Answer:
true
Step-by-step explanation:
[Sin A + Sin 3A + Sin 5A + Sin 7A]÷
[Cos A + Cos 3A + Cos 5A + Cos 7A]
=Tan 4A
Do the following rewrites:
sin(x) = sin(4x - 3x) = sin(4x) cos(3x) - cos(4x) sin(3x)
sin(7x) = sin(4x + 3x) = sin(4x) cos(3x) + cos(4x) sin(3x)
sin(3x) = sin(4x - x) = sin(4x) cos(x) - cos(4x) sin(x)
sin(5x) = sin(4x + x) = sin(4x) cos(x) + cos(4x) sin(x)
cos(x) = cos(4x - 3x) = cos(4x) cos(3x) + sin(4x) sin(3x)
cos(7x) = cos(4x + 3x) = cos(4x) cos(3x) - sin(4x) sin(3x)
cos(3x) = cos(4x - x) = cos(4x) cos(x) + sin(4x) sin(x)
cos(5x) = cos(4x + x) = cos(4x) cos(x) - sin(4x) sin(x)
So in the numerator, we have
sin(x) + sin(3x) + sin(5x) + sin(7x)
= 2 sin(4x) cos(3x) + 2 sin(4x) cos(x)
= 2 sin(4x) (cos(3x) + cos(x))
In the denominator,
cos(x) + cos(3x) + cos(5x) + cos(7x)
= 2 cos(4x) cos(3x) + 2 cos(4x) cos(x)
= 2 cos(4x) (cos(3x) + cos(x))
So we have
(sin(x) + sin(3x) + sin(5x) + sin(7x)) / (cos(x) + cos(3x) + cos(5x) + cos(7x))
= (2 sin(4x) (cos(3x) + cos(x))) / (2 cos(4x) (cos(3x) + cos(x)))
= sin(4x) / cos(4x)
= tan(4x)
QED
Susan buys a movie ticket for $12.50 and 3 buckets of popcorn that cost $14.20 each with her
$100. Which statement is true?
Answer: the answer is NO
Step-by-step explanation:
Khan academy
The amount of fertilizer needed for a lawn varies directly with the area of the lawn Mr. Dundee lawn is a rectangular shape and measures 78' x 93' 4 pounds of fertilizer are needed for 750 ft.² of lawn how much is needed for Mr. Dundees lawn to the nearest whole pound
Answer:
39 pounds is needed
Step-by-step explanation:
Given
Lawn Dimension: 78' by 93'
4 pounds fertilizer for 750ft² area
Required
Determine the amount needed for the given dimension
First, we need to calculate the area of the lawn
[tex]Area = 78' * 93'[/tex]
' means feet
So:
[tex]Area = 78ft * 93ft[/tex]
[tex]Area = 7254 ft^2[/tex]
Let the amount of fertilizer need be x
So, we have:
4 pounds = 750ft²
and
x = 7254ft²
Cross Multiply:
[tex]x * 750 = 4 * 7254[/tex]
[tex]x * 750 = 29016[/tex]
Solve for x
[tex]x = 29016/750[/tex]
[tex]x = 38.688[/tex]
[tex]x = 39[/tex] (approximated)
AXYZ is in Quadrant 1. It is rotated 90° counterclockwise around the origin.
Then AX'Y'Z' is reflected across the y-axis. Then AX"Y"Z" is translated 5 units to
the right. In which Quadrant is AX"Y"" Z"'? How do you know?
Answer:
Quad 1
Step-by-step explanation:
AXYZ is in the 2nd quad bc of the rotation, then goes back to 1st quad bc of reflection (y axis). After this, the translation doesn't affect the movement of quadrants. A""X""Y""Z"' lands in quadrant 1.
Answer:
1st quadrant
Step-by-step explanation:
1. Rotated 90° counterclockwise from the 1st quadrant, moves object to the second quadrant.
2. Reflection across y-axis, moves object back to the 1st quadrant.
3. Translation to the right is moving to the right inside the 1st quadrant.
Harley ate 3 Oreos each day of the week. If Ceire eats 2 Oreos each day of the week,
how many did they eat combined?
Answer:
35
Step-by-step explanation:
You take 3 times 7 and that's 21. Then 2 times 7 and that's 14. So, 21+14=35
What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?
Answer:
(-4,0)(4,-4)
slope(m) = (-4 - 0) / (4 - (-4) = -4/(4 + 4) = -4/8 = -1/2. A parallel line will have the same slope.
y = mx + b
slope(m) = -1/2
(2,3)...x = 2 and y = 3
now we sub and find b, the y int
3 = -1/2(2) + b
3 = -1 + b
3 + 1 = b
4 = b
y = -1/2x + 4
1/2x + y = 4....multiply by 2
x + 2y = 8 <== ur parallel line
Answer:
D: 2x + y = 8
Step-by-step explanation:
on edge2021! hope this helps!!~ （=´∇｀=）
Question 4 (3 points)
It take Andre 4 minutes to swim 5 laps.How many minutes per lap is that?
