Answer:
[tex]\cos(2\, x) = 1 - 2\, (\sin(x))^2[/tex].
Step-by-step explanation:
Angle sum identity for cosine: [tex]\cos(a + b) = \cos(a) \, \cos(b) - \sin(a) \, \sin(b)[/tex].
Pythagorean identity: [tex](\cos(a))^{2} + (\sin(a))^{2} = 1[/tex] for all real [tex]a[/tex].
Subtract [tex](\cos(x))^{2}[/tex] from both sides of the Pythagorean identity to obtain: [tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex].
Apply angle sum identity to rewrite [tex]\cos(2\, x)[/tex].
[tex]\begin{aligned}&\cos(2\, x)\\ &= \cos(x + x) \\ &= \cos(x) \, \cos(x) - \sin(x)\, \sin(x) \\ &= (\cos(x))^{2} + (\sin(x))^{2}\end{aligned}[/tex].
[tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex] follows from the Pythagorean identity. Hence, it would be possible to replace the [tex](\cos(x))^{2}[/tex] in the previous expression with [tex](1 - (\sin(x))^{2})[/tex].
[tex]\begin{aligned}&(\cos(x))^{2} - (\sin(x))^{2}\\ &= \left[1 - (\sin(x))^{2}\right] - (\sin(x))^{2} \\ &= 1 - 2\, (\sin(x))^{2} \end{aligned}[/tex].
Conclusion:
[tex]\begin{aligned}&\cos(2\, x) \\ &= (\cos(x))^{2} + (\sin(x))^{2} \\ &=1 - 2\, (\sin(x))^{2}\end{aligned}[/tex]
Evaluate the function.
f(x)=2x^2+8x
Find f(−1)
PLease help!
a:-10
b:-6
c:6
d:10
Answer:b
Step-by-step explanation:
The pie chart below shows the percentage of total revenue that a publisher receives from various types of publications. Use this chart to answer the questions
below.
Answer:
a. Cookbooks
b. 50%
c. 30%
Step-by-step explanation:
According To the Question,
We have a total revenue of a publisher describe in a circle (360°).a. Now, Approximately Cookbooks & Textbooks revenue Form 180°, but textbook revenue is more than cookbooks as clearly visible in the diagram
Thus, cookbooks are less than 90°.
Now, we have to find 1/5th of total publisher revenue which is 360°/5= 72°. & the Cookbooks is nearest to 72° ( less than 90°)
So, Answer For (a) is Cookbooks
b. Here in Diagram Clearly Visible that The Cookbooks & Textbooks Revenue Form 180° which is Approximately 50% of total Publisher's Revenue.
So, the Total Revenue Comes From Textbooks & Cookbooks is 50%.
c. Now We know the Cookbooks + Textbooks Revenue form 180° Approximately & Cookbook is approximately equal to 72° (as we solve above)
So, textbooks are 180°-72° = 108°, which is 30% of 360° ∴ 30% Revenue Come From Textbooks.
For what value of x is the rational expression below equal to zero?
20+2x
5-x
O A. -10
O B. -5
C. 10
O D. 5
Answer:
A.-10 should be the answer to the question..
The rational expression is zero at x = -10.
What is rational expression?The ratio of two polynomials is known as a rational expression.
The given rational expression can equate to zero
[tex]\frac{20+2X}{5-X} =0[/tex]
Then, 20+2x=0
Therefore, x = (-20/2) = -10.
At x = -10, the given rational expression is zero.
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The length of a rectangle should be 20 meters longer than 8 times the width. If the length must be
between 116 and 180 meters long, what are the restrictions for the width, z?
Write the solution set as an algebraic inequality solved for the variable
Answer:
The width of the rectangle lies between 12 and 20.
Step-by-step explanation:
Let the width of the rectangle is w.
length of the rectangle,
L = 8 w + 20
116 < L < 180
So,
116 < 8 w + 20 < 180
96 < 8 w < 160
12 < w < 20
So, the width of the rectangle lies between 12 and 20.
