This question asks for the degree, leading coefficient, zeroes, factors, factors with multiplicity, and the final answer
Answers
Answer:
[tex]\textsf{Degree:}\quad 6[/tex]
[tex]\textsf{Leading\;coefficient:}\quad \dfrac{1}{3456}[/tex]
[tex]\textsf{Zeroes:}\quad -6, 2, 5, 8[/tex]
[tex]\textsf{Factors:}\quad (x + 6), (x - 2), (x - 5), (x - 8)[/tex]
[tex]\textsf{Factors\;with\;multiplicity:}\quad (x + 6)^3(x - 2)(x - 5)(x - 8)[/tex]
[tex]\textsf{Equation\;of\;function:}\quad f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]
Step-by-step explanation:
ZeroesThe zeroes are the x-values of the points where the function crosses the x-axis, so the x-values when f(x) = 0.
Therefore, the zeroes of the given function are:
x = -6x = 2x = 5x = 8[tex]\hrulefill[/tex]
FactorsAccording to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x - a) is a factor of f(x). Therefore, the factors of the function are the x-values that satisfy f(x) = 0.
Therefore, the factors of the given function are:
(x + 6)(x - 2)(x - 5)(x - 8)[tex]\hrulefill[/tex]
MultiplicitiesThe multiplicity of a factor is the number of times the factor appears in the factored form of the equation of the polynomial.
If the behaviour of the x-intercept is like that of a line, i.e. the curve passes directly through the intercept, its multiplicity is one.
Therefore, the factors (x - 2), (x - 5) and (x - 8) have multiplicity one.
The behaviour of the x-intercept at x = -6 is like that of a cubic function (S-shape). There, this zero has multiplicity 3: (x + 6)³.
[tex]\hrulefill[/tex]
DegreeSo far we have found the zeros, factors and their multiplicities, so we can write a factored form of the function:
[tex]\implies f(x)=a(x+6)^3(x-2)(x-5)(x-8)[/tex]
The degree of the function is the highest exponent value of the variables in the polynomial. Therefore, to find the degree of the function, simply sum the exponents of the factors:
[tex]\implies \textsf{Degree}=3 + 1 + 1 + 1 = 6[/tex]
Therefore, the degree of the function is 6.
[tex]\hrulefill[/tex]
Leading CoefficientFrom inspection of the given graph, the y-intercept is (0, -5).
Therefore, to find the leading coefficient (value of a), substitute (0, -5) into the equation and solve for a:
[tex]\begin{aligned}\implies f(0)=a(0+6)^3(0-2)(0-5)(0-8)&=-5\\a(216)(-2)(-5)(-8)&=-5\\-17280a&=-5\\a&=\dfrac{1}{3456}\end{aligned}[/tex]
Therefore, the leading coefficient of the function is 1/3456.
[tex]\hrulefill[/tex]
Equation of the functionPutting everything together, the function in factored form is:
[tex]f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]
In standard form:
[tex]f(x)=\dfrac{1}{3456}x^6+\dfrac{1}{1152}x^5-\dfrac{1}{36}x^4-\dfrac{37}{432}x^3+\dfrac{17}{24}x^2+\dfrac{13}{8}x-5[/tex]
Related Questions
Kremena took out a $500 discounted loan for a period of 3 months. The amount she actually received into her bank account was $460. Assuming simple interest rates, what is effective interest rate re?
Answers
The effective interest rate on the loan is also 32%.
What is effective interest rate ?
Effective interest rate is the actual interest rate that is paid or earned on an investment, loan, or other financial product. It takes into account not only the nominal interest rate, which is the stated rate of interest, but also the frequency of compounding or other factors that affect the overall return.
According to the question:
To find the effective interest rate, we first need to calculate the amount of interest Kremena paid on the loan. We can do this by subtracting the amount she received from the amount of the loan:
Interest = Loan amount - Amount received
Interest = $500 - $460
Interest = $40
Next, we can use the formula for simple interest to calculate the interest rate:
I = P * r * t
where I is the interest, P is the principal (loan amount), r is the interest rate, and t is the time in years.
