.060 If tax is paid at 12%. How much is the man's net income
A man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27
The taxable income = $3060
The tax percentage = 12%
Income tax is the a type of tax impose on income generated by businesses and individuals by the government
Consider the net income as x
Then,
12% of the income = x×(12/100)
Therefore the equation will be
x - x×(12/100) = 3060
x(1-(12/100) = 3060
x(1-0.12) = 3060
0.88x = 3060
x = 3060/0.88
x = $3477.27
Hence, a man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27
Learn more about income tax here
brainly.com/question/13219434
#SPJ1
The figure shows the design of a rectangular windowpane. The four horizontal lines are parallel. The measure of angle 6 is 53 degrees. What is the measure of angle 12? Write and solve an equation to find the answer.
∠6 and ∠12 are supplementary angles. That means, they add up to 180°
[tex]\angle6+\angle12=180\degree[/tex]Substitute ∠6 by 53° to find ∠12.
[tex]53+\angle12=180[/tex]Subtract 53 from both sides to find ∠12.
[tex]\begin{gathered} 53+\angle12-53=180-53 \\ \angle12=127\degree \end{gathered}[/tex]Answer: ∠12 = 127°.
3.5²-√8.6
Answer to the 2nd decimal places
Answer:
9.32 if question is [tex]3.5^2-\sqrt{8.6}[/tex]
or
10.55 if question is [tex]3.5^2 - \sqrt{8} \cdot 6[/tex]
(see explanation below)
Step-by-step explanation:
I took the question as
[tex]3.5^2-\sqrt{8.6}[/tex]
since it was not clear if it was [tex]\sqrt{8.6}[/tex] or [tex]\sqrt{8} \cdot 6[/tex]
If it is [tex]3.5^2 - \sqrt{8} \cdot 6[/tex] then the answer would be 10.55
So check out your question and choose
Given the diagram above and bd= 12 and ac= x+ 23, find ac
The value of AC when BD= 12 and AC = x+ 23 is 28
What is a line segment?A line segment can be defined as the part of a straight line that is being bounded by two different end points, and also contains all the points on the line between its endpoints.
From the information given, we have that line AD is a line with segments, line AB, line BC, line CD with B and C as the midpoints.
Given the points as;
AC = x + 23BD = 12BC = 14 + xAD = 26 + xWe have that;
AC + BC = AD
But line BD = 14 + x, we have;
Line AC = x + 23 - 14 + x
Line AC = 2x + 9
substitute the values into the equation
2x + 9 +12 = 26 + x
collect like terms
2x - x = 26 - 21
Add or subtract like terms
x = 5
But, we have that;
Line AC = x + 23
Line AC = 5 + 23
Add the values
Line AC = 28
Hence, the value is 28
Learn more about line segment here:
https://brainly.com/question/2437195
#SPJ1
25.42 marked down by 33%
25.42 marked down by 33 % is 17.0314.
This is a question of percentages.
Percentage
A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentages have no dimension. Hence it is called a dimensionless number.
33 % of 25.42 is given by:-
(33/100)*(25.42) = (33*25.42)/100 = 838.86/100 = 8.3886
25.42 marked down by 33 % = 25.42 - 8.3886 = 17.0314.
To learn more about percentage, here:-
https://brainly.com/question/28269290
#SPJ1
help nakaouebenaooaujwbennfnfnd pls
Answer:
Value of x is 22 because there are alternative angles
Step-by-step explanation:
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
Enter the correct answer in the box.
What are the solutions of this quadratic equation?
x² = 16x - 65
Substitute the values of a and b to complete the solutions.
x = a + bi
x = a - bi
The solutions of the quadratic equation x² = 16x - 65 are:
x = 1/2 + 1/32i
x = 1/2 - 1/32i
What is the solution?We know that a quadratic equation is an equation that is of the sort ax^2 + bx + c = 0. Hence, the equation would be solved and it could have a complex root. By this I mean that the root of the equation could be a complex number as we have in the case of the equation here.
x² = 16x - 65 = 0
x² - 16x + 65 = 0
When we solve by the formula method;
x = -b ±√b^2 - 4ac/2a
x = -(-16) ±√(-16)^2 - 4 (1) (65)/2(16)
x = 16 ±√256 - 260/32
x = 16/32 ±√-4/32
x = 1/2 ± 1/32i
Thus
a = 1/2
b = 1/32
We then obtain;
x = 1/2 + 1/32i
x = 1/2 - 1/32i
Learn more about quadratic equation:https://brainly.com/question/17177510
#SPJ1
Factor out the GCF -27z^3-9z^4+18z^6
The simplified expression for -27z^3-9z^4+18z^6, using the greatest common factor, is given as follows:
9z³(-3 - z + 2z³).
