All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
We have to given that;
Rule for sequence is,
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Now, WE can find first five terms of sequence as;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Put n = 1;
⇒ a (1) = - 11 × (1/2)¹⁻¹
⇒ a (1) = - 11
Put n = 2;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (2) = - 11 × (1/2)²⁻¹
⇒ a (2) = - 11 × (1/2)¹
⇒ a (2) = - 11 / 2
Put n = 3;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (3) = - 11 × (1/2)³⁻¹
⇒ a (3) = - 11 × (1/4)
⇒ a (3) = - 11 / 4
Put n = 4;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (4) = - 11 × (1/2)⁴⁻¹
⇒ a (4) = - 11 × (1/2)³
⇒ a (4) = - 11 / 8
Put n = 5;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (5) = - 11 × (1/2)⁵⁻¹
⇒ a (5) = - 11 × (1/2)⁴
⇒ a (5) = - 11 / 16
Thus, All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
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CAN SOMEONE TELL ME IS HE CORRECT OR WRONG HOW TO DO IT
Answer:
The answer is 33°
Yes you are correct
Step-by-step explanation:
angles on a straight line equal 180°
57+90+x=180
x+147=180
x=180-147
x=33°
Hi, I can't tell if there's a little square drawn in red to indicate that there's a right angle in the middle. There's some squiggly lines and so it's kind of hard to tell.
I am going to assume that there is. Let me know if there isn't.
The sum of these 3 angles would be 180 degrees.
As an equation, 57 + 90 + x = 180
Solve for x.
147 + x = 180
x = 33 degrees.
So this would be correct ASSUMING that there's a little red square drawn indicating that there's a right angle.
evaluate 3x+5y when x=11 and y=4.
(a)23
(b)67
(c)53
(d)13
Answer:
(c):53
Step-by-step explanation:
Let's start with the equation:
3x+5y
Since we already have the values of x and y, we can just solve the equation.
3(11)+5(4)
33+20=53
The answer is (c)53
Can someone help me? Find the sum of the first 24 terms of the arithmetic series if the first term is 3 and the common difference is 3.
The sum of the 24 terms of the arithmetic series is 900
How to solve:
To find the sum of an arithmetic series, we can use the formular:
Sn = (n/2)(2a + (n-1)d)
Where;
Sn is the series sum, n is the number of terms, a is the first term, and d is the common difference.
The first term (a) in this scenario is 3, and the common difference (d) is 3. With n equal to 24, we want to find the sum of the first 24 terms.
When the values are entered into the formula, we get:
The sum of the first 24 terms of the arithmetic series is 900 because;
S24 = (24/2)(2(3) + (24-1)(3))
= 12(6 + 23(3))
= 12(6 + 69)
= 12(75)
= 900.
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Question: 4/8
Mr. Oswald, the head of human resources, has
been in the company for 24 years, which
corresponds to three times as many as the
number of years Mrs. Bright, the finance
director, is also employed there.
Considering neither of them leaves their jobs,
how many years will Mr. Oswald have worked for
the company when that corresponds to twice as
many as Mrs. Bright's number of years there?
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.
The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.
So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.
Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.
Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.
Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.
16 more years - 24 years = -8 years.
The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.
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Regina is comparing two checking accounts. One has a monthly fee of $12
and a per-check fee of $0.10, and the other has a monthly fee of $9 and a per-
check fee of $0.25. What is the minimum number of monthly checks Regina
needs to write for the first account to be a better option?
A. 15
B. 30
OC. 21
OD. 20
The minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.
To solve this problemOn the basis of the quantity of checks written, we can compare the overall costs of the two accounts.
Let's calculate the total cost for each account based on the given information:
First Account:
Monthly fee: $12
Per-check fee: $0.10
Total cost = Monthly fee + (Per-check fee * Number of checks)
Second Account:
Monthly fee: $9
Per-check fee: $0.25
Total cost = Monthly fee + (Per-check fee * Number of checks)
We must determine the point at which the first account's total cost is less than the second account's total cost. Let's construct the formula:
$12 + ($0.10 * Number of checks) < $9 + ($0.25 * Number of checks)
Simplifying the equation
$12 - $9 < ($0.25 - $0.10) * Number of checks
$3 < $0.15 * Number of checks
Dividing both sides by $0.15:
$3 / $0.15 < Number of checks
20 < Number of checks
Therefore, the minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.
