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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Choose the correct box of the best buy available. a can of tomatoes for 53¢ one can of tomatoes with a 20% discount when the regular price is 70¢ per can
The solution is: a can of tomatoes for 53 cents, is the best buy available.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
So, we have two options:
option 1: a can of tomatoes for 53 cents.
option 2: a can of tomatoes for 70 cents with a 20% discount.
First we have to determine the price of the 2nd option.
10 % of 70 cents is 7 cents
20 % of 70 cents is 14 cents.
So, we have 14 cents of discount, which makes the new price (70-14=) 56 cents.
Now our two options are either 53 or 56 cents.
Therefore option 1 is the best buy available.
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Credit card A offers an APR of 25.68% compounded monthly, while credit card B offers an APR of 25.32%, compounded daily. All else being equal, which card offers a better deal for the consumer?
Answer:
Credit card B, because its effective interest rate is about 0.13% less than that of credit card A.
The deal of Credit card A is du to higher interest rate.
What is compound interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given
APR of credit card A = 25.68% compounded monthly
APR of credit card B = 25.32% compounded daily
other details are same
let principle be 100
time = 1 year
Amount for Credit card A = P[tex](1 + \frac{r}{n})^{n t}[/tex]
where r = rate, t = time, n = time frequency
A = 100[tex](1 + \frac{0.2568}{12})^{12*1 }[/tex]
A = 128.92
amount for credit card B
A = 100[tex](1 + \frac{0.2532}{360})^{360*1 }[/tex]
A = 128.78
Hence amount for both the APR is approx. same so Credit card A is better deal with more interest rate.
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What is 3/tan(30°) in radical form? (meant to be a fraction)
A tree standing vertically on level ground casts a 140 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 24.7°. Find the height of the tree to the nearest foot.,
A recovering heart attack patient is told to get on a regular walking program. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of 10 weeks. At that point the patient is to maintain the distance walked during the 10th week. How far will the patient walk during the 10th week? a. Is the sequence arithmetic or geometric? Explain your answer.
The sequence in this scenario is arithmetic, with the patient increasing their distance walked by 3 km each week. Using the formula for the nth term of an arithmetic sequence, the patient will walk a distance of 32 km during the 10th week.
Explanation:The sequence in this case is arithmetic. This can be determined by observing that the difference between the distances walked each week is consistent. In this case, the difference is 3 km, as the patient increases their distance by 3 km each week.
To find out how far the patient will walk during the 10th week, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
Where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
Given that the first term is 5 km, the common difference is 3 km, and we want to find the 10th term, we can substitute the values into the formula:
a10 = 5 + (10-1)3
a10 = 5 + 9 * 3
a10 = 5 + 27
a10 = 32
Therefore, the patient will walk a distance of 32 km during the 10th week.
A square has an area of 256 square meters. How long is each side?
what two numbers have a sum of 24 and have a quotient of 3?
The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?
What is the length of a leg of the pre-image, triangle RST? 4 units 8 units 16 units 20 units
Answer:
C) 16 units
Step-by-step explanation:
The length of a leg of the pre-image is 16 units
What is Dilation?The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger. The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image. Dilation comes in two varieties:
Increase in an object's size is referred to as expansion.Contraction is the reduction of an object's size.Given:
Δ RST was dilated by a scale factor of 1/2
and, Δ R'S'T' is an isosceles triangle with measurement 8 units.
As, Pre-image = measure of pre-image x scale factor
So, the measure of pre-image = 8 ÷ 1/2
= 8 x 2/1
= 16 units.
Hence, the length of a leg of the pre-image is 16 units
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Four polynomials are shown below: A. 4 − 7x5 + x2 B. 5x3 + 5 − 3x4 C. 3x + 2x4 − x2 + 6 D. 3x3 − 5 + 2x5 + x Which of the above polynomials is a 4th degree trinomial? Polynomial A Polynomial B Polynomial C Polynomial D
Answer:
Polynomial B
Step-by-step explanation:
We are given 4 different polynomial. We need to choose 4th degree polynomial from given.
Degree is maximum power of x of polynomial.
Option A: [tex]4-7x^5+x^2[/tex]
Degree = 5, False
Number of term = 3 (Trinomial)
Option B: [tex]5x^3+5-3x^4[/tex]
Degree = 4
Number of term = 3 (Trinomial)
True
Option C: [tex]3x+2x^4+x^2+6[/tex]
Degree = 4
Number of term = 4 (Not Trinomial)
False
Option D: [tex]3x^3-5+2x^5[/tex]
Degree = 5
Number of term = 3 (Trinomial)
False
Hence, Polynomial B is correct whose degree 4 and number of term 3.