Answer:
0.8 minutes
Step-by-step explanation:
Answer:
Andre would take approximately 1.25 minutes
In the arithmetic sequence 5,2,-1,-4 what term is -25?
Answer:
Thus, the eleventh term is -25.
Step-by-step explanation:
Arithmetic Sequences
The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)r[/tex]
Where
an = nth term
a1 = first term
r = common difference
n = number of the term
We are given the sequence:
5,2,-1,-4,...
We can directly find the common difference by subtracting two successive terms:
r = 2 - 5 = -3
The same result is obtained by subtracting any pair of successive terms.
The first term is a1 = 5. The general equation is:
[tex]a_n=5-3(n-1)[/tex]
[tex]a_n=5-3n+3[/tex]
[tex]a_n=-3n+8[/tex]
We need to find which term is -25, thus:
-3n + 8 = -25
Subtracting 8:
-3n = -25 - 8 = -33
Dividing by -3:
n = -33 / (-3)
n = 11
Thus, the eleventh term is -25.
Two similar figures have a scale factor of 3/5. One side of the larger figure is 20 inches. how long is the corresponding side in the smaller figure?
Answer:
12 inStep-by-step explanation:
Side of the larger figure = 20 inScale factor = 3/5Side of the smaller figure:
20 * 3/5 = 12 inA computer costs $725.85 and a printer costs $87.55. The state sales tax is 6%. What would be the total cost of
both items including sales tax? (round to the nearest cent)
Answer: It would be $862.20
Step-by-step explanation:
A farmer raises goats and cows. Each goat
requires 400 square feet of grazing area and
each cow requires 1200 square feet of grazing
area. The farmer has 36,000 square feet of
grazing area. Write a function to represent
the combination of goats and cows the farmer
can raise. If the farmer raises only cows, how
many can he raise? If the farmer raises only
goats, how many can he raise?
Answer:
I'm guessing
Step-by-step explanation:
My calculations assume at least 456
Tim purchases a new bike for $72.99. A 5% sales tax is charged for these items. What is the total cost, including
tax?
Tax = (Original Amount)(Percent)
please helpp and if you do know the awnser pleaseee tell me how to get itt... thank uuu!!!
Answer:
76.64 hope this helps!
Two times the quantity, a number plus four, is no more than three times the sum of a number and seven, decreased by four. What is the minimum value of the number?
PLEASE HELP ME OUT ALSO SHOW THE EQUATION ON HOW YOU GOT THE ANSWER sorry for caps I just want to clarify
Its 0
0x2=0
0+4=4
0x7=0
4-4=0
solve the proportion
Answer:
x=13
Step-by-step explanation:
Pleaseeeee hellllppppp and explainnn
Will do anything for someone to help me on my homework please I need it!
A sixth-grade science club needs $180 to pay for the tickets to a science museum. All tickets cost the same amount. What could \large 180\div15 mean in this context? Describe two interpretations of the expression. Then, find the quotient and explain what it means in each interpretation. Your answer:
Answer:
Two interpretations:
1. Ticket price for each student
2. Number of students
Quotient = 12
Step-by-step explanation:
Given that:
Total money to be paid for the tickets to the science museum = $180
To find:
Two interpretations, what does the expression [tex]\large 180\div15[/tex] represent ?
Solution:
The expression [tex]\large 180\div15[/tex] has two terms:
1st is 180, which is the amount of money to be paid for the tickets to the science museum.
As price of all the tickets is same, 15 might be one of the two things:
1. Total Number of candidates:
If 15 is the total number of candidates, then the expression [tex]\large 180\div15[/tex] represents the price of each ticket.
2. Price of each ticket:
If 15 is the price of each ticket, then the expression [tex]\large 180\div15[/tex] represents the Total number of candidates.
Now, let us find the quotient:
[tex]\large 180\div15=\bold{12}[/tex]
please help, if you get it right you’ll get brainliest :))
Answer:
The answer is A
Step-by-step explanation:
The answer is A because if you flip it over the y-axis it will be on the same line as before.
Hope this helps!!
the grace your family is driving from Sacramento California to Key West Florida and 5 days they had travel 2045 miles at this rate, how long will it take them to travel from Sacramento to key west.
Step-by-step explanation:
it will take them 104 hours.
The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by R(p) = −25p^2 + 1600p where p is the price per unit (in dollars).