How to factor an expression by GCF?To find a symbolic expression by the greatest common factor, we have to:
Find the greatest common factor of the numeric coefficients.Find the greatest common factor of the exponents.Then we multiply these GCFs.
For this problem, the numeric coefficients are given as follows:
27, 9 and 18, hence the GCF is of 9.
The exponents are given as follows:
z³, z^4 and z^6, hence the GCF is of z³, which is the expression with the lowest exponent.
Then the GCF of the expression is given as follows:
9z³.
To simplify the expression, each term of the expression is divided by 9z³, hence the factored expression is:
9z³(-3 - z + 2z³).
More can be learned about the greatest common factor and factorization at https://brainly.com/question/28302749
#SPJ1
The length of a violin string varies inversely as the frequency of its vibrations. A violin string 14 inches long vibrates at a frequency of 450 cycles per second. Find the frequency of a 10-inch violin string.
The frequency of the 10 inch violin string will be 630 cycles per second or Hertz if the violin string 14 inches long vibrates at a frequency of 450 cycles per second.
As per the question statement, A violin string 14 inches long vibrates at a frequency of 450 cycles per second and we are supposed to find out the frequency of a 10-inch violin string.
We should be knowing that the length of a violin string varies inversely as the frequency of its vibrations.
f = m/l, where "f" is the frequency and "l" is the length and "m" is the constant number
450 = m / 14
m = 6300
Therefore New frequency = 6300 / 10 = 630 cycles per second
Frequency: The number of oscillations or cycles per second or per unit time and it's SI unit is Hertz or cycles per second.To learn more about frequency, click on the link given below:
https://brainly.com/question/17014472
#SPJ1
f(n) = n - 7
f(-9k) =
Answer:
[tex]-9k-7[/tex]
Step-by-step explanation:
Replace n with -9k.
What is 3™+a= a+r, for m
Answer: m = (3/2)r
Step-by-step explanation:
2/3m+a=a+r, for m
----
(2/3)m + a = a + r
---
(2/3)m = r
. If four players on the twenty-man baseball roster are left-handed, what
percent of the players are left-handed?
Answer:
20%
Step-by-step explanation:
4/20
20 x 5 = 100
4x 5 =20
20/100=20%
Write an equation for the line that is parallel to the given line y=3/4x + 7 and that passes through the given point G(8,3)
The equation for the line that is parallel to the given line y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.
As given in the question,
Equation of the given line :
y=3/4x + 7
Slope of the given line = (3/4)
Equation of line with slope (3/4) & passing through point (8, 3) is given by:
y - 3 = [tex]\frac{3}{4}[/tex] (x - 8)
⇒ 4 (y - 3) = 3 (x - 8)
⇒ 4y - 12 = 3 x - 24
⇒ 4 y = 3 x - 24 + 12
⇒ 4 y = 3 x - 12
⇒ y = (3/4)x - 3
Therefore, the equation for the line that is parallel to the given line
y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.
Learn more about equation here
brainly.com/question/13738061
#SPJ1
If a car has 80-liter petrol and after one hour driving the car use 6-liter petrol, how
much petrol will remain after x-hours driving?
Answer:
13.3 liters of petrol left
Step-by-step explanation:
80 ÷ 6 = 13.3
Which number is located between 11 and 12 on a number line?
A.
√150
B.
√134
C.
√115
D.
√121
√134 is the number which is located between 11 and 12 on a number line.
What is a Number Line?A number line is a horizontal straight line on which real numbers are arranged in equal intervals. This line extends both sides at infinity.
Comparison and operations of numbers can be better explained using number lines.
Taking consecutive perfect squares of integers which lies above and below the given numbers on the number line and taking it's square root, we can find the answer.
The perfect squares below and above 150 are 144 = 12² and 169 = 13². So √150 lies in between 12 and 13.