Since Kremena took out the loan for 3 months, which is a quarter of a year, we have:
I = P * r * t
$40 = $500 * r * (3/12)
$40 = $500 * r * 0.25
r = $40 / ($500 * 0.25)
r = 0.32 or 32%
So the interest rate on the loan is 32%. However, this is the nominal interest rate, which does not take into account the effects of compounding. To find the effective interest rate, we need to take into account the fact that Kremena only received $460, which means that she effectively paid more interest than she would have if she had received the full $500.
To calculate the effective interest rate, we can use the formula:
[tex]re = (1 + r/n)^n - 1[/tex]
where re is the effective interest rate, r is the nominal interest rate, and n is the number of compounding periods per year. Since the problem specifies simple interest, there is no compounding, so we can take n = 1. Plugging in the values, we get:
[tex]re = (1 + 0.32/1)^1 - 1[/tex]
re = 0.32 or 32%
So the effective interest rate on the loan is also 32%.
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST PLEASE HELP
Answers
The value of f(9), the y-intercept, and the equation will be -3, 15, and f(x) = -2x + 15, respectively.
Given that:
Points, (-1, 17) and (4, 7)
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation of the line passing through (-1, 17) and (4, 7) is given as,
(y - 17) = [(7 - 17)/(4 + 1)](x + 1)
y - 17 = -2x - 2
f(x) = -2x + 15
The value of f(9) is calculated as,
f(9) = -2(9) + 15
f(9) = - 18 + 15
f(9) = - 3
The graph is given below.
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If two adjacent angles (x+18) and x are inside a 90° angle, what is the equation for the two adjacent angles?
Answers
Answer:
Step-by-step explanation:
For a right angle triangle we use Pythagoras theorem
hypotenuse²=x²+(x+18)²
=x²+x²+36x+324
=2x²+36x+324
Find the measure of line segment JK.
Answers
The measure of line segment JK using the Secant Theorem is found as 7 units.
Explain about the Secant Theorems?According to the intersecting secants theorem, the product of one whole secant segment but also its outer segment is equivalent to the product of the other whole secant segment as well as its external segment when two secants cross at an exterior point.
According to the Secant Theorem,
If two secants are drawn from an identical point through a circle, their products, A times their external segment and B times their external segment, are equal.
So, using Secant Theorem:
JK*JL = RM*RL
8* (2x + 7) = 24 * 7
Solving the equation:
x = 7
Thus, the measure of line segment JK using the Secant Theorem is found as 7 units.
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Alfred is y years old
Libby is 4 years younger
than Alfred.
John is 4 times as old as
Libby.
Write down an expression in terms of y, for john’s age.
Answers
Answer:
therefore, the expression for John's age in terms of y is 4y - 16.
Step-by-step explanation:
Answer:
John's age = 4y - 16
Step-by-step explanation:
We can start by using the information given to write expressions for the ages of Libby and John in terms of Alfred's age y.
We know that Libby is 4 years younger than Alfred, so her age can be written as:
Libby's age = Alfred's age - 4
We also know that John is 4 times as old as Libby, so his age can be written as:
John's age = 4 × Libby's age
Substituting the expression for Libby's age from the first equation into the second equation, we get:
John's age = 4 × (Alfred's age - 4)
Simplifying this expression, we get:
John's age = 4 × Alfred's age - 16
Therefore, an expression in terms of y for John's age is:
John's age = 4y - 16
what is the debt to equity ratio for 2024
Answers
Answer:
75.6%
Step-by-step explanation:
Reducing Debt: 2024's debt to equity ratio has increased from 67.6% to 75.6% over the past 5 years. Debt Coverage: 2024's operating cash flow is negative, therefore debt is not well covered.
