(4-3m)8 distributive property
Whats the constant term for y=3x + 5
1. 3
2. 5
i answered this one already on your other post for it
3 is the constant/slope
5 is the y intercept
f(x) = cube root 2x
g(x) = 2x + 1
Find (f/g) (X) Include any restrictions on the domain
Answer:
B.
Step-by-step explanation:
any arithmetic operation with functions just means to do this operation with the functional expressions.
f/g is really just the expression of f divided by the expression of g.
so, this results in a fraction with the denominator (bottom part) = 2x + 1
as you know, a division by 0 is not a valid operation, and therefore we have to forbid any value for x that would create a 0 in the denominator.
so, for what x do we get
2x + 1 = 0
2x = -1
x = -1/2
therefore, we have to exclude x = -1/2.
[tex] \rm \int_{ \infty }^{ - \infty } \frac{ { {e}^{ { - x}^{2} } }(5 {x}^{2} + 2 {x}^{4} )}{ {x}^{2}( {x}^{2} + 1)} dx \\ [/tex]
Consider the integral
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx[/tex]
which is the negative of yours. Bit strange to integrate over [tex](\infty,-\infty)[/tex], but if that's what you actually intended, just multiply the final result by -1. Of course, I've already canceled the superfluous factors of [tex]x^2[/tex].
Expand the integrand into partial fractions.
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \int_{-\infty}^\infty \left(2 + \frac3{1+x^2}\right) e^{-x^2} \, dx[/tex]
Recall that for [tex]\alpha>0[/tex],
[tex]\displaystyle \int_{-\infty}^\infty e^{-\alpha x^2} \, dx = \sqrt{\frac\pi\alpha}[/tex]
Now let
[tex]\displaystyle I(a) = \int_{-\infty}^\infty \frac{e^{-ax^2}}{1+x^2} \, dx[/tex]
Together, these give
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = 2\sqrt\pi + 3I(1)[/tex]
Differentiate [tex]I(a)[/tex] under the integral sign with respect to [tex]a[/tex] to obtain a simple linear differential equation.
[tex]\displaystyle \frac{dI}{da} = -\int_{-\infty}^\infty \frac{x^2 e^{-ax^2}}{1+x^2} \, dx \\\\ ~~~~~~~~ = - \int_{-\infty}^\infty \left(1 - \frac1{1+x^2}\right) e^{-ax^2} \, dx \\\\ ~~~~~~~~ = -\sqrt{\frac\pi a} + I(a)[/tex]
Solve for [tex]I(a)[/tex] with the initial value [tex]I(1) = \sqrt\pi[/tex]. Using an integrating factor,
[tex]\displaystyle \frac{dI}{da} - I(a) = -\sqrt{\frac\pi a} \\\\ e^{-a} \frac{dI}{da} - e^{-a} I(a) = -\sqrt{\frac\pi a}\,e^{-a} \\\\ \frac{d}{da}\left[e^{-a} I(a)\right] = -\sqrt{\frac\pi a}\,e^{-a}[/tex]
By the fundamental theorem of calculus,
[tex]\displaystyle e^{-a} I(a) = e^{-a}I(a)\bigg|_{a=0} - \sqrt\pi \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi \\\\ I(a) = \pi e^a - \sqrt\pi \, e^a \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]
so that
[tex]\displaystyle I(1) = \pi e - \sqrt\pi\,e \int_0^1 \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]
Substitute [tex]t=\sqrt\xi[/tex].
[tex]\displaystyle I(1) = \pi e - 2\sqrt\pi\,e \int_0^1 e^{-t^2} \, dt[/tex]
Recall the error function,
[tex]\mathrm{erf}(x) = \displaystyle \frac2{\sqrt\pi} \int_0^x e^{-t^2} \, dt[/tex]
which we can use to write
[tex]I(1) = \pi e - 2\sqrt\pi e \cdot \dfrac{\sqrt\pi}2\,\mathrm{erf}(1) = \pi e - \pi e \,\mathrm{erf}(1)[/tex]
Finally, we arrive at
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \boxed{2\sqrt\pi + 3\pi e - 3\pi e \, \mathrm{erf}(1)}[/tex]
A small publishing company is planning to publish a new book. Let C be the total cost of publishing the book (in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 200 copies of the book. Suppose that C= 10/N + 800 gives C as a function of N during the first printing. Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
The domain is the set of all integers lying in the interval [0 , 200] and range is the set of all reals lying in the interval [800 , 2800].