What is the missing constant term in the perfect square that starts with x²+6x?
The expression given to us is: x²+6x
Now, we know that the second term is twice the square root of the first and the last terms. Let us call the last term as [tex] y^2 [/tex]. Thus our given expression will become:
[tex] x^2+6x+y^2 [/tex].
Now, since the middle term is 6x and since we know that the second term is twice the square root of the first and the last terms, therefore,
[tex] 6x=2\times \sqrt{x^2} \times \sqrt{y^2} [/tex]
[tex] 6x=2\times x\times y [/tex]
[tex] \therefore y=3 [/tex] (By dividing both sides by 2x)
Therefore, the missing term is 3.
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9
5.363
52.63
53.62
5.263
Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410
The estimation to determine whether the result is reasonable or not. 108.93 x 355.112
Reasonable
Not reasonable
Which figure shows the correct dimensions of a 14 scale drawing of the given figure?
Angle K in △MKL is a right angle.
What is the value of tan M ?
15/17
8/17
8/15
15/8
Solution :
Given that, In triangle MKL, angle K is a right angle.
To find the value of tan M,
As we know by trigonometric ratio, that In a right angled triangle
[tex] tan (\theta)= \frac{opposite }{Adjacent} [/tex]
Here Opposite means opposite side of the angle and adjacent means side adjacent to the angle.
So, [tex] tan M= \frac{KL}{KM} = \frac{15}{8} [/tex]
Hence, Value of [tex] tan M = \frac{15}{8} [/tex] .
Option D is the correct solution.
Jake runs either 15 kilometers or 8,500 meters each day.He alternates short and long runs. how many meters farther will he run on his two long run days than on his two short run days?Describe how you found your answer
What is the length of BB' ?
Answer:
The answer is sqrt29
Step-by-step explanation:
If you are doing the same program as me, there will be other questions similar to this one. What is the length to AA', BB', and CC'. All of these share the same answer which is also sqrt29. We are almost finished with the semester, hang on!
You and your friend each drive 50.0 km. you travel at 90.0 km/h. your friend travels at 95 km/h. how long will your friend be waiting for you at the end of the trip?
Answer:
He will reach 0.02 hours before me.
Step-by-step explanation:
A we know that,
Speed = Distance ÷ Time
Here we have given that Distance = 50 km
My Speed is 90 km/h
So time taken to complete my trip = Distance ÷ Speed
⇒ My Time = 50 ÷ 90 = 0.55 hours
Also, Speed of my friend is 95 km/h
So time taken to him to complete his trip = Distance ÷ Speed
His Time = 50 ÷ 95 = 0.53 hours
Thus he will reached before me as his speed is fast
He will reach 0.55 - 0.53 = 0.02 hours before me.
Which identity needs to be used to prove tan (pi/2-x)=cot x?
To prove the identity tan (pi/2-x) = cot x, we can use the identity tan(pi/2-x) = 1/tan x and simplify the expression.
To prove tan (pi/2-x) = cot x, we can use the identity tan(pi/2-x) = 1/tan x. First, rewrite tan(pi/2-x) as 1/tan x. Then, simplify 1/tan x to cot x using the definition of cot x = 1/tan x. Therefore, we have proven that tan (pi/2-x) = cot x.
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To prove tan(π/2 - x) = cot x, we use the co-function identity for tangent and cotangent, showing the relation of these functions in complementary angles. This identity confirms that tan(π/2 - x) equals cot x.
To prove the identity tan (π/2 - x) = cot x, we can use a fundamental trigonometric identity. Here's how:
Recall the co-function identity: tan (π/2 - x) = cot x. This identity is derived from the relationship between tangent and cotangent in complementary angles.
Using the identity tan (π/2 - x) = cot x, we know that the tangent of an angle's complement is equal to the cotangent of the angle.
By definition, tan θ (tangent) is the ratio of the opposite side to the adjacent side in a right triangle. For the complementary angle, the roles of the opposite and adjacent sides switch, which aligns with the definition of cot x (cotangent), i.e., the adjacent side over the opposite side.
This proves that tan (π/2 - x) = cot x.
At summer camp, 150 kids had the opportunity to choose their activities. 1/3 of those kids selected archery for their morning activity. Of that group,1/5 also chose to study drama in the afternoons. How many kids chose both archery in the morning and drama in the afternoons? kids chose archery for their morning activity. Of those kids who chose archery in the mornings, also chose drama in the afternoons.
Answer:
50&10...
Step-by-step explanation:
The average of 3 numbers is 22, and the smallest of these numbers is 2. what is the value of the other two numbers if they are equal?
if csc( weird squiggly thing) = 13/5 then what would sec sin cos and tan = ?,
Please help ASAP!!! 15 points!