Write the first four terms of a maclaurin series for f(x) = e^x
Answers
On solving the question we have that the answer of the equation will be [tex]Answer: "f(x) = 1 + x +\frac{1}{2}{x^2} + \frac{1}{6}{x^3} + ..."[/tex]
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
[tex]"f(x) = {e^x} \Rightarrow f'(x) = {e^x} \Rightarrow f''(x) = {e^x} \Rightarrow f'''(x) = {e^x}"[/tex]
Then
[tex]"f(x) = f(0) + \frac{{f'(0)}}{{1!}}x + \frac{{f''(0)}}{{2!}}{x^2} + \frac{{f'''(0)}}{{3!}}{x^3} + ... = {e^0} + \frac{{{e^0}}}{1}x + \frac{{{e^0}}}{2}{x^2} + \frac{{{e^0}}}{6}{x^3} + ... = 1 + x + \frac{1}{2}{x^2} + \frac{1}{6}{x^3} + ..."[/tex]
[tex]Answer: "f(x) = 1 + x + \frac{1}{2}{x^2} + \frac{1}{6}{x^3} + ..."[/tex]
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HELP ASAP WILL GIVE BRAINLIEST
When rolling a 6-sided die twice, determine P(sum of 4).
3
36
5
36
8
36
2/6
Answers
The probability of the sum of 4 is 3/36
How to determine the probability of the sum of 4From the question, we have the following parameters that can be used in our computation:
rolling a 6-sided die twice
So, the sample space are
S1 = {1, 2, 3, 4, 5, 6}
S2 = {1, 2, 3, 4, 5, 6}
For the sum of 4, we have]
(1, 3), (2, 2) and (3, 1): Count of 3
The sample size of the event is
Size = 6 * 6
Size = 4
Using the above as a guide, we have the following:
P = Count/Size
So, we have
P = 3/36
Evaluate
P = 1/12
Hence, the probability is 1/9
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PLEASE HELP WILL GIVE BRAINLISET AND 60 PTS I APPRECIATE IT !!:)
Answers
Answer:
Step-by-step explanation:
domain is negative infinity, positive infinity
range is -3, positive infinity
Answer:
F(x) is all values that x can be. so the answer is the domain is (-∞,4)
Step-by-step explanation:
Chapter 8 test geometry
Does anyone know how to do this? Pls help
Answers
a. The sketch is attached
b. The vertical height is 18.13 feet
c. The given angle 65° is the angle of elevation.
d. The foot of the ladder is 8.45 feet away from the wall.
7. The angle of elevation is congruent to angle of depression because they are on the alternate sides of two parallel lines.
8.
a. Diagram of triangle CDE is attached
b. The formula that can be used to solve triangle CDE is the Law of Sines
c.
∠ e = 11
c = 75.47
d = 8.77
How to vertical height of the ladderb. To find the vertical height of the ladder that is touching the wall, we use the trigonometric function
sin 65 = vertical height / height of ladder
sin 65 = vertical height / 20
vertical height = sin 65 * 20
vertical height = 18.13 feet
c. The given angle 65° is the angle of elevation.
d. To find how far the foot of the ladder is from the wall, we can use the trigonometric function cosine.
cos 65° = x / 20
x = 20 cos 65°
x ≈ 8.45 feet
7. The statement is true. The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the object above the horizontal line.
The angle of depression is the angle between the horizontal line and the line of sight from the observer to the object below the horizontal line.
If the two objects are on parallel lines (e.g., the ground and a bridge above it), then the angle of elevation from one object is congruent to the angle of depression from the other object.
8. a. Diagram of triangle CDE is attached
b. The formula that can be used to solve triangle CDE is the Law of Sines
∠ e = 180 - 52 - 17 = 111
sin E / 28 = sin C / c = sin D / d
c = 28 sin 52 / sin 111 = 23.63
d = 28 sin 17 / sin 111 = 8.77
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If the total amount of wealth in the world is $418.3 Trillion, and the wealth of the top 1% combined is worth more than $190 Trillion, what percent of global wealth is concentrated in the hands of the top 1%
?
Answers
Answer: The top 1% of the world's population holds more than 45% of global wealth.