(a) Find the revenues when the price per unit is $20, $25, and $30.
(b) Find the unit price that will yield a maximum revenue.
(c) What is the maximum revenue?
(d) Explain your results.
Answer:
B because I elmenite the ansgdkebs smbsjmsvsjsosvejajscr
From 150 minutes to 172 minutes
A hostess earned a 5% tip. What decimal is equivalent to 5%?
Answer:
.05 is the equivalent of 5 percent.
Step-by-step explanation:
Factorise x(x+z) -y(y+z)
Show calculation and please give correct answers.
Answer:
(x-y)(x+y+z)
Step-by-step explanation:
[tex]x^{2} +xz-y^{2} -yz\\x^{2} -y^{2} +z(x-y)\\(x+y)(x-y)+z(x-y)\\(x-y)(x+y+z)\\[/tex]
Answer:
(x - y)(x + y + z)
Step-by-step explanation:
Given
x(x + z) - y(y + z) ← distribute both parenthesis
= x² + xz - y² - yz ← rearrange
= x² - y² + xz - yz ← x² - y² can be factored as a difference of squares
= (x - y)(x + y) + z(x - y) ← factor out (x - y) from each term
=(x - y)(x + y + z)
if i make 118 bucks an hour how much would i make in a year
Answer:
118*360=42480..........
6. Solve for x: 8x - 2 - 5x = 8.
Can someone help
Answer:
Hope this helps have a good day! :)
Step-by-step explanation:
Exact form = 10/3
Decimal form = 3.3
Mixed number form = 3 1/3
the solution for x is x = 10/3 or approximately x = 3.33.
To solve for x in the equation 8x - 2 - 5x = 8, we need to simplify and combine like terms, then isolate x on one side of the equation.
Let's start by combining the x terms on the left side:
(8x - 5x) - 2 = 8
Simplifying further:
3x - 2 = 8
Next, we want to isolate the x term. We can do this by adding 2 to both sides of the equation:
3x - 2 + 2 = 8 + 2
Simplifying the equation:
3x = 10
Finally, to solve for x, we divide both sides of the equation by 3:
(3x) / 3 = 10 / 3
The division yields:
x = 10/3
Therefore, the solution for x is x = 10/3 or approximately x = 3.33.
Learn more about equation here
https://brainly.com/question/32490578
#SPJ6
GCF distributive property of 42+14
Answer:
56
Step-by-step explanation:
You will add 42+14 together to get 56 and you will distribute 42 and 14 to get 2 cubed times 14.
I am glad to help and have a great day
Find the sum or difference.
(- 2h + 1) + 2(3h - 4) SHOW YOU WORK FOR POINTS AND BRAINIEST
Answer: (- 2h + 1) + 2(3h - 4) = 4h -7
Step-by-step explanation:
First, remove unnecessary parentheses
- 2h + 1 + 2(3h - 4)
then distribute 2 through the parentheses
- 2h + 1 + 2(3h - 4) = -2h + 1 + 6h -8
Combine like terms
-2h + 1 + 6h -8 = 4h + 1 - 8
1-8= 7
So the answer is
4h - 7
using the slope formula find the slope of the line that passes through these points (2,5) and (8,-3)
Answer:
-4/3
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ].
-3-5/8-2
-8/6
-4/3
Best of Luck!
Answer:
-4/3
Step-by-step explanation:
You can use rise/run. The rise (y values) goes from 5 to -3. You subtract 8 for this. The run (x values) goes from 2 to 8. You add 6 for this. the proportion is -8/6, which can be simplified to -4/3.
Therefore, the slope is -4/3!
Hope I helped!!!!!!
whats the slope intercept form for the points [5,2] and [0,-1]
Answer:
[tex]\displaystyle y=\frac{3}{5}x-1[/tex]
Step-by-step explanation:
The Equation of a Line
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
We are given the points (5,2) and (0,-1), thus:
[tex]\displaystyle y-2=\frac{-1-2}{0-5}(x-5)[/tex]
Operating:
[tex]\displaystyle y-2=\frac{-3}{-5}(x-5)[/tex]
[tex]\displaystyle y-2=\frac{3}{5}(x-5)[/tex]
To find the slope-intercept form, we continue to simplify the expression:
Removing the parentheses:
[tex]\displaystyle y-2=\frac{3}{5}x-\frac{3}{5}\cdot 5[/tex]
[tex]\displaystyle y-2=\frac{3}{5}x-3[/tex]
Adding 2:
[tex]\displaystyle y=\frac{3}{5}x-3+2[/tex]
[tex]\mathbf{\displaystyle y=\frac{3}{5}x-1}[/tex]
Which are the solutions of the quadratic equation?
Answer:
The answer is C
Step-by-step explanation: