The function f(x) in completely factored form is (4x+1)(5x-1)(x+5).
To write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, we can use synthetic division with the given zero of (-(5)/(2)).
Step 1: Set up the synthetic division with the given zero and the coefficients of the polynomial.
(-(5)/(2)) | 20 44 -17 -5
|______________
Step 2: Bring down the first coefficient, 20, and multiply it by the given zero.
(-(5)/(2)) | 20 44 -17 -5
| -50
|______________
| 20
Step 3: Add the result of the multiplication to the next coefficient and repeat the process until all coefficients have been used.
(-(5)/(2)) | 20 44 -17 -5
| -50 3 10
|______________
| 20 -6 -14 5
Step 4: The last number in the bottom row is the remainder. If it is zero, then the given zero is a factor of the polynomial. In this case, the remainder is 5, so (-(5)/(2)) is not a factor of f(x).
Since (-(5)/(2)) is not a factor of f(x), we cannot use synthetic division to write f(x) in completely factored form. Instead, we can use factoring to find the factors of f(x).
f(x) = 20x^(3)+44x^(2)-17x-5
= (4x+1)(5x-1)(x+5)
Therefore, f(x) in completely factored form is (4x+1)(5x-1)(x+5).
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Use the one-to-one property of logarithms to solve: 15.Ln(10−3x)=ln(−4x)16.log4(6−m)=log43(m)
The solutions to the given equations are x = 10 and m = 1.5.
Using the one-to-one property of logarithms, we can solve the given equations as follows:
First, we will solve the equation: 15.Ln(10−3x)=ln(−4x)
The one-to-one property of logarithms states that if logb(a) = logb(c), then a = c. Therefore, we can use this property to set the arguments of the logarithms equal to each other:
10 - 3x = -4x
Simplifying this equation gives:
10 = x
So the solution to the first equation is x = 10.
Next, we will solve the equation: 16.log4(6−m)=log43(m)
Again, using the one-to-one property of logarithms, we can set the arguments of the logarithms equal to each other:
6 - m = 3m
Simplifying this equation gives:
6 = 4m
m = 6/4
m = 1.5
So the solution to the second equation is m = 1.5.
Therefore, the solutions to the given equations are x = 10 and m = 1.5.
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If the rate of inflation is 3.4% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)=25000(1.034)^t. Find the current price of the item and the price 10 years from today.
The price of the item 10 years from today will be approximately $37,607.56
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To find the current price of the item, we need to substitute t = 0 in the given equation.
So we get:
[tex]p(0) = 25000(1.034)^0 = 25000(1) = 25000[/tex]
Therefore, the current price of the item is $25,000.
To find the price 10 years from today, we need to substitute t = 10 in the given equation. So we get:
[tex]p(10) = 25000(1.034)^{10} = 37607.56[/tex]
Therefore, the price of the item 10 years from today will be approximately $37,607.56.
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PLEASE HELP I NEED HELP PLEASE
Answer:
Step-by-step explanation:
You take 528- divided by 2000- and then you get your answer.
whats the answer? I have to finish this quiz since I missed it
Answer:
Step-by-step explanation:
For this triangle, we can find the angle adjacent to side length 4 using trig:
tan(theta) = 7/4
theta = tan^-1(7/4)
theta = 60.26
Now we use sine to find x:
sin(60.26) = 7/x
x = 7/sin(60.26)
x = 8.06
I don't know how far you need to round, so it can either be this or 8.1
Hope this helps!
Sean planted seeds in 0.2 square yards of his garden in 1.5 hours. How long will it take Sean to plant seeds in 0.5 square yards of the garden?
3 hours
3 hours
3.5 hours
3.5 hours
3.75 hours
3.75 hours
30 hours
It will take Sean 3.75 hours to plant seeds in 0.5 square yards of the garden. Answer: 3.75 hours.
What is multiplication ?Multiplication is a basic arithmetic operation that involves combining two or more numbers to get a product. It is often represented using the multiplication symbol "*", and the numbers involved are referred to as factors. The result of a multiplication operation is called the product.