Step-by-step explanation:
To find the percentage of global wealth concentrated in the hands of the top 1%, we need to divide the wealth of the top 1% by the total amount of global wealth, and then multiply by 100 to get the percentage.
Percentage of global wealth held by top 1% = (Wealth of top 1% / Total global wealth) x 100
We are given that the total amount of global wealth is $418.3 trillion, and the wealth of the top 1% is more than $190 trillion.
So, the percentage of global wealth held by the top 1% is:
(190 trillion / 418.3 trillion) x 100 = 45.38%
Therefore, the top 1% of the world's population holds more than 45% of global wealth.
Answer:
45.42%
Step-by-step explanation:
To find:-
What percent of global wealth is concentrated in the hands of the top 1% .Answer:-
We are here given that, the total global wealth is 418.3T dollars and more than 190T dollars is in hands of top 1% of the people. We are interested in finding out the percentage of global wealth in the hands of top 1% . We can find the percentage as ,
[tex]:\sf\implies \pink{ \% =\dfrac{Wealth\ owned\ by \ 1\% }{Total\ wealth}\times 100}\\[/tex]
On substituting the respective values, we have;
[tex]:\sf\implies \% =\dfrac{\$ 190T}{\$ 418.3T}\times 100\\[/tex]
[tex]:\sf\implies \pink{\% = 45.42\% } \\[/tex]
Hence the required percentage is 45.42% .
Find the savings plan balance after 6 months with an APR of 2% and monthly payments of $150.
www
The balance is $.
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answers
The savings plan balance after 6 months with an APR of 2% and monthly payments of $150 is approximately $913.35.
What distinguishes nominal interest rates from effective interest rates?The stated interest rate on a loan or investment is known as the nominal interest rate; it does not account for compounding or any other elements that may have an impact on the real return or expense. Often, it is stated as an annual percentage rate (APR).
The effective interest rate, in contrast, takes into account compounding and other elements that may have an impact on the true cost or return of a loan or investment. It is often represented as an annual percentage yield and represents the actual rate of return or cost that is earned or paid on the principal amount over a certain time (APY).
Given that,
APR = 2% and monthly payments = $150.
For future value of annuity we use the following formula:
FV = Pmt × [(1 + r)⁽ⁿ⁻¹⁾] /r
Substituting the values:
r = 0.02/12 = 0.0016667, n = 6, and Pmt = $150:
FV = $150 × [(1 + 0.0016667)⁽⁶⁻¹⁾]/0.0016667
FV ≈ $913.35
Hence, the savings plan balance after 6 months with an APR of 2% and monthly payments of $150 is approximately $913.35.
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Estimated Salary=29,608.40+2632.98(Years of Experience)
What is the estimated salary for an employee with 18
years of experience?
Answers
The estimated salary fοr an emplοyee with 18 years οf experience is $77,201.24.
What is BODMAS?BODMAS stands fοr Brackets, Order, Divisiοn/Multiplicatiοn, Additiοn/Subtractiοn, and it represents the οrder οf mathematical οperatiοns tο be perfοrmed when evaluating an expressiοn. It ensures that expressiοns are evaluated in a cοnsistent and unambiguοus manner.
Tο calculate the estimated salary fοr an emplοyee with 18 years οf experience using the prοvided fοrmula, we can substitute 18 fοr "Years οf Experience" and sοlve fοr the salary:
Estimated Salary = 29,608.40 + 2632.98(18)
Estimated Salary = 29,608.40 + 47,592.84
Estimated Salary = 77,201.24
Therefοre, the estimated salary fοr an emplοyee with 18 years οf experience is $77,201.24.
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Which is the factor for all numbers ?
Answers
Answer: 1
Step-by-step explanation: From the above data, we observe that 1 is the greatest factor of itself and the smallest factor of any other number. Therefore, 1 is the factor of every number.
What is the value of x?
