The given sequence 48, 12, 3, .... written in the explicit formula is as follows:
aₙ = 48·(1/4)^(n-1)
What is the explicit formula?The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.
An arithmetic sequence has the explicit formula aₙ = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms.
The nth term of arithmetic, geometric, or harmonic series is usually the explicit formula.
So, the sequence we have is as follows:
48, 12, 3, ....
The common ratio of the terms is 1/4, and the first term is 48.
The universal equation for a geometric sequence's n-th term is:
aₙ = a1·r^(n-1)
This is true when r = 1/4 and a1 = 48:
aₙ = 48·(1/4)^(n-1)
Therefore, the given sequence 48, 12, 3, .... written in the explicit formula is as follows:
aₙ = 48·(1/4)^(n-1)
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Find the equation of the line joining the points (2,-8) and (5,6)
Answer:
y=3/2x-11
x,=2 and x2=5y1= -8 and y2= 6change in y over change in x get x use the formulae[tex]y = mx + c[/tex]thats the formular u got mfind c using one pairThe Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt? Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The amount of baking powder would they need to used 1 teaspoon of salt will be 6 teaspoons.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.
Now,
Since, The Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.
Hence, The amount of baking powder would they need to used 1 teaspoon of salt = 2 × 3
= 6
Thus, The amount of baking powder would they need to used 1 teaspoon of salt will be 6 teaspoons.
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Find the surface area of the cylinder in terms of pi
Answer:[tex]522\pi[/tex] [tex]sq. inches[/tex]
Step-by-step explanation:
formula for surface area of cylinder =[tex]2\pi r^{2} +2\pi rh[/tex] , where r is radius of cylinder given 9 inches and h is height of the cylinder which is 20 inches.putting the values we get,[tex]2\pi (9)^{2} +2\pi (9)(20)\\162\pi +360\pi \\=522\pi sq. inches[/tex]
Tim answered all the questions on the math test but got 10 wrong answers. He got 4 points for each correct answer, there were no penalty points for incorrect answers. His score was 76 points. Write an equation to find the total number of questions (q) on Tim’s math test
The equation to find the total number of questions (q) on Tim's math test is 76 = 4x + 0
How to write and solve equation?
Number of wrong questions = 10
Points received for right question = 4 points
Points received for wrong question = 0 points
Total of Tim's score = 76%
According to the given question:
Let the number of questions right answered by Tim be x.
Total points gained by Tim for the right answer = number of questions right answered x Points received for a right answer
= x × 4
= 4x
Points gained by Tim for the wrong answer = number of questions wrong answered x Points received for a wrong answer
= 10 × 0
= 0
Total points scored by Tim = Points gained for the right answer + Points gained for the wrong answer
76 = 4x + 0
76 = 4x
divide both sides by 4
x = 76/4
x = 19
Hence, the number of question answered right by Tim are 19.
Total number of questions attempted by Tim
Total number of questions attempted by Tim
= number of questions answered right +number of questions answered Wrong
= 19 + 10
= 29
Hence, the total number of questions attempted by Tim is 29.
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Write a polynomial function f of least degree that
has rational coefficients, a leading coefficient of 1,
and the given zeros.
5. -4, 1, 2
6. -6, -1, 3
7. 7, 1+ i
8. 2i, 1-i
The polynomial functions of the given zeroes are:
5) f=x³+x²-10x+8
6) f=x³+4x²-15x-18
7) f=x²-x(1-i-7)+7i+7
8) f=x²-x(1-i)+2i+2
What is a polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
5) The given zeroes are -4, 1, 2
(x+4)(x-1)(x-2)=0
x³+x²-10x+8=0
6) (x+6)(x+1)(x-3)=0
x³+4x²-15x-18=0
7) (x-7)(x-(1+i))=0
x²-x(1-i-7)+7i+7=0
8) (x-2i)(x-(1-i))=0
(x-2i)(x-1+i)=0
x²-x(1-i)+2i+2=0
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Ahmad drove 350 miles in 5 hours.
At the same rate, how many miles would he drive in 7 hours?
Answer:
490 miles
Step-by-step explanation:
Since Ahmad is driving 350 miles in 5 hours, he's averaging 70 miles per hour.
350/5 = 70 mph
Driving 7 miles at 70 mph:
7 x 70 = 490 miles
Answer: 490 miles!
Step-by-step explanation:
350 x 7hrs divided by 5hrs would be = 490miles
multiple 350 and 7 ( 350x7) which will equal 2450 then divide by 5 and you will get 490 milesHow did I get 490? or why didn't you do 350 x 5?