What is 30% of 280 passengers
Answer:
84 Passengers
Step-by-step explanation:
30/100(280)
= 3/10(280)
= 84
Answer:
84
Step-by-step explanation:
30/100x280
So 84 is the answer
HW HELP ASAP PLZZZZZ
Answer:
ur ans is here...
find the area
steps, please
Answer:
45) 35.75 sq km
46) 24.5 sq km
Step-by-step explanation:
Area of Square:
A= [tex]\frac{(base)(height)}{2}[/tex]
45) A = (11)(6.5) ÷ 2 =
46) A = (10)(4.9) ÷ 2 =
Answer:
45) [tex]35.75[/tex] [tex]km^2[/tex]
46) [tex]24.5[/tex] [tex]km^2[/tex]
Step-by-step explanation:
------------------------------
The formula to find the area of a triangle is [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.
So, let's solve and find out the answer.
--------------->>>>
45)
[tex]A=\frac{1}{2}(11)(6.5)[/tex]
[tex]A=\frac{1}{2}(71.5)[/tex]
[tex]A=35.75[/tex]
The area of this triangle is [tex]35.75[/tex] [tex]km^2[/tex]
--------------->>>>
46)
[tex]A=\frac{1}{2} (10)(4.9)[/tex]
[tex]A=\frac{1}{2} (49)[/tex]
[tex]A=24.5[/tex]
The area of this triangle is [tex]24.5[/tex] [tex]km^2[/tex]
------------------------------
Hope this is helpful
Alejandro used a mathematical property to create two equivalent expressions.
6(x + 2) = 6x + 30
Which of the following is the missing term?
O 24
Х
O 5x
6
5
Mr. Jones lives in City A and drives at a constant speed to City B, which is 400 km 2 of the distance at that same away. On the way back to City A, Mr. Jones drives 5 constant speed. Then, because of rain, he decreases his speed by 20 km/h. The round trip takes 11 hours. How fast did Mr. Jones drive during the rainy part of his trip from City B to City A?
Answer:
He traveled at 72km/hr during the rain
Step-by-step explanation:
Question is not well formatted. See comment
Given
[tex]d=400km[/tex] --- distance
[tex]t = 11hrs[/tex] --- total time
Let his speed from city A till the rain starts on his return trip be [tex]s_1[/tex]
Let his speed from city during the rain be [tex]s_2[/tex]
So:
[tex]s_2 = s_1 -20[/tex]
Required
Calculate [tex]s_2[/tex]
From the question, we understand that; he drives the whole 400 km and 2/5 of 400 km at [tex]s_1[/tex]
The distance covered during this period is:
[tex]d_1 = 400 + \frac{2}{5} * 400[/tex]
[tex]d_1 = 400 + 160[/tex]
[tex]d_1 = 560[/tex]
And the time during this period is:
[tex]t_1 = \frac{2}{5} * 11[/tex]
[tex]t_1 = 4.4[/tex]
So, the distance during the rain is:
[tex]d_2 = 2 * 400 - d_1[/tex]
[tex]d_2 = 2 * 400 - 560[/tex]
[tex]d_2 = 800 - 560[/tex]
[tex]d_2 = 240[/tex]
And the time during the rain is:
[tex]t_2 = 11 - t_1[/tex]
[tex]t_2 = 11 - 4.4[/tex]
[tex]t_2 = 6.6[/tex]
So, we have:
[tex]d_1 = 560[/tex] --- distance covered before the rain
[tex]d_2 = 240[/tex] --- distance covered when raining
[tex]s_2 = s_1 -20[/tex]
[tex]t_1 = 4.4[/tex] ---- time spent before the rain
[tex]t_2 = 6.6[/tex] --- time spent in the rain
Speed is calculated as:
[tex]Speed = \frac{distance}{time}[/tex]
Make distance the subject
[tex]distance = speed * time[/tex]
So:
[tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex]
Recall that:
[tex]s_2 = s_1 -20[/tex]
Make [tex]s_1[/tex] the subject
[tex]s_1 = s_2 + 20[/tex]
The expression [tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex] becomes:
[tex]560 + 240 = (s_2 + 20) * 4.4 + s_2 * 6.6[/tex]
[tex]800 = 4.4s_2 + 88+ 6.6s_2[/tex]
Collect like terms
[tex]6.6s_2 + 4.4s_2 = 880 - 88[/tex]
[tex]11s_2 = 792[/tex]
Solve for [tex]s_2[/tex]
[tex]s_2= \frac{792}{11}[/tex]
[tex]s_2=72km/h[/tex]
The distance and time 400 km and 11 hours as well as the speed
reduction gives the speed during the rainy part as 60 km/h.
Which method can be used to find the speed in the rain?Based on the comment in the question, we have;
Given:
Distance between City A and City B = 400 km
Distance travelled at the same speed on his way back = [tex]\mathbf{\frac{2}{5}}[/tex] of the distance
Amount by by which his speed is reduced in the remaining [tex]\frac{3}{5}[/tex] of the distance because of rain = 20 km/h
The duration of the trip = 11 hours
Required:
How fast Mr. Jones was driving during the rainy part of his trip from City
B to City A?
Solution:
Let v represent the constant speed, we have;
[tex]Time = \mathbf{ \dfrac{Distance}{Speed}}[/tex]
The distance for which his speed is v = ([tex]\frac{2}{5}[/tex] + 1) × 400 km = 560 km
Total distance of the round trip = 400 km + 400 km = 800 km
The distance for which the speed = v - 20 = 800 km - 560 km = 240 km
Therefore, we have;
[tex]\mathbf{\dfrac{560}{v} + \dfrac{240}{v - 20}}= 11[/tex]
Which gives;
[tex]\mathbf{\dfrac{560 \times (v - 20) + 240 \cdot v}{v\times (v - 20) } } = 11[/tex]
11 × (v² - 20·v) = 560·v - 20 × 560 + 240·v
11·v² - 220·v - 560·v - 240·v + 11200
11·v² - 1020·v + 11,200 = 0
Using the quadratic formula, to solve the above quadratic equation we have;
[tex]v = \dfrac{1020 \pm\sqrt{(-1020)^2 - 4 \times 11 \times 11200} }{2 \times 11} = \dfrac{1020 \pm740 }{22} = \mathbf{ \dfrac{1020 \pm740 }{22}}[/tex]
v = 80 or v = [tex]12 . \overline{72}[/tex]
The possible value for the constant speed is therefore;
v = 80 km/h
The speed during the rain = v - 20, which gives;
The speed during the rain = 80 km/h - 20 km/h = 60 km/hLearn more about quadratic formula here;
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How many different 5 digit natural numbers are there starting with odd numbers or ending with even numbers.
if marvin bought 490 soda cans and candy bars, where the ratio is 3:4, respectively, how many of each did marvin buy?
9514 1404 393
Answer:
210 soda cans280 candy barsStep-by-step explanation:
The 3+4 = 7 ratio units represent the total of 490 snacks, so each ratio unit represents 490/7 = 70 snacks.
The number of soda cans is 3·70 = 210.
The number of candy bars is 4·70 = 280.
Marvin bought 210 soda cans and 280 candy bars.
Hallar la ecuación de la recta (2,3) y (1,-2)
Answer:
[tex]y=5x-7[/tex]
Step-by-step explanation:
the points -6/5 and -5/6 will line in which quadrant
A negative x is to the left of the y axis and a negative y value is below the x axis. Any value to the left and below the axis’ will be in the 3rd quadrant.
Answer: 3rd quadrant
WILL MARK YOU IF YOU HELP ME !!!!