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Answer is option a, c, d
Ik it may seem like too easy question but how option C is answer since vector depend on both magnitude and 'direction' T-T
Won't direction will change?
The value of a scalar does not depend on the orientation.
The magnitude of a vector does not depend on the orientation of the axes.
(a) The value of a scalar does not depend on the orientation of the axes. Scalar is a quantity that has only magnitude and no direction, so it is independent of the coordinate system. Examples of scalars include temperature, mass, and time.
(b) Component of a vector depends on the orientation of the axes. If the coordinate axes are rotated or shifted, the components of a vector will change accordingly.
(c) A vector depends on the orientation of the axes. A vector has both magnitude and direction and changes when the orientation of the axes is changed.
(d) The magnitude of a vector does not depend on the orientation of the axes. The magnitude of a vector is defined as the length of the vector, which is independent of the coordinate system. For example, the magnitude of a velocity vector is the speed, which is the same regardless of the orientation of the axes.
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Find the 15th term of the geometric sequence 2,6,18...
The first term of a geometric sequence is 2 and the common ratio is 3. The general term formula for the nth term of a geometric sequence is given by: an = a₁ × rⁿ⁻¹ Where, an is the nth term of the sequence, a₁ is the first term of the sequence, and r is the common ratio of the sequence. The 15th term of the sequence is 86,093,442.
To find the 15th term of the sequence, we need to use the above formula to find a₁ and r.The sequence is: 2, 6, 18, 54, ...Since the first term is 2, then a₁ = 2.The common ratio can be found by dividing any term by its preceding term. We will use the second and first term:6 / 2 = 318 / 6 = 3Again, the common ratio is 3. Now, we can use the formula to find the 15th term of the sequence: an = a₁ × rⁿ⁻¹a15 = 2 × 3¹⁵⁻¹a15 = 2 × 3¹⁴a15 = 2 × 43,046,721a15 = 86,093,442 The 15th term of the sequence is 86,093,442.
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here is my algebra 13 homework, can someone please help me fast! Quick!!
The function h(x) = (2ˣ) + 1 does not have an x intercept.
A function has an x-intercept when the value of the function is equal to zero at some point on the x-axis.
(a) f(x) = -x + 2 is a linear function with a negative slope (-1) and a y-intercept of 2.
To find the x-intercept, we set f(x) equal to zero and solve for x:
0 = -x + 2
x = 2
Therefore, the function f(x) has an x-intercept at (2, 0).
(b) g(x) = -(x²) is a quadratic function that opens downward and has a vertex at (0, 0).
To find the x-intercept, we set g(x) equal to zero and solve for x:
0 = -(x²)
x²= 0
x = 0
Therefore, the function g(x) has an x-intercept at (0, 0).
(c) h(x) = (2ˣ) + 1 is an exponential function
To find the x-intercept, we set h(x) equal to zero and solve for x:
0 = (2ˣ) + 1
-1 = 2ˣ
However, there is no real value of x that satisfies this equation.
h(x) = (2ˣ) + 1 has no x intercept.
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PLEASE HELPP!!!!!
If the sample follows a normal distribution, does this make sense? Why?
It is possible for a sample to follow a normal distribution, depending on the nature of the data being accumulated.
The regular distribution is a bell-shaped curve that is symmetric across the mean, and it's far typically used to model various natural phenomena and measurements in fields such as information, engineering, and social sciences.
If the data being gathered is continuous and the sample length is large sufficient, it is regularly assumed that the pattern follows a normal distribution.
This assumption is based at the critical limit Theorem, which states that the sampling distribution of the suggest of any independent, random variable will tend toward a ordinary distribution because the sample size increases.
But, it's far critical to notice that not all samples will observe a ordinary distribution, and in a few cases, different distributions may be greater suitable for the records being amassed.
It's far consequently essential to analyze the information and evaluate the assumptions being made before using the regular distribution as a model.
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What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
The probability that either event will occur is 0.62
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
Event A = 6 + 6 = 12
Event B = 20 + 6 = 26
Both A and B = 6
Other Events = 20
Using the above as a guide, we have the following:
Total = A + B + C + Others - Both
So, we have
Total = 12 + 26 - 6 + 20
Evaluate
Total = 52
So, we have
P(A) = 12/52
P(B) = 26/52
Both A and B = 6/52
For either events, we have
P(A or B) = (12 + 26 - 6)/52
Evaluate
P(A or B) = 0.62
Hence, the probability that either event will occur is 0.62
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Identify a situation that would fit into this scenario and explain how would you organize this calculation to solve it without a calculator. Assume a 5% sales tax rate. For full credit, you will need the cost of the it, an explanation of how you would calculate the sales tax and the total cost.
You would add the sales tax amount to the cost of the meal to get the total cost. In this case, the sales tax amount is $1, so the total cost would be $26.
One situation that would fit into this scenario is calculating the total cost of a meal at a restaurant that costs $25. Firstly, to calculate the sales tax, you would need to convert the percentage of sales tax into a decimal.
In this case, the sales tax rate is 5%, so you would convert it to 0.05.Next, you would multiply the cost of the meal by the sales tax rate to calculate the sales tax amount.
To do this calculation without a calculator, you can use mental math or estimation techniques.For example, you could estimate 5% of $25 by breaking the 5% into a 1% and 4% calculation.
To calculate 1%, you would simply move the decimal point two places to the left, which gives you $0.25. Then, to calculate 4%, you could multiply $0.25 by 4, which equals $1.
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The two ways to indicate an empty set are
a square pyramid sitting on its base. The sides are 8cm, 14cm, and 14cm. whats the surface area of the pyramid in square centimeters?
The surface area of the square pyramid is 224 square centimeters.
Since the base of the square pyramid is a square, all sides are equal in length.
Let's call the length of one side of the square base "s".
Then the surface area of the pyramid can be found using the formula:
Surface area = Area of base + Area of four triangles
The area of the base is just s², and the height of each triangle can be found using the Pythagorean theorem.
Let's call the height "h". Then:
h² = 14² - (s/2)² (using the longer side of the triangle as the hypotenuse)
h² = 196 - (s²/4)
Now, we need to find the surface area in terms of "s" and simplify:
Surface area = s² + 4(1/2)(s)(h)
Surface area = s² + 2sh
Surface area = s² + 2s√196 - s²/4))
Surface area = s²+ 2s√(784 - s²))/2
Surface area = s² + s√(784 - s²))
We are given that one side of the square base is 8cm, so:
Surface area = 8² + 8√784 - 8²
Surface area = 64 + 8√400
Surface area = 64 + 8(20)
Surface area = 224
Therefore, the surface area of the square pyramid is 224 square centimeters.
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Solve. Prisms. Surface area.
The surface areas of the solids are listed below:
Case I: A = 216 ft²
Case O: A = 204 mm²
Case H: A = 216 ft²
Case L: A = 284.6 cm²
Case E: A = 25.657 yd
Case N: A = 356 yd²
Case S: A = 361.88 ft²
Case T: A = 150 cm²
How to determine the surface area of a solidIn this problem we find eight solids, whose surface areas, that is, the sum of the areas of all faces of the solid, must be found. Each face can be represented by the following area formula:
Rectangle
A = w · h
Triangle
A = 0.5 · w · h
Where:
w - Widthh - HeightNow we proceed to determine the surface areas:
Case I:
A = 6 · (6 ft)²
A = 216 ft²
Case O:
A = 4 · 0.5 · (6 mm) · (14 mm) + (6 mm)²
A = 204 mm²
Case H:
A = 2 · (8 ft) · (6 ft) + (8 ft) · (5 ft) + (6 ft) · (5 ft) + (10 ft) · (5 ft)
A = 216 ft²
Case L:
A = 2 · 0.5 · (7 cm) · (5 cm) + 2 · (6.1 cm) · (13 cm) + (7 cm) · (13 cm)
A = 284.6 cm²
Case E:
A = 2 · 0.5 · (2 yd)² + 2 · (2 yd) · (4 yd) + (√2 yd) · (4 yd)
A = 25.657 yd
Case N:
A = 2 · (3 yd) · (8 yd) + 2 · (8 yd) · (14 yd) + 2 · (14 yd) · (3 yd)
A = 356 yd²
Case S:
A = 2 · 0.5 · (8 ft) · (6 ft) + 2 · (14 ft) · (7.21 ft) + (14 ft) · (8 ft)
A = 361.88 ft²
Case T:
A = 6 · (5 cm)²
A = 150 cm²
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Graph the inequality y ≤1/3x+1
The graph of the inequality y ≤ 1/3x + 1 is added as an attachment and it is represented with option (c)
How to determine the graph of the inequalityFrom the question, we have the following parameters that can be used in our computation:
y ≤ 1/3x + 1
The above expression is an inequality that implies that
It is a linear inequalityIt has a slope of 1/3It has a y-intercept of 1The upper part and the left part of the graph is shadedNext, we plot the graph
See attachment for the graph of the inequality
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help me solve my math
Answer:
653.3 bacteria
Step-by-step explanation:
A continuously growing population of bacteria is modeled by the function:
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
where:
[tex]P(t)[/tex] is the population after [tex]t[/tex] time periods[tex]P_0[/tex] is the initial population[tex]r[/tex] is the relative rate of growthIn this problem, we are given the following values:
[tex]P_0 = 484 \text{ bacteria}[/tex][tex]r = 15\% = 0.15[/tex][tex]t = 2[/tex]We can plug these into the function to solve for [tex]P(2)[/tex].
