hich function is the same as y = 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2? y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2 y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2 y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2 y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2
Answers
Answer:
B) y = -3 sin(2(x + π/4)) - 2
Step-by-step explanation:
Which function is the same as y = 3 cos(2 (x + π/2)) - 2
A) y = 3 sin(2(x + π/2)) - 2
B) y = -3 sin(2(x + π/4)) - 2
C) y = 3 cos(2 (x + π/4)) - 2
D) y = -3 cos(2 (x + π/2)) - 2
y = 3 cos(2 (x + π/2)) - 2
Sine and cosine have the following relationship:
cos(θ) = sin (π/2 - θ)
y = 3 cos(2 (x + π/2)) - 2
⇒ y = 3 cos(2x + π) - 2
Let θ = 2x + π, therefore using Sine and cosine have the following relationship:
cos(2x + π) = sin (π/2- (2x + π))
= sin (π/2 - 2x - π)
= sin (-2x - π/2)
= sin (-2(x + π/4))
but sin(-θ) = -sin (θ)
Therefore:
sin (-2(x + π/4)) = -sin (2(x + π/4))
⇒ - sin (2(x + π/4)) = cos(2x + π)
y = 3 cos(2x + π) - 2 = 3[ - sin (2(x + π/4))] -2
y = -3 sin (2(x + π/4)) -2
Answer:
b
Step-by-step explanation:
Related Questions
Does someone mind helping me with this problem? Thank you!
Answers
Answer:
y = - \(\frac{1}{4}\) x - 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x - 2 ← is in slope- intercept form
with slope m = 4
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{4}\) , then
y = - \(\frac{1}{4}\) x + c ← is the partial equation
to find c substitute (4, - 11 ) into the partial equation
- 11 = - \(\frac{1}{4}\) (4) + c = - 1 + c ( add 1 to both sides )
- 10 = c
y = - \(\frac{1}{4}\) x + (- 10) , that is
y = - \(\frac{1}{4}\) x - 10 ← equation of line
What is the sum of three fourths and
seven fourths?
Answers
How can you determine the equation that represents this relationship?
Answers
Answer:
FINDING THE EQUATION OF A LINEAR RELATIONSHIP. We can use the points on a graph of a linear relationship to write an equation for the relationship. The equation of a linear relationship is y = mx + b, where m is the rate of change, or slope, and b is the y-intercept (The value of y when x is 0). Example 1 : A handrail runs alongside a stairway. As the horizontal distance from the bottom of the stairway changes, the height of the handrail changes.
If a is a 4×4 matrix with characteristic polynomial λ4+λ3+λ2+λ, then a is not invertible.a. Trueb. False
Answers
The statement is true. If a matrix has a characteristic polynomial of degree n, then it means that it has n eigenvalues, some of which may be repeated.
The determinant of a matrix is equal to the product of its eigenvalues. If any of the eigenvalues are 0, then the determinant is also 0, meaning the matrix is not invertible. In this case, the characteristic polynomial has degree 4, meaning there are four eigenvalues. If we assume that the matrix a is invertible, then all of its eigenvalues are nonzero, which would mean that the determinant of a is nonzero. However, the characteristic polynomial evaluated at λ=0 is 0, meaning that at least one of the eigenvalues is 0, which contradicts the assumption that the matrix is invertible. Therefore, the statement is true.
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A data value is considered _______ if its z-score is less than 2 or greater than 2.
Answers
A data value is considered significantly low or significantly high if its z-score is less than -2 or greater than 2.
What does it mean if z-score is 2?
A positive z-score indicates the raw score is higher than the mean average.For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.A negative z-score reveals the raw score is below the mean average.For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.What does a standard deviation of 2 mean?
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean.In any distribution, about 95% of values will be within 2 standarddeviations of the mean.
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The correct question is -
A data value is considered _______ if its z-score is less than minus−2 or greater than 2.
Bailey has 45 minutes to exercise. It takes Bailey 3 minutes to jog around the track and 5 minutes to stretch. She jogs 6 laps around the track and stretches 2 times. Write and evaluate an algebraic expression to find the amount of time Bailey has left. Use j for the number of laps she jogs and s for the number of times she stretches.
Answers
Answer:
a) Time left = [45 - (3j + 5s)] minutes
b) 17 minutes
Step-by-step explanation:
a) Using j for the number of laps she jogs and s for the number of times she stretches. Since Bailey has a total of 45 minutes to complete his exercise, then;
Time left = [45 - (3j + 5s)] minutes
If she jogs 6 laps and stretches 2 times , then;
Time left = [45 - (3j + 5s)]
b) Where j = 6 and s = 2,
Time left = 45 - (3(6) + 5(2))
= 45 - (18 + 10)
= 45 - 28
= 17
Amount of time Bailey has left is 17 minutes.
What is the range of the following graph? A. {xx 0,E R} B. {yly # 2, ER} C. {yl y = 0,9 € R} D. {x| x + 2 x + R} X" →X 0
Answers
The graph of the function is shown below
The range of a function is the set of all output values (Y-values).
From the graph, the graph is discontinuous on y= 0
Hence there is no output at y = 0
This implies that the range of the function is all real numbers except y = 2
That is
\(\mleft\lbrace y\mright|y\ne2,y\in\mathfrak{\Re }\}\)
Y-2/3x=-6. Find the value of y.
Answers
y-2/3=-6
y-2/3 = -6
+2/3 +2/3
simplify: add the numbers
y=-16/3
hope that helped
a man 6-ft tall walks at a rate of 5 ft/sec away from a lamppost that is 22-ft high. at what rate is the length of his shadow changing when he is 60 feet away from the lamppost?
Answers
The rate of change of the length of the man's shadow when he is 60 feet away from the lamppost is approximately 1.11 ft/sec.
To solve this problem, we can use similar triangles and the chain rule of differentiation. Let y be the length of the man's shadow and x be his distance from the lamppost. Then we have the following ratio of corresponding sides: (6 ft)/(y ft) = (60 ft + x ft)/(22 ft). Solving for y, we get y = (22/6)(60 + x). To find the rate of change of y with respect to time, we differentiate both sides with respect to time and apply the chain rule: dy/dt = (22/6) d/dt (60 + x) = (22/6)(dx/dt). Plugging in the given values, we get dy/dt = (22/6)(5/12) = 1.11 ft/sec. Therefore, the rate of change of the length of the man's shadow when he is 60 feet away from the lamppost is approximately 1.11 ft/sec.
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Given triangle DOG is congruent to triangle CAT, which reason could you use to prove that angle G is congruent to angle T?
Answers
Answer:
The correct option is;
d) CPCTC
Step-by-step explanation:
The phrase Corresponding Parts of Congruent Triangles are Congruent with the acronym CPCTC, is used as valid reasoning in the provision of a proof, after the existence of congruency between two triangles has been proven
Given that the triangles ΔDOG and ΔCAT have been proven congruent, we have that the corresponding vertices are;
Vertex D corresponds to vertex C
Vertex O corresponds to vertex A
Vertex G corresponds to vertex T
Therefore, given that ΔDOG ≅ ΔCAT, we have;
∠D ≅ ∠C by CPCTC
∠O ≅ ∠A by CPCTC
∠G ≅ ∠T by CPCTC.
Help asap please im failing
Answers
Step-by-step explanation:
Convert each fraction by setting up proportion out of 100.
\( \frac{60}{90} = \frac{?}{100} \)
\( \frac{78}{150} = \frac{?}{100} \)
\( \frac{75}{120} = \frac{x}{100} \)
Cross multiply each fraction. let x represent the missing number.
\(6000 = 90x\)
\(7800 = 150x\)
\(7500 = 120x\)
Solve for x
For the first equation.
\(x = 66.66666\)
For the second equation
\(x = 52\)
For the third equation,
\(x = 62.5\)
Round each missing value to the nearest whole value and add the % sign.
60/90=67%
78/150=52%
75/120=63%
He scored the highest on his English test.
On his science test he scored 52%
On his math test he scored 63%
To calculate these you would divide by putting the amount of points he earned over the total possible points. Then convert the decimal to a percentage.
He scored the highest on his english test.
Computation 1. Suppose the number of workers at a company is given by w and the average annual salary per worker is given by S(w) when there are w workers over the year. Then the average annual payroll (in dollars) for the company is given by A(w) where A(w) = w:S(w) = = dA dw a) Find lw=5 if S(5) = 35000 and S'(5) = 2000 b) Briefly interpret lw=5. Be sure to include units and values. dA dw
Answers
When the company has 5 workers and the average salary per worker is $35000, then increasing the number of workers by one will increase the average payroll by $45000.
a) We need to find dA/dw when w = 5 and S(5) = 35000 and S'(5) = 2000.
We know that A(w) = wS(w).
By product rule, dA/dw = wdS/dw + S.
We need to find dA/dw when w = 5.So, dA/dw = 5dS/dw + S ...............................(1)
Given, S(5) = 35000.
So, we know the value of S at w = 5.
Given, S'(5) = 2000.
So, dS/dw at w = 5 is 2000.
Now, putting w = 5, dS/dw = 2000 and S = 35000 in equation (1), we get
dA/dw = 5dS/dw + S= 5 × 2000 + 35000= 45000
Therefore, the value of dA/dw at w = 5 when S(5) = 35000 and S'(5) = 2000 is 45000.b) In part (a), we found that dA/dw = 45000 when w = 5. Therefore, when the company has 5 workers and the average salary per worker is $35000, then increasing the number of workers by one will increase the average payroll by $45000. The units of dA/dw are in dollars/worker. Therefore, if we increase the number of workers by one, then the average payroll will increase by $45000 per worker.
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Select the correct answer. If function f has zeros at -3 and 4, which graph could represent function f?
Answers
Answer:
first one
Step-by-step explanation:
The graph intersects x-axis at (4,0) and (-3,0)
If function f has zeros at -3 and 4 then the first graph represents the function f.
When a function has zeros at -3 and 4, it means that the function's value is equal to zero at those x-values.
In other words, when x = -3 and x = 4, the function f(x) becomes 0.
To represent this on a graph, you should look for two points where the graph intersects the x-axis at -3 and 4.
When the graph crosses the x-axis at these points, it indicates that the function has zeros at those x-values.
When we observe the graphs, the first graph has zeros at -3 and 4.
Hence, the first graph could represent the function f with zeros at -3 and 4.
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Mrs. Rogers sold 49 out of 78 crafts at the fair. What percent of her crafts did she sell? Show your
proportion or equation set-up.
Answers
Answer:
62.8, 63% if you around it off.
Step-by-step explanation: Do 49 Divided by 78, then times it by 100 to get your percentage. I just rounded it off to the nearest tenth and whole number just in case. Hope this helped!
Will GIVE BRAINLIEST IF CORRECT
The diagram shows a convex polygon.
Find the value of a.
Answers
Answer:
The value of a is 15.
Step-by-step explanation:
First, you have to find the total interior angles of the polygon using the formula, sum = (n-2)×180°, where n represents the number of sides :
sum = (n-2)×180°
sum = (5-2)×180°
sum = 540°
Given that the sum of the interior angle is 540° so in order to find the value of a, you have to add up all the angles in terms of a :
3a + 150 + 8a + 6a + 9a = 540
26a + 150 = 540
26a = 390
a = 390 ÷ 26
a = 15
A polynomial is a single term or the sum of two or more terms containing variables with exponents that are
Answers
whole numbers and coefficients that can be constants or variables. The exponents in a polynomial must be non-negative integers (whole numbers).
The polynomial terms can be added or subtracted, but the exponents of the variables must still be whole numbers.
For example, the following are polynomials:
1. 3x^2 + 5x - 2
2. 2y^3 + 4y^2 - 7y + 1
3. x^4 + 2x^3 - x^2 + 3x - 1
In these examples, the exponents are all whole numbers (2, 3, and 4), and the coefficients (the numbers multiplied by the variables) can be constants or variables themselves.
However, expressions like 2x^(1/2) or 3x^(-2) are not considered polynomials because the exponents in these cases are not whole numbers.
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Find the slope of the line that passes through the points A(-3, 1) and B(2, -5).
Answers
Answer:
\(m = \frac{ - 5 - 1}{2 - ( - 3)} = - \frac{6}{5} \)
Write a real word situation involving multiplication comparison that may be represented by the equations shown 24=4times6;24=6 times 2. 45=9 times 5; 45 = 5 times 9 3. 36= 3 times12; 36 =12 times 3 4. 60 =12 times 5; 60 = 5times 12
Answers
1. 24=4times6;24=6 times 4 is represented by apple orchard
2. 45=9 times 5; 45 = 5 times 9 is represented by classroom of students
3. 36= 3 times12; 36 =12 times 3 is represented by A construction site
4. 60 =12 times 5; 60 = 5times 12 is represented by A grocery store
How write the real word situation1. An apple orchard is comparing the productivity of two of its workers in terms of the number of baskets of apples picked. Worker A picked 4 baskets in 6 hours, while Worker B picked 6 baskets in 2 hours.
The situation can be represented by the equations 24 = 4 x 6 and 24 = 6 x 2, where 24 represents the total number of baskets picked.
2. Another example is a classroom of students comparing the number of pencils each student has. In one row, there are 9 students and each student has 5 pencils. In another row, there are 5 students and each student has 9 pencils. This situation can be represented by the equations 45 = 9 x 5 and 45 = 5 x 9, where 45 represents the total number of pencils in each row.
3. A construction site is comparing the efficiency of two workers in terms of the number of bricks they can lay in a certain amount of time. Worker A can lay 3 bricks in 12 minutes, while Worker B can lay 12 bricks in 3 minutes. The situation can be represented by the equations 36 = 3 x 12 and 36 = 12 x 3, where 36 represents the total number of bricks laid.
4. A grocery store is comparing the size of two crates of oranges. Crate A contains 12 rows of oranges, with 5 oranges in each row. Crate B contains 5 rows of oranges, with 12 oranges in each row. This situation can be represented by the equations 60 = 12 x 5 and 60 = 5 x 12, where 60 represents the total number of oranges in each crate.
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Alang took a taxi from his house to the airport. The taxi company charged a pick-up fee of $1.80 plus $2 per mile. The total fare was $21.80, not including the tip. Which tape diagram could be used to represent the context if mm represents the number of miles in the taxi ride?
Answers
The number of miles Alang took a taxi is 10
Alang took a taxi from his house to the airport. The taxi company charged a pick-up fee of $1.80
The fare per mile is $2
The total fare was $21.80, not including the tip.
Let the number of mile is x
total fare = pick up fee + fee per mile
21.80 = 1.80 + 2x
2x = 20
x = 10
Therefore, the number of miles Alang took a taxi is 10
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Which of the following algebraic represents shows a dilation that is an enlargement ?
Answers
The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)
A dilation is a type of transformation that changes the size of the shape or object. It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.
A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).
For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.
Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)
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What is m∠P? There is a five sided polygon PQRST in which the measure of angle PQR is 132 degrees, the measure of angle QRS is (4x-10) degrees, the measure of angle RST is (5x-11) degrees, the measure of angle STP is 128 degrees and the measure of angle TPQ is (4x+2) degrees.
Answers
Answer:
94°
Step-by-step explanation:
There is a five sided polygon PQRST in which the measure of angle PQR is 132 degrees, the measure of angle QRS is (4x-10) degrees, the measure of angle RST is (5x-11) degrees, the measure of angle STP is 128 degrees and the measure of angle TPQ is (4x+2) degrees.
Sum of angles in a pentagon = 540°
Hence:
PQR + QRS + RST +STP + TPQ = 540 °
132 + (4x-10)° + (5x-11)° + 128° + (4x+2) degrees = 540°
132 + 4x - 10 + 5x - 11 + 128 + 4x + 2 = 540
132 - 10 - 11 + 128 + 2 + 4x + 5x +4x = 540°
241 +13x = 540
13x = 540 - 241
13x = 299
x = 299/13
x = 23
What is m∠P?
m∠P in Pentagon PQRST = TPQ
TPQ = 4x + 2
= 4 × 23 + 2
= 94°
the information contained in a probability distribution has to be summarized into a single measure to be used to make decisions. what is this measure called?
Answers
Poisson distribution is the measure to summarize the information contained in a probability distribution in a single parameter.
Poisson distribution gives the probability of an event occurring a certain number of times (k) within a specified time period.
It is denoted by λ , which is the mean number of events.
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The temperature at noon at a ski resort is 3°F. The temperature drops 8°F by midnight.
What is the temperature at midnight?
Answers
Answer:
-5
Step-by-step explanation:
8 - 3
Which in fraction reprecent 80%
Answers
Answer:
answer is 4/5
which answer shows 4^-2=1/16 in logarithmic form
Answers
Answer:
log4 (116)=−2
Step-by-step explanation:
Convert the exponential equation to a logarithmic equation using the logarithm base (4)(4) of the right side (116)(116) equalsthe exponent (−2)(-2).
Suppose each time you toss this loaded coin, you win $20 if the result of a toss is a tail, and you lose $10 if the result of a toss is a head. What is your expected gain or loss
Answers
If the coin is fair, the expected gain would be $5. However, without information about the probabilities, we cannot determine the exact expected gain or loss.
To calculate the expected gain or loss, we need to determine the probability of getting a tail or a head when tossing the loaded coin.
Let's assume that the probability of getting a tail is represented by p and the probability of getting a head is represented by q. Since these are the only two possible outcomes, we know that p + q = 1.
Given that we win $20 for a tail and lose $10 for a head, we can calculate the expected gain or loss using the following formula:
Expected gain or loss = \((p \times $20) + (q \times -$10)\)
Since the question doesn't provide any information about the probabilities, we cannot provide an exact calculation for the expected gain or loss. However, if we assume that the coin is fair (50% chance of getting a tail and 50% chance of getting a head), we can substitute the values into the formula:
Expected gain or loss = \((0.5 \times $20) + (0.5 \times -$10) = $10 - $5 = $5\)
Therefore, if the coin is fair, the expected gain would be $5. However, without information about the probabilities, we cannot determine the exact expected gain or loss.
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how to concentrate in maths
Answers
Answer:
by learning from 1 to 1million numbers first and second place value third addition subtraction multiplication division fourth equations
Please help with this I give
Brainliest thank you!
Answers
Hope this helps
Answer:
We are learning median, mean, range, and stuff related to that and box plots etc...
and I think its the first quartile.
Step-by-step explanation:
CHILD ANYWAYSSSS SOOOOO... YEAH ITS THE 1ST QUARTILE.
BYE HAVE A NICE BOO.
a 95 confidence interval for p1-p2 is (-0.185, -0.093). explain how the confidence interval provides the same information as the significance test in part a
Answers
We can conclude that the difference between p1 and p2 is statistically significant at the 5% level of significance.
The confidence interval and significance test in part A both provide similar information. The significance test in part A tests if the difference between p1 and p2 is statistically significant, while the confidence interval provides an estimated range of values for the true difference between p1 and p2 with a certain degree of confidence (95% in this case).A confidence interval is a range of values that we believe will include a population parameter with a specified level of confidence.
It can be computed to estimate the population mean or the difference between two population means, such as p1 and p2.In contrast, a significance test assesses whether the difference between two population proportions is statistically significant.
The test calculates a p-value, which is the likelihood of obtaining the observed difference between two proportions, assuming the null hypothesis (that there is no difference between the two proportions) is true. A p-value less than the level of significance (usually 0.05) indicates that the difference between the two proportions is statistically significant, while a p-value greater than the level of significance indicates that the difference is not statistically significant.
Both the confidence interval and the significance test inform us about the difference between two population proportions. The confidence interval provides a range of plausible values for the difference, while the significance test tells us whether the difference is statistically significant or not. In this particular case, since the confidence interval does not contain zero,
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if f(x)=3x+5 and g(x)=x-2 , what is ( f - g)(x)
Answers
Answer:
(f - g)(x) = 2x + 7
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x + 5 - (x - 2) ← distribute parenthesis by - 1
= 3x + 5 - x + 2 ← collect like terms
= 2x + 7