According to given information :We can start by using the ratio of square yards to time as a proportion:
0.2 sq yd / 1.5 hrs = 0.5 sq yd / x hrs
Cross-multiplying, we get:
0.2 sq yd * x hrs = 1.5 hrs * 0.5 sq yd
Simplifying, we get:
x = (1.5 hrs * 0.5 sq yd) / 0.2 sq yd
x = 3.75 hrs
Therefore, it will take Sean 3.75 hours to plant seeds in 0.5 square yards of the garden. Answer: 3.75 hours.
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A rectangular prism is 6 centimeters long and 16 centimeters high. Its volume is 1,152 cubic centimeters. What is the width of the rectangular prism?
The width of the rectangular prism as required to be determined is 12 centimetres.
What is the measure of the prism's width?As evident in the task content; the rectangular prism is 6 centimeters long and 16 centimeters high while Its volume is 1,152 cubic centimeters.
Since for rectangular prisms;
Volume = length × width × height
Where,
Length = 6 centimeters
Width = w
Height = 16 centimeters
So,
Volume = length × width × height
1152 = 6 × w × 16
w = 1152 / 96
w = 12 centimeters
Ultimately the width of the rectangular prism in discuss is;12 centimetres.
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Express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form.
The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
To express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form, we need to multiply the two expressions together and then simplify. Here are the steps:
1. Distribute the first term of the first expression to the second expression: (4/3)x * (5/6)x + (4/3)x * (5/3) = (20/18)x^2 + (20/9)x
2. Distribute the second term of the first expression to the second expression: -6 * (5/6)x + -6 * (5/3) = (-30/6)x + (-30/3)
3. Combine the like terms: (20/18)x^2 + (20/9)x + (-30/6)x + (-30/3) = (20/18)x^2 + (-10/9)x + (-30/3)
4. Simplify the fractions: (10/9)x^2 + (-10/9)x + (-10)
So the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
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need help you all with this question:(
Answer:
True both each.
Step-by-step explanation:
Your teacher would probably like you to remember the Trig Identities or allow you to have a cheat sheet for the Quiz or Test.
[tex]\frac{sin(\alpha )}{sin^{2}(\alpha) +cos2\alpha } \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +[cosx^{2} (\alpha)-sinx^{2} (\alpha )]} \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +cosx^{2} (\alpha)-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{[sin^{2}(\alpha) +cosx^{2} (\alpha)]-sinx^{2} (\alpha )}[/tex]
[tex]\frac{sin(\alpha )}{1-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )*cos(\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )}*\frac{1}{cos(\alpha )} \\\\tan(\alpha )*sec(\alpha )\\\\\frac{1}{cot(\alpha )}*sec(\alpha )\\\\\frac{sec(\alpha )}{cot(\alpha )}[/tex]
Im really confused .
Answer:
Triangle A is not a scale drawing
Triangle B is a scale drawing
Triangle C is not a scale drawing
Help I don't understand.
Answer:
Below
Step-by-step explanation:
f(-5) = 85 * .95^(-5) = 109.9 mg remaining after -5 hours this does not fit the context of the problem
( domain ( values of 'x') should be 0 ---> infinity)
f(24) = 85 * .95^24 = 24.8 mg remaining after 24 hours this does fit the context of the problem
2. What is the product of (-3x3 + 2x – 5) and (2x4 – 4x2 – 3)?
(a) Show your work
(b) Is the product of (-3x3 + 2x – 5) and (2x4 – 4x2 – 3) equal to the product of (2x4 –
4x2 – 3) and (-3x3 + 2x – 5) Explain your answer.
The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)
What is expressiοn?An expressiοn in mathematics is made up οf different numbers, variables, and mathematical prοcesses, such as expοnents, lοgarithms, trigοnοmetric functiοns, and arithmetic. It can symbοlise a number οr a fοrmula, but it lacks an equals sign (=) and cannοt be evaluated οr sοlved withοut being cοmbined οr simplified. Expressiοns can be straightfοrward, like 3x + 4, οr they can be cοmplicated, like (2x - 1)/(x + 3).
given:
(a) We must multiply each term in the first expressiοn by each term in the secοnd expressiοn befοre cοmbining like terms tο determine the prοduct οf (-3x³ + 2x - 5) and (2x4 - 4x² - 3). The distributive principle allοws us tο write:
= (-3x³ + 2x - 5) * (2x⁴ - 4x² - 3) * (3x³ + 2x - 5) * = 3x³ * 2x⁴ + (-3x³) * (-4x²) * (-3)
= 2x * 2x⁴ + 2x * (-4x²) + 2x * (-3)
= -6x⁷ + 12x⁵ + 9x³ + 4x⁵ - 8x³ - 6x - 10x⁴ + 20x² + 15 = 5 * 2x⁴ - 5 * (-4x²) - 5 * (-3)
The result οf the οperatiοns (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is as fοllοws: -6x⁷ + 10x⁴ + 16x⁵ - 17x³ - 6x + 15
(b) The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3). Due tο the fact that multiplicatiοn is cοmmutative, changing the οrder οf the variables has nο effect οn the οutcοme οf the prοduct. Cοnsequently, we can write:
(2x⁴ - 4x² - 3) * (-3x³ + 2x - 5) = (-3x³ + 2x - 5) * (2x⁴ - 4x² - 3)
The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)
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Find the null space of \( A \). a. \( A=\left[\begin{array}{ccc}1 & -2 & 0 \\ 1 & 0 & 2\end{array}\right] \) b. \( B=\left[\begin{array}{cccc}1 & 3 & 4 & 0 \\ 0 & 2 & 4 & 4 \\ 1 & 1 & 0 & -4\end{array
The null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \) and the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
To find the null space of a matrix, we need to solve the equation \( Ax=0 \), where \( x \) is a vector in the null space.
For matrix \( A \), we can set up the following system of equations:
\begin{align*}
x-2y &= 0 \\
x+2z &= 0
\end{align*}
Solving for \( x \) and \( y \) in terms of \( z \) gives us:
\begin{align*}
x &= -2z \\
y &= -z
\end{align*}
So the null space of \( A \) is the set of all vectors of the form \( \left[\begin{array}{c}-2z \\ -z \\ z\end{array}\right] \), where \( z \) is any scalar. This can also be written as the span of the vector \( \left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right] \), so the null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \).
For matrix \( B \), we can set up the following system of equations:
\begin{align*}
x+3y+4z &= 0 \\
2y+4z+4w &= 0 \\
x+y-4w &= 0
\end{align*}
Solving for \( x \), \( y \), and \( z \) in terms of \( w \) gives us:
\begin{align*}
x &= 4w \\
y &= -2w \\
z &= w
\end{align*}
So the null space of \( B \) is the set of all vectors of the form \( \left[\begin{array}{c}4w \\ -2w \\ w \\ w\end{array}\right] \), where \( w \) is any scalar. This can also be written as the span of the vector \( \left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right] \), so the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
Therefore, the null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \) and the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
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Explain how to convert a number of months to a fractional part of a year.Divide the number of months by 6
Hence, to convert a number of months to a fractional portion of a year, linear function divide the number of months by either 6 or 12 to get the answer in terms of half-years or complete years.
What is linear function ?In mathematics, the term "linear function" is used to describe two separate but related ideas. Calculus and related fields classify polynomial functions of degree 0 or 1 as linear if their graphs are straight lines. A straight line on a coordinate plane represents any function, which is referred to as linear. Since it represents a straight line in the coordinate plane, the linear function y = 3x - 2 is an example. As the function may be connected to y, it can be represented as f(x) = 3x - 2.
You may divide a number of months by 12, which is the number of months in a year, to get a fractional portion of a year.
Consider the case when you have nine months. Nine months are equal to 0.75 years when you divide nine by twelve. But, if you divide 9 by 6, you obtain a result of 1.5, indicating that 9 months are equal to 1.5 half-years or 1 year and 6 months.
Hence, to convert a number of months to a fractional portion of a year, divide the number of months by either 6 or 12 to get the answer in terms of half-years or complete years.
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what does x equal to? 10x+48=18x+-34
Answer: 41/4 or 10.25 or 10 1/4
Step-by-step explanation:Exact Form:
x
=
41
4
Decimal Form:
x
=
10.25
Mixed Number Form:
x
=
10
1
4
Find the period of the function f(x) = cos(2.22x+0.19). Provide four decimal places. Answer:______ Find the period of the function f(x) = sin(1.05x). Provide four decimal places. Answer:______
The period of the function f(x) = cos(2.22x+0.19) is 2.8323 and the period of the function f(x) = sin(1.05x) is 5.9834
The period of a trigonometric function, we use the formula:
Period = 2π/|B|
where B is the coefficient of x in the function.
For the first function, f(x) = cos(2.22x+0.19), the coefficient of x is 2.22. Therefore, the period is:
Period = 2π/|2.22| ≈ 2.8323
For the second function, f(x) = sin(1.05x), the coefficient of x is 1.05. Therefore, the period is:
Period = 2π/|1.05| ≈ 5.9834
So, the period of the first function is 2.83 and the period of the second function is 5.98. Both answers are rounded to four decimal places.
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In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?
2x^2 + 7x + 3 factors into (2x + 1)(x + 3).
What is factoring?
The factoring approach can be used if the quadratic polynomial can be divided into two linear factors:
Look for two numbers that add up to b and multiply to c.
With these numbers, rewrite the quadratic polynomial as the sum of two terms.
Choose the term that has the most in common with each group of terms.
Remove the common binomial factor between the two groups.
Take the quadratic polynomial 2x2 + 7x + 3, for instance. We must choose two values that sum up to seven and multiply by three in order to factor this polynomial. These are the numbers 3 and 1. The quadratic can then be rewritten as follows:
2x² + 3x + 4x + 3
Then, for each collection of terms, we factor out the term with the highest common factor:
x(2x + 3) + 1(4x + 3)
Lastly, we remove the common binomial factor between the two groups:
(2x + 1)(x + 3)
As a result, 2x2 + 7x + 3 equals (2x + 1)(x + 3).
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2
A geometric sequence is shown below.
Which function describes this sequence?
5, 11, 29, 83, ...
These values match the given sequence, so the function that describes the sequence is:
an = 5(2.2 + 0.8182n)ⁿ⁻¹
What is the meaning of the word "function"?According to one definition, a function is a relationship between a number of inputs where each input has exactly one output.
To find the function that describes the given geometric sequence, we need to find the common ratio r. We can do this by dividing any term in the sequence by the previous term:
11/5 = 2.2
29/11 = 2.63636...
83/29 = 2.86206...
We can see that the common ratio is increasing, which suggests that the sequence is not a perfect geometric sequence. However, the differences between the ratios are getting smaller, so we can approximate the sequence as a geometric sequence with a changing common ratio.
Let's use the first two terms of the sequence to find an initial approximation for the common ratio:
r ≈ 11/5 = 2.2
Then, we can write the nth term of the sequence as:
an = 5(2.2)ⁿ⁻¹
However, we noticed that the common ratio is increasing, so we need to adjust our formula to account for this. Let's try a formula where the common ratio is a linear function of n:
an = 5(2.2 + 0.8182n)ⁿ⁻¹
Plugging in n = 1, 2, 3, and 4, we get:
a1 = 5(2.2 + 0.8182(1))⁰ = 5
a2 = 5(2.2 + 0.8182(2))¹ ≈ 11
a3 = 5(2.2 + 0.8182(3))² ≈ 29
a4 = 5(2.2 + 0.8182(4))³ ≈ 83
These values match the given sequence, so the function that describes the sequence is:
an = 5(2.2 + 0.8182n)ⁿ⁻¹
where n is the index of the term in the sequence.
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Perform the multiplication or division and simplify
x2 + 2xy + y2
x2 − y2
·
3x2 − xy −
2y2
2x2 − xy −
3y2
After performing multiplication or division and simplify we get 2x2 − xy − 3y2 as the answer of this question.
The question is asking you to perform the multiplication or division and simplify:
x2 + 2xy + y2 ÷ x2 − y2 =
(x2 + 2xy + y2)(3x2 − xy − 2y2) ÷ (x2 − y2) =
3x4 − x3y − 2x2y2 − 3xy2 + 2xy3 + 2y4 ÷ (x2 − y2) =
3x4 − x3y − 2x2y2 − 2y4 ÷ (x2 − y2)
= 2x2 − xy − 3y2
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6. Consider the expansion of x^2 (3x^2 + k/x)^8. The constant term is 16128. Find k. [7 marks]
The value of k is ∛√199.
Consider the expansion of x^2(3x^2 + k/x)^8. The constant term is 16128. We need to find the value of k.
The expansion of (3x^2 + k/x)^8 will have terms of the form (3x^2)^a(k/x)^b, where a + b = 8. The constant term will be the term where the powers of x cancel out, so we need to find a and b such that 2a - b = 0.
Solving for a and b, we get a = 4 and b = 8. So the constant term will be (3x^2)^4(k/x)^8 = 81x^8(k^8/x^8) = 81k^8.
Setting this equal to 16128 and solving for k, we get:
81k^8 = 16128
k^8 = 16128/81
k^8 = 199
k = ∛√199
Therefore, the value of k is ∛√199.
k = ∛√199.
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6. A man drops a penny from the top of a 500 m tall building. After / seconds, the penny has fallen a distance 16 of's metres, where s(t)- 500-S0SS10.
a. Determine the average velocity between 1 s and 5s.
b. Determine the average velocity between 5s and 9 s.
c. Determine the velocity at -5.
a. The average velocity between 1s and 5s is -30 m/s.
b. The average velocity between 5s and 9s is -70 m/s
c. The velocity at -5 is -50 m/s.
A. The average velocity between 1 s and 5 s can be calculated by finding the displacement divided by the time interval. The displacement is the difference between the final and initial positions, which can be found by plugging in the values of t into the equation s(t) = 500 - 5t^2.
So, s(1) = 500 - 5(1)^2 = 495 m and s(5) = 500 - 5(5)^2 = 375 m.
The displacement is 375 - 495 = -120 m. The time interval is 5 - 1 = 4 s.
Therefore, the average velocity is -120 m / 4 s = -30 m/s.
B. The average velocity between 5 s and 9 s can be calculated in the same way. s(5) = 375 m and s(9) = 500 - 5(9)^2 = 95 m.
The displacement is 95 - 375 = -280 m. The time interval is 9 - 5 = 4 s.
Therefore, the average velocity is -280 m / 4 s = -70 m/s.
C. The velocity at t = 5 can be found by taking the derivative of the position function s(t) = 500 - 5t^2.
The derivative is s'(t) = -10t. Plugging in t = 5 gives s'(5) = -10(5) = -50 m/s.
So the velocity at t = 5 is -50 m/s.
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Write the following linear equation in function notation. y = 2x + 5
Answer:
y=mx+b
It's already in function notation. Unless you need to graph it or show it.
Help a girl out I need help his due for tomorrow please help guys
The function that generates the sequence 1, 2, 4, 8, ... is:
Of(x) = 2^(x-1)
We can check this by plugging in the first few values of x:
Of(1) = 2^(1-1) = 1
Of(2) = 2^(2-1) = 2
Of(3) = 2^(3-1) = 4
Of(4) = 2^(4-1) = 8
Therefore, the answer is option B.
help me please I want to be done
a) The exponential growth equation is y = ( 1.2 )ˣ
b) The exponential decay equation is y = ( 0.71 )ˣ
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the exponential growth equation be represented as A
Now , the value of A is
y = ( 1.2 )ˣ
where the growth rate is r = 20 %
Let the exponential decay equation be represented as B
Now , the value of B is
y = ( 0.71 )ˣ
where the decay rate is r = 29 %
The graph A represents an exponential decay graph and the graph B represents an exponential growth graph
Hence , the exponential equations are solved
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Graph f(x) = (x+1) (x-5)
The graph of the quadratic function is on the image at the end.
How to graph the quadratic function?Here we have the quadratic function:
f(x) = (x + 1)*(x - 5)
To graph this, we need to find some points of the parabola and then connect them.
So let's evaluate the function.
if x = -1
f(-1) = (-1 + 1)*(-1 - 5) = 0
if x = 0
f(0) = (0 + 1)*(0 - 5) = -5
if x = 1
f(1) = (1 + 1)*(1 - 5) = 2*-4 = -8
if x = 5 then:
f(5) = (5 + 1)*(5 - 5) = 0
So we have the points (-1, 0), (0, -5), (1, -8) and (5, 0).
With these we can graph the parabola (you can try to find more points to get a better graph).
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A car travels 1 mile every
minute, what is its speed in
mi/hr?
Answer:
Step-by-step explanation:
60mi/hr
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 21 HCF of water is
$35.39, and the cost for using 57 HCF is $83.99. What is the cost for using 56 HCF of water?
Monthly cost
(in dollars)
Water usage
(In HCF)
E
If the cost for using 21 HCF of water is $35.39. the cost for using 56 HCF of water is $82.64.
How to find cost for using 56 HCF of water?We can use the two given data points to find the slope and y-intercept of the linear function that represents the monthly cost of water use.
Let's use (21, 35.39) and (57, 83.99) as our two data points.
First, let's find the slope of the line:
slope = (y2 - y1) / (x2 - x1)
slope = (83.99 - 35.39) / (57 - 21)
slope = 48.6 / 36
slope = 1.35
Now that we have the slope, we can use either of the two data points to find the y-intercept. Let's use (21, 35.39):
y = mx + b
35.39 = 1.35 * 21 + b
35.39 = 28.35 + b
b = 35.39 - 28.35
b = 7.04
So the linear function that represents the monthly cost of water use is:
y = 1.35x + 7.04
where y is the cost (in dollars) and x is the amount of water used (in HCF).
Now we can use this function to find the cost for using 56 HCF of water:
y = 1.35x + 7.04
y = 1.35 * 56 + 7.04
y = 82.64
So the cost for using 56 HCF of water is $82.64.
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Given sinx=3/5 and x is in quadrant 2, what is the value of tanx/2
let's keep in mind that in the II Quadrant, sine is positive and cosine is negative, so just about the same for the opposite and adjacent sides of the angle "x", so
[tex]\sin(x )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=adjacent\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ a=\pm\sqrt{ 5^2 - 3^2} \implies a=\pm\sqrt{ 16 }\implies a=\pm 4\implies \stackrel{II~Quadrant }{a=-4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cos(x )=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}}\hspace{9em} \tan\left(\cfrac{\theta}{2}\right)=\cfrac{\sin(\theta)}{1+\cos(\theta)} \\\\\\ \tan\left(\cfrac{x}{2}\right)\implies \cfrac{\frac{3}{5}}{1-\frac{4}{5}}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{\frac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{5}{1}\implies \text{\LARGE 3}[/tex]
Write a story problem:
100 - 20 - 4 =
Answer: a ticket to an amusement park is $100 per person. you have a coupon for $20 off of the admission price. the amusement park is also having a promotion where if you bring an empty pepsi can you can take an additional $4 off of the total admission cost. how much do you have to pay to be admitted to the amusement park after the coupons? (it would be $76)
Step-by-step explanation: my brain thought this up
Answer:
Step-by-step explanation:
Mikes mom gave him 100 dollars to spend and his favorite toy shop. Mike bought a Lego set which cost him 20 dollars. When he bought a lollipop which cost him 4 dollars.
PKEASE HELPPP 15 POINTSSSSSSSSSSss
Answer: you can see herhere
Step-by-step explanation:
try times like x=1 and find the answer true
Find a polynomial function completely multiplied out with real coefficie that has the given zeros: 1,-4,(3+1) x^(3)+3x^(2)-4x
a polynomial function completely multiplied out with real coefficient that has the given zeros is f(x) = x³-x²-16x+16
To find a polynomial function with the specified zeros that is fully multiplied out with real coefficients, we can use the fact that if a polynomial has a zero at x = a, then (x-a) is a factor of the polynomial. Therefore, we can write the polynomial as a product of its factors:
(x-1)(x+4)(x-(3+1)) = (x-1)(x+4)(x-4)
Now, we can multiply out the factors to get the polynomial in standard form:
(x-1)(x+4)(x-4) = (x²+3x-4)(x-4) = x³+3x^(2)-4x-4x²-12x+16 = x³-x²-16x+16
Therefore, the polynomial function completely multiplied out with real coefficients that has the given zeros is:
f(x) = x³-x²-16x+16
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