Answers
The exact value of the trigonometric function by half-angle formula is cos 22.5° = √(2 + √2) / 2. (Correct choice: B)
How to determine the exact value of a trigonometric function
In this problem we are asked to determine the exact value of a trigonometric function by means of a trigonometric formula known as half-angle formula:
cos 0.5θ = √[(1 + cos θ) / 2]
If we know that θ = 45°, then the exact value of the half-angle formula:
cos 22.5° = √[(1 + cos 45°) / 2]
cos 22.5° = √[(1 + √2 / 2) / 2]
cos 22.5° = √(2 + √2) / 2
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Related Questions
Help me solve this pretty please. Doesn't make sense to me
Answers
Answer:
[tex]A \approx 421.1[/tex]
Step-by-step explanation:
We can split this figure into two simpler shapes:
a parallelogram anda semicircleFirst, we can find the area of the parallelogram.
[tex]A_\square = b \cdot h[/tex]
[tex]A_\square = 24 \cdot 11[/tex]
[tex]A_\square = 264[/tex]
Next, we can find the area of the semicircle. We know that its diameter ([tex]2r[/tex]) is 20 because opposite sides of a parallelogram are the same length. Therefore, its radius is [tex]20 \div 2 = 10[/tex].
[tex]A_\circ = \dfrac{1}{2} \cdot \pi r^2[/tex]
[tex]A_\circ = \dfrac{1}{2} \cdot \pi (10)^2[/tex]
[tex]A_\circ = \dfrac{1}{2} \cdot 100 \pi[/tex]
[tex]A_\circ = 50\pi[/tex]
Finally, we can find the area of the entire figure by adding the areas of each of its parts.
[tex]A = A_\square + A_\circ[/tex]
[tex]A= 264 + 50\pi[/tex]
[tex]\boxed{A \approx 421.1}[/tex]
Activity
Each month, Stacey places a portion of her earnings in a retirement account. Her savings are invested in two companies. For every $9 invested in company A, $2 is invested in company B. Stacey quizzes her children, Krista and Kevin, about how much money she will invest in company A if she invests $24 in company B.
Krista and Kevin used two different methods to arrive at the answer to Stacey’s problem. Let’s see who found the correct answer and how. You’ll answer some questions along the way.
Part A
What is the ratio of the amount invested in company A to the amount invested in company B? Write the answer as a fraction using the values given. Do not include any variables.
Answers
the ratio of the amount invested in company A to the amount invested in company B is 9:2 or simply say 9/2 fraction.
What is the ratio of the amount?Based on the information in the question, for every $9 invested in company A, $2 is said to be invested in company B. So, from the above, the ratio of the amount invested in company A to the amount invested in company B can be written aa:
$9 : $2
One can express this ratio as a fraction, and thus it is written as:
9/2
Therefore, the ratio of the amount invested in company A to the amount invested in company B is 9/2.
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Factor the following expression.
OA. (5-7) (2x + 1)
OB. (523
(5x³7) (2x² + 1)
OC. (5x³ + 7) (2x² - 1)
D.
(5x + 7) (2x - 1)
Answers
Answer:
B
Step-by-step explanation:
(5׳-7)(2x²+1)
=10x⁵+5x³-14x²-7
What is the mean of 47, 47, 26, 73, 61
Answers
Answer:
50.8
Step-by-step explanation:
To find the mean, add the values, and then divide by the number of data points.
1. 47+47+26+73+61=254
2. 254/5=50.8
Answer:
42 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
47+47+26+73+61=254
254÷6=42.333333 or 42 [tex]\frac{1}{3}[/tex]
What is the meaning of "[tex]\varnothing =\left \{ u:u\neq u \right \}[/tex]"?
Answers
y is inversely proportional to x
when y=7,x=9
a) work out an equation connecting y and x.
b) workout the value of y when x=21
Answers
(a) The equation connecting y and x is y = 63/x
(b) the value of y is 3
a) work out an equation connecting y and x.From the question, we have the following parameters that can be used in our computation:
Inverse proportion
An inverse proportion is represented as
y = k/x
Where
k = constant of variation
Using the values, we have
7 = k/9
So, we have
k = 63
So, the equation is
y = 63/x
b) workout the value of y when x=21This means that
y = 63/x
So, we have
y = 63/21
Evaluate
y = 3
Hence, the value of y is 3
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can you find the slope and if you I will make a brailest
Answers
Explanation: You count the rise over run and get 2/1, which equals 2.
Answer:
is 2
Step-by-step explanation:
Unit 8 right triangles and trigonometry homework 2 special right triangles
Answers
Answer:
what are the advantages of standard contract
can you help me solve these and you will be made brainlest
Answers
In the given graph, the slope of the line is 2
Calculating the slope of a lineFrom the question, we are to determine the slope of the line in the diagram.
The diagram shows a straight line of the graph.
To determine the slope of the line, we will determine two points on the line and then use the slope formula to determine slope.
The slope is
Slope = Change in y / Change in x = (y₂ - y₁) / (x₂ - x₁)
Picking the points (-1, -1) and (0, 1)
Thus,
Slope = (1 - (-1)) / (0 - (-1))
Slope = (1 + 1) / (0 + 1)
Slope = 2/1
Slope = 2
Hence,
The slope of the line is 2
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How do i solve this question?
Answers
To find the volume of one ice cube use volume formula and plug in the given values.
2. You flip a fair, two-sided coin 100 times. Define a ‘run’ as a sequence of coin flips with the same value (heads or tails). for example, the sequence HTTHH has 3 runs: the first H, then the TT block, then the HH block.
Let X be the number of runs we observe in n flips. We’ve discussed how to find E(X) using indicators. Now, approximate E(X) for large n by imagining this process as a Markov Chain.
Answers
For example, if the current state is "HH" and the next flip is a tails, the state transitions to "HHT." We can represent these transitions as a transition matrix, where the probability of transitioning from state i to state j is simply the probability of observing a coin flip that extends from the last run in i to the new run in j. For example, the probability of transitioning from "HH" to "HHT" is 1/2, since the next flip can be either heads or tails.
Using this Markov chain framework, we can approximate E(X) as the expected number of transitions required to reach the absorbing state where all flips are in the form of one long run. This is because once we reach this absorbing state, we have observed all possible runs and no further transitions are possible.
Using the transition matrix, we can find the expected number of transitions required to reach the absorbing state by solving a system of linear equations. Specifically, we can find the expected number of transitions from state i to the absorbing state by setting up the system of equations:
E(T_i) = 1 + p_ij*E(T_j) where j is some state that can be reached from i with probability p_ij.
We can then solve for E(T_i) for all possible states i using matrix inversion. The expected number of runs observed in n flips is then given by the sum of the expected number of transitions required to reach the absorbing state from each possible starting state, weighted by the probability of starting in that state.
Simplify express your answer as a single term without a denominator cd3•c-5d-2
Answers
The simplified expression is d/ c⁴.
To simplify the expression cd³ c⁻⁵ x d⁻², we can combine the variables with the same base (c and d) by adding their exponents:
Using the property of exponents as
Product Rule:When multiplying two exponential expressions with the same base, you can add the exponents. This can be expressed as follows:
aᵇ x aⁿ= aᵇ⁺ⁿ
Quotient Rule:When dividing two exponential expressions with the same base, you can subtract the exponents. This can be expressed as follows:
aᵇ / aⁿ= aᵇ⁻ⁿ
So, cd³ c⁻⁵ x d⁻²
= c¹⁻⁵ x d³⁻²
= c⁻⁴ x d¹
= dc⁻⁴
Again from the property of exponents
a⁻ᵇ = 1/aᵇ
So, dc⁻⁴
= d/ c⁴
Therefore, the simplified expression is d/ c⁴.
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Let f(x) = 3x+4 and g(x) = 2x². Perform the function operation and then find the domain of the result.
(f+g)(x)
(f+g)(x)= ___ (simply your answer)
Answers
The composition of the functions is solved and ( f + g ) ( x ) = 2x² + 3x + 4
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 3x + 4
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = 2x²
Now , the composition of functions is
( f + g ) ( x ) = f ( x ) + g ( x )
( f + g ) ( x ) = 2x² + 3x + 4
Hence , the function is ( f + g ) ( x ) = 2x² + 3x + 4 and domain of the function is all real numbers (-∞, ∞).
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Tanya performs two transformations on ABC to form A"B" and C" as shown on the coordinate grid below.
Answers
the transformation ABC is not similar to A”B”C”. hence the statement is false.
How do we know?We say the statement is false because the ratios of the grid squares are not similar.
We notice that the first triangle is up to over 3 and the other triangle is up 4 over 4 so in order for them to be similar the first triangle would have to be up 3 over 3.
A transformation is described as a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
#complete question:
Please help this is due today and I’m so stressed!I will mark Branliest!!!
Tanya performs two transformations on ABC to form A"B"C" as shown on the coordinate grid below.
True or False:ABC is similar to A”B”C”?
a + b=c make (a) the subject with working
Answers
Step-by-step explanation:
a= c-b pls let me know if it is correct or not
Question 14 (1 point)
Chris sells computer equipment for his company. He receives a base pay of $300
plus commission on his sales. He receives 10% for the first $5000 in sales and 15%
anything over $5000.
Last week, he sold $17000 in computer equipment. Find his gross pay.
Round to the nearest whole dollar.
For your answer, do NOT include symbols, commas, words, etc.
HELP PLS
Answers
Chris' gross pay for the week after selling computer equipment worth $17,000 is $2,600.
How is the gross pay determined?The gross pay is the addition of the base pay and the sales commission.
The sales commission is graduated and computed as follows:
Chris' base pay = $300
Sales Commissions:
First $5,000 = 10%
Above $5,000 = 15%
Last week's sales = $17,000
10% Commission = $500 ($5,000 x 10%)
15% Commission = $1,800 ($17,000 - $5,000 x 15%)
Total Commission = $2,300
Gross pay = Base Pay + Commission
= $2,600 ($300 + $2,300)
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The hole needs to be twice as wide as the diameter of the root ball and deep enough for the entire root ball to fit inside. After placing the tree in the hole, Mahari will fill the rest of the hole with soil.
Answers
Mahari needs 3.97 cubic feet of soil to fill the hole.
Convert the diameter of the root ball from inches to feet:
Diameter = 18 inches = 18/12 feet = 1.5 feet
Since the hole needs to be twice as wide as the diameter, the width of the hole would be 2 times the diameter:
Width = 2 × Diameter = 2× 1.5 feet = 3 feet
The depth of the hole is the same as the height of the root ball, which we don't have information about.
Volume = π × (radius)² × height
Let's assume the height of the root ball is 1.5 times the diameter:
Height = 1.5 × Diameter = 1.5 × 1.5 feet = 2.25 feet
Now we can calculate the approximate volume of the hole:
Volume = π × (radius)² × height
= π × (1.5/2)² × 2.25 cubic feet
= 2.25 × 1.77 cubic feet
= 3.97 cubic feet
Therefore, Mahari needs 3.97 cubic feet of soil to fill the hole.
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I WILL GIVE BRAINLYEST
Answers
Answer:
The answer is C.
I counted the rows by 4s and got 48.
Step-by-step explanation:
thr answer is c, just count
ƒ(t) = –1∕2t2 + 2t + 6
Answers
This function represents a downward-opening parabola with a vertical shift of 6 units upward.
How to explain the functionThe given function is Ƒ(t) = –1/(2t²) + 2t + 6.
This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.
Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.
So, the function Ƒ(t) can be written as:
Ƒ(t) = (-1/2)t² + 2t + 6
This function represents a downward-opening parabola with a vertical shift of 6 units upward.
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100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answers
The solution set to the trigonometric equation 3 · cos² θ - sin² θ = 0 are θ = π / 3 ± i · π or θ = - π / 3 ± i · π, where i is a whole number.
How to solve a trigonometric equation
Herein we find the case of a trigonometric equation, whose solution set can be found both by algebra properties and trigonometric formulas:
3 · cos² θ - sin² θ = 0
3 · cos² θ = sin² θ
tan² θ = 3
tan θ = ± √3
θ = π / 3 ± i · π or θ = - π / 3 ± i · π, where i is a whole number.
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Select each expression that is equivalent to 18x + 3.
A. 6(3x + 1/2
)
B. 9(2x + 1/3
)
C. 4(4x + 1) – 1
D. 2(9x + 5) – 7
E. 3(6x + 2) + 3
--Please tell me which ones are correct ASAP--
Answers
A. 6(3x + 1/2) simplifies to 18x + 3
B. 9(2x + 1/3) simplifies to 18x + 3
D. 2(9x + 5) - 7 simplifies to 18x + 3
E. 3(6x + 2) + 3 simplifies to 18x + 3
Expression C is not equivalent to 18x + 3. It simplifies to 15x + 3.
PS: give more points when saying ASAP or no one will do it
101. A number cube with sides labeled 1 through 6 is rolled two times, and the
sum of the numbers that end face up is calculated. What is the probability that the
sum of the numbers is 3?
A.) 1/18
B.) 1/12
C.) 1/9
D.) 1/2
Answers
1/18 is the probability that the sum of the number is 3.
The number of favourable outcomes (where the sum is 3) and the total number of potential outcomes must be determined in order to calculate the likelihood that the sum of the numbers rolled on a number cube is 3.
Six possibilities are conceivable for each roll, for a total of six times six or 36 outcomes.
Let's now find the positive results, where the sum is 3:
There are just two events that might happen: (1, 2) and (2, 1).
Therefore, the probability of obtaining a sum of 3 is 2 (favorable outcomes) out of 36 (possible outcomes):
Probability = favorable outcomes / total outcomes
Probability = 2 / 36
Probability = 1 / 18
Thus, the correct answer is A.) 1/18.
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This table shows the numbers of cars owned by 20 different families living in one street.
Number of cars
0
1
2
3
4
Number of families
5
8
4
2
1
a Work out the modal number of cars.
b Work out the mean number of cars per family.
Answers
1. The modal number of cars is 1.
2. The mean number of cars per family is 1.3.
1. From the given table, we can see that the number of cars owned by the highest number of families is 1 (appearing 8 times). Therefore, the modal number of cars is 1.
2. To work out the mean number of cars per family, we need to calculate the average number of cars per family.
= (0 cars x 5 families) + (1 car x 8 families) + (2 cars x 4 families) + (3 cars x 2 families) + (4 cars x 1 family)
= 0 + 8 + 8 + 6 + 4
= 26
So, Mean number of cars per family
= Total number of cars / Total number of families
= 26 / 20 = 1.3
Therefore, the mean number of cars per family is 1.3.
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find the value of 1500 deposited for 15 years in an account paying 3.75% annual interest compounded quarterly.
Answers
Answer:
$2625.69
Step-by-step explanation:
Formula for quarterly compounded interest is A = P (1 + r/4)^4t
Where P is initial amount, t is time in years, r is rate in decimals.
A = 1500 (1 + 0.0375/4)^(4 X 15)
= $2625.69
calculate with reasons the value of a, b and c:
(please help i’d really appreciate it)
Answers
Answer:
Step-by-step explanation:
By first glance, you can see that in line CHF, it has two given and one unknown angle. The total angle of one straight line is 180. Given that:
a = 180 - 50 -70 = 60
The angle intersecting the CHFD line can be computed by the the total angle inside the triangle. Angle on EFH would give 180-40-60 = 80 and on EFD the angle would be 100 from 180-80. Since angle C is congruent to the angle EFD.
c = 100
Take note that in a 4 sided polygon (GEFH), the total exterior angle is 360 degrees.
The different angle would be
angle GHF = 50 + a = 50+60 = 110
angle EFH = 80
angle FEG = 180- c = 180-100 = 80
ANGLE EGH = 360 - GHF -EFH -FEG = 360 - 110-80-80 = 90
since angle AG is congruent to EGH, we can calculate for the angle b which is congruent to its opposite. This would give us formula of
360 = (90+90) + (b) +(b)
360 = 180 +2b
b = 90
If a storage tank is holding 450 litres when it is three quarters full, how much will it contain when it is two thirds?
Answers
Answer:
400 litres
Step-by-step explanation:
Which of the following is closest to the area, in square inches, of the shaded sector of circle Y?
A. 25.7 square inches
B. 51.3 square inches
C. 128.3 square inches
D. 153.9 square inches
And What is the length, to the nearest tenth of an inch, of minor arc XZ?
Blank inches
Answers
Answer is B
The box plots show a summary of scores for Class A and Class B on the same test. Both classes have the same number of students.
Determine whether each statement is true based on these box plots. Select True or False for each statement.
The median score of Class B is at least 10 points less than the median score of Class A.
True or false
At least 25% of students in each class scored less than 70.
True or false
At least 50% of students in each class scored between 75 and 95.
True or false
Answers
True
At least 25% of students in each class scored less than 70.
False
At least 50% of students in each class scored between 75 and 95.
True
Ray deposits $5000 into a savings account that pays 1.4% annual interest compounded quarterly. Enter a function to represent the balance A in the account after t years.
Answers
The function to represent the balance A in the account after t years is [tex]A = 5000(1 + 0.014/4)^(^4^t^)[/tex]
To represent the balance A in the savings account after t years with quarterly compounding, we can use the formula for compound interest
[tex]A = P(1 + r/n)^(^n^t^)[/tex]
Where:
A is the balance in the account after t years,
P is the principal amount (initial deposit),
r is the annual interest rate (as a decimal),
n is the number of compounding periods per year.
Ray deposits $5000, the annual interest rate is 1.4% (or 0.014 as a decimal), and the interest is compounded quarterly (n = 4).
Substituting the values into the formula, we get:
[tex]A = 5000(1 + 0.014/4)^(^4^t^)[/tex]
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Krista designs quilts using the pattern shown. The table of values describes the shaded area of the pattern in square units, y, as a function of the length of a side,X units. Which equation describes this relationship?
Answers
The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²
Modeling relationship between two variablesSide length, x = 1,3,4,5,8
Shaded Area, y = 0.5, 4.5, 8, 12.5, 32
The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c
a = 0.5 ; b = 0 ; c = 0
Therefore, the quadratic function can be written as y = 0.5x²
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