If the equation is
- sin²(x) = cos(2x)
rewrite the left side using the Pythagorean identity,
sin²(x) = 1 - cos²(x)
and the right side using the double angle identity for cosine,
cos(2x) = 2 cos²(x) - 1
Then the equation transforms to
- (1 - cos²(x)) = 2 cos²(x) - 1
Solve for cos²(x) :
-1 + cos²(x) = 2 cos²(x) - 1
cos²(x) = 0
Take the square root of both sides to get
cos(x) = 0
Solve for x :
x = cos⁻¹(0) + 2nπ or x = cos⁻¹(0) - π + 2nπ
x = π/2 + 2nπ or x = -π/2 + 2nπ
where n is any integer. We get solutions in the interval [-π, π] when n = 0, giving the solutions
x = π/2 or x = -π/2
8. Lisa types 6 pages in 36 minutes. Frank types 5 pages in 30 minutes. Do they type at the same rate? Use a proportion to explain.
Answer:
Yes
Step-by-step explanation:
Lisa and Frank type at the same rate.
They both type 1 page every six minutes.
Lisa types 6 pages every 36 minutes, and if we divide the minutes by the pages, we get
[tex]\frac{36}{6} = 6[/tex]
And Frank types 5 pages ever 30 minutes, when we divide we get
[tex]\frac{30}{5} = 6[/tex]
Select Yes or No to indicate whether each of the ordered pairs is most likely a solution to the equation represented by the graph.
For a Biology assignment, Lisa collected data on plant growth of a sunflower every week for 9 weeks. When Lisa first planted the sunflower, it was 10 centimeters tall. The time (in weeks) is plotted against the height (in centimeters) as shown below. Using the best-fit line, approximately how tall was the sunflower plant during the fifth week? 33 centimeters 34 centimeters 35 centimeters 30 centimeters
Answer:
I think it was 34 cm because it should be not too long
Step-by-step explanation:
this is from my logic perspective
0.5= x djdododododododdodod
Answer:
25
Step-by-step explanation:
cuz
1) -1 = x – 5
2) -5x + 2 = 17
PLS ANSWER PLS PLS PLS
Plzzz answer it :( :
All fraction or mixed number answers are in simplest form or reduced form .
True or false
Answer:
false it is not always reduced form
Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?
Answer:
50%
Step-by-step explanation:
*In this question, the 6 does not matter*
If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.
Percentages are just fancy fractions and decimals. 50% means 1/2.
Thus, the answer is 50%
Delete this already.
Juanita earns $36 for 3 hours of work. At that rate, how long would she have to work to earn $720?
Answer:
She has to work for 60hours in order to earn $720.
Step-by-step explanation:
Amount of money earned in 1hour=36÷3
=12$
Total time required=720÷12
=60hours
pitcher can hold 1,200 milliliters of tea. How many liters of tea are in the pitcher?
Answer:
1.2 Liters
Step-by-step explanation:
There are 1000 mL in 1 L. divide 1200 by 1000 and you get 1.2
Given
f
(
x
)
=
−
x
−
3
f(x)=−x−3, solve for
x
x when
f
(
x
)
=
−
2
f(x)=−2.
Answer:
-5
Step-by-step explanation:
Substitute every part of the equation where x appears with the value of x, which is -2
f(-2)=-2-3
f(-2)=-5
So, f(x)=-5
MY HRW ‼️ Solve the equation. You may find using algebra tiles helpful in solving this problem.
X +6=-X-6
Answer:
x=-6
Step-by-step explanation:
x+6=-x-6
(-6)+6=(6)-6
0=0
Answer:
Solve the equation. You may find using algebra tiles helpful in solving this problem. X +6=-X-6 X= -6
what is wswssssssssss 4+4?
Answer: 4+4=8
Hope this helps :)
Step-by-step explanation:
Say you have four apples, and your friend gives you four more. You put together the amount of apples you have and you get 8.
Help me with this plz!?!? I will mark brainliest!!!
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
Look at the equation. y=2x−2 Which situation is best described by the equation?
A. The temperature at 2.00AM 2°c and rises 2°C each hour for x hours
B. The temperature at 2.00AM is -2°C and rises 2°C each hour for x hours
C.The temperature at 2:00AM is 2°C and drops 2°C each hour for X hours
D. The temperature at 2:00AM is -2°C and drops 2°C each hour for x hours.
Answer: A
Step-by-step explanation:y=2x−2 2.00AM 2°c and rises 2°C each hour for x hours
The largest prime number that is a factor of 35 is multiplied by the smallest prime number
Answer:
the largest factor of 35 is 35 and the smallest prime number is 2 so 35 times two is 70
Step-by-step explanation:
plz help! will give brainliest! really easy!
Answer:
C
Step-by-step explanation:
I explained it in the comments of the other one
Consider this function.
(r) = -3r + 3
Which graph represents the inverse of function ?
9514 1404 393
Answer:
C. graph Y
Step-by-step explanation:
Starting with f(r) = -3r +3, the inverse function can be found from ...
r = f(y)
r = -3y +3
r -3 = -3y
(r -3)/-3 = y
y = -1/3r +1
The inverse function will have a slightly negative slope and a y-intercept of 1. This matches graph Y.
which of the following is a characteristic of the circumcenter of a triangle? multi-choice. A. it is the center of the only circle that can be inscribed in the triangle. , B. it is the center of the circle that can be inscribed in given a given triangle. C. it is the center of the only circle that can be circumscribed about the triangle. D. it is equidistant from all three sides of the triangle.
Answer:
C
Step-by-step explanation:
The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.
I hope this helps!
Further explanation:
For a circle to circumscribe something, it circles it so that each of the vertices are on the circle, so each of the vertices are equidistant from the circumcenter. The circumcenter of a triangle is formed by the perpendicular bisectors of its sides.
Side note:
The rest of the choices describe an incenter.
Explain how to graph 8 is greater than it equal to y
Answer:
t w e n t y c h a r e c t e r s l o n g
need this done quick pls
Answer:
50 degrees
Step-by-step explanation:
40+50=130
130-180
50
Answer:
50
I have not done this in years!
Put these numbers in order from least to greatest.
3 4/5 3 3/4 3.5
Answer:
3/4, 4/5, 3, 3, 3.5
Answer:
3.5,3 3/4,3 4/5
Step-by-step explanation:
Least to greatest 0.4, 5/8, 74%, 3/5
Answer:
0.4,3/5,5/8,74%
Step-by-step explanation:
Change them all into decimals.
Get 0.4,0.625,0.74,0.6
Then reorder and see what their original values were
Christina has 50 coins consisting of quarters and dimes. The coins combined value is $9.50. Write a system of equation to determine how many quarters and dimes Christina has.
Answer:
Christina has 30 quarters and 20 dimes.
Step-by-step explanation:
Given that a quarter is worth 0.25 dollars and a dime is worth 0.10 dollars, if Christina has 50 coins and these add up to a total of $ 9.50, to determine the number of quarters and dimes that she has in her possession, the following calculation must be carried out, taking into account that the difference between a quarter and a dime is 0.15 dollars:
50 x 0.25 = 12.5
12.5 - 9.5 = 3
Thus, the difference between the value that Christina has and the value that she would have if all of her coins were quarters is 3 dollars. Thus, since 0.15 x 20 equals 3, of the 50 coins Christina has, 30 are quarters and 20 are dimes.
This is confirmed through the following equation:
30 x 0.25 + 20 x 0.1 = X
7.5 + 2 = X
9.5 = X
What is the value of x in the rhombus below?
O A. 17
O B. 35
O C. 53
O D. 37
Answer:
∴ x= 17
Step-by-step explanation:
the total of angel in 90°
∴ 2x+3+3x+2 =90
∴ 5x +5 =90
5x=90-5
5x = 85 (divide both side by 5)
∴ x= 17
Answer:17
Step-by-step explanation:
big brain knowledge
whats 7, −6, 4, −10, 3 least to greatest
Answer:
-10, -6, 3, 4, 7
Step-by-step explanation:
Hope it helps ^^
Need help geometric sequences see pic for details
Given:
The recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]
[tex]a_1=-3[/tex]
To find:
The explicit formula of the given geometric sequence.
Solution:
We know that, first term of geometric sequence is [tex]a_1=-3[/tex].
Recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\times r[/tex] ...(i)
where, r is common ratio.
We have,
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]r=\dfrac{1}{8}[/tex]
The explicit formula of a geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get
[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]
Therefore, the correct option is D.
1/13 times 1/2.54 show your work
Answer:
0.03028467595
Step-by-step explanation:
calculator?
Stephanie needs to cover her yard with 410taft2of soil. She has enough for 125ft2in one bag and 65 ft2in another bag. How much more square feet of soil will she need covered?
Answer:
Stephanie needs 220ft² of more soil to cover the rest of her yard.
Step-by-step explanation:
First add the bags she already has:125ft²+65ft²+x=410ft² --> 190ft²+x=410ft²
Second use the subtraction property of equality: 190ft²-190ft²+x=410ft²-190ft² ---> x=220ft²
BRANLIEST TO CORRECT ANSWER!!!
Which statements describe vascular tissue?
Check all that apply.
The primary purpose of vascular tissue is to support the plant and help it stand upright.
Phloem carries food made during photosynthesis to other parts of the plant.
Phloem contains the chloroplasts.
Xylem moves water and nutrients throughout the plant.
Xylem is the protective, waxy layer on a plant that prevents water loss.
Answer:
Xylem moves water and nutrients throughout the plant.
Answer:
B and D
Step-by-step explanation:
most people in the comments said it was right so I tried it and got it right