Which of the following could be the equation of the function below? On a coordinate plane, a curve crosses the y-axis at y = 2. It has a maximum at 5 and a minimum at negative 1. It goes through one cycle at pi. y = negative 3 sine (2 (x + pi)) + 2 y = negative 3 sine (x + pi) + 2 y = 3 sine (4 (x minus pi)) + 4 y = 3 sine (2 (x + pi)) + 2
Answers
Answer:
b
Step-by-step explanation:
We want to find a sine function such that:
it has a y-intercept equal to 2.it has a maximum of at 5, and a minimum at -1.it goes through one cycle at pi.The given options are:
y = -3*sin(2*(x + pi)) + 2 y = -3*sin(x + pi) + 2 y = 3*sin(4*(x - pi)) + 4 y = 3*sin(2*(x + pi)) + 2Notice that the first information that we have, implies that y must be equal to 2 when x = 0.
Knowing that we can discard the third option which has a y-intercept of 4.
Now the second. Remember that for a general function:
y = A*sin(k*x) + M
Where A is the amplitude and M is the midline, the maximum and minimum are given by:
A + M
-A + M
In all the remaining options we have:
A = ± 3
M = 2
We can see that with these we get the maximum and minimum of 5 and -1.
Finally, we know that it goes through one cycle at pi.
This means that if f(x) is the function, then:
f(x) = f(x + pi)
Also remember that for a general sine function, we have:
sin(x) = sin(x + 2*pi)
Ok, now let's analyze the options (only the sine part)
1) sin(2*(x + pi)) = sin( 2*x + 2*pi) = sin(2*x)
if we evaluate this in x + pi, we will get:
sin(2*( x + pi + pi)) = sin(2*(x + 2*pi)) = sin( 2*x + 4*pi) = sin(2*x)
So yes, option 1 is a correct option (you also can see that option 4 has the exact same sine part, so that option is also correct.)
2) for the second option the sine part is:
sin(x + pi)
if we evaluate this in x + pi we get:
sin(x + pi + pi) = sin(x + 2*pi) = sin(x)
and we have:
sin(x +pi) ≠ sin(x)
Then this function does not go through one cycle at pi.
We can conclude that the two options that meet all the conditions are the first one and fourth one:
1) y = -3*sin(2*(x + pi)) + 2
4) y = 3*sin(2*(x + pi)) + 2
We can't say which one is correct if we do not look at the graph.
If the function starts increasing, then (2) is the correct one, if the graph starts decreasing, then (1) is the correct one.
Below, you can see a graph of both functions:
The green one is y = 3*sin(2*(x + pi)) + 2, the blue one is y = -3*sin(2*(x + pi)) + 2
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Related Questions
Giving Brainliest if correct!!
Adam bought a treadmill and a dirt bike from a sports equipment store for y dollars. He signed an installment agreement requiring an 8% down
payment and monthly payments of x dollars for 18 months. Which expression correctly represents Adam's finance charge?
A. 0.8y
B. 18y
C. 18x-0.92y
D. 18x-0.08y
E. 18y-0.92x
Answers
Answer:
D. 18x-0.08y
Step-by-step explanation:
He will make 18 monthly payments of x dollars on the total amount leftover after paying an 8% down payment. So his finance charge is payment minus down payment: 18x-0.08y
The expression correctly represents Adam's finance charge is
C. 18x-0.92y.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
From, The given information,
8% of the downpayment is (8/100)×y = 0.08y and te total monthly payment is 18x.
Therefore,
The phrase that accurately describes Adam's finance charge is,
y = 0.08y + 18x.
y - 0.08y = 18x.
0.92y = 18x.
18x - 0.92y = 0.
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Evaluate tan²0 for 0 = 60°.
1/3
3/4
1
3
Answers
Answer:
3
Step-by-step explanation:
i Substituted the value ofthe variable into the equation and simplified it.
What is the volume of the right cone below?
Answers
Answer:
The answer is A.
Step-by-step explanation:
You have to use the formula of volume of cone,
[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
Given that the diameter of cone is 10 units so the radius is 5. Then substitute the followung values into the formula :
Let r = 5 units,
Let h = 45 units,
[tex]v = \frac{1}{3} \times \pi \times {5}^{2} \times 45[/tex]
[tex]v = \frac{1}{3} \times \pi \times 1125[/tex]
[tex]v = 375\pi \: \: {units}^{3} [/tex]
Answer:
[tex]375\pi \: \: units ^{3} [/tex]
Answer A is correct.Step-by-step explanation:
[tex]v = \pi {r}^{2} \frac{h}{3} \\ =\pi \times 5 \times 5 \times \frac{45}{3} \\ = \pi \times 25 \times 15 \\ = 375\pi \: \: units ^{3} [/tex]
Which number is divisible by 3
Answers
Answer:
6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,...
Step-by-step explanation:
Which is the graph of g(x) = [X + 3]?
Answers
Answer
D or the fourth one because i took the quiz and got it right
If $3000 is placed in an account at 5% and is compounded quarterly for 5 years. How much is
in the account at the end of 5 years? *
(1 Point)
A.$3674.68
B.$3828.85
C.$3846.11
D.$3923.07
Answers
$3828.85 is in the account at the end of 5 years which is correct option(B).
What is Compound interest?
Compound interest is defined as interest paid on the original principal and the interest earn on interest of principal.
p = $3000
r = 5%
t = 5 years
[tex]A = p(1+\frac{r}{100} )^t[/tex]
substitue the values of p,r and t in formula,
[tex]A = 3000(1+\frac{5}{100} )^5[/tex]
[tex]A = 3000(1+0.05} )^5[/tex]
[tex]A = 3000(1.05} )^5[/tex]
A = 3000(1.276)
A = 3828.85
Hence, $3828.85 is in the account at the end of 5 years.
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1. A ball is thrown off of a balcony and it's height can be
modeled using the function, f(x) = -x2 + 4x + 12, where x is
the number of second after the ball was released. After
how many seconds will it the ball to hit the ground?
Answers
Answer:
After 6 seconds, the ball will hit the ground.
Step-by-step explanation:
f(x)=-x^2 + 4x + 12
Since we want to see when it touches the ground, the height must be equal to 0, so f(x) has to equal 0.
0=-x^2 + 4x + 12
If you factor this equation, you'd get:
(-x + 6)(x + 2) = 0
We get the 2 and the 6 from the factors of 12. The two factors of 12 have to be able to add or subtract into 4, and in this case, 6-2 is 4. (If you multiply this equation out, you'd get the same one you started with)
Since we need it to equal 0, the way to multiple to 0 is to have a zero itself. This means that either (-x+6) is equal to 0 or (x+2) is equal to 0. The only x values that satisfy this is 6 and -2. You can't have -2 seconds after, so it has to be 6.
Hope that helps.
Which steps should be used to compare the fractions StartFraction 2 Over 9 EndFraction and StartFraction 5 Over 6 EndFraction? Find a common numerator. Add the numerators and denominators to determine which sum is larger. Use the “greater than” symbol to show which denominator is larger. Multiply the first fraction by StartFraction 2 Over 2 EndFraction and the second fraction by StartFraction 3 Over 3 EndFraction
Answers
Answer:
The answer is C
Step-by-step explanation:
because if you do Use the “greater than” symbol to show which denominator is larger. than you can see and find out which one is greater
There is a population of 1,000 bacteria in a colony. If the number of bacteria doubles every 4 minutes, what will the population be 8 minutes from now? Please help me I might Fail Algebra.
a. 8000 b. 500 c. 4000 d. 2000
Answers
4,000= 8 minutes
Part A: The area of a square is (4a2 − 20a + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (9a2 − 16b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Answers
Answer:
(2a -5)²(3a -4b)(3a +4b)Step-by-step explanation:
There are a couple of factored forms that are used here:
(a +b)² = a² +2ab +b² . . . . the sign of "2ab" will match the sign of b
a² -b² = (a -b)(a +b)
__
Part A:
Since this trinomial is known to be a perfect square, you can find the binomial(s) by looking at the roots of the first and last terms.
√(4a²) = 2a
√25 = 5
The factoring is ...
4a² -20a +25 = (2a -5)²
__
Part B:
This is the difference of perfect squares, so the terms of the factors can be found as in the previous part.
√(9a²) = 3a
√(16b²) = 4b
Using the above factored form, we have ...
9a² -16b² = (3a -4b)(3a +4b)
A B C or D PLZ help!!!!!!!!!!!!!!!
Answers
Answer:
id say D
Step-by-step explanation:
Factor 8y+36please help thank you
Answers
Answer:
4(2y + 9)
Step-by-step explanation:
divide by 4.
What’s the answer to this???
Answers
Answer:
A i think
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Find the radius of the sphere with the given volume 36πin^3
Answers
Answer:
3 in.
Step-by-step explanation:
PLSSSS help
Marking BRainlist
Answers
Answer: x = 14 for the first one, x = 4 for the second
Step-by-step explanation:
8x - 9 = 7x + 5
subtract 7x from both sides
x - 9 = 5
add 9 to both sides
x = 14
8x + 9 = 3x + 29
subtract 3x from both sides
5x + 9 = 29
subtract 9 from both sides
5x = 20
divide both sides by 5
x = 4
x = 14
the second one is
x = 4
Plzzzzzzzz help me worth 20 points
what is: - 5 1/4- [-7 1/2] =
Answers
Answer:
2 1/4
Step-by-step explanation:
- 5 1/4- [-7 1/2]
Get a common denominator of 4
- 5 1/4- [-7 1/2*2/2]
- 5 1/4- [-7 2/4]
We know subtracting a negative is adding
- 5 1/4 + [7 2/4]
Rewriting
7 2/4 - 5 1/4
Subtract the whole numbers
7-5 =2
Subtract the fractions
2/4 -1/4 = 1/4
2 1/4
Answer:
2 ¼
Step-by-step explanation:
-5 ¼ - [-7 ½]
-5 ¼ + 7 ½
7½ - 5¼
(7-5) + (½-¼)
2 + ¼
2 ¼
State the 3 primary Trigonometrie Formulas and draw a well labelled triangle to help illustre, cely
indicating the unknown angle you are labelling the sides in reference to
Answers
Answer:
I think this is what you want:
Step-by-step explanation:
Carson uses cubes to make a pattern of shapes. The first shape has a height of
2 cubes and a length of 2 cubes, as shown below. For each step in the pattern,
Carson adds 1 cube to the height and 1 cube to the length. Which sentence
about the shapes in Carson's pattern is true?
Step 1
height
length
» The total number of cubes in each
shape will alternate between even and
odd.
)) The length of each shape will alternate
between even numbers and odd
numbers.
1) The length of each shape will be an
even number
()) The total number of cubes in each
shape will be even.
Answers
Answer:
1
Step-by-step explanation:
Please please please please please please thank please please please help me please ASAP
Answers
Answer:
4
Step-by-step explanation:
3x^2 + 2(y-1)/x+y^2
3(4)^2 + 2(3-1)/4+3^2
3x16+2x2/4+9
48+4/13
52/13
4
I NEED HELP PLZZZZZZZ !!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
6.28 yards
Step-by-step explanation:
C=3.14(2 yards)
Answer:
6.28 is the answer
in a survey of 80 people.it was found that 60 liked oranges only and 10 liked both oranges and apples.the number of people who liked oranges is five times the number of people who liked apples. by using venn-diagram, find the number of people who liked apples only and who didn't like any of these fruits
Answers
There are 4 people who only like apples, and 6 people who do not like any fruit.
Since in a survey of 80 people it was found that 60 liked oranges only and 10 liked both oranges and apples, and the number of people who liked oranges is five times the number of people who liked apples, to determine the number of people who liked apples only and the number of people who didn't like any of these fruits, the following calculations must be performed:
First, the number of people who like apples must be determined, knowing that it is 5 times less than the number of people who like oranges.
(60 + 10) / 5 = X 70/5 = X 14 = X
Thus, 14 people like apples, of which 10 of them also like oranges. So there are 4 people who only prefer apples, added to 60 people who prefer oranges and 10 who like both fruits. This gives a total of 74 people, which implies that 6 people do not like any fruit.
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Plzz help me its is math
Answers
Answer:
A
Step-by-step explanation:
Whenever you square a real number, the result will always be positive, because even if you are squaring a negative number a negative times a negative is a positive. However, when you cube a negative number, the result CAN be negative, because you are multiplying a negative number by itself three times. Therefore, the answer is only A. Hope this helps!
please help ASAP.
find:
1/6 of 48=__
1/10 of 40=__
3/4 of 24=__
2/5 of £65= £__
7/10 of £90= £__
Answers
4
18
£26
£63
Please mark thx or brainliest ❤️
Answer:
1/6 of 48 is 8
1/10 of 40 is 4
3/4 of 24 is 18
2/5 of £65 is £26
7/10 of £96 is £67.2.
Step-by-step explanation:
I did the math.
At Ken's boutique, 33 customers wore a size small, and 51 customers wore a different size.
What is the probability that a randomly selected customer wore a size small?
Write your answer as a fraction or whole number.
Answers
Answer:
11/28
Step-by-step explanation:
1. Add up all of the customers to get the sample size.
33 + 51 = 84
2. Since we are finding the chance of it being a size small, 33 will be out numerator.
3. Create the final fraction, (33/84)
4. Simplify (11/28)
Hope this helps! Comment if you have any questions. :)
Answer:
11/28
Step-by-step explanation:
First, you add 33 and 51 to get a total of 84 customers. Then you put the number of selections you want (33) as the numerator to 84, to get 33/84. Finally you simplify and get the probability of selecting a customer at random. Answer= 11/28 is your probability
Describe how ice-albedo feedback causes global warming
Answers
Which expression shows a way to find 20% of 950? Please I need help thanks.
Answers
Answer:
the answer of the expression is 190
Step-by-step explanation:
Given expression as :
20 % of 950
Or, [tex]\frac{20}{100}[/tex] times 950
Or, [tex]\frac{20}{100}[/tex] × 950
Or, 20 × [tex]\frac{950}{100}[/tex]
or, 20 × 9.5
∴ 190
Answer:
1/5 times 950
Step-by-step explanation:
I did this on iready and got it correct
If the weight of a blue square is 4 pounds, what is the weight of one green triangle.
Answers
Answer:
2
Step-by-step explanation:
Subtract.
(5x-1)-(3xy+c)
Answers
Answer:
5 x − 1 − 3 x y − c
The solution to the expression (5x-1)-(3xy+c) would be 5x - 1 - 3xy - c.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0.
The given expression is (5x-1)-(3xy+c)
The subtraction between them is
5x - 1 - 3xy - c
Thus, the subtraction would be 5x - 1 - 3xy - c.
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The dot plot shows the number of particpants in each age group in a science fair. 11 12 15 16 17
Answers
Complete Question
The dot plot shows the number of participants in each age group in a science fair. Which of the following statements is not supported by the dot plot?
A The range is 6.
B The mean of the ages is about 14.4.
C The mode of the ages is 13.
D The median of the ages is 15.
Answer:
(C) The mode of the ages is 13.
Step-by-step explanation:
The given dot plot is attached.
From the dot plot, there is no participant aged 13. Therefore, the mode of the ages cannot be 13. The mode is actually 15.
Therefore, Option C is not supported by the dot plot.
Find the missing side length
A man rides his bike 15 miles southeast
and then 12 miles west. How far is he
from his starting point?
Answers
Answer: 19.21
Step-by-step explanation:
12^2 + b^2 = 15^2
subtract 12^2 from both sides
b^2 = 15^2 - 12^2
b^2 = 81
b = 9
credit to melissanix90 for helping
Hope this helps :)
