Answers
Answer:
The bottom one ....see below
Step-by-step explanation:
Using reference angle of pi/8 and half angle trig identity:
cos ( angle/2) = -sqrt (1 + cos (angle) /2)
cos ( pi/4 / 2) = - sqrt (1+ cos ( pi/4)/2)
cos (pi/8) = - sqrt (1 + sqrt (2) / 2)
= - sqrt (1 + sqrt 2) / sqrt 2 rationalize the denominator
= - sqrt ( sqrt 2 + 2) / 2
re arrange to
- sqrt ( 2 + sqrt2) / 2 the fourth answer
Related Questions
6E and 7 with full explanation
Answers
Answer:
See below ~
Step-by-step explanation:
Question 6(e) :
⇒ x² ≤ 16
Take square root on each side :
⇒ √x² ≤ √16
⇒ x ≤ 4 and x ≥ -4
⇒ -4 ≤ x ≤ 4
⇒ x² ≤ 16
Apply the absolute rule if x² < a then -√a < x < √a
⇒ -√16 ≤ x ≤ +√16
⇒ -4 ≤ x ≤ 4
Part 7First of all, The student should have subtracted both sides by 4
What he should have done:
[tex]\rightarrow \sf \dfrac{3}{x-2} > 4[/tex]
[tex]\rightarrow \sf \dfrac{3}{x-2} -4 > 4 -4[/tex]
[tex]\rightarrow \sf \dfrac{3}{x-2} -\dfrac{4(x-2)}{x-2} > 0[/tex]
[tex]\rightarrow \sf \dfrac{3-4(x-2)}{x-2}} > 0[/tex]
[tex]\rightarrow \sf \dfrac{3-4x+8}{x-2}} > 0[/tex]
[tex]\rightarrow \sf \dfrac{-4x+11}{x-2}} > 0[/tex]
[tex]\sf \large \boxed{\sf {\left \{ {{-4x+11 = 0} \atop {x-2 = 0}} \right. }}[/tex]
⇒ -4x + 11 = 0, x - 2 = 0
⇒ -4x = -11, x = 2
⇒ x = 11/4 , x = 2
Solution satisfying the inequality:
⇒ 2 < x < 11/4
By using a problem-solution structure, the author is able to show readers how people are hurting the planet. The structure also shows how we can change and what we can do to help solve the problems we have caused. It inspires people to take action
Answers
Answer:
One of the problems humans have made is a large amount of pollution.
And so some of the ways we can fix this is;
1- Using electric cars.
2- Using reusable packaging.
3- For the final one you could use stuff that easily and quickly to break down naturally materials.
Step-by-step explanation:
In a class of 28 students, 21 have a cat and 9 have a dog. There are 7 students who
have a cat and a dog. What is the probability that a student has a dog given that they
do not have a cat?
Answers
The probability that a student has a dog given that they do not have a cat is 1/14.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
In a class of 28 students, 21 have a cat and 9 have a dog.
There are 7 students who have a cat and a dog.
The probability that a student has a dog given that they do not have a cat
= 2/ 28
= 1/14
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Which expression is equivalent to – 2 log2 x + 4 log2 y + 4 log2 z? log base 2 of the quantity x squared y to the fourth all divided by z to the fourth log base 2 of the quantity y to the fourth z to the fourth all divided by x squared log base 2 of the quantity y times z to the fourth all divided by x squared log base 2 of the quantity yz divided by x end quantity raised to the sixth
Answers
The expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².
To answer the question, we need to know the laws of logarithm
Laws of logarithmpower law - nlogₐx = logₐxⁿaddition law - logₐx + logₐy = logₐxySince we want to find the expression equivalent to -2log₂x + 4log₂y + 4log₂z, we simplify using these laws, we have
-2log₂x + 4log₂y + 4log₂z = log₂x⁻² + log₂y⁴ + log₂z⁴ (appying the power law)
= log₂x⁻²y⁴z⁴ (applying the multiplication law)
= log₂y⁴z⁴/x²
= log₂(yz)⁴/x²
So, the expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².
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Answer:
C.log_2(yz^4/x^2)
Step-by-step explanation:
I took the Algebra exam
HELP WITH THE RIGHT ASNWER FOR BRAINLIEST!!!!
Graph the line with slope 3 passing through the point (2,1).
Answers
From the set {1, 2, 3, 4}, use substitution to determine which value of x makes the equation true. 4x = 8
Answers
Substitute each number into equation
4x = 8
4 (1) = 8. No
4 (2) = 8. Yes
4 (3) = 8. No
4 (4) = 8. No
A cylinder has a base radius of 9 feet and a height of 4 feet. What is its volume in
cubic feet, to the nearest tenths place?
Answers
The volume of the cylinder will be equal to 1017.87 cubic feet.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. For the cylinder, the volume will be calculated by radius and the height of the cylinder.
Given that:-
The volume of the cylinder will be calculated by using the formulas below:-
V = πr²h
V = π ( 9 )² 4
V = 1017.87 cubic feet.
Therefore the volume of the cylinder will be equal to 1017.87 cubic feet.
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What percent of the first 20 natural numbers are prime one-digit numbers?
Answers
Answer:
5%
Step-by-step explanation:
The first 20 single digit first numbers are 2,3,5 and 7. Thus they are four.
So next we calculate the percentage:
⇒ 4 × 100% = 1 × 100% = 5%
20 20
The table lists the test scores William and Andre received on five math assessments.
William’s Scores Andre’s Scores
89
90
97
74
78
73
81
87
91
82
Which statement best describes the difference of the mean of the two data sets?
Answers
statement best describes the difference of the mean of the two data sets 2.8 is about 1.5 times the mean absolute deviation of either set.
What is mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
The mean of William's set.
To find the mean, add all of the data points together and divide by the number of data points:
=89+90+97+74+78/5
=85.6
Now, mean absolute deviation,
=|89-85.6|+|90-85.6|+|97-85.6|+|74-85.6|+|78-85.6|/5
= 3.4+4.4+11.4+11.6+7.6/5
=7.68.
The mean of Andre's set.
To find the mean, add all of the data points together and divide by the number of data points:
=73+81+87+91+82/5
=82.8
Now, mean absolute deviation,
=|73-82.8|+|81-82.8|+|87-82.8|+|91-82.8|+|82-82.8|/5
=9.8+1.8+4.2+8.2+0.8/5
= 4.96.
Hence, the difference between the means of the two sets is
85.6-82.8=2.8.
2.8 is about 1.5 times the mean absolute deviation of either set.
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Answer:
Step-by-step explanation:
nothing im just as lost as everyone else
Sheila counted 9 blue jays and 21 sparrows at the bird feeder. What was the ratio of blue jays to sparrows?
Answers
Answer:
9/21
= 1/7
Step-by-step explanation:
ratio means the comparison of two things
A tower, 50 feet high, is secured with a guy wire anchored 8
feet from the base of the tower. What angle will the guy wire
make with the ground?
Answers
The tangent of an angle is the ratio of perpendicular to the base. The angle will the guy wire makes with the ground will be 80.91°.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
A tower, 50 feet high, is secured with a guy wire anchored 8 feet from the base of the tower.
The angle will the guy wire makes with the ground will be given by the tangent.
The tangent of an angle is the ratio of perpendicular to the base.
Then we have
tan θ = 50/8
tan θ = 6.25
θ = tan ⁻¹ (6.25)
θ = 80.9097
θ ≅ 80.91°
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this is probability can someone please give me an answer
Answers
Answer:
The experimental probability is 4%
Step-by-step explanation:
50pts PLEASE HURRY UP I WILL GIVE BRAINLEST SHOW ALL OF YOUR WORK ANSWER ALL THE QUESTIONS
Use the spinner to answer the practice problems below:
Alice spins the spinner 2 times
What is the probability that the spinner stops on A and then B. or on B and then A?
Maria will spin the arrow on the spinner 2 times.
What is the probability that the arrow will stop on the same letter twice?
Answers
Answer:
In two spins, there are 9 possible outcomes: AA, AB, AC, BA, BB, BC, CA, CB, CCIf we assume each of these is equally likely, then the probability of AB or BA is ... 2/9
Step-by-step explanation:
Use the functions a(x) = 7x + 10 and b(x) = 12x - 18 to complete the function operations listed below.
Part A: Find (a + b)(x). Show your work.
Part B: Find (a - b)(x). Show your work.
Part C: Find (a - b)(x). Show your work.
Part D: Find a[b(x)]. Show your work.
Answers
The value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively
Sum and difference of functionsGiven the following functions a(x) = 7x + 10 and b(x) = 12x - 18
Take the sum
(a+b)(x) = a(x) + b(x)
(a+b)(x) = 7x + 10 + 12x - 18
(a+b)(x) = 19x- 8
Take the difference
(a-b)(x) = a(x) - b(x)
(a-b)(x) = 7x + 10 - 12x + 18
(a-b)(x) = -5x + 28
For the composite function a[b(x)].
a(12x- 18) = 7(12x-18) - 10
a[b(x)] = 84x - 126 - 10
a[b(x)] = 84x - 136
Hence the value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively
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You bought 3 pounds of strawberries and 1 pound of blueberries for $8.40 to make pies for the summer festival. Your friend helped and bought 2 pounds of strawberries and 2 pounds of blueberries for $10.08. How much did a pound of blueberries cost? Let the cost of each pound of strawberries =x and the cost of each pound of blueberries = y
Answers
Step-by-step explanation:
3x + y = 8.4
2x + 2y = 10.08
x + y = 5.04
y = 5.04 - x
we use this then in the first equation
3x + 5.04 - x = 8.4
2x = 3.36
x = 3.36/2 = $1.68
y = 5.04 - x = 5.04 - 1.68 = $3.36
blueberries cost $3.36 per pound.
Nayeli lights a 4\,\text{m}^24m 2 4, start text, m, end text, squared space with 121212 candles. Citlali lights a 10\,\text{m}^210m 2 10, start text, m, end text, squared space with 303030 of the same type of candles. Whose space is lit brighter? Choose 1 answer: help me im graded at this
Answers
Using proportions, it is found that both spaces have the same brightness, as both have 3 candles per m².
The correct question is as given below:-
Nayeli lights a 4 square meter space with 12 candles. Citlali lights a 10 square meter space with 30 of the same type of candles. Whose space is lit brighter? Choose 1 answer: help me im graded at this
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For Nayeli and Citlali, the rate of candles per m² is given by:
N = 12/4 = 3 candles per m².
C = 30/10 = 3 candles per m².
Hence both spaces have the same brightness, as both have 3 candles per m².
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Find the slope of a line parallel to the line that passes through (-4, -1) and (-1, 3)
Answers
Answer:
[tex] \boxed{\rm \: Slope(m)= \cfrac{4}{ 3} }[/tex]
OR
[tex] \boxed{\rm \: Slope(m) \approx \: 1.30} \rm \: (nearest \: tenth)[/tex]
Step-by-step explanation:
Given two coordinates:
(-4, -1) and (-1, 3)To Find:
The slope of given two coordinatesSolution:
In this case,we'll need to use the slope's formula,to get the slope.
Here's the formula:
[tex] \rm \: Slope(m)= \: \cfrac{ y_2 -y_1 }{x_2 - x_1} [/tex]
Slope is usually denoted as m.According to the question:
[tex] \rm (y_2 , y _1) = (3,-1)[/tex][tex]\rm (x_2 , x_1) = (-1,-4)[/tex]Substitute them accordingly:
[tex] \rm \: Slope(m)= \cfrac{3 - ( - 1)}{ - 1 - ( - 4)} [/tex]
Simplify then, using a rule called PEMDAS.
[tex] \rm \: Slope(m)= \cfrac{3 + 1}{ - 1 +4 } [/tex]
[tex] \rm \: Slope(m)= \cfrac{4}{ 3} [/tex]
[tex] \rm \: Slope(m) \approx \: 1.30[/tex]
Hence, we can conclude that:
The slope of a line parallel to the line that passes through (-4, -1) and (-1, 3) is 4/3 in exact form and 1.30 in approximate decimal form.Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of a line parallel to the line that passes through
[tex]\star~\mathrm{(-4,-1)}\star[/tex]
[tex]\star~\mathrm{(-1,3)}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The slope formula will help us out! :)Here's the formula:
[tex]\star\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]
y2 and y1 are y-coordinates
x2 and x1 are x-coordinates
Substitute the given values:
[tex]\star\mathrm{\cfrac{3-(-1)}{-1-(-4)}}[/tex]
Simplify!
[tex]\star\mathrm{\cfrac{3+1}{-1+4}}[/tex]
Simplify more!
[tex]\star\mathrm{\cfrac{4}{3}}[/tex]
Now, what is the slope of the line parallel to this one?
Well, parallel lines have the same slope.
[tex]\star \ \mathrm{The \ slope \ of \ the \ line \ parallel \ to \ this \ one \ is \ \cfrac{4}{3}}.[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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If f(n) = 2n^2 + 2 and g(n) = n + 1, what is (f -g)(n) when n = -1?
Answers
2n^2+2-n-1 => 2n^2-n+1
now we replace n with -1
2(-1)^2-(-1)+1 => 2+2=4
"4" is teh final answer
Activity 2 :Collect the information on any one of the famous Mathematician :a) b) Bhaskara c) Shri Niwasan Ramanujan Aryabhatta please
Answers
Answer:
Bhāskara was a 7th-century mathematician and astronomer, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.
Aryabhatta is the father of Indian mathematics. He was a great mathematician and astronomer of ancient India. His major work is known as Aryabhatiya. It consists of spherical trigonometry, quadratic equations, algebra, plane trigonometry, sums of power series, arithmetic.
Step-by-step explanation:
hope it helps you and give brainliest
i needs help with it please
Answers
The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )
Meaning of congruent trianglesA triangle can be defined as a plain shape that has three sides and three angles.
Congruent triangles are triangles that satisfy one or more congruence postulates or laws. The triangles could either be similar based on their angles or sides or angles and side being similar.
In conclusion, The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )
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Write the converse of the statement
below.
If it is 9 a.m., then I am awake.
Answers
Answer:
if I am awake then it is 9 am.
Step-by-step explanation:
if p then q the converse is if q then p.
CAN SOMEONE HELP ME PLEASE? I’LL GIVE YOU FREE EASY POINTS IF YOU GIVE ME THE RIGHT ANSWER.. NO WRONG ANSWERS PLS!!
Answers
see the attachment..........
Work out the value of y in the equation
below.
бу
6y = 44 - 5у
Answers
Answer: Y = 6 1/2
Step-by-step explanation: Let's begin,
step 1) Isolate the variable by dividing each side by factors that don't contain the variable.
Then, Exact Form:
y = 13/2
Decimal Form:
y = 6.5
Mixed Number Form:
y = 6 1/2
need help would be apperacited .
Answers
A function on a graph to figure it out you can do the line test where you draw a line through the graph and if the line touches two points its not a function. With this in mind bottom right is for sure one and the top left looks like one but i cant really tell...
Step-by-step explanation:
Decagon, a=22 m, s=14.3 m
Answers
The area of the decagon is 1573.39 square meters
How to determine the area of the decagon?The given parameters are:
Side length, s = 14.3 mApothem, a = 22 mThe area of a decagon is calculated using:
[tex]A = \frac 52s^2\sqrt{5 + 2\sqrt 5[/tex]
Substitute 14.3 for s
[tex]A = \frac 52 * 14.3^2\sqrt{5 + 2\sqrt 5[/tex]
Evaluate the exponent
[tex]A = \frac 52 * 204.49\sqrt{5 + 2\sqrt 5[/tex]
Evaluate the product and the roots
A = 1573.39
Hence, the area of the decagon is 1573.39 square meters
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What is the value of x???
Answers
The given polygon isa pentagon and the sum of its exterior angle is 360°. The value of x from the given polygon is 8
Sum of the exterior angle of a polygonThe given polygon isa pentagon and the sum of its exterior angle is 360°.
Take the sum of the angles and equate to 360° as shown;
77 + 66 + 62+ 59 + 12x = 360°
264 + 12x = 360
12x = 96
x = 8
Hence the value of x from the given polygon is 8
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Two dice are rolled. Event A is that the sum of the numbers is 7 or 11. Event B is that the sum of the numbers is 11 or 12. Find the probability of Event A or B(A union B)
Answers
Answer:
the probability is %25 percent :P
Step-by-step explanation:
-6 3/5 - (-7 4/15) + 2 1/5
Answers
The answer to your question would be 43/15 or 2.866 and ongoing.
What is the value of x? 2 3 6 7
Answers
Answer:
6
Step-by-step explanation:
Answer:
2 or A
Step-by-step explanation:
Correct on edge22
ch of these is the absolute value parent function?
A. f(x) = x
B. f(x) = x^2
C. f(x) = |x|
D. f(x) = 2^x
Answers
Answer:
[tex] \text{C.} \: f(x) \: = \: |x| [/tex]
Step-by-step explanation:
To identify the absolute value of a number, it will always be represented between two sticks.
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