Well because the question asks how many miles would he drive in 7 hours? you will need to multiple the droven miles which is 350miles because that is part of the getting answer, and the question of having to know how many miles would he drive in 7 hours, you wouldn't do 350 x 5 because its not asking " Ahmad drove 350 miles in 5 hours, how many miles would he drive in 5 hours? and which would equal 250 which not correct because it doesn't make sense if he's drove 350 miles in 5 hours and then drove 250miles in 7 hours, back to the explanation, after multiplying 350 into 7 you will end up at 2450, no this isn't the answer you need to divide because it would take more than 7 hours to drive 2450 miles, next you divide by the hours driven in 350 miles which in this in this case would be 5 because your diving 2450 by 5 because sense u cannot get the answer by multiplying 350x5 so this is time where your gonna use the 5 because 350 x 7= 2450 is too large in miles for 7 hours your gonna divide the 2450 to lower it down to 490 miles, doesn't that sound more accurate? the miles increase by 1.4 ( 140 miles ) so another way u could have gotten the answer was by doing 350 + 140 = 490 but however you would need to know how much the miles have increase which u can do by 490 - 350 which equals to 140 miles.
The administrative assistant at a software company often provides breakfast when there is a morning meeting. For last week's sales meeting, she purchased 4 dozen doughnuts and 1 dozen croissants, spending a total of $34. In preparation for yesterday's safety meeting, she spent $52 on 7 dozen doughnuts and 1 dozen croissants. Write a system of equations that could be used in this situation.
Hint: I JUST WANT THE EQUATIONS NOT THE FINAL SOLUTION.
A dozen of doughnuts cost $6 and a dozen of croissants cost $10.
What is meant by a linear equation?A linear polynomial over a field, from which the coefficients are taken, can be reduced to a linear equation by equating it to zero.
Such an equation's solutions are the values that, when used as placeholders for the unknowns, result in the equality being true.
When there are just two variables, it is possible to interpret each solution as the Cartesian coordinates of a particular point on the Euclidean plane. In the Euclidean plane, a linear equation's solutions are represented by lines, and each line can be thought of as the collection of all the solutions to a linear equation with two variables.
Let,
The cost of dozen doughnuts be x
And the cost of dozen croissants be y
Given,
4x+y=34
7x+y=52
By solving both the equations, we get
-3x=-18
x=6
4x+y=34
4(6)+y=34
24+y=34
y=10
Therefore, a dozen of doughnuts cost $6 and a dozen of croissants cost $10.
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A fruit-packing company produced peaches last summer whose weights were normally distributed with mean 14 ounces and standard
deviation 0.8 ounce. Among a sample of 1000 of those peaches, about how many could be expected to have weights of more than
11.2 ounces?
About 999 plants have weights more than 11.2 ounce.
What is z- score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree
Given:
Mean= 14
Standard deviation = 0.8
So, P( x > 11.2) = P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] > (11.2- 14/ 0.8)
= P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] > -3.5)
= 0.999767
Hence, about 999 plants have weights more than 11.2 ounce.
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The area of a circle is 113.04 square miles. What is the circle's radius?
Use 3.14 for л.
Submit
miles
Answer: 6 miles exactly
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
A=πr^2
113.04=3.14×r^2
113.04/3.14=r^2
36=r^2
√36=r
r=6
how manys pounds of mixed nuts that contain 20% peanuts must eugene add to 16 pounds of mixed nuts that contain 70% peanuts to make a mixture with 60% peanuts?
By resolving equations, we know that we can add 10 pounds of mixed nuts that include 20% peanuts.
What are equations?An equation is a statement that demonstrates the equality of two mathematical expressions, according to mathematics.
For instance, the equation 3x + 5 = 14 is composed of equation 2 3x + 5 and 14, which are separated by the equal sign.
So, we require x pounds of the mixed nuts in total.
This mixture contains 0.70 pounds of peanuts.
The 20% mix, or 0.20*15, is made out of 3 pounds of peanuts.
Equation obtained: 0.70 x + 3 = 0.40(x + 15)
Solve the equation as shown below:
0.70 x + 3 = 0.40(x + 15)
0.70 x + 3 = 0.40(x + 15)
0.70x + 3 = 0.40x + 6
0.70x - 0.40x = 6 - 3
0.30x = 3
x = 10 pounds
Therefore, by resolving equations, we know that we can add 10 pounds of mixed nuts that include 20% peanuts.
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will someone help me with this geometry please
Answer:
[tex]\huge\boxed{\sf HF=71.4}[/tex]
Step-by-step explanation:
If ΔCDE is similar to ΔFGH, their sides are proportional.
So,
[tex]\displaystyle \frac{23}{HF} =\frac{19}{59} \\\\Cross \ Multiply\\\\23 \times 59 = 19 \times HF\\\\1357 = 29HF\\\\Divide \ 19 \ to \ both \ sides\\\\1357/19 = HF\\\\71.4 = HF\\\\HF=71.4\\\\\rule[225]{225}{2}[/tex]
Annual high temperatures in a certain location have been tracked for several years. Let
X
represent the year and
Y
the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).
x y
2 20.35
3 21.6
4 21.45
5 22.8
6 23.25
7 20.6
8 20.95
9 22.1
10 18.85
11 21.1
12 17.75
13 19.5
14 19.25
15 17.1
Answer:
haha
Step-by-step explanation:
How can you find value of n in this equation 40+n=55+22
Answer:
n=37
Step-by-step explanation:
The first thing to do would be to eliminate the 40 from the left side of the equation, leaving n by itself. Then, you subtract the 40 from the 55, then add the result to 22.
hope this helps!!! :3
John's bank account was overdrawn. The status of his account was $-141. He did not realize the problem and wrote another check for $29. The bank charged him a $15 fee for being overdrawn. What was the new status of John's account at this point ?
Answer:
$-185
Step-by-step explanation:
If Johns bank account is at $-141, and he continues to use money, then the equation would look something like this:
-141 + -29 + -15 =?
It's simple! Just add the numbers together!
141 + 29 = 170
170 + 15 = 185
Johns bank account status is now $-185.
If the figure above is rotated 90° counterclockwise, in which quadrant will it appear?
A. I
B. II
C. III
D. IV
Answer: Depends on what quadrant it starts in/on.
Step-by-step explanation:
Quadrant 1 is the top-right corner.
Quadrant 2 is the top-left corner.
Quadrant 3 is the bottom-left corner.
Quadrant 4 is the bottom-right corner.
Depending on what quadrant you started on will determine what quadrant you're on after rotating 90 degrees counter-clockwise.
You take your car in to get the oil changed. It costs $40 for the oil and $25 an hour for labor.
Write a linear equation that represents the total cost in dollars of the oil change if it requires x hours of labor.
A linear equation that represents the total cost in dollars of the oil change is Y = 25X + 40
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Linear Equations in Standard Form
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.
Given :
Cost of the oil (calculated once) = $40
Cost of labour (calculated per hour) = $25
Thus , a linear equation that represents the total cost in dollars of the oil change if it requires x hours of labor can be expressed as Y = 25X + 40 where X represents no . of working hours of labour and Y represents total cost .
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A restaurant prepares 250 side salads per day and estimates that 15% of the salads will spoil. What s the spoilage amount for the side salads? (Round up to nearest whole number.) A. 38 salads B. 15 salads C. 40 salads D. 6 salads
Answer:
A
Step-by-step explanation:
15 : 100 = x : 250
x = 250 * 15 / 100
x = 2.5 * 15
x = 37.5
x = 38
2/5*6/7 multiple and write fraction or mixed number in simplest form
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
multiple the numerators together 2 x 6 = 12 and multiply the denominators togethers 5 7 = 35
Dilating point A using center C and scale factor 2.5 gives A'. Dilating point B using Center C and scale factor 2.5 gives image B'. What can you say about line AB and A'B'? What is the length of segment A'B'?
line AB is original figure, line A'B' is transformed figure. the length A'B' is given by √[(2.5x₂-2.5x₁)²+(2.5y₂-2.5y₁)²]
What is dilation?
A process of transformation in which an image or figure changes from the original shape.
What is dilating point?
The point which is acted as the center for all contraction and expansion is termed as dilation point.
let, point A is (x₁,y₂) and point B is (x₂,y₂). By using scale factor 2.5, both A and B transformed to the position A' and B'.
hence, A' = (2.5x₁, 2.5y₁) and B'=(2.5x₂,2.5y₂)
now length of A'B' =√[(2.5x₂-2,5x₁)²+(2.5y₂-2.5y₁)²]
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How do I find the value in n of the equation 40+n=50+22
Angela uses 6.1 pints of white paint and blue paint to paint her bedroom walls.
4
5
of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Blue paint she has used in her bedroom walls is, 1.22 paints.
Fraction definition?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure below the line.
The walls of Angela's bedroom are painted with 6.1 paints each of blue and white paint.
So to find the blue paint ,
she used 4/5 of whole pigments as white paint.
Firstly we multiple it by whole paint that is 6.1 and find white paint and then whole paint subtracted with white paint will give blue paint.
She painted using 4/5 of the whole amount of pigments as white paint
That amount in pints of white paint is equal to
4/5 * 6.1.
= 4.88 paints of white
The number of paints used to paint blue is therefore:
whole paint - white paint.
= 6.1 - 4.88
As a result, 1.22 blue paints she has used.
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Hey I need help understanding how to solve application problems involving rational equations
Select the correct answer.
Consider the graph and the equation of function f.
f(x)=2 sin (1/2x) + 1
Answer:
y = 1
Step-by-step explanation:
The middle of the equation on the graph is y = 1.