Answers
Answer:
x = 26 degrees
Step-by-step explanation:
Supplementary angles mean that they sum up to be 180 degrees therefore
C + D = 180 degrees
128 degrees + D = 180 degrees
D = 180 degrees - 128 degrees
D = 52 degrees
If the measure of the angle D is two times the value of x then x is...
x = D/2
x = 52 degrees / 2
x = 26 degrees
A manufacturer of lighting fixtures has daily production costs of C 800 - 50x+ 0.25x2, where C is the total cost (in dollars) and x is the number of units produced. What daily production number
yields a minimum cost?
x fixtures
Submit Answer
Answers
We can find the minimum point of the quadratic function by using the formula:
x = -b/(2a)
where a = 0.25, b = -50.
Substituting these values into the formula, we get:
x = -(-50)/(2*0.25)
x = 100
Therefore, the daily production number that yields a minimum cost is 100 fixtures.
Question 6 of 10
Fill in the blank to complete the following sentence.
If a polynomial has one root in the form a- √5, it has a second root in the
form of a√5.
Answers
Considering the complex-conjugate root theorem, the statement is given as follows:
If a polynomial has one root in the form a - √5, it has a second root in the
form of a + √5.
What is the complex-conjugate theorem?The complex conjugate theorem for rational roots states that if a polynomial with real coefficients has a complex root of the form a + bi (where a and b are real numbers and i is the imaginary unit), then its complex conjugate a - bi is also a root of the polynomial.
In the case of a rational root, we have that:
If [tex]a + \sqrt{b}[/tex] is a root, then the number [tex]a - \sqrt{b}[/tex] is also a root, which justifies the answer for this problem.
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At her Fourth of July party, Lexi serves her famous grilled chicken. Her secret is to use 6 fluid ounces of lemon-garlic marinade for every pound of chicken. Lexi plans to grill 4 pounds of chicken. How many cups of marinade should she use? cups
Answers
Which of the following statements are true about the diagram
Answers
The statements that are true about the diagram given above = Line JL is an angle bisector and L is the midpoint of a segment in the diagram. That is option B and F.
What is an angle bisector?An angle bisector is defined as the lone the
at is drawn through an angle such that it divides the angle into two equal parts.
From the diagram above, line JL divided the angle < J into two equal angles while diving the line segment KI into two equal parts such as KL and LI.
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Solve the equation 4tan+5=0 on the interval[0,360 )
Answers
answer
306.87 degrees and 666.87 degrees.
steps
4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Equation with tangent function.
Title: Solving an equation involving tangent function
Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).
Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).
Numbered list:
Start with the equation 4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
Take the arctangent (or inverse tangent) of both sides to find θ.
Specify the interval [0,360) when giving the solution.
Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.
One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).
To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.
Subtracting 5 from both sides gives us: 4tanθ = -5
Dividing both sides by 4: tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Sure, here's just the math:
4tanθ + 5 = 0
Subtracting 5 from both sides:
4tanθ = -5
Dividing both sides by 4:
tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides:
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
ChatGPT
PLEASE HELP ME!!!!!!!!!!
Reflect △ABC across the y-axis
PLEASE LOOK AT THE PICTURE!!!!!!!
Answers
A: (4,-2)
B: (1,-1)
C: (1,-4)
Hope this helps! Just graph it.
Tickets for The Phantom of the Opera cost $6 for children and $12 for adults. A local school group paid $252 for 36 tickets. How many of each did they purchase?
Answers
x + y = 36 (equation 1)
6x + 12y = 252 (equation 2)
Equation 1 represents the total number of tickets purchased, which is 36. Equation 2 represents the total cost of the tickets, which is $252. The coefficients of x and y in equation 2 are the prices of the respective tickets.
To solve for x and y, we can use any method of solving systems of equations. Here, we will use the substitution method. Solving equation 1 for x, we get:
x = 36 - y
Substituting this expression for x into equation 2, we get:
6(36 - y) + 12y = 252
Expanding the left side of the equation, we get:
216 - 6y + 12y = 252
Combining like terms, we get:
6y = 36
Dividing both sides by 6, we get:
y = 6
Substituting this value of y into the expression we derived for x, we get:
x = 36 - y = 36 - 6 = 30
Therefore, the school group purchased 30 children's tickets and 6 adult tickets.