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]
[tex]P(2) = 484 \cdot e^{0.3}[/tex]
Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.
[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]
Select ALL TRUE statements
A) There are no zeroes
B) There is one zero
C) There are two zeroes
D) The vertex is (1, 14)
E) The vertex is (14, 1)
F) The vertex is (2, 14)
G) The vertex is (14, 2)
H) The axis of symmetry is x = 1
I) The axis of symmetry is x = 2
J) The "a" of the parabola is positive
K) The "a" of the parabola is negative
M) The parabola has a minimum
N) The parabola has a maximum
O) The zeroes are -2 and 6
P) The zeroes are 1 and 6
Q) The zero is 6
R) The zero is 14
Answer:
The correct statements are:
A) There are no zeroes
D) The vertex is (1, 14)
H) The axis of symmetry is x = 1
J) The "a" of the parabola is positive
M) The parabola has a minimum
Therefore, the options B, C, E, F, G, I, K, N, O, P, Q, and R are all false.
Step-by-step explanation:
Step-by-step explanation:
Remember that, this is quadratic function graph.
Let's analyze fact the graph. We get :
There are two roots/zeroes
Two roots are x1 = -2 , x2 = 6
Vertex is maximum value of parabola (2,14)
Symmetry function is x = 2 (you can show that, x-axis from vertex)
"a" parabola indicated negative
The parabola with "a" negative, thus have maximum value (show that vertex is (2,14))
Conclusion :
The true statements are C,F,I,K,N,O (6 statements are shown)
Subject : Mathematics
Level : JHS
Chapter : Quadratic Functions
Multiply using the Vertical Method: (x+4)(2x^2−3x+5).
Using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.
What is vertical multiplication?
In vertical multiplication, the numbers to be multiplied are placed vertically over one another with their least significant digits aligned.
The top number is named the multiplicand and the lower number is the multiplier. The result of the multiplication is the product.
The given expressions;
(x+4)(2x² −3x+5).
We will multiply as follows;
2x² - 3x + 5
× x + 4
_________________
2x² - 3x + 5 (Multiply by x)
+ 8x² - 12x + 20 (Multiply by 4)
_________________
10x² - 15x + 25
Thus, using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.
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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, the period, phase shift, and vertical shift of the function. Then graph the function. Thank you!
For the function y = 3sin[2(θ-90°)] + 2, the amplitude is 3, the period is π, the phase shift is -45° and the vertical shift is 2 units up.
The amplitude of a sine function represents the maximum displacement from the midline.
The coefficient in front of the sine function is 3, so the amplitude is 3.
The period of a sine function is the length of one complete cycle. It can be calculated using the formula T = 2π/b, where b is the coefficient of θ inside the sine function brackets.
Here, b = 2, so the period is T = 2π/2 = π.
The phase shift of a sine function indicates a horizontal shift to the left or right.
In this case, c = 90°, so the phase shift is θ = 0° - 90°/2 = -45°.
The vertical shift indicates a shift up or down on the y-axis.
The constant term outside the sine function is 2, so the vertical shift is 2 units up.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
The correct answer:
(B) SAS Similarity
Can someone answer this question
Answer: 4th one is the correct one
Step-by-step explanation:
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Measure of angle 1 is,
Angler ACB = 36 degree
We have to given that;
In a parallelogram we get;
Angler CAD = 36 degree
Now, We know that;
Opposite sides are parallel to each other in a parallelogram.
Hence, We get;
Angler CAD = Angle ACB
Since, Angler CAD = 36 degree
Hence, We get;
Measure of angle 1 is,
Angler ACB = 36 degree
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MISTERBRAINLYY!!
The paint in a certain container is sufficient to paint an area equal to 9.375m2. How many bricks of dimensions 22.5cm×10cm×7.5cm can be painted out of this container?
There are three area options for the number of bricks:
4165551250How many bricks can be painted out of a container?
The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:
n = A / A'
A' = w · h
Where:
w - Width of the brick, in centimeters.h - Height of the brick, in centimeters.There are three possible answers:
Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm
A' = 22.5 · 10
A' = 225
n = 93750 / 225
n = 416.667
n = 416
Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm
A' = 22.5 · 7.5
A' = 168.75
n = 93750 / 168.75
n = 555.556
n = 555
Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm
A' = 10 · 7.5
A = 75
n = 93750 / 75
n = 1250
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Write in standard form.
Please help with this. Two different tutors gave me two different answers!
Answer:
16x+4y=2
Step by step explanation
desperately need help!!!
The classification , symmetry , maximum r-values and the zeroes of the function are solved
Given data ,
a)
Let the function be represented as A
Now , the value of A is
r² = 25 sin( 2θ )
The equation represents a cardioid
It is symmetric about the polar axis.
The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.
The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0
b)
The equation represents a limaçon.
It is symmetric about the polar axis.
The maximum value of r is 7.
The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).
c)
The equation represents an Archimedean spiral.
It does not possess any symmetry.
There is no maximum r value.
The equation has a zero at θ = 1/2.
Hence , the zeroes of the function are solved
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Assuming the formula of a cylinder, with a height of 2r, if the square area of a can of beans is x square inches, and the volume is x cubic inches, what's the value of x?
Eight upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 7. The smallest domino, #0, is 4.00 cm tall and will be toppled by a person to start the chain reaction. Each subsequent domino is 12% taller than the one before. What is the height of domino #7?
The height of domino #7 is approximately 6.89 cm tall.
How to solve for the heightThe formula for the nth term of a geometric progression is:
[tex]a_n = a * r^(^n^-^1^)[/tex]
where:
a is the first term (the height of the smallest domino, 4.00 cm),
r is the common ratio (the growth rate, 1.12), and
n is the term number (for domino #7, n = 7 + 1 = 8, because the sequence starts with domino #0).
Let's plug these values into the formula:
[tex]a_8 = 4.00 cm * (1.12)^7[/tex]
(Note that we're using 7, not 8, because the first domino is #0, not #1.)
Now, compute the value:
[tex]a_8 = 4.00 cm * (1.12)^7[/tex]
= 6.89 cm
So, domino #7 is approximately 6.89 cm tall.
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What trinomial can be added to x^2+5x-8 to give me a sum of 2x-5
Write a sine function that has a midline of y=4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right.
The sine function with a midline of y=4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2sin(2(x - π/4)) + 4.
To write a sine function with the given properties, we can use the general form of a sine function: y = A * sin(B(x - C)) + D, where A represents the amplitude, B represents the frequency (or inverse of the period), C represents the horizontal shift, and D represents the vertical shift (or midline).
In this case:
The midline is y = 4, so D = 4.
The amplitude is 2, so A = 2.
The period is π, so the frequency is B = 2π/π = 2.
The horizontal shift is π/4 to the right, so C = -π/4.
Plugging these values into the general form, we get the sine function:
y = 2 * sin(2(x - (-π/4))) + 4
Simplifying further:
y = 2 * sin(2(x + π/4)) + 4
Therefore, the sine function with a midline of y = 4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2 * sin(2(x + π/4)) + 4.
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A washer and a dryer cost $995 combined. The washer costs $95 more than the dryer. What is the cost of the dryer?
Answer:
$450
Step-by-step explanation:
995/2 = 497.5
95/2 = 47.5
497.5 + 47.5 = 545
495 - 95 = 450