help please!
I need to prove this using identites
show all steps
cosx+cos7x/sinx-sin7x=-cot3x
Answer: see proof below
Step-by-step explanation:
Use the following Sum to Product Identities:
[tex]\cos A+\cos B=2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B}{2}\bigg)\\\\\\\sin A-\sin B=2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)[/tex]
Use Even/Odd Identities: cos (-A) = - cos A
sin (-A) = sin (A)
Use Quotient Identity: [tex]\cot A=\dfrac{\cos A}{\sin A}[/tex]
Proof LHS → RHS:
[tex]\text{LHS:}\qquad \qquad \qquad \dfrac{\cos x+\cos 7x}{\sin x - \sin 7x}[/tex]
[tex]\text{Sum to Product:}\qquad \dfrac{2\cos \bigg(\dfrac{x+7x}{2}\bigg)\cdot \cos \bigg(\dfrac{x-7x}{2}\bigg)}{2\cos \bigg(\dfrac{x+7x}{2}\bigg)\cdot \sin \bigg(\dfrac{x-7x}{2}\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{2\cos \bigg(\dfrac{8x}{2}\bigg)\cdot \cos \bigg(\dfrac{-6x}{2}\bigg)}{2\cos \bigg(\dfrac{8x}{2}\bigg)\cdot \sin \bigg(\dfrac{-6x}{2}\bigg)}[/tex]
[tex]= \dfrac{ \cos (-3x)}{\sin(-3x)}[/tex]
[tex]\text{Even Odd:}\qquad \quad \dfrac{ -\cos (3x)}{\sin(3x)}[/tex]
[tex]\text{Quotient:}\qquad \quad -\cot(3x)[/tex]
LHS = RHS [tex]\checkmark[/tex]
ANSWER CORRECTLY FOR 25 POINTS!!!
Use this rule to fill in the table.
Rule: Add 8 to the input to get the output.
Add 8
Input Output
1 8
3 24
_ 18
Please fill out the "_"
Answer:
10
Step-by-step explanation:
just minus 8
orrr ig you could do:
x is the input
y is the output
y = 8 + x
18 = 8 + x
(minus 8 on both sides)
x = 10
Answer:10
Step-by-step explanation:
Your subtract 8 from 18 and get 10
Samuel found the difference of the polynomials.What value is missing from his solution? What value is missing from his solution?
is there a picture I can see
Answer:
A or 8
Step-by-step explanation:
You measure containers for international shipments. The height of the standard container is 6 feet and 7 inches. What is its height in meters?
Answer:
2.042 meters hope this helps
The height of the container in meters is 2.0066.
What is unitary method ?Unitary method is a mathematical way of first determining the value of a single unit then deriving the given unit from it.
According to the given question containers for international shipments measures 6 feet and 7 inches.
We know 1 feet is 12 inches.
∴ 6 feet is (12 × 6) = 72 inches.
So, 6 feet 7 inches is (72 + 7) inches which is 79 inches.
We know 1 inches is 0.0254 meter.
∴ 79 inches is ( 79 × 0.0254 ) meter which is
= 2.0066 meters.
learn more about unitary method here :
https://brainly.com/question/21648365
#SPJ2
Jane took a train traveling at an average speed of 60 mph from Boston, MA to Washington, D.C. The trip took 8 hours. On her way back to Boston, Jane decides to take an express train that travels at an average speed of 75 mph. How long will the trip home take?
Answer:
6 hours and 24 minStep-by-step explanation:
The distance is:
60*8 = 480 milesReturn trip will take:
480/75 = 6.4 hours = 6 hours and 24 minWhich graph has a rate of change of zero?
Answer:
not on screen
Step-by-step explanation:
rate of change of 0 is a horizontal line
A practice field is in the shape of a rectangle. The area of the practice field is represented by 5x^2 + 30x -7xy -42y. Find the expressions that represent the length and width of the practice field.
Answer:
length and width are x + 6 and 5x - 7y
Step-by-step explanation:
5x² + 30x - 7xy - 42y
= 5x(x + 6) - 7y(x + 6)
= (x + 6)(5x - 7y)
so
length and width are x + 6 and 5x - 7y
Find the measures of all of the angles.
Step-by-step explanation:
I've shown the process in the picture
hope it helps
What is the value of 5.7 x 1089
Answer:
570,000,000 is the answer hope this helps ^^
Step-by-step explanation:
Answer:
6,207.3
Step-by-step explanation:
=> 5.7 x 1089
multiply 1089 by 5.{=[tex]6,207.3[/tex]
I NEED HELP PLEASE I don't know how to do it
Answer:
$1.68
Step-by-step explanation:
To find the answer we have to find the unit price of the coffee per one ounce.
$11.78 ÷ 7 = $1.68285714
Round your answer to the nearest cent.
$1.68
The cost per ounce is $1.68.
You were asked to factor 16x^4 + 25. Which of the following is true? ANSWER ASAP
Answer: Please explain what you mean by "Which of the following is true?"
Overall, This is the step to solve the equation.
Step-by-step explanation:
16x4=64
64+25=89
An item is regularly priced at $40. It is now priced at a discount of 20% off the regular price. What is the price now?
Answer:
$32
Explanation:
40 x .2 = 8
40 - 8 = 32
I have three times as many cats as Alice but Bob has 7 less cats than me. In total we have 56 cats. How many cats do I have?
The number of cats that you have is; 27 cats
How to calculate algebra word problems?
Let the number of cats alice has be x.
Since you have thrice the amount of cats that alice has, then you have 3x cats.
Bob has 7 less cats than you. Thus, bob has; 3x - 7
If they have a total of 56 cats, then;
x + 3x - 7 + 3x = 56
7x - 7 = 56
7x = 56 + 7
7x = 63
x = 63/7
x = 9
Thus, number of cats you have = 3x = 3 * 9 = 27 cats
Read more on algebra word problems at; https://brainly.com/question/13818690
Brainliest if correct
Answer:
27
Step-by-step explanation:
-3 - (-6) x 5
(-6) x 5 = -30
-3 - (-30)
two minuses makes a plus
-3 + 30
= 27
Answer:
27
Step-by-step explanation:
-3 - (-6) * 5
-3 + 6 * 5
-3 + 30
27
Hope this helps! Have a lovely day! :)
(btw this time i made sure to read the question properly lol)
APR of 7% how much should you deposit monthly to accumulate 85000 in 15 years
Answer:
472.222222222
Step-by-step explanation:
Helllllllllpppppppppp
Answer:
C
Step-by-step explanation:
Literally just do the work yourself man...
A rectangular city is 2 miles long and 7 miles wide. What is the distance between opposite corners of the city? The exact distance is ______________ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ___________ miles.
Answer:
√53 ≈ 7.3 miles
Step-by-step explanation:
The Pythagorean theorem can be used to find the length of a diagonal of a rectangle. The diagonal is effectively the hypotenuse of a right triangle with leg lengths equal to the side lengths of the rectangle.
__
If c represents the distance between opposite corners, and 'a' and 'b' represent the length and width of the city, then we have ...
c² = a² +b²
c² = 2² +7² = 53
c = √53 . . . . . exact corner-corner distance in miles
c ≈ 7.3 . . . . . . approximate corner-corner distance
The exact distance is √53 miles; to the nearest tenth, the distance is approximately 7.3 miles.
10. Given a = 7, b = 6, and c = 10, use the Law of Cosines to solve for A. Round your answer to the nearest degree.
11. Find the area of the triangle given a = 13, c = 21, and B = 87 degrees. Round your answer to the nearest tenth.
12. Find the area of the triangle given a = 6, b = 16, and C = 95 degrees. Round your answer to the nearest tenth.
Answer:
10) 44° (nearest degree)
11) 136.6 units² (nearest tenth)
12) 47.8 units² (nearest tenth)
Step-by-step explanation:
Please see the attached pictures for the full solution.
Answer:
All 20 people must go as one group if they want to save $500.
The equation y=-3x² describes a parabola. Which way does the parabola open?
A. Left
B. Right
C. Up
D. Down
1/7 x 2/3
whats the answer? show ur work
Answer:
Step-by-step explanation:
1/7×2/3=2/21
Solution with Steps
1/7×2/3=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
1×2 and 7×3=2/21
This fraction cannot be reduced.
Therefore:
1/7×2/3=2/21
Solution by Formulas
Apply the fractions formula for multiplication, to
1/7×2/3
and solve
1×2 and 7×3
=2/21
Answer:
1/7 × 2/3 is 2/21
becuase, if you times the numerators, which are the top numbers; and then the denominators which are the bottom numbers; like if you multiply 1×2 you get 2 and 7×3 is 21.
Mary drove 355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles?
Answer: 13.60 gallons divide 355 by 17 to get the base miles per gallon then use that and divide it 284 by 20.88
Step-by-step explanation:
Step-by-step explanation:
17g = 335miles
1g = 335÷17
= 19.70588235
284miles = (284÷19.70588235) × 1
284miles = 14.4119403
Answers:
284miles = 14.41gallons (2.dp)
OR
284miles = 15gallons (nearest whole number)
please help please help
Answer:
1/16 meters
Step-by-step explanation:
perimeter of a square = 4 x length of each side,
so the length of each side is (1/4)/4 = 1/16 meters
Find the slope of the line passing through the pair of points (5,8) (-4,6)
Answer:
0.222
Step-by-step explanation:
the slope of a line is equal to (y2-y1)/(x2-x1)
y1= 8
y2= 6
x1=5
x2=-4
(6-8)/(-4-5)
=0.222
The answer to this question.
Answer: B
Step-by-step explanation: It’s just about respect and good attention. Watching body language can help you know how they are feeling or if their verbal words match their feelings.
Which of the following would be a correct interpretation of a 99% confidence interval such as 4.1<μ<5.6?
Choose the correct answer below.
A.
It means that 99% of all data values are between 4.1 and 5.6.
B.
There is a 99% chance that μ will fall between 4.1 and 5.6.
C.
It means that 99% of sample means fall between 4.1 and 5.6.
D.
We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.
Explanation:
Imagine you randomly selected n items to form a sample, and you did this 100 times. Each time doing a trial like this, we generate a confidence interval. We expect about 99 of those times to have a confidence interval containing the true value of μ. This is what it means when we say "We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ."
5. Find the number of distinguishable arrangements of the letters of the word.
TREDECILLION
Answer:
The word has nine(9) letters with two(2) letters occurring twice each
Step-by-step explanation:
Please mark me brainliest
What is the slope intercept form of (-4,-5); and slope 1/2
Answer:
[tex]y=0.5x-3[/tex]
Step-by-step explanation:
Given the following question:
Point A = (-4, -5) = (x, y)
[tex]m=\frac{1}{2} =0.5[/tex]
To find the slope intercept form of the given information we will have to use the formula y = mx + b where m equals the slope.
[tex]y=mx+b[/tex]
[tex]-5=0.5(-4)+b[/tex]
[tex]0.5\times-4=-2[/tex]
[tex]-5=-2+b[/tex]
[tex]-2+2=0[/tex]
[tex]-5+2=-3[/tex]
[tex]b=-3[/tex]
[tex]y=0.5x-3[/tex]
Which means your answer is "y = 0.5x - 3."
Hope this helps.
calculate the value of two times three squared minus eight
Answer:
10first find the value of 3 squared.
3 x 3
now multiply.
It would be 9.
Now multiply by 2.
2 x 9 = 18
Finally, subtract.
18 - 8 = 10
▬▬▬▬▬▬▬▬
With this information, the answer is 10.
A swimming pool holds 2,640,000 quarts of water.
How many gallons does it hold?
Enter your answer as a number, like this: 42
Answer:
660,000 gallons.
Step-by-step explanation:
Quarts refers to a unit of measurement of volume of a fluid such as water. Quart is typically a standard unit in the British Imperial (imperial quarts) and United States of America (U.S) Customary systems (liquid and dry quarts) of measurement as a unit of volume or capacity.
Generally, there are three (3) types of quarts still in use today; dry quarts, imperial quarts and the liquid quarts.
A quart has the symbol "qt" and it's typically calculated as a quarter (¼) of a gallon.
Mathematically, it is given by the expression;
[tex] 1 \; Quart = 0.25 \; Gallon[/tex]
Therefore, [tex] Gallon = Quart * 0.25[/tex]
Given that the volume or capacity of the swimming pool is 2,640,000 quarts.
[tex] Gallon = 2,640,000 * 0.25[/tex]
[tex] Gallon = 660,000 [/tex]
Hence, the gallons of water of a swimming pool holding 2,640,000 quarts of water is 660,000 gallons.
WILL GIVE BRAINLIEST
Complete each trinomial such that it can be rewritten in the form a(x+b)^2 or a(x-b)^2
1.5x^2+6x+...
Answer:
[tex]1.5x^2+6x+6[/tex]
Step-by-step explanation:
Collect 1.5 from everything, noticing that [tex]6= 1.5\times 4)[/tex]
[tex]1.5(x^2+4x + b^2)[/tex]
Now let's remember that the square of a binomial is [tex](x+b)^2 = x^2+2xb+b^2[/tex], confronting with what we have inside the bracket, [tex]2bx = 4x \implies b=2[/tex]
Our completed bynomial becomes [tex]1.5(x^2+4x+4) = 1.5x^2+6x+6[/tex]
Answer:
1.5x² + 6x + 6
Step-by-step explanation:
1.5x² + 6x + ? = a(x + b)²
a = 1.5
2ab = 6
ab = 3
b = 3/1.5
b = 2
So, inputting all the values :-
a(x + b)²
1.5(x + 2)²
1.5(x² + 4x + 4)
1.5x² + 6x + 6