The perfect squares below and above 134 are 121 = 11² and 144 = 12². So √134 lies in between 11 and 12.
The perfect squares below and above 115 are 100 = 10² and 121 = 11². So √115 lies in between 10 and 11.
The number 121 is itself a perfect square. √121 = 11.
Hence √134 is the number which lies in between 11 and 12.
To learn more about Number line, click:
https://brainly.com/question/13425491
#SPJ1
simplify the equation if a=3. b=-1 and c=5
4a+6-ac+b
Answer:
12 + 6 - 15 + (-1) = 2
Step-by-step explanation:
4a = 3 × 4 = 12
ac = 3 × 5 = 15
12 + 6 - 15 + (-1) = 2
The table shows a country’s average fuel consumption for light duty vehicles for several years. Let XP the number of years since 1985 so that executes five cents for 1990 and so forth. Find the linear regression model for the status. What does slope and regression model represent
Using linear function concepts, it is found that:
The slope is of 0.172 means that the fuel economy increases by 0.172 mpg each year.The intercept of 17.04 means that the fuel economy was of 17.04 mpg in 1985.What do the slope and the intercept of a linear function represent?The slope-intercept representation of a linear function is:
y = mx + b.
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we will use a calculator from the points on the table to build a linear function of best-fit. The points are given as follows:
(5, 17.9), (10, 18.7), (15, 19.7), (20, 20.5), (25, 21.3).
Then the function is:
y = 0.172x + 17.04.
Then:
The slope is of m = 0.172, meaning that each year, the fuel economy increases by 0.172 mpg.The intercept of b = 17.04 was the fuel economy in 1985.What is the missing information?The table is missing, and is given by the image at the end of the answer.
More can be learned about linear function concepts at https://brainly.com/question/24808124
#SPJ1
Jillian and Nikki each filled their cars with gasoline. The graphs below show the amount of gas in each car and the miles driven since filling the tank. A graph titled Jillian's Car has miles driven on the x-axis, and gallons of gas left on the y-axis. A line goes through (0, 22) and (100, 16). A graph titled Nikki's Car has miles driven on the x-axis and gallons of gas left on the y-axis. A line goes through points (0, 20) and (100, 16). Which statement is supported by the graphs? Jillian’s car holds more gasoline and gets better gas mileage. Nikki’s car holds more gasoline and gets better gas mileage. Jillian’s car holds more gasoline, but Nikki’s car gets better gas mileage. Nikki’s car holds more gasoline, but Jillian’s car gets better gas mileage.
The statement that is best supported by the graph is; Jillian's car holds more gasoline, but Nikki's car gets better gas mileage.
How to Interpret Linear Graphs?The total amount of gasoline each car tank can hold is shown on the left of each graph on the y-axis.
Jillian's car holds 22 gallons.
Nikki's car holds 20 gallons.
Jillian's car holds more gasoline.
Now we need to see which car gets better gas mileage. Getting better gas mileage means you can go farther with each gallon of gas.
With Jillian's car, after using 22 gallons of gas, you have gone 350 miles, and the gas tank is empty.
350 miles with 22 gallons is 350/22 = 15.9 miles per gallon.
With Nikki's car, you start with only 20 gallons. By the time you drive 350 miles, you still have some gas left. Not only did you start with less gas, 20 gal vs. 22 gal, but after driving the same distance, 350 miles, there is still some gas left in the tank, 6 gallons.
That means Nikki's car used 20 - 6 = 14 gallons to drive 350 miles. 350/14 = 25 miles per gallon.
The more miles per gallon you get, the better the mileage. Thus;
25 miles per gallon is better mileage than 15.9 miles per gallon.
Nikki's car has a smaller gas tank, but it gets better mileage.
Read more about Linear Graphs at; https://brainly.com/question/28393413
#SPJ1
What is 84,787 in expanded form?
Answer:
Your number written in expanded form is: 80000 + 4000 + 700 + 80 + 7
what is 3/12 converted into over 100
The value of 3/12 of 100 is 25 .
In the question ,
a fraction 3/12 is given ,
we have to find the value of 3/12 of 100 .
to find the value , we first convert both the numbers into fraction
So 100 in fraction form can be written as 100/1
So the value 3/12 of 100 means
= [tex]\frac{3}{12} *\frac{100}{1}[/tex]
multiplying the numerator with numerator
and multiplying denominator with denominator .
we get = 300/12
on further simplification ,
we have ,
= 75/3
= 25
So , 3/12 of 100 = 25
Therefore , The value of 3/12 of 100 is 25 .
The given question is incomplete , the complete question is
What is the value of 3/12 of 100 ?
Learn more about Fraction here
https://brainly.com/question/1937550
#SPJ1
4. Find “a” so that the parabola y = ax² + 3x + 11 goes through the point (3,2).
Answer:
a = - 2
Step-by-step explanation:
since the point (3, 2 ) lies on the parabola, then it makes the equation true.
substitute x = 3, y = 2 into the equation and solve for a
y = ax² + 3x + 11
2 = a(3)² + 3(3) + 11
2 = 9a + 9 + 11
2 = 9a + 20 ( subtract 20 from both sides )
- 18 = 9a ( divide both sides by 9 )
- 2 = a
Answer:
a = -2
Step-by-step explanation:
Given quadratic equation:
[tex]y=ax^2+3x+11[/tex]
In order to find "a", substitute the given point on the curve (3, 2) into the equation and solve for a:
[tex]\begin{aligned}y&=ax^2+3x+11\\\textsf{Substitute $(3,2)$} \implies 2&=a(3)^2+3(3)+11\\2&=9a+9+11\\2&=9a+20\\2-20&=9a+20-20\\-18&=9a\\9a&=-18\\\dfrac{9a}{9}&=\dfrac{-18}{9}\\\implies a&=-2 \end{aligned}[/tex]
Therefore, the value of "a" so that parabola y = ax² + 3x + 11 goes through the point (3, 2) is:
[tex]\large \boxed{a=-2}[/tex]
Change 23 out of 25 to a percentage
This how we change 23 out of 25 to a percentage
The numerator of a question is the number that appears above the bar; in this case, the numerator is 23.
The denominator is the number beneath the bar, and in this question, it is 25.
To calculate the value of a fraction, divide the numerator by the denominator.
Therefore, we must divide 23 by 25.
23/25 = 0.92
To determine the percentage, multiply the outcome by 100.
The percentage value will be obtained by multiplying 0.92 by 100.
0.92 x 100 = 92%
As a result, 92% is the answer to the question.
To know more about percentages click at
https://brainly.com/question/27760921
What is 12 divided by .5
(help please i’m bad at division)
Answer:
24
Step-by-step explanation:
Think of .5 as 2 and instead of dividing, you're multiplying.
So instead of 12/.5, it would be 12x2, which is 24.
Hope that helps!
A spinner with 8 equally sized slices has 2 red slices, 3 blue slices, and 3 yellow slices. What is the probability of stopping on a red or blue slice?
Answer:
The probability is 5/8
Step-by-step explanation:
is 10,000,000,001 prime? explain your reasoning
Answer:
Answer down below!
Step-by-step explanation:
It is not prime!!
10,000,000,001 is an odd eleven-digits composite number following 10000000000 and preceding 10000000002. In scientific notation, it is written as 1.0000000001 × 10^10. The sum of its digits is 2. It has a total of 3 prime factors and 8 positive divisors. There are 9,897,840,000 positive integers (up to 10000000001) that are relatively prime to 10000000001.
2/3 times the quantity n plus 16
(n+16)
O(2n+16)
O(n-16)
O(16-n)
Answer:
24
Step-by-step explanation:
it just is, I don't know how I get this. I just did.
[tex]\frac{2n+48}{3}[/tex]
Find b
A 16
B 23
C 92
D76
Answer:
b 23 is your answer okisussu
can anyone decompose 240 - 135 = 105 ?
need new calculation after decomposing? help
The decomposition of 240 - 135 = 105 will be 15(16 - 9) = 15(7) = 105
What is decomposition?It should be noted that decomposition simply means breaking down of the numbers that are given or illustrated.
It should be noted that the numbers 240 - 135 = 105 all have a common factor of 15. This will be broken down as:
240 - 135 = 105
15(16 - 9)
= 15(7)
= 105
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
What is 903 Divided by 72 In Fraction form
Answer: The answer would be 12 39/72
Step-by-step explanation:
903 divided by 72, you'd get 12.5417. You could also express 903/72 as a mixed fraction: 12 39/72.