Answer:
Perpendicular bisector
Answer:
perpendicular bisector
Express in roster form. Set of B is the set of all elements x such that x is an element of natural numbers and x is a multiple of 8
=========================================================
Explanation:
The set of natural numbers is {1,2,3,...} basically anything positive and a whole number.
Any multiple of 8 is of the form 8x. Since x is a natural number, the smallest it can be is x = 1 which corresponds to 8x = 8*1 = 8. So 8 is the first multiple of the set. Then 16 is next because 8x = 8*2 = 16, and so on.
That's how we end up with {8, 16, 24, 32, ...}
The three dots, or ellipses, tell the reader that the pattern goes on forever. This set is infinitely large. We wouldn't stop at 800 because we could plug in say x = 200 to get 8x = 8*200 = 1600 and that's a multiple of 8.
i need to see the steps for simplifying 3(m-5)+m
Answer:
4m - 15
Step-by-step explanation:
a( x + y) = ax + ay
[tex]3( m - 5 ) + m\\\\3m - 15 + m \\\\4m - 15[/tex]
Answer:
4m-15
Step-by-step explanation:
Distrubite 3 through the parentheisis
3m-15+m
Collect like terms
4m-15
I can clean my apartment in two hours. My roommate could clean it in three hours. How long will it take use the clean the apartment if we work together?
Answer:
So in this question you want the average because both of y'all are working together. To take the average you want to multiply 2x3=6/2=3
3 hours if y'all work together!
Step-by-step explanation:
A circle has a circumference of 28 centimeters. If an arc subtends a central angle of 55 degrees, what is the arc length?
A.4.28 centimeters
B.26.88 centimeters
C.53.76 centimeters
D.8.56 centimeters
Answer:
s = 4.28 cm (Answer A)
Step-by-step explanation:
1) The formula for the circumference of a circle of radius r is C = 2(pi)r, and this corresponds to a full circle, with central angle 360 degrees.
2) Here the circumference is 28 cm. Therefore, solving for the radius involves the following calculation: 28 cm = 2(pi)r, or
r = (28 cm) / (2 pi), or (28 cm) / 6.28 = 4.46 cm.
3) The arc length s = r(theta), when the central angle (theta) is 55 degrees, is (55/360) times the circumference of the circle: (55/360)(28 cm), or
s = 4.28 cm (Answer A)
Two cities are 3450 miles apart. A plane leaves one of them, traveling towards the other at an average speed of 310 miles per hour. At the same time a plane leaves the other, traveling towards the first, at an average speed of 380 miles per hour. How long will it take them to meet?
Answer:
5 hours.
Step-by-step explanation:
let they meet after t hours.
310t+380t=3450
690t=3450
69t=345
t=345/69=5
Crhistine paid $633.68 for a handbag the sales tax in her state is 6.5% what was the price of the hand bag before the sales tax was added
Answer:
Step-by-step explanation:
X * (1.065) = $633.68
X = $633.68/1.065
X= $595.00
The price of the handbag before the sales tax was added is $595
What is sale tax?A sales tax is a tax paid to a governing body for the sales of certain goods and services. Usually laws allow the seller to collect funds for the tax from the consumer at the point of purchase.
Given that, Christine paid $633.68 for a handbag the sales tax in her state is 6.5%
Let the cost of the handbag before sales tax be x,
Therefore,
x + 6.5% of x = 633.68
x + 6.5 / 100 × x = 633.68
x(1 + 6.5 / 100) = 633.68
x(106.5 / 100) = 633.68
x = 633.68 × 100 / 106.5
x = 595
Hence, the price of the handbag before the sales tax was added is $595
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Two parallel lines, e and f, are crossed by two transversals.
What is the measure of <15
m<15 = 77°
m< 15 = 83°
m<15 = 93°
m<15= 97°
9514 1404 393
Answer:
∠15 = 97°
Step-by-step explanation:
At any given transversal of parallel lines, all obtuse angles are congruent, and all acute angles are congruent. Obtuse angle 15 is congruent to the one market 97°.
∠15 = 97°
Which rules of exponents will be used to evallate this expression? Select three options.
Figure ABCD is a rectangle find the value of x
Answer:
Espanol la vecsu
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
The diagonals of a rectangle bisect each other , so
DE = EB , that is
7x - 1 = 2x + 4 ( subtract 2x from both sides )
5x - 1 = 4 ( add 1 to both sides )
5x = 5 ( divide both sides by 5 )
x = 1
HELP ME PLSSSSSS
if f(x) = 2x-3/5 , which of the following is the inverse of f(x)?
Find the volume of this rectangular pyramid.
Be sure to include the correct unit in your answer.
6 m
3 m
9 m
Answer:
54 m^3
Step-by-step explanation:
this is the answer = 54 m^3
Volume of the rectangular pyramid will be 54[tex]m^{3}[/tex].
What is Rectangular Pyramid?Rectangular pyramid has 5 faces where one face is rectangular which is at bases and other 4 faces are triangular which is connected at the one point .
How to calculate the volume of the rectangular pyramid?If we assume that l is the length of the base and b is the width of the base and h is height of the rectangular pyramid then we can calculate the volume of the rectangular pyramid using the formula stated below
Volume of the rectangular pyramid = V= (1/3)×l×b×h
According to the asked question
l = 6m
b = 3m
h = 9m
then we can calculate the volume of the rectangular pyramid by using the above formula
= V= (1/3)×l×b×h
= (1/3)×6m×3m×9m
= 54[tex]m^{3}[/tex]
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Will mark BRAINLIEST!! This is pt.2
Answer:
See below.
Step-by-step explanation:
Problem 3.
1. <3, <4
Given
2. <1, <2
Given
3. KG
Congruence of segments is reflexive.
4. HKG, LKG
ASA
Problem 4.
1. MR, OR
Given
2. PR, NR
Given
3. <2
Vertical angles are congruent.
4. MPR, ONR
SAS
Xác suất xảy ra môt sự kiện là 0.3. Xác suất để sự kiện đó không xảy ra là?
Câu trả lời:
0,7
Giải thích từng bước:
Xác suất để một sự kiện xảy ra = 0,3
Cho sự kiện = A
P (A) = 0,3
Xác suất mà sự kiện không xảy ra có thể thu được bằng cách sử dụng quy tắc bổ sung;
P (A ') = 1 - P (A)
Vì thế,
P (A ') = 1 - 0,3 = 0,7
27/7n > 4/3 select all the value of n that make the inequality true
A. 2/5
B. 1/5
C.1
D.2/9
E. 3/2
Answer:
A ajjajsjsjsjajsiyisisksksk
Simplify the expression √(4-1)^2+(3+1)^2 using the order of operations.
Answer:
[tex]\sqrt{\left(4-1\right)^2}+\left(3+1\right)^2[/tex]
[tex]\longmapsto \sqrt{(4-1)^2} =3[/tex]
[tex]\longmapsto (3+1)^2=4^2[/tex]
[tex]\hookrightarrow 3+4^2[/tex]
[tex]\hookrightarrow 4^2=16[/tex]
[tex]\hookrightarrow 3+16[/tex]
[tex]\hookrightarrow 19\checkmark[/tex]
hope it helps
Answer:
5
Step-by-step explanation:
Given :
[tex]\sqrt{(4-1)^{2} +(3+1)^{2} }[/tex]
Now,
[tex]\sqrt{(3^{2} )+4^{2} } \\\sqrt{9+16}\\\sqrt{25} \\5[/tex]
Answer of the given expression will be 5.
199 rounded up to the nearest hundred
Answer:
199
Step-by-step explanation:
Answer:
It would be 200 because 199 is closer to 200 rather than 100.