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Jose measures the diameter of a ball as 15 inches. How many cubic inches of air can the ball hold, to the nearest tenth?
Answers
Answer:
Assuming the ball is a perfect sphere, we can use the formula for the volume of a sphere to calculate the amount of air it can hold.
The formula for the volume of a sphere is:
V = (4/3)πr^3
where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.
To calculate the radius of the ball from its diameter of 15 inches, we divide by 2:
r = d/2 = 15/2 = 7.5 inches
Substituting this value into the formula, we get:
V = (4/3)π(7.5)^3 ≈ 1767.15 cubic inches
Therefore, the ball can hold approximately 1767.15 cubic inches of air to the nearest tenth.
Step-by-step explanation:
Find the area of the figure. (Sides meet at right angles.)
Answers
Answer:
Step-by-step explanation:
The area of the figure is 1120
the time taken to fill a tank was 2 hours and 43 minutes. write this time to the nearest 5 minutes
Answers
Answer:
To write the time taken to fill a tank to the nearest 5 minutes, we first need to convert 2 hours and 43 minutes to minutes. 2 hours = 2 x 60 = 120 minutes So, the total time taken in minutes is: 120 + 43 = 163 minutes To round this to the nearest 5 minutes, we need to consider the last digit of the number of minutes, which is 3. Since 3 is less than 5, we round down to the nearest multiple of 5, which is 160. Therefore, the time taken to fill the tank to the nearest 5 minutes is: 2 hours and 43 minutes = 160 minutes = 2 hours and 40 minutes
To write the given time to the nearest 5 minutes, round down the minutes value if the last digit is less than 5, and keep the hours value as it is.
Explanation:To write the given time to the nearest 5 minutes, we need to round it to the closest multiple of 5. The given time is 2 hours and 43 minutes. To round to the nearest 5 minutes, we look at the last digit of the number of minutes, which is 3. Since 3 is less than 5, we round down the minutes to 0 and keep the hours as it is. Therefore, the time to the nearest 5 minutes is 2 hours and 40 minutes.
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The ordered pair ( 3 , 2 7 ) is on the graph of a proportional relationship. 2 5 10
a. Show how to find the constant of proportionality. b. Write an equation for this relationship.
Answers
a) The constant of proportionality is solved to be 9
b) The equation of the relationship is y = 9x
How to find the constant of proportionalitya. To find the constant of proportionality, we can use the formula:
K = y/x
where
k is the constant of proportionality,
y is the dependent variable (output), and
x is the independent variable (input).
In this case, The ordered pair (3, 27) will be used them to solve for k.
where
x = 3
y = 27
k = y/x = 27/3
k = 9
b. The equation for this relationship is written using the formula
K = y/x
rewriting in terms of y
y = kx
y = 9x
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DEDUCTION AND APPLICATION Do not use a calculator when answering Part 3. 3.1 Apply the compound angle expansion sin(x + y) = sin x cos y + cos x sin y to expa sin 2x and simplify your answer: sin 2x = sin(x+x) 3.2 Expand each of the following, using your answer from 3.1: 3.2.1 sin 100° = ..... 3.2.2 sin 46° = .... 3.2.3 sin 40° =. Write the following expressions as a single trigonometric ratio: 3.3.1 2 sin 19° cos 19° = 3.3.2 2 cos 40° sin 40° - 3.3.3 sin 25° cos155° .........
Answers
Answer:
Step-by-step explanation:
3.1:
Using the compound angle expansion, we have:
sin 2x = sin(x + x) = sin x cos x + cos x sin x
sin 2x = 2 sin x cos x
Therefore, sin 2x = 2 sin x cos x.
3.2:
Using the result from 3.1:
3.2.1: sin 100° = 2 sin 50° cos 50° = sin 100° = 0.766
3.2.2: sin 46° = 2 sin 23° cos 23° = sin 46° = 0.719
3.2.3: sin 40° = 2 sin 20° cos 20° = sin 40° = 0.642
3.3:
Using the identity sin(a ± b) = sin a cos b ± cos a sin b:
3.3.1: 2 sin 19° cos 19° = sin 38° = sin (45° - 7°) = sin 45° cos 7° - cos 45° sin 7° = (1/√2)cos 7° - (1/√2)sin 7° = -sin (7° - 45°) = -sin 38°
Therefore, 2 sin 19° cos 19° = -sin 38°.
3.3.2: 2 cos 40° sin 40° = sin 80° = sin (45° + 35°) = sin 45° cos 35° + cos 45° sin 35° = (1/√2)cos 35° + (1/√2)sin 35° = sin (35° + 45°) = sin 80°
Therefore, 2 cos 40° sin 40° = sin 80°.
3.3.3: sin 25° cos 155° = (1/2)(sin 180°) = 0
Therefore, sin 25° cos 155° = 0.
Solving Square Root Equations
Solve the following equations. Be sure to label any extraneous solutions.
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The solution of each equation are;
1) x = 6, x = 0
2) x = 3, x = 2
3) x= 4 ±√6
4) x = 6 ± √24/2
What is an extraneous solution?An extraneous solution is a solution obtained in a mathematical equation that does not satisfy the original equation, even though it appears to be a valid solution when plugged into the equation.
1) (√6x)^2 = x^2
6x = x^2
x^2 - 6x = 0
x = 6, x = 0
2) √5x - 6 = x
5x - 6 = x^2
x^2 - 5x + 6 = 0
x = 3, x = 2
3) √2x - 1 = x - 3
2x - 1 = (x - 3)^2
2x - 1 = x^2 - 6x + 9
x^2 - 6x - 2x + 9 + 1 = 0
x^2 -8x + 10 = 0
x= 4 ±√6
4) x = 2 + √2x - 11
x -2 = √2x - 11
x^2 - 4x + 4 = 2x - 11
x^2 -4x -2x + 4 + 11 = 0
x^2 - 6x + 15 = 0
x = 6 ± √24/2
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Rodolfo has two checks that he needs to deposit into his checking account.
One check is for $108.93, and the second check is for $372.47. He wants to receive $75 cash back from his deposit. What is Rodolfo's net deposit?
Answers
Answer:
Rodolfo has two checks, one for $108.93 and the other for $372.47. Let's add the amounts of the checks to get the total amount of the deposit:
$108.93 + $372.47 = $481.40
Next, Rodolfo wants to receive $75 cash back from his deposit. We need to subtract $75 from the total amount of the deposit to get the net deposit:
$481.40 - $75 = $406.40
Therefore, Rodolfo's net deposit is $406.40.
Step-by-step explanation:
Answer:
Step-by-step explanation:
To find Rodolfo's net deposit, we need to add the values of his two checks and subtract the amount of cash he wants to receive back:
Net deposit = (Value of Check 1) + (Value of Check 2) - (Amount of Cash Back)
Net deposit = $108.93 + $372.47 - $75
Net deposit = $406.40 - $75
Net deposit = $331.40
Therefore, Rodolfo's net deposit is $331.40.
Which expression is equivalent to 1/3b+2/3b-5/6(b+1)
Answers
the answer is (a) [tex]\frac{1}{6}b-\frac{5}{6}[/tex]
In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):
1/3b + 2/3b = 3/3b = 1/b
what are expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
from the question:
In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):
1/3b + 2/3b = 3/3b = 1/b
We can now reintroduce this value into the first expression:
1/b - 5/6(b+1)
We can distribute the 5/6 term in order to further simplify this:
1/b - 5/6b - 5/6
Now that the first two terms share a common denominator of 6b, we may combine them:
6/6b - 5/6b - 5/6
Simplifying this gives us:
1/6b - 5/6
Therefore, the answer is (a) 1/6b - 5/6.
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