Identify the null and alternative hypotheses for the following problems.
a. The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch.
b. Economists have stated that the marginal propensity to consume is at least 90¢ out of every dollar.
c. It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.
The null hypothesis is it takes a customer less than or equal to 25 minutes to eat lunch.
The alternate hypothesis is it takes a customer more than 25 minutes to eat lunch.
What is null and alternate hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. The alternative hypothesis is one of the suggested hypotheses in statistical hypothesis testing.
We are given a statement,
The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch.
According to null hypothesis, There is no difference or change
Hence the null hypothesis is, it takes a customer less than or equal to 25 minutes to eat lunch.
Where as in alternate hypothesis, There should be a difference of change
Hence the alternate hypothesis is it takes a customer more than 25 minutes to eat lunch.
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(need help asap please this is urgent)
Use the systems of inequalities graphed below to answer the questions.
what is the inequality symbol of the green line?
-y is greater than ax+b -y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
what is the inequality symbol of the green line?
-y is greater than ax+b
-y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
is the point (-3, -5) a solution to the system of inequalities?
-yes -no
is the point (1,6) a solution to the system of inequalities?
-yes -no
Answer:
Green line: y is greater than or equal to ax+b
Purple line: y is less than ax+b
(-3, -5) : Yes
(1, 6) : No
Step-by-step explanation:
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Green line
From inspection of the given graph, the green line is a solid line and the shading is above the line.
Therefore, the inequality symbol of the green line is ≥.
"y is greater than or equal to ax+b"
Purple line
From inspection of the given graph, the purple line is a dashed line and the shading is below the line.
Therefore, the inequality symbol of the purple line is <.
"y is less than ax+b"
The solutions to a graphed system of inequalities are found in the overlapping shaded region.
Yes, point (-3, -5) is a solution to the system of inequalities as this point is in the overlapping shaded region.
No, point (1, 6) is not a solution to the system of inequalities as this point is not in the overlapping shaded region.
The school events committee is planning to buy a banner and some helium balloons for graduation night. A store charges them $35 for the banner and $3.50 for each helium balloon. If the committee has at most $125 to spend, how may helium balloons can they buy?
Answer: About 25
Step-by-step explanation: So, to find how many helium balloons, we need to subtract 35 from 125, then divide it by 3.50. So, 125-35 = 90. So, 90 / 3.50 = 25.714285714285715. So, we are around 25.7 up to 26. But, we can't do this. This is because they can't spend over $91 on balloons. So, we have to round down. If it was 26, they would spend $91, 1 dollar over their budget. So, it would be about 25, which would be 87.50. So, they would have $3.50 left over.
what is the solution to -3x-3<6
Answer:
x>-3
Step-by-step explanation:
1
Add
3
to both sides
-3x-3<6
-3x-3+
2
Simplify
Add the numbers
Add the numbers
-3x<9
3
Divide both sides by the same factor, and flip the relation because the factor is negative
-3x<9
4
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
x>-3
A car starts out at a speed of 50mph. A second car starts out 3 hours later at 65mph to overtake the first one. How many hours will the first car be on the road at the point where it is overtaken?
50 PTS! Please answer quick. you will get brainliest
Answer:
13 hours----------------------------------
Both cars will make same distance but the first one will be on road for 3 more hours.
Let the number of hours the first car in travel be x.
Then set an equation:
50x = 65(x - 3)50x = 65x - 19565x - 50x = 19515x = 195x = 13write the equation of the trigonometric graph.
A trigonometric equation is an equation containing one or more trigonometric ratios of unknown angles. It is expressed as the ratio of the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.
What are examples of trigonometric equations?
Trigonometric equations are equations containing trigonometric functions with one variable. For example, sin x + 2 = 1 is an example of a trigonometric equation. The equation can be as simple as this, or as complex as sin2 x – 2 cos x – 2 = 0.
What are the 4 types of trigonometry?
Side length ratios can be found with six trigonometric functions. The six functions are sine (sin), cosine (cos), tangent (tan), cosecant(cosec), secant (sec), and cotangent (cot).
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Answer(s):
[tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2 \\ y = -3cos\:(\frac{2}{3}x \pm \pi) + 2 \\ y = 3cos\:\frac{2}{3}x + 2[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{3}{4}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{2}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\:\frac{2}{3}x + 2,[/tex]in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{3}{4}\pi\:units[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{3}{4}\pi\:units,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{3}{4}\pi} = \frac{-\frac{\pi}{2}}{\frac{2}{3}}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-4\frac{1}{2}\pi, -1],[/tex]from there to [tex]\displaystyle [-1\frac{1}{2}\pi, -1],[/tex]they are obviously [tex]\displaystyle 3\pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 3\pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 2,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
what is the value of b?
Answer:
b = 44°
Step-by-step explanation:
Opposite angles are congruent.