45 POINTS! HELP ASAP AND ILL MARK AS BRAINLIEST!
What are the amplitude, period, and midline of the function? (1 point)
Amplitude: 8; period: π; midline: y = 1
Amplitude: 8; period: 2π; midline: y = 5
Amplitude: 4; period: 2π; midline: y = 5
Amplitude: 2; period: π; midline: y = 1
Answers
Amplitude = 2; period T = π; midline y = 1.
This sinusoidal wave is a even function which means that it has a positive half-cycle and a negative half-circle of equal size, from the image we can see that the midline is y = 1 which is the point where the function is centered.
The amplitude is the measure from the midline to the positive half-cycle, and the midline to the negative half-cycle which is 2.
The period corresponds to a complete cycle of the function or the repetition of the wave seen from a point. In this case, we can see that the wave, starting from π/2 it repeat in 3π/2. So, to calculate the period just substract 3π/2 by π/2
T = 3π/2 - π/2 = (3π - π)/2
T = 2π/2
T = π
Related Questions
If sinθ = 2/3 and θ is located in Quadrant II, then tan2θ = _____.
Answers
Answer:
[tex] -4 \sqrt{5} [/tex]
Step-by-step explanation:
Quadrant 2 means cosine is negative.
So [tex] \sin(\theta)=\frac{2}{3} =\frac{\text{ opp }}{\text{ hyp }} [/tex]
So the adjacent side is [tex] \sqrt{3^2-2^2}=\sqrt{9-4}=\sqrt{5} [/tex]
So [tex] \cos(\theta)=-\frac{\sqrt{5}}{3} [/tex]
Now to find [tex] \tan(2 \theta) [/tex]
[tex] \tan(2 \theta) =\frac{2\tan(\theta)}{1-\tan^2(\theta)}[/tex]
We will need [tex] \tan(\theta) [/tex] before proceeding.
[tex] \tan(\theta) =\frac{\sin(\theta)}{\cos(\theta)}=\frac{\frac{2}{3}}{\frac{-\sqrt{5}}{3}}=\frac{-2}{\sqrt{5} } [/tex]
Now plug it in and the rest is algebra.
[tex] \tan(2 \theta) =\frac{2\tan(\theta)}{1-\tan^2(\theta)} =\frac{2 (\frac{-2}{\sqrt{5}}}{1-\frac{4}{5}} [/tex]
Now the algebra, the simplifying.... We need to get rid of the compound fraction. We will multiply top and bottom by [tex] 5 \sqrt{5} [/tex]
This will give us
[tex] \frac{-4(5)}{5 \sqrt{5}-4 \sqrt{5}} [/tex]
[tex] \frac{-20}{\sqrt{5}} [/tex]
Multiply top and bottom by [tex] \sqrt{5} [/tex]
[tex] \frac{-20 \sqrt{5}}{5} [/tex]
The answer reduces to
[tex] -4 \sqrt{5} [/tex]
Final answer:
To find tan2θ when sinθ = 2/3 and θ is in Quadrant II, we use the Pythagorean identity to find cosθ and the double angle identity for tangent. After calculation, tan2θ = -4√5.
Explanation:
If sinθ = 2/3 and θ is located in Quadrant II, we first have to find cosθ and then use the double angle identity for tangent to find tan2θ. Since sinθ is positive in Quadrant II and cosθ must be negative (as the x-values are negative in Quadrant II), we can use the Pythagorean identity sin2θ + cos2θ = 1 to find cosθ. Thus, cosθ = -√(1 - sin2θ) = -√(1 - (2/3)2) = -√(1 - 4/9) = -√(5/9) = -√5/3.
The double angle identity for tangent is tan2θ = 2tanθ / (1 - tan2θ). But first, we find tanθ = sinθ/cosθ = (2/3) / (-√5/3) = -2/√5. Then, tan2θ = 2(-2/√5) / (1 - (-2/√5)2) = -4/√5 / (1 - 4/5) = -4/√5 / (1/5) = -20/√5. Simplifying further, we multiply by √5/√5 to rationalize the denominator, which gives us tan2θ = -20√5/5 = -4√5.
What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3
3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0
Answers
Answer:
x-3y-7=0
Step-by-step explanation:
Given
m=1/3
The standard form of point slop form is:
y=mx+b
To find the value of b, we will put the point in the standard form
So,
[tex]-2=\frac{1}{3}(1)+b[/tex]
Solving for b[tex]-2=\frac{1}{3}+b\\-2-\frac{1}{3}=b\\\frac{-6-1}{3}=b\\b=\frac{-7}{3}[/tex]
Putting the values of b and m in standard form:
[tex]y=\frac{1}{3}x+\frac{-7}{3}\\y=\frac{1}{3}x-\frac{7}{3}Multiplying\ both\ sides\ by\ 3\\3y=x-7\\-x+3y+7=0\\Can\ also\ be\ written\ as\\x-3y-7=0[/tex]
Which of these expressions will give the unpaid balance after 6 years on a $90,000 loan with an APR of 7.2%, compounded monthly, if the monthly payment is $708.61?
A. 90,000(1+0.072)^72+708.61[1-(1+0.072)^72/0.072]
B. 90,000(1+0.006)^6+708.61[1-(1+0.006)^6/0.006]
C. 90,000(1+0.006)^72+708.61[1-(1+0.006)^72/0.006]
D. 90,000(1+0.072)^6+708.61[1-(1+0.072)^6/0.072]
Answers
Answer:
none of the expressions shown is correct
The appropriate expression is ...
90,000(1+0.006)^72+708.61[(1-(1+0.006)^72)/0.006] . . . best matches C
Step-by-step explanation:
The formula used to calculate the remaining balance is ...
A = P(1 +r)^n +p((1 -(1 +r)^n)/r) . . . . . note the parentheses on the fraction numerator
In this formula, r is the monthly interest rate: 7.2%/12 = 0.006, and n is the number of monthly payments: 6×12 = 72. Putting these values into the formula along with the loan amount (P=90,000) and the payment amount (p=708.61) gives ...
A = 90,000(1.006)^72 +708.61((1 -(1.006)^72)/0.006)
A = 74,871.52
Answer: the answer is
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find the solution(s) to the system of equations. Select all that apply
y=x^2-1
y=2x-2
Answers
Step-by-step explanation:
y = x^2 - 1
y = 2x - 2
x^2 - 1 = 2x - 2
x^2 - 2x + 1 = 0
(x - 1)^2 = 0
x = 1
Because x = 1 the answer must be D (1, 0).
Answer:
(1,0)
Step-by-step explanation:
Replace x values and y values with the answer choices.
[tex]y=(1)^2- 1 = 0[/tex]
[tex]y= 2(1)-2=0[/tex]
Since the coordinate pair [tex](1,0)[/tex] it is safe to assume that D will be the correct answer.
Use the graph to confirm that the solution is (1,0)
The blue line intersects at (1,0), so the solution for the system of equations is (1,0)
Graph the following system of linear inequalities. Identify at least two points in the solution: y < 5 - 2x | x + 5y > -7
Answers
Answer:
(1,2) and (2,-1)
Step-by-step explanation:
we have
[tex]y< 5-2x[/tex] ----> inequality A
The solution of the inequality A is the shaded area below the dashed line [tex]y=5-2x[/tex]
[tex]x+5y>-7[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the dashed line [tex]x+5y=-7[/tex]
The solution of the system of inequalities is the shaded area between the two dashed lines
If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area
Two points in the solution are
(1,2) and (2,-1)
see the attached figure
Isaac downloaded 7 ringtones. Each polyphonic ringtone costs $3.25, and each standard ringtone costs $1.50. If he spends a total of $21 on ringtones, find the number of polyphonic and standard ringtones he downloaded.
Answers
Answer:
[tex]6\ polyphonic\ ringtones[/tex] and [tex]1\ standard\ ringtone[/tex]
Step-by-step explanation:
Let
x -----> the number of polyphonic ringtones
y ----> the number of standard ringtones
we know that
[tex]x+y=7[/tex]
[tex]x=7-y[/tex] -----> equation A
[tex]3.25x+1.50y=21[/tex] -----> equation B
Solve the system of equations by substitution
Substitute equation A in equation B and solve for y
[tex]3.25(7-y)+1.50y=21[/tex]
[tex]22.75-3.25y+1.50y=21[/tex]
[tex]3.25y-1.50y=22.75-21[/tex]
[tex]1.75y=1.75[/tex]
[tex]y=1\ standard\ ringtones[/tex]
Find the value of x
[tex]x=7-1=6\ polyphonic\ ringtones[/tex]
Answer:
6 polyphonic, 1 standard
Step-by-step explanation:
Woodland Mound Park sells annual visitor passes for $12.50. Last year the park raised $53,500 in annual visitor pass sales. How many annual visitor passes were sold?
Answers
Answer:
4280 passes were sold
Step-by-step explanation:
The unknown we are looking for the number of passes that were sold. We don't know how MANY were sold, but we do know that the cost of ONE is 12.50. We represent the number of passes at that price per pass as
12.50x
We also know that money earned from the sale of this unknown number of passes came to 53,500. Our equation then becomes
12.50x = 53,500
Solving for x, we divide both sides by 12.50 to get that
x = 4280
Final answer:
To find the number of annual visitor passes sold at Woodland Mound Park, divide the total sales ($53,500) by the price per pass ($12.50), resulting in 4,280 passes sold.
Explanation:
The question asks how many annual visitor passes were sold at Woodland Mound Park last year if each pass costs $12.50 and the total amount raised from pass sales was $53,500. To find the number of passes sold, you'll need to divide the total sales by the price per pass. Here is the step-by-step calculation:
Identify the total revenue from sales: $53,500.Identify the price of one annual visitor pass: $12.50.Divide the total revenue by the price per pass to get the quantity sold: $53,500 / $12.50 = 4,280.Priscilla graphed function g, a transformation of the quadratic parent function f(x)=1/2f(x+2)-1 which statement is correct?
A.)Priscilla made a mistake when applying the horizontal shift.
B.)Priscilla made a mistake when applying the vertical shift.
C.)Priscilla made a mistake when applying the vertical compression.
D.)Priscilla correctly graphed the transformed function .
Answers
Answer:
Step-by-step explanation:
A.)Priscilla made a mistake when applying the horizontal shift. That "x+2" indicates a horiz. shift to the LEFT, not to the right.
Answer:
Option A.
Step-by-step explanation:
Priscilla graphed function g(x), a transformation of the quadratic parent function f (x) = [tex]\frac{1}{2}[/tex] f ( x+2 ) - 1
(1) She graphed the vertical compression correctly
(2) Priscilla graphed the vertical shift of (-1) means 1 unit downwards on y-axis correctly.
(3) In the last she made a mistake because for f(x+2) the parent function should have been shifted left on x-axis by two units f (x) ⇒ f[ x- (-2)]
Therefore Option A will be the answer.
find f(g(x)) for the functions f(x) = (x+1)^3 -5 and g(x) = ^3sqrt(x) -1
are these functions inverses?
Answers
Answer:
f(g(x)) = x-5the functions are NOT inversesStep-by-step explanation:
Substitute g(x) for x in f(x) and evaluate:
f(g(x)) = f(x^(1/3) -1)
= ((x^(1/3) -1) +1)^3 -5
= (x^(1/3))^3 -5
= x^(3/3) -5
f(g(x)) = x -5
This is confirmed by a graphing calculator. (See attached.)
If the functions were inverses, the value of f(g(x)) would be x. It is not, so the functions are not inverses.
Given the following linear function identify the slope in the Y intercept of the function
Answers
Answer:
Choice #2
Step-by-step explanation:
Your linear function is in the slope-intercept form of a line, y = mx + b, where m is the value of the slope, and b is the value of the y-intercept. The number in the m position in your equation is 1/6, and thee number in the b position in your equation is 7. So the second choice is the one you want.
the number of bacteria growing in an incubator culture increases with time according to b(x)=8500(3)^x where x is the time in days. After how many days will the number of bacteria in culture be 2,065,500?
Answers
Answer:
5 days
Step-by-step explanation:
Put the given number in the formula and solve for x.
2065500 = 8500·3^x
243 = 3^x . . . . . . . . . . . divide by 8500
log(243) = x·log(3) . . . take logarithms
log(243)/log(3) = x = 5 . . . . divide by the coefficient of x
After 5 days, the number of bacteria in culture will be 2,065,500.
please help!
The total number of fungal spores can be found using an infinite geometric series where a1 = 11 and the common ratio is 2. Find the sum of this infinite series that will be the upper limit of the fungal spores.
465
280
The series is divergent
125
Answers
Answer:
The series is divergent
Step-by-step explanation:
An infinite geometric series with a common ratio greater than 1 does not converge to a sum. The series is divergent.
If tan x° = a divided by 4 and cos x° = 4 divided by b what is the value of sin x°? (1 point) \
Answers
Answer:
Sin x = a / b.
Step-by-step explanation:
The opposite side =a and the adjacent side = 4 (because tan x = a/4.
Cos x = 4/b so the hypotenuse = b ( because Cos = adjacent /hypotenuse.
So sin x = opposite /hypotenuse = a / b.
Answer:
sin x° = a divided by b is the answer
Step-by-step explanation:
I got 100% on the test!
Harry asked a sample of 4 people how many siblings they had. Here are their responses:
0, 0, 1, 3
The mean is x-bar = 1 sibling.
What formula gives the standard deviation?
Answers
Answer:
Formula of standard deviation = √Variance
Standard deviation = 1
Step-by-step explanation:
X-bar is the variance
Therefore, the answer would be
√X-bar
√1 = 1
!!
Answer:
C
Step-by-step explanation:
What must be done to each side of the equation to find the value of n?
-4n = 696
A)
add -4
B)
multiply by -4
C)
subtract -4
D)
divide by -4
Answers
Answer:
Divide both sides by -4.
Step-by-step explanation:
If you divide both sides by -4, you'll get the answer n=−174.
Please mark brainliest!
Answer:
D
Step-by-step explanation:
-4n = 696
What must be done to each side of the equation to find the value of n?
Divide both sides by -4 to find the value of n
∴ -4n/-4 = 696/-4
n = -174
Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1,000 earthworms. How many earthworms can he have if his square of compost has a side length that is five times longer?
A.) 20,000
B.) 25,000
C.) 100,000
D.) 5,000
Please be original!!! I am torn between B and D. THANKS!
Answers
Answer:
The answer is D: 5,000
Step-by-step explanation:
That is the easiest question to solve. Good luck!
The number of earthworms he have if his square of compost has a side length that is five times longer is 5000.
How many earthworms can he have?
The first step is to determine the number of earthworms in a compost with a side length of 1.
1000 / 4 = 250
Number of earthworms with side length five time longer : (4 x 5) x 250 = 5000
To learn more about multiplication, please check: https://brainly.com/question/13814687
#SPJ5
For the functions f(x) = x^2+ 8x + 2 and g(x) = -5+9, find (f•g)(x)and (f.g)(-1).
Answers
Answer: (f·g)(x) = -5x³ - 31x² + 62x + 18
(f·g)(-1) = -70
(fog)(x) = 25x² - 130x + 155
(fog)(-1) = 310
Step-by-step explanation:
f(x) = x² + 8x + 2 g(x) = -5x + 9
(f·g)(x) = (x² + 8x + 2)(-5x + 9)
= -5x³ + 9x²
- 40x² + 72x
- 10x + 18
= -5x³ - 31x² + 62x + 18
(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18
= -5(-1) - 31(1) - 62 + 18
= 5 - 31 - 62 + 18
= -70
****************************************************************************************
(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2
= 25x² - 90x + 81
- 40x + 72
+ 2
= 25x² - 130x + 155
(fog)(-1) = 25(-1)² - 130(-1) + 155
= 25 + 130 + 155
= 310
It wasn't clear if you wanted multiplication or composition so I solved both.
The composition (f⋅g)(x) is 50, and the product of functions (f.g)(-1) is -20.
To find the composition of the functions f(x) and g(x), denoted as (f⋅g)(x), we first need to determine g(x). Given g(x) = -5 + 9, we simply add these numbers together to get g(x) = 4. With g(x) found, we can now substitute g(x) into f(x) to find the composition. To do this, wherever there is an x in f(x), we replace it with 4.
So, (f⋅g)(x) = f(g(x)) = f(4) = 4^2 + 8(4) + 2 = 16 + 32 + 2 = 50.
Next, to find (f.g)(-1), which represents the product of the two functions evaluated at x = -1, we evaluate both f(-1) and g(-1). We already know that g(x) is constant at 4, so g(-1) = 4. Now we find f(-1):
f(-1) = (-1)^2 + 8(-1) + 2 = 1 - 8 + 2 = -5.
Thus, the product at x = -1 is:
(f.g)(-1) = f(-1) ⋅ g(-1) = (-5) ⋅ 4 = -20.
The sum of two consecutive integers is 9. Find the numbers.
Answers
[tex]n,n+1[/tex] - two consecutive integers
[tex]n+n+1=9\\2n=8\\n=4\\n+1=5[/tex]
4 and 5
Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y
Answers
Answer:
y = 2x + 20
Step-by-step explanation:
2 * x is the number of minutes from the math problems
20 is the number of minutes for the history homework
Answer:
y= 2x=20
Step-by-step explanation:
A car, originally valued at 70,000 in 2006 depreciates exponentially at a rate of 4% each year. Round the expected value of the car in 2018 to the nearest dollar. Round the expeated value of the car in 2018 to the nearest dollar
Answers
Answer:
$42,890
Step-by-step explanation:
The standard form for an exponential equation is
[tex]y=a(b)^x[/tex]
where a is the initial amount value and b is the growth rate or decay rate and t is the time in years. Since we are dealing with money amounts AND this is a decay problem, we can rewrite accordingly:
[tex]A(t)=a(1-r)^t[/tex]
where A(t) is the amount after the depreciation occurs, r is the interest rate in decimal form, and t is the time in years. We know the initial amount (70,000) and the interest rate (.04), but we need to figure out what t is. If the car was bought in 2006 and we want its value in 2018, a total o 12 years has gone by. Therefore, our equation becomes:
[tex]A(t)=70,000(1-.04)^{12}[/tex] or, after some simplification:
[tex]A(t)=70,000(.96)^{12}[/tex]
First rais .96 to the 12th power to get
A(t) = 70,000(.6127097573)
and then multiply.
A(t) = $42,890
squared or cubed is indicated to the top right of a number - what does 3/2 stand for? Is it a number cubed? Or squared?
Answers
Answer:
Step-by-step explanation:
3/2 is a power of 1.5 or equivalently 1 1/2. This is another way to write a radical.
[tex]x^\frac{3}{2}=\sqrt[2]{x^3}[/tex]
Ammo 67 match each definition on the left with the correct term.
Answers
Which of the following values are in the range of the function graphed below? Check all that apply
Please help! - Will give the answer "brainliest!"
Answers
The equation is y = 1, so the only number of the range is 1
Option: D is the correct answer.
The values that lie in the range of the function which is graphed is:
D. 1
Step-by-step explanation:Range--
The range of the function is the possible values which are attained by the function.
i.e. the values of y as is obtained corresponding to different x as in the domain.
By looking at the graph of the function is defined over the interval [-2,1] and the graph passes through (0,1) and is parallel to the x-axis.
Hence, the range of the function is: 1
( Since it takes just a single value i.e. 1 over the interval [-2,1] )
PLEASE HELP
How can I find the measure of Angle A?
Answers
Answer:
∠A ≈ 58.1°
Step-by-step explanation:
Since the triangle is right use the tangent ratio to solve for ∠A
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{8.2}{5.1}[/tex], hence
A = [tex]tan^{-1}[/tex] ( [tex]\frac{8.2}{5.1}[/tex] ) ≈ 58.1°
Sam recorded the number of points she scored on each weekly test out of the number of points possible for the test. In which two subjects did Sam score the lowest? Choose exactly two answers that are correct. Language Arts History Science Math Sam's Test Scores Math 2225 Science 1920 Language Arts 84100 History 910
Answers
Makes no sense.
He scored the lowest in History and Science. Compare the numbers to help you prepare the obvious chart.
Sam scored the lowest in Language Arts with 84% and Math with 88%.
To determine this, We need to calculate Sam's percentage scores for each subject:
Math: [tex]\frac{25}{25}*100[/tex] = 88%Science: [tex]\frac{19}{20}*100[/tex] = 95%Language Arts: [tex]\frac{84}{100} *100[/tex] = 84%History:[tex]\frac{9}{10}*100[/tex] = 90%Based on these calculations, the two subjects where Sam scored the lowest are Language Arts (84%) and Math (88%).
complete question:
Sam recorded the number of points she scored on each weekly test out of the number of points possible for the test.In which two subjects did Sam score the lowest?Choose exactly two answers that are correct. Sam's Test Scores in Math 22/25 ,in Science 19/20 ,in Language Arts 84/100 ,in History 9/10.
Julie has 5 cherry lollipops,1 lime lollipops, and 2 grape lollipops in a bag. She is going to select one lollipop, replace the lollipop in the bag, and then select a second one. What is the probability that Julie will select a cherry lollipop and then a lollipop other than grape?
a.)6/8
b.)11/16
c.)15/32
d.)10/64
Answers
Answer: [tex]\dfrac{15}{32}[/tex]
Step-by-step explanation:
Given : The number of cherry lollipop = 5
The total number of lollipop = 8
the number of lollipops other than grape =6
The probability of selecting a cherry lollipop is given by :_
[tex]\text{P(Cherry)}=\dfrac{5}{8}[/tex]
The probability of selecting a lollipop other than grape is given by :_
[tex]\text{P(Other than grape)}=\dfrac{6}{8}[/tex]
Since, there is replacement , then the events are independent of each other.
Now, the probability that Julie will select a cherry lollipop and then a lollipop other than grape is given by :-
[tex]\text{P(Cherry and other than grape)}=\dfrac{5}{8}\times\dfrac{6}{8}=\dfrac{15}{32}[/tex]
Hence, the required probability =[tex]\dfrac{15}{32}[/tex]
If $34,500 is invested at 6.9% for 30 years, find the future value if the interest is compounded:
A-annually
E- daily
Answers
Answer:
A) 255,358.46
E) 273,353.92
Step-by-step explanation:
The formula for future value of principal P at interest rate r per year compounded n times per year for t years is ...
FV = P(1 +r/n)^(nt)
Filling in the numbers and doing the arithmetic, we have ...
A) FV = $34,500(1 + 0.069)^30 ≈ $255,358.46
__
E) FV = $34,500(1 + 0.069/365)^(365·30) ≈ $273,352.92
Paul received a $12,000 loan from the bank the bank charges 6. 99% Do you eat interest-rate after four years how much money does Paul owe in the interest?
Answers
Answer:
$3355.20
Step-by-step explanation:
The formula for simple interest is ...
i = Prt
where P is the principal amount, r is the annual rate, and t is the number of years. Fill in the given values and do the arithmetic.
i = 12,000×0.0699×4 = 3355.20
Paul owes $3355.20 in interest.
Which equation can be used to solve for the unknown number? Seven less than a number is thirteen.
n-7=13
7-n=13
n+7=13
n+13=7
Answers
Answer:
n-7=13
Step-by-step explanation:
We need to find an equation that represents the expression: "Seven less than a number is thirteen".
It means that a number minus 7 equals 13. So, the correct option is: n-7=13
Bonus: Solving for 'n' we have that n=20.
So, Seven less than 20 equals 13!!
Answer:
the anwser is: n-7=13
Step-by-step explanation:
i took the test:)
PLEASE HELP ME FAST
The table shows values for functions f(x) and g(x). What are the two solutions to f(x) = g(x)? (Hint: What X values have the same y values?)
x = -3
x = -2
x = -1
x = 0
x = 1
x = 2
x = 3
Answers
Answer:
The Answer is: -1 and 1
Step-by-step explanation: