What is the equation of the midline for the function y = 2sin(x - π) + 3
The equation of the midline for the function 2sin (x - π) + 3 is y = 3.
What is the Midline of a Function?The midline of a function is the line horizontal to the minimum value and maximum value of the function.
Given function is 2sin (x - π) + 3.
We know the trigonometric formula,
sin (A - B) = sin A cos B - cos A sin B
sin (x - π) = sin x cos π - cos x sin π
= (sin x × -1) - (cos x × 0) [Since cos π = -1 and sin π = 0]
= -sin x
So, 2sin (x - π) + 3 = -2sinx + 3
Now, we know that,
-1 ≤ sin x ≤ 1
Multiplying whole sides by -2,
2 ≥ -2sin x ≥ -2
[since the inequality sign changes when negative is multiplied or divided]
Adding 3 throughout,
5 ≥ -2sin x + 3 ≥ 1
Maximum value is 5 and minimum value is 1.
Midline value = (5 + 1) / 2 = 3
So the equation of the midline is y = 3.
Hence the equation of midline is y = 3.
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i need help PLEASEEEEEEEEEE!:P Susan is paying $0.30 per $100 on her $483,000 home in homeowners insurance annually. If her annual homeowners insurance premium is divided into twelve equal monthly installments to be included on each of her monthly mortgage payments of $2128.00, what is her total monthly payment?
a.
$2,248.75
b.
$2,409.75
c.
$3,381.00
d.
$3,577.00
The owner of a garden center delivers bags of mulch. Each bag is sold for $6. The owner spends $16 for transportation to deliver the bags. Which of the following is the slope of the profit function for the garden center owner per delivery? Answer Choices m=6 m=−6 m=16 m=−16
If the height of Mount Everest is about 8.8×103 meters, and the height of the Empire State Building is about 3.8×102 meters, which of these statements is true?
Answer:
option C is correct, i.e. Mount Everest is about 23 times as tall as the Empire State Building .
Step-by-step explanation:
Given options are:-
A. There is no way to compare these heights .
B. Mount Everest is about 40 times as tall as the Empire State Building .
C. Mount Everest is about 23 times as tall as the Empire State Building .
D. The Empire State Building is about 23 times as tall as Mount Everest.
Given the height of Mount Everest is about 8.8×10^3 meters, and the height of the Empire State Building is about 3.8×10^2 meters.
Finding ratios of given heights:-
[tex]\frac{Mount\;\;Everest}{Empire\;\;State\;\;Building} =\frac{8.8*10^3m}{3.8*10^2m} \\\\\frac{Mount\;\;Everest}{Empire\;\;State\;\;Building} =23.15789474 \approx 23 \\\\Mount\;\;Everest=23*(Empire\;\;State\;\;Building)[/tex]
Hence, option C is correct, i.e. Mount Everest is about 23 times as tall as the Empire State Building .
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Could you plz help me id appreciate it so much: )
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14. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5). Show your work.
Question 4 find the indicated probability or percentage for the normally distributed variable. the volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. what is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?
HELP PLS with this geometry problem
What is the answer to this question please explain...
Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(1.25, 0.75) , B′(0.75, 1.75) , and C′(0.25, 1) . The center of dilation is the origin. What is the scale factor of the dilation? 0.25 0.5 2 4
This is the answer the other is right
one light year is 5.88 x 10^12 miles. suppose a star is 2.23 x 10^2 light years away from earth. In scientific notation how many miles is it?
A playground is being designed where children can interact with their friends in certain combinations.
If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 3 interactions.
If there are 3 children, there can be 12 interactions.
If there are 4 children, there can be 39 interactions.
Which recursive equation represents the pattern?
an = an – 1 + 3(n – 1)
an = an – 1 + 3(n – 1)
an = an – 1 + (3n – 1)
an = an – 1 + (n – 1)3
Answer:
[tex]a_n=a_{n-1}+3^{n-1}[/tex]
Step-by-step explanation:
It is given that
If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 3 interactions.
If there are 3 children, there can be 12 interactions.
If there are 4 children, there can be 39 interactions.
It means we have,
[tex]a_1=0, a_2=3, a_3=12, a_4=39[/tex]
We need to find the recursive equation that represents the pattern.
[tex]a_2=3\Rightarrow 0+3=a_1+3[/tex]
[tex]a_3=12\Rightarrow 3+9=a_2+3^2[/tex]
[tex]a_4=39\Rightarrow 12+27=a_3+3^3[/tex]
Similarly,
[tex]a_n=a_{n-1}+3^{n-1}[/tex]
Therefore, the required recursive formula is [tex]a_n=a_{n-1}+3^{n-1}[/tex].