What is a function?
A function defined from A to B, associates each and every element of the set A tò the element of set B. In mathematics, it is represented using the symbol, f : A -> B. Here, set A is called the domain of the function while set B is called the range of a function.
Calculation of domain and range of a given function
The domain is the set of all possible values of x. According to this question, the domain of N lies in the interval [0 , 200] i.e. all the integers lying in the given interval. Only integers are chosen because the number of books cannot be in fraction.
The range is the set of possible costs and lies in the interval [800 , 2800] i.e. all the reals lying in the given interval.
Hence, the domain is the set of all integers lying in the interval [0 , 200] and range is the set of all reals lying in the interval [800 , 2800].
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Tom and Louise share £40 in the ratio 1 : 3 work out how much money Tom gets
Answer:
5
Step-by-step explanation:
because I give him and the answer is incorrect I know but I gave him believe me
Please answer this screenshot please 10 points good idea yes.
Answer:
Yes it is a function
Step-by-step explanation:
There is a relationship between x and y. It is not linear but quadratic
Answer:
yes it is a function
Step-by-step explanation:
that is the answer bc I said I was
At the beginning of each of her four years in college, Miranda took out a new Stafford loan. Each loan had a principal of $5,500, an interest rate of 7.5% compounded monthly, and a duration of ten years. Miranda paid off each loan by making constant monthly payments, starting with when she graduated. All of the loans were subsidized. What is the total lifetime cost for Miranda to pay off her 4 loans? Round each loan's calculation to the nearest cent.
a.
$23,650.00
b.
$29,481.08
c.
$7,834.32
d.
$31,337.27
The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27.
What is interest?Interest is the sum of money paid for using someone else's funds. You must pay interest when you borrow money from lenders. You receive interest when you lend money to borrowers. It could be stated in terms of money or the rate of payment. You will learn more about interest in this article, including the different sorts of interest, what they are, and how to determine how much interest will be charged on a loan or a loan amount.
Given that,
At the beginning of each of her four years in college
Miranda took out a new Stafford loan.
Each loan had a principal of $5,500,
An interest rate of 7.5% compounded monthly
A duration of ten years.
Miranda paid off each loan by making constant monthly payments, starting with when she graduated.
All of the loans were subsidized.
The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27
Therefore, the total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27
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Answer: D 31,337.27
Step-by-step explanation:
x - y = 7
x - y = -1
Solve the system of equations by graphing
Answer:
There is no solution. The lines are parallel. They will never intercept. There will be no point that is on both lines.
Step-by-step explanation:
The length of a rectangle is twice its width.
If the perimeter of the rectangle is 36 m, find its area
Answer:
length= 12 width=6
Step-by-step explanation:
when adding perimeter you add the length and width twice each so divide 36 by two and get 18
if the length is twice the width then you could make the equation w+2w=18
by adding like terms you get 3w=18
to get n by itself you divide 18 by 3 and get w=6
if the width is 6 and the length is twice that then the length is 12
Answer:
A=72
Step-by-step explanation:
The length of a rectangle is TWICE it's width meaning 2 times. (Note that L= length, W=width, and A=Area)
L=2w
4w+2w=36
6w=36 <- ( 6 is width)
then
2x6=12
Then
12x6=72
So the area of the rectangle is 72.
Hope that makes sense!
In the last year school board election Mrs Jackson received 60.1% of the votes write three equivalent fractions for 60.1% with denominator of 1000 and 100and 10
if 2/5 kilogram of soil fills 1/3 of a container,can1 a kilogram of soil fit in the container? Explain or show your reasoning
Answer:
Yes
Step-by-step explanation:
1 kilogram of soil will fill:
1/3 ÷ 2/5 = 5/6 (of a container)
Because 5/6 < 1
=> 1 kilogram of soil will fit in the container
(Adding and Subtracting with Scientific Notation MC)
Simplify (9 x 10−13) − (6.3 x 10−15).
8.937 x 10−15
8.937 x 10−13
2.7 x 10−15
2.7 x 10−13
Answer:
C) 2.7 x 10-15
Step-by-step explanation:
Sorry if I'm wrong. hope you're having a great day
The computation shows that the value of (9 x 10−13) − (6.3 x 10−15) is C. 2.7 x 10−15
How to compute the value?Simplify (9 x 10−13) − (6.3 x 10−15).
This will be solved as follows. It should be noted that one just have to subtract the values.rhat are given based on the information above.
Therefore, (9 x 10−13) − (6.3 x 10−15).
= 2.7 x 10−15
In conclusion, the correct option is C.
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What is the value of −7 + |−25|?
Step-by-step explanation:
the absolute value function always delivers the positive value of the internal expression, no matter if it is actually negative or already positive.
so,
|-25| = 25
therefore,
-7 + 25 = 18
Find the rate of change of f(x) = x² - 2x + 3 on [-1,2].
Answer:
-1.
Step-by-step explanation:
Rate of change = [ f(2) - f(-1)] / [2 - (-1)]
= [(2)^2 - 2(2) + 3) - ((-1)^2 - 2(-1) + 3] / 3
= ( 3 - 6)/3
= -1.
solve the equation for x (3x/4)+2=4x-1
Answer:
Step-by-step explanation:
Scientific notation question HW
Answer:
the scientific notation of 83300 is 8.33*10^4
i really need help! please
What is an equation of the line that passes through the points (3, 6) and (-1, -6)?
f(x) = 5x-7, then what is the solution to f(x) = 4?
(1) 13
(3) -87
(2)-7
(4) 2}
I need some work or explanation please ASAP
The solution to function f(x) = 4 is 2 1/5.
Given that, f(x) = 5x - 7
Now, function f(x) = 4 implies that
i.e. 5x - 7 = 4
i.e. 5x = 4 + 7
i.e. 5x = 11
i.e. x = 11/5
x =2 1/5
So, option (4) is correct.
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
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The function is f(x)= 5x-7. The solution to f(x)=4 is when x is 11/5.
Given that,
The function is f(x)= 5x-7
A function is nothing but in mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain),where there is exactly one output for every input, and the output can be connected to its input.
f(x), where x is the input, is a common way to refer to a function. A function represented as y = f(x).
We have to find the solution to f(x)=4
Take 5x-7 in the place of f(x) because they are equal.
5x-7=4
5x=4+7
5x=11
x=11/5
Therefore, the solution x value is 11/5.
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Urgent (I added 50 points)
The diagram below is drawn on a one-centimetre square grid
Work out the area of the shaded triangle:
The area of the shaded triangle will be 11.5 square centimeters.
What is the area of the shaded region?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The area of the square will be given as,
A₁ = 5 x 5
A₁ = 25
The area of the triangles will be given as,
A₂ = 1/2 (1 x 5 + 4 x 3 + 2 x 5)
A₂ = 1/2 (27)
A₂ = 27/2
Then the area of the shaded triangle will be given as,
A = A₁ - A₂
A = 25 - 27/2
A = (50 - 27) / 2
A = 23/2
A = 11.5 square cm
The area of the shaded triangle will be 11.5 square centimeters.
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Answer:
In the graph, excluding the shaded triangle, there are three right angled triangles surrounding the shaded triangle in a square
Area of shaded triangle = area of square - area of three triangles
[tex]{ \sf{area = (5 \times 5) - ( \frac{1}{2} \times 4 \times 3) - ( \frac{1}{2 } \times 5 \times 2) - ( \frac{1}{2} \times 5 \times 1)}} \\ \\ { \sf{area = 25 - 6 - 5 - 2.5}} \\ \\ { \sf{area = 11.5 \: {cm}^{2} }}[/tex]QUESTION 94
Percentages
In January 2021, a study by the Bureau of Transportation statistics found that 12 out of 35 flights arrived
on time. What percent of the flights were on time?
Choose one 4 points
O 72%
O 34.3%
O 34%
O 27%
Answer: 34.3%
Step-by-step explanation:
[tex]Given:\ 12/35\ flights\ on\ time[/tex]
To find the percent, divide then multiply by 100:
[tex]\frac{12}{35} = 0.343\times100=\large\boxed{34.3}[/tex]
3y^3+20y^2=7y
Solve the polynomial by factoring. The answer is y(3y-1)(y+7)
I can't seem to figure out how they got the answer. I need an explanation before my test tomorrow.
Answer:
Hello,
Step-by-step explanation:
[tex]3y^3+20y^2-7y=y(3y^2+20y-7)\\\\=y(3y^2+21y-y-7)\\\\=y(3y(y+7)-(y+7))\\\\=y(y+7)(3y-1)\\[/tex]
Which expression simplifies to 2√/15? A. V17 OB. √19 OC √30 OD. √60
please help just have 3 minutes left
Answer:
Step-by-step explanation:
solve the equation by performing two operations on both sides. State the operation in order of use
Answer:
C. Multiply by 5, then subtract 7.
Step-by-step explanation:
You want to know the two steps required to solve this 2-step linear equation.
SolutionThe variable x has 7 added to it, and the sum is divided by 5. To find the value of x, we must undo these operations in reverse order.
To undo division by 5, we must multiply by 5.
Then, to undo the addition of 7, we must subtract 7.
Here is the "work":
[tex]\dfrac{x+7}{5}=10\qquad\text{given}\\\\x+7 = 50\qquad\text{multiply both sides by 5}\\\\x=43\qquad\text{subtract 7 from both sides}[/tex]
The operations in order of use are ...
Multiply both sides by 5 first, then subtract 7 from both sides.
__
Additional comment
The properties of equality tell you that you must do the same operation to both sides of the equation.
Approximate √10 to the nearest tenth
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar.
The computation shows that the tons of sugar when they'll have same price is 18 tons.
How to compute the value?The first company charges $5500 to rent trucks plus an additional fee of $200.25. Thai will be:
= 5500 + (200.25 × s)
= 5500 + 200.25s
where s = tons of sugar
The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. This will be:
5041 + 225.75s
Then we will equate both of them. This will be:
5500 + 200.25s = 5041 + 225.75s
5500 - 5041 = 225.75d - 200.25s
459 = 25.5s
s = 459/25.5
s = 18
At 18 tons, they'll have same price.
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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. For want mount if sugar do they charge the same price.
Find the values of x and y. Write all radicals in simplest form.
Answer:
For the 60-30-90 degree triangle:
x=12
y=[tex]12\sqrt{3}[/tex]
For the 30-60-90 degree triangle:
x=16
y=[tex]8\sqrt{3}[/tex]
For the 45-45-90 degree triangle:
x=7
y=[tex]7\sqrt{2}[/tex]
Step-by-step explanation:
For 30-60-90 triangles, the side opposite the 30 degree angle is x, while the side opposite the hypotenuse is 2x, while the side opposite the 60 degree angle is [tex]x\sqrt{3}[/tex].
For 45-45-90 triangles, the sides opposite the 45 degree angles are x, while the hypotenuse is [tex]x\sqrt{2}[/tex].
Suppose the odds are 38 to 1 that someone will lie to you at least once in the next seven days. State this as a probability.
Answer:
38/39
Step-by-step explanation:
P=s/(s+f)
P=38/(38+1)
P=38/39
A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 3 feet in length. How many 18-inch pieces can the dressmaker cut from 15 of these rolls of ribbon?