Solve the equation using the quadratic formula.x squared minus 4 x plus 3 equals 0 (1 point)x equals 2 semicolon x equals 4x equals 0 semicolon x equals 4x equals 1 semicolon x equals 3x equals negative 1 semicolon x equals 92. Solve the equation using the quadratic formula. x squared plus 10 x equals negative 25 (1 point)x equals 5x equals negative 5x equals 15x equals 253. Using the discriminant, determine the number of real solutions.negative 4 x squared plus 20 x minus 25 equals 0 (1 point)no real solutionsone real solutiontwo real solutions4. Using the discriminant, determine the number of real solutions.2 x squared plus 7 x minus 15 equals 0 (1 point)no real solutionsone real solutiontwo real solutions5. Using the discriminant, determine the number of real solutions.negative 2 x squared plus x minus 28 equals 0 (1 point)no real solutionsone real solutiontwo real solutions6. If the discriminant of a quadratic is zero, determine the number of real solutions. (1 point)no real solutionsone real solutiontwo real solutions7. Solve the equation using the quadratic formula.3 x squared equals 2 left-parenthesis 2 x plus 1 right-parenthesis (1 point)x equals StartFraction 3 plus minus StartRoot of 13 EndRoot over 6 EndFractionx equals StartFraction 2 plus minus StartRoot of 10 EndRoot over 3 EndFraction x equals one-sixth semicolon x equals one-halfx equals 3 semicolon x equals negative 18. Solve the equation using any technique.x squared plus 8 x plus 12 equals 0 (1 point)x equals negative 4 semicolon x equals 4x equals negative 6 semicolon x equals negative 2x equals 3 semicolon x equals 7x equals 6 semicolon x equals 89. Solve the equation using any technique.6 x squared minus 5 x minus 1 equals 0 (1 point)x equals one-fifth semicolon x equals one thirdx equals 2 semicolon x equals 6x equals 3 semicolon x equals negative one-halfx equals negative one-sixth semicolon x equals 110. Solve the equation using any technique.x squared equals 3 x minus 1 (1 point)x equals StartFraction 2 plus minus StartRoot 7 EndRoot over 3 EndFractionx equals StartFraction 1 plus minus StartRoot 3 EndRoot over 2 EndFractionx equals StartFraction 3 plus minus StartRoot 5 EndRoot over 2 EndFractionx equals StartFraction negative 2 plus minus 2 StartRoot 3 EndRoot over 3 EndFraction
This answer details the use of the quadratic formula to solve quadratic equations and the discriminant's role in determining the number of real solutions.
Explanation:The question involves solving quadratic equations and using the discriminant to determine the number of real solutions. The quadratic formula, \(x = \frac{-b \pm \sqrt[tex]{b^2[/tex] - 4ac}}{2a}\), is a powerful tool in finding the roots of any quadratic equation of the form \([tex]ax^2[/tex]+ bx + c = 0\). The discriminant, \(\Delta =[tex]b^2[/tex] - 4ac\), helps in understanding the nature of the roots without actually solving the equation. If \(\Delta > 0\), there are two distinct real solutions; if \(\Delta = 0\), there is exactly one real solution; and if \(\Delta < 0\), there are no real solutions and instead two complex solutions.
What did the Beat generation writers try to defeat in America?
A) pacifism
B)traditionalism
C)individualism
D)Feminism
Option: B is the correct answer.
B) Traditionalism.
Step-by-step explanation:Beat generation was a literary movement that was started by a group of authors and belongs to the post World War || period.
They started this movement to reject literary formalism and the American culture built on capitalism and materialism.
It has a major impact on both poetry as well as culture in America.
Hence, the Beat generation writers try to defeat in America is:
Traditionalism.
X^2-7x+10=0
It says to “solve each equation by factoring and using the Zero Product Rule
can someone help me please? i'm not sure if 4 is right and i don't understand how to do 3
Find an equivalent function for the following:
f(x) = 3(2)4x
Assume a team plays 6 games. If the team is equally likely to win as to lose each game, what is the probability that they win a string of at least 4 games in a row? I found my sample size to be 2^6=64 and I've tried listing out all the sequences, what I found was. W W W W W W ; W W W W W L ; W W W W L L ; L W W W W L ; L W W W W W ; L L W W W W,
Answer:
I THINK A
Step-by-step explanation:
MATHHHHHHHHHHHHHHHHHHHHHHHHA
A volume of ______ is formed by revolving a plane figure through 360 degrees around a line.
Answer:
Correct Answer: Revolution
Step-by-step explanation: