prove that:
cos20°cos40°cos80°=1/8
Answer:
see explanation
Step-by-step explanation:
Using the double angle identity for sine
sin2x = 2sinxcosx
Consider left side
cos20°cos40°cos80°
= [tex]\frac{1}{2sin20}[/tex] (2sin20°cos20°)cos40°cos80°
= [tex]\frac{1}{4sin20}[/tex] (2sin40°cos40°)cos80°
= [tex]\frac{1}{4sin20}[/tex] (sin80°cos80° )
= [tex]\frac{1}{8sin20}[/tex] (2sin80°cos80° )
= [tex]\frac{1}{8sin20}[/tex] . sin160°
= [tex]\frac{1}{8sin20}[/tex] . sin(180 - 20)°
= [tex]\frac{1}{8sin20}[/tex] . sin20°
= [tex]\frac{1}{8}[/tex] = right side , thus proven
Step-by-step explanation:
hope its helps you have a great day keep smiling be happy stay safe ☺
Solve.
Enter any fraction as a simplified fraction.
[tex](5\sqrt{5})^{-2x+1} = \frac{1}{5} * 125^{x-3}[/tex]
Step-by-step explanation:
(5√5)^(1-2x) = 1/5 * 125^(x-3)
(5^1.5)^(1-2x) = 5^(-1) * 125^x / 125^3
5^1.5 / 5^3x = 5^(-1) * 5^(3x) / 5^9
5^1.5 / 5^3x = 5^(3x) * 5^(-10)
5^(1.5 - 3x) = 5^(3x - 10)
=> 1.5 - 3x = 3x - 10
=> 6x = 11.5
=> x = 23/12.
A triangle has a perimeter represented by the expression 9x + 7
A square has a side length represented by 4x – 3.
Which expression represents the total perimeter of the two figures?
A) 20x
B) 4x2 + 9x – 5
C) 13x + 4
D) 25x – 5
Answer:
D. 25x-5
Step-by-step explanation:
you need to add all the sides of the square to get 16x-12 and then add 9x+7 to get D.
Which of the following values for x is true for 4x > 10?
3
O x=
4
O x = 2
O x = 2.5
OX= 3
Question 4
10 pts
Question 6
Question 7
Question 8
What is the length of line segment DK to the nearest tenth of an inch?
Time Running Hide
1 Hour, 26 Minutes, 25 Sec
16 in
430
D
O 10.9 in
0 21.9 in
O 23.5 in.
O 11.7 in.
« Previous
Next
Answer:
C = 23.5 in
Step-by-step explanation:
θ = 43°
The length of the side opposite to θ = 16 in.
Hypotenuse = DK
Apply trigonometric ratio, thus:
sin(θ) = opp/hyp
Plug in the values
sin 43 = 16/DK
Multiply both sides by DK
DK*sin 43 = 16
Divide both sides by sin 43
DK = 16/sin 43
DK = 23.5 (nearest tenth of an inch)
PLEASE HELP ME WITH THIS PROBLEM I WILL FAIL
Answer:
The answer is b
Step-by-step explanation:
please help me !!!!
Flying against the wind , an airplane travels 3660 kilometers in 6 hours. flying with the wind , the same plane travels 3800 kilometers in 4 hours. what is the rate of the plane in still air and what is the rate of the wind?
Answer:
...
against the wind, an airplane travels 3640 km in 7 hours.
with the wind, the same plane travels 6000 km in 6hrs.
...
let speed of plane in still air be x mph
speed of wind be y mph.
..
t=d/r
..
against wind speed = x-y mph
with wond speed = x=y mph
...
3640/(x-y)=7
3640 = 7x-7y
/7
520=x-y.....................1
...
6000/x+y = 6
6000 = 6x+6y
/6
1000=x+y.....................2
...
Add (1) & (2)
2x=1520
/2
x=760 mph speed of plane in still air
...
plug value of x in 2
1000=760+y
100-760=y
240 = y
240 mph speed of wind
fivestar farm purchased 2400 apple trees. If 80 trees can be planted on each acre of land, how many acres will be needed to plant all the trees?
Answer:
30
Step-by-step explanation:
To find the answer you would need to do 2400 divided by 80 which = 30
Hope this helped :)
A is directly proportional to B when A = 12, B = 3 a) find a formula for A in terms of B b) find the value of A when B = 5 c) find the value of B when A = 36
Answer:
a) A = kB
b) 20
c) 9
Step-by-step explanation:
A is directly proportional to B when A = 12, B = 3
a) find a formula for A in terms of B
A ∝ B
A = kB
Where k is constant of proportionality
when A = 12, B = 3
12 = 3k
k = 12/3
k = 4
b) find the value of A when B = 5
A = kB
k = 4
A = 4 × 5
A = 20
c) find the value of B when A = 36
k = 4
A = kB
B = A/k
B = 36/4
B = 9
plzz help me
Solve -24 = 6x. Show your work.
Answer:
x = -4
Step-by-step explanation:
-24 = 6x
________
Switch sides:
6x = -24
________
Divide both sides by 6:
6x/6 = -24/6
________
Simplify:
X = -4
Answer:x = -4
Step-by-step explanation:
what is the solution of √5x+1-√x=5
Answer: x= 16
Step-by-step explanation:
Solve for x
√(5x + 1) − √x = 5
Add √x to both sides of the equation.
√(5x + 1)^2 = 5( + √x )^2
To remove the radical on the left side of the equation, square both sides of the equation.
√5x + 12 = (5 + √x)^2
Simplify each side of the equation.
5x + 1 = 25 + 10√x + x
Solve for 10√x.
10√x = 4x − 24
To remove the radical on the left side of the equation, square both sides of the equation.
(10√x)^2 = (4x − 24)^2
Simplify each side of the equation.
100x = 16x^2 − 192x + 576
Solve for x.
x = 9/4 , 16
Exclude the solutions that do not make √5x + 1 − √x = 5 true.x = 16
The graph of h(x)=|x-10|+6 is shown on whitch interval is the graph increasing
Given the diagram and AB || CD, which of the following
statements is most likely to be used to show that
AECD - AEAB?
A
С
A
E
3
D
ZECD=ZECD
ZABEZECD
ZEABELECD
LEDCZEAB
In a school, 2/3 of the students study a language.
Of those who study a language 2/5 study French
Find the ratio of students who study French to students who do not study French.
Give your answer in its simplest form.
Answer:
4 : 11
Step-by-step explanation:
Given that:
Fraction of language students = 2/3
Number of students who study French :
2/5 of 2/3
2/5 * 2/3 = 4 /15
Those who do not study French :
Total fraction of entire student :
1 - 4/ 15
(15 - 4) / 15
11/15
Ratio of French to non-french
4/15 : 11/15
4/15 ÷ 11/15
4/15 * 15/ 11
4 / 11
4 : 11
what is thirty five percent
Answer:
i dont know what you need 35% as but..
Step-by-step explanation:
Decimal : 0.35
Fraction: 7/20
7 times what equals 17?
Answer:
119
Step-by-step explanation:
PLEASE HELP!!!!!!
Rotate the given triangle 270°
counter-clockwise about the
origin.
2 21
-1 -1 3
-1
[1 1
?
[
-1
1
11
9514 1404 393
Answer:
[tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
Step-by-step explanation:
The 270° CCW rotation is described by the transformation ...
(x, y) ⇒ (y, -x)
That is, the first row of the transformed coordinate matrix is the same as the second row of the input matrix. The second row of the output matrix is the opposite of the first row of the input matrix.
[tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
g(x)=2x-1
h(x)=x^2-3x
find g(x)+h(x)
Answer:
[tex](2x - 1) + ({x}^{2} - 3x) \\ = {x}^{2} - 1x - 1 \\ [/tex]
10.3
divided by 200.3865
Answer: 0.0514006682 and yes i looked it up bc nobody has time for that
Step-by-step explanation:
Answer:
0.051
Step-by-step explanation:
Hope this helps!
How many 1/4 cup servings are in an 8 -cup box of cereal? 32 servings 1/4 servings 6 servings 2 servings?
Answer:
32
Step-by-step explanation:
In a company, 90% of the workers are women . If 440 people work for the company who aren't women , how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
There are total 4400 workers
Process is in photo...
The total number of workers if, In a company, 90% of the workers are women, If 440 people work for the company who aren't women is 4400.
What is percentage?
As it is clear from the term per-cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
In a company, 90% of the workers are women,
If 440 people work for the company who aren't women,
Calculate the percentage of people who aren't women as shown below,
The percentage of people who aren't women = 100% - the percentage of women
The percentage of people who aren't women = 100% - 90%
The percentage of people who aren't women = 10%
Assume that there are a total of x workers then according to the statement,
10% of x = 440
10 / 100 × x = 440
x = 440 × 100 / 10
x = 4400
To know more about percentages:
brainly.com/question/20818421
#SPJ2
Find the balance in Grace's account after 2 years for a principal of $2500 if the bank pays simple interest at a rate of 5.25%. A.)29762.50 B.)2862.50 C.)2762.50 D.)2772.50
Answer: C.)2,762.50
Step-by-step explanation:
The bank is paying a simple interest of 5.25%.
After 2 years, Grace's account will have:
Simple interest:
= Principal * ( 1 + rate * years)
= 2,500 * ( 1 + 5.25% * 2)
= $2,762.50
Anybody know the answer for this? ;-;
Answer: the first answer choice
Step-by-step explanation:
Answer:
i think its the bottom one but i dont know
Step-by-step explanation:
Let m=7 , r = 8, and t=2
Evaluate the expression. mr/t
Answer:
28
Step-by-step explanation:
7 times 8 /2
56/2
28
if that was what you were supposed to do,,
Answer:
mr/t=28
Step-by-step explanation: If m=7, r=8 and t=2, then the equation is 7(8)/2. 7*8=56 and then 56/2=28.
Solve for x!!!!!.....
Number of weeks and amount of money in account chart
Mortgage loan of $84,000.
Interest rate is 6 percent.
Monthly payment is $504.
How much of the first monthly payment is for interest?
Answer: $420
Step-by-step explanation:
The monthly payment has both an interest component and a principal repayment component.
The interest component is based on the total loan amount(principal) still due at the time and the principal repayment component will be the rest of the payment.
First convert the interest rate to a monthly interest rate as the payments are done monthly:
= 6%/12
= 0.5%
Interest = Principal remaining * interest rate
= 84,000 * 0.5%
= $420
Answer:
420
Step-by-step explanation:
PLEASEEE HELPPPP ASAPPP PLEASE
please help i will give Brainliest to the correct one. Use the Distributive Property to rewrite the expression in its equivalent formImmersive Reader -2x(3y+5)
Answer:
−
6
−
1
0
Step-by-step explanation:
there you go!
DESCRIBE THE GENERAL STRUCTURE OF THE OCEAN FLOOR! (Not math)
Answer:
A lot of sand :D