The angle between 0 and 2 π in radians that is coterminal with the angle 62 9 π in radians is
8π/9 is coterminal with 62π/9 and lies between 0 and 2π.
Given that, the angle between 0 and 2 π in radians that is coterminal with the angle 62π/9 in radians.
What is the coterminal with the angle?The coterminal angles are the angles that have the same initial side and the same terminal sides. We determine the coterminal angle of a given angle by adding or subtracting 360° or 2π to it.
To find a coterminal angle, add or subtract any multiple of 2π, that is
62π/9 - 2π = (62π-18π)/9
44π/9 - 2π = 26π/9
26π/9 - 2π = 8π/9
Therefore, 8π/9 is coterminal with 62π/9 and lies between 0 and 2π.
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4.Krissa drew a circle with a radius of 4 inches.
Fill in the blanks.
The area of the circle is _______ square inches and the circumference is _______ inches.
64π, 16π
16π, 8π
16π, 64π
8π, 16π
To calculate the area of a circle, use the formula A = πr², where r is the radius. For this specific circle with a radius of 4 inches, the area is 16π square inches, and the circumference formula is C = 2πr, resulting in a circumference of 8π inches.
To find the area of a circle: A = πr². Substituting the given radius of 4 inches, we get Area = π(4)² = 16π square inches. The circumference of a circle is C = 2πr. Substituting the radius, we get C = 2π(4) = 8π inches.
PLEASE HELP 20 POINTS!!!!!!!!! The graph below shows a system of equations: Draw a line labeled y equals x plus 4 by joining the ordered pairs negative 4, 0 and 1, 5. Draw a line labeled 3 times y equals minus 2 x plus 2 by joining the ordered pairs negative 2, 2 and 4, negative 2 The x-coordinate of the solution to the system of equations is__________
A product transformation _____.
multiplies coordinates to transform the image
combines the coordinates of multiple transformations
finds the result of combining multiple transformations
uses a scale factor to multiply coordinates of the image
Answer:
The answer is C
Step-by-step explanation:
PLEASE HELP ME ON THIS!!!!
Help! Please. I don't get this.
Please help me. Thank you.
1. Your total restaurant bill is _____. (1 point)
Captionless Image
*
the items purchased minus sales tax, and plus tip.
the items purchased plus sales tax and tip.
the items purchased minus sales tax, and plus tip.
2. A check is _____. (1 point)
Captionless Image
*
required to be paid by your bank when presented
a promissory note (I.O.U.)
not able to be forged
3. There are several different ways to pay for items. In most modern economies, which is not a way to pay? (1 point)
Captionless Image
*
credit cards
bartering
cash
First question:
Your total restaurant bill is the items you have purchased plus the sales tax and plus the tip (if there’s any). Sales tax is added to your purchase because this is tax imposed to the consumer and not to the buyer. The buyer is only required to collect this tax from the buyer.
Second question:
A check is a financial instrument wherein the bank is required to pay when presented or encashed to them. You just have to make sure that you have account balance to that certain bank.
Third question:
The way of payment not any more common in the most modern economies is the bartering. Both credit cards and cash are the most common way of paying for your purchases.
Answer:
1. the items purchased plus sales tax and tip.
2. a promissory note (I.O.U.)
3. bartering
The distance from the origin to the point (-24, 32) is
The opening of the tunnel can be modeled by the graph of the equation y=-0.18x^2+4.4x-12 where x and y are measured in feet. Find the maximum height of the tunnel.
Jacob drew the similar triangles below to represent the sides of two bicycle stunt jumps. The area of the smaller triangle is 36 square inches. what is the area of the larger triangle?
A. 54
B.108
C. 324
D. 432
Anyone have the proper answer to this?
MATH HELP PLEASE UGRGENT WILL GIVE BRAINIEST!!
In the figure, YX−→− and YZ−→− are tangents to circle A at points X and Z, respectively.
mXZ=140∘
mXSZ=220∘
What is the measure of ∠XYZ ?
Answer:
40
Step-by-step explanation:
Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of
12 inches. He will make the "X" by stretching red ribbon diagonally from corner to corner. How many inches of ribbon will Peter need to make the "X"? Round your answer to the nearest inch.
Consider the following pair of equations:
y = x + 4
y = −2x − 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Janey bought a used bicycle for $640. the bike was 3 years old when she bought it, and cost $850 new. assuming it decreases in value by the same amount each year, write a linear equation for the value of the bicycle, v, when it is t years old (so t = 0 was when it was new).
Can someone do question 3 by showing step by step solutions