Domain = ∈ [2, ∞]
Range = ∈ [0, ∞]
Graph [tex]\sqrt{x - 2 [-10, 10, -5, 5]}[/tex]
Just outline the function.
The typical root operation is:
[tex]y = a * \sqrt{(x - h)} + k[/tex]
where x - h ≥ 0
The value within the root sign of a square root function CANNOT be < 0
∴ x - h ≥ 0
∴ x ≥ 2
Therefore, Domain = ∈ [2, ∞]
Regarding range, the function we were provided doesn't have a K value.
As a result, the range spans from 0 to infinity.
Therefore, Range = ∈ [0, ∞]
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a baseball coach spent $118.25 on 11 pizzas. estimate ate the cost of each pizza using a number with one nonzero digit. then find the exact cost per pizza
Answer:
10.75
Step-by-step explanation:
$118.25 / 11
We're finding the cost of each pizza. So, If a Coach bought 11 Pizza's for $118.25, We need to find how much x is. x = amount of cost per pizza. Divide $118.25 by 11 to get $10.75.
Each Pizza Costs $10.75.
What is the answer
6000 +300+20+5
Answer:
6325
Step-by-step explanation:
[tex]6000 \\ \: \: 300 \\ \: \: \: \: 20 \\ \: \: \: + 5[/tex]
___________
6325
Answer:
Your answer would be [tex]6325[/tex]
Step-by-step explanation:
[tex]=6325[/tex]
[tex]6000 +300+20+5[/tex]
[tex]=6325[/tex]
hopefully this helps! TwT
. Rewrite Y = √4x+16 +5 y to make it easy to graph using a translation. Describe the graph.
Answer:
The graph of [tex]y=\sqrt{4x+16}+5[/tex] is the graph of [tex]y=\sqrt{x}[/tex] translated 4 units left, stretched horizontally by a factor of 1/4, and translated 5 units up.
Step-by-step explanation:
Transformations
[tex]\textsf{For }a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Given function
[tex]y=\sqrt{4x+16}+5[/tex]
Parent function
Parent functions are the simplest form of a given family of functions.
[tex]y=\sqrt{x}[/tex]
The graph of the parent function is related to the graph of the given function by a series of transformations. To determine the series of transformations, work out the steps of how to go from the parent function to the given function.
Factor the expression under the square root sign:
[tex]y=\sqrt{4(x+4)}+5[/tex]
Transformations
Parent function:
[tex]f(x)=\sqrt{x}[/tex]
Translated 4 units left:
[tex]f(x+4)=\sqrt{x+4}[/tex]
Horizontally stretched by a factor of 1/4 (compressed by a factor of 4):
[tex]\begin{aligned}f(4(x+4)) & =\sqrt{4(x+4)}\\ & = \sqrt{4x+16} \end{aligned}[/tex]
Translated 5 units up:
[tex]f(4x+16)+5=\sqrt{4x+16}+5[/tex]
Therefore, the graph of [tex]y=\sqrt{4x+16}+5[/tex] is the graph of [tex]y=\sqrt{x}[/tex] translated 4 units left, stretched horizontally by a factor of 1/4, and translated 5 units up.
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true or false 3:7=3/7
true, 3:7 is a ratio and is equal to 3/7
Write a function g whose graph is a reflection in the x-axis of the graph of f(x)=|x|−5
The function g(x) reflected along x-axis is |x| + 5.
What is a mod function ?A modulus function always outputs positive values, hence the outputs are greater than or equal to zero,f(x) ≥ 0.
When a graph is reflected along x-axis f(x) becomes -f(x).
∴ The function f(x) = |x| - 5 when reflected along x-axis it will become
f(x) = - (|x| - 5).
f(x) = - |x| + 5.
Or
g(x) = - |x| + 5.
Graph of g(x) is shown in the image attached.
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Raphi buys 1 rubber and 1 pen for £1.25.
Dylan buys 4 rubbers and 3 pens for £4.75.
Work out the cost of one rubber and one pen.
rubber: £
pen: £
Submit Answer
Answer:
Step-by-step explanation:
Cost of one rubber = $1
Cost of one pen = 0.25
what’s the answer to area=11in2
Car A travels a distance of 22.5 miles in 30 minutes and car B travels a distance of 34.5 miles in 45 minutes. which car is traveling faster.
someone plssssss ITS URGENT.
Write the English phrase as an algebraic expression. Let the variable X represent the number
The sum of 15 divided by a number and that number divided by 15.
The expression is: ???
Answer:
(15 ÷ n) + (n ÷ 15)
Step-by-step explanation:
The sum of 15 divided by a number and that number divided by 15.
15 divided by a number
= (15 ÷ n)
15 is being divided by an unknown number (put n as a variable)
that number divided by 15
= (n ÷ 15)
An unknown number (put n as a variable) is being divided by 15.
The sum
Add (15 ÷ n) and (n ÷ 15)
(15 ÷ n) + (n ÷ 15)
Hope this helped and have a lovely rest of your day! :)
Consider the three functions below.
- (4) -(41* *--*
Which statement is true?
The range of h(x) is y> 0.
The domain of g(x) is y> 0.
The ranges of f(x) and h(x) are different from the range of g),
The domains of f(x) and g(x) are different from the domain of h(x).
Answer: c
Step-by-step explanation:
1. A rectangle has area 48cm². a) What might its perimeter be?
There are multiple but here are 2
13+13+11+11 = 42
10+10+14+14 = 42
Answer the filling questions in your own words.
1. Which figure above is a line segment?
2. Which figure above is a ray?
3. Explain, in detail, the differences between a line, a line segment, and a ray.
A line has no endpoints (line FG), a line segment has two endpoints (line segment AB), and a ray has one endpoint (ray CD).
What is a Line Segment?A line segment can be described as a line having two definite endpoints.
What is a Ray?A ray is a part of a line that has just one fixed endpoint and extends in the opposite direction of the endpoint to infinity.
What is a Line?A line has no endpoint. It extends in opposite directions to infinity.
1. The figure that is a line segment is the green figure. (line segment AB).
2. The blue figure is a ray (ray CD)
3. The red figure is a line (line FG).
In summary, a line has no endpoints (line FG), a line segment has two endpoints (line segment AB), and a ray has one endpoint (ray CD).
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[tex] \rm\sum_{n=1}^{\infty}\sum_{m=1}^{\infty} \frac{( - 1 {)}^{n + 1} }{ {mn}^{2} + mn + {m}^{2} n} \\ [/tex]
Let [tex]S[/tex] denote the sum. We can first resolve the sum in [tex]m[/tex] by factorizing and decomposing into partial fractions.
[tex]\displaystyle S = \sum_{n=1}^\infty \sum_{m=1}^\infty \frac{(-1)^{n+1}}{mn^2 + mn + m^2n} \\\\ ~~~~ = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n \sum_{m=1}^\infty \frac1{m(m+n+1)} \\\\ ~~~~ = \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n(n+1)} \sum_{m=1}^\infty \left(\frac1m - \frac1{m+n+1}\right)[/tex]
Rewrite the [tex]m[/tex]-summand as a definite integral. Interchange the integral and sum, and evaluate the resulting geometric sums.
[tex]\displaystyle \sum_{m=1}^\infty \left(\frac1m - \frac1{m+n+1}\right) = \sum_{m=1}^\infty \int_0^1 \left(x^{m-1} - x^{m+n}\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \sum_{m=1}^\infty \left(x^{m-1} - x^{m+n}\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \frac{1 - x^{n+1}}{1 - x} \, dx \\\\ ~~~~~~~~ = \int_0^1 \sum_{\ell=0}^n x^\ell \, dx \\\\ ~~~~~~~~ = \sum_{\ell=0}^n \int_0^1 x^\ell \, dx \\\\ ~~~~~~~~ = \sum_{\ell=0}^n \frac1{\ell+1} \\\\ ~~~~~~~~ = \sum_{\ell=1}^{n+1} \frac1\ell = H_{n+1}[/tex]
where
[tex]H_n = \displaystyle \sum_{\ell=1}^n \frac1\ell = 1 + \frac12 + \frac 13 + \cdots + \frac1n[/tex]
is the [tex]n[/tex]-th harmonic number. The generating function will be useful:
[tex]\displaystyle \sum_{n=1}^\infty H_n x^n = -\frac{\ln(1-x)}{1-x}[/tex]
To evaluate the remaining sum to get [tex]S[/tex], let
[tex]\displaystyle f(x) = \sum_{n=1}^\infty \frac{H_{n+1}}{n(n+1)} x^{n+1}[/tex]
and observe that [tex]S=\lim\limilts_{x\to-1^+} f(x)[/tex], which I'll abbreviate to [tex]f(-1)[/tex]. Differentiating twice, we have
[tex]\displaystyle f'(x) = \sum_{n=1}^\infty \frac{H_{n+1}}n x^n[/tex]
[tex]\displaystyle f''(x) = \sum_{n=1}^\infty H_{n+1} x^n[/tex]
[tex]\displaystyle \implies f''(x) = -\frac{\ln(1-x)}{x^2(1-x)} - \frac1x[/tex]
By the fundamental theorem of calculus, noting that [tex]f(0)=f'(0)=0[/tex], we have
[tex]\displaystyle \int_{-1}^0 f'(x) \, dx = f(0) - f(-1) \implies f(-1) = -\int_{-1}^0 f'(x) \, dx[/tex]
[tex]\displaystyle \int_x^0 f''(x) \, dx = f'(0) - f'(x) \implies f'(x) = -\int_x^0 f''(t) \, dt[/tex]
[tex]\displaystyle \implies S = f(-1) = \int_{-1}^0 \int_x^0 \left(\frac{\ln(1-t)}{t^2(1-t)} + \frac1t\right) \, dt \, dx[/tex]
Change the order of the integration, and substitute [tex]t=-u[/tex].
[tex]S = \displaystyle \int_{-1}^0 \int_{-1}^t \left(\frac{\ln(1-t)}{t^2(1-t)} + \frac1t\right) \, dx \, dt \\\\ ~~~ = - \int_{-1}^0 \left(\frac{(1+t) \ln(1-t)}{t^2(1-t)} + \frac1t + 1\right) \, dt \\\\ ~~~ = -1 - \int_{-1}^0 \left(\left(\frac2{1-t} + \frac2t + \frac1{t^2}\right) \ln(1-t) + \frac1t\right) \, dt \\\\ ~~~ = -1 - \int_0^1 \left(\left(\frac2{1+u} - \frac2u + \frac1{u^2}\right) \ln(1+u) - \frac1u\right) \, du[/tex]
For the remaining integrals, substitute and use power series.
[tex]\displaystyle \int_0^1 \frac{\ln(1+u)}{1+u} \, du = \int_0^1 \ln(1+u) d(\ln(1+u)) = \frac{\ln^2(2)}2[/tex]
[tex]\displaystyle \int_0^1 \frac{\ln(1+u)}u \, du = - \int_0^1 \frac1u \sum_{k=1}^\infty \frac{(-u)^k}k \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~ = - \sum_{k=1}^\infty \frac{(-1)^k}k \int_0^1 u^{k-1} \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~ = - \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = \frac{\pi^2}{12}[/tex]
[tex]\displaystyle \int_0^1 \frac{\ln(1+u) - u}{u^2} \, du = - \int_0^1 \frac1{u^2} \left(\sum_{k=1}^\infty \frac{(-u)^k}k + u\right) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = -\int_0^1 \frac1{u^2} \sum_{k=2}^\infty \frac{(-u)^k}k \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = - \sum_{k=2}^\infty \frac{(-1)^k}k \int_0^1 u^{k-2} \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = -\sum_{k=2}^\infty \frac{(-1)^k}{k(k-1)} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \sum_{k=1}^\infty \frac{(-1)^k}{k(k+1)} = 1 - 2\ln(2)[/tex]
Tying everything together, we end up with
[tex]S = -1 - \left(2 \cdot \dfrac{\ln^2(2)}2 - 2 \cdot \dfrac{\pi^2}{12} + (1-2\ln(2))\right) \\\\ ~~~ = \boxed{\frac{\pi^2}6 - 2 + 2\ln(2) - \ln^2(2)}[/tex]
A point is plotted on the number line at 2. A second point is plotted at 4.
What is the length of a line segment joining these points?
Enter your answer as a simplified mixed number in the box.
units
units
A computer programmer had two flies with a total size of 77.56 gigabytes if one of the files was 45.46 gigabytes how big is the second file
Answer:
Step-by-step explanation:
32.1 gb is answer
77.56
-45.46
second file would be 32.10 gb
prove that the sequence {Xn ] Such that
Xn Converges to Zero
The sequence or pattern [[tex]x_{n}[/tex]] [tex]x_{n}[/tex] Converges to Zero, meaning that the power, limit, and final solution all get closer to zero.
What do you mean by mathematical sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. The length of the series is the number of elements (potentially infinite).Unlike a set, a sequence may contain the same things more than once at different locations, and unlike a set, the sequence's order is crucial.
According to given information;
First put;
[tex]x_{n}[/tex]−1=−√(1+x[tex]_n_-_2[/tex]+1)
into
[tex]x_{n}[/tex]=(−1+x[tex]_n_-_1[/tex]+1)
You'll notice a general form:
[tex]x_{n}[/tex]=−1+(x[tex]_n_-_r[/tex]+1)^2^−r
Then put r = n-1, and take the limit of both sides with n tending to infinity. On the right hand side, you have
−1 +[tex]\lim_{n \to \infty}[/tex](x+1)^[tex]\frac{1}{2n-1}[/tex]
n→∞
he power approaches 0, the limit approaches 1 and the final answer approaches 0.
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Solve 2x + 2 > 10.
PLEASE HELP
Answer:
x > 4
Step-by-step explanation:
2x + 2 > 10
2x > 10 - 2
2x > 8
x > 8/2
x > 4
In a class in which the final course grades depends entirely on the average of four equally weighted 100 point test David has scored 81, 92, and 74 on the first three. What range of scores on the fourth test will give David a b for the semester ( an average between 80 and 89 inclusive) assume that all the test scores have a non negative value
The range of scores on the fourth test to give David a B grade for the semester is at least 73 but less than or equal to 89.
What is a range?A range refers to the difference between the lowest and the highest score.
A range of scores gives two values, the lowest and the highest scores.
Data and Calculations:Scores secured by David = 81, 92, and 74
Total scores in three exams = 247
The average score for a B grade is:
80 ≤ B grade < 90 ["at least" means ≤]
Therefore,
80 ≤ (81 + 92 + 74 + x) / 4 < 89 [assume equal weights for exams]
80 ≤ (247 + x) / 4 ≤ 89 [add values]
320 ≤ (247 + x) ≤ 356 [multiply by 4, retains a sense of inequality]
73 ≤ x < 109 [subtracting 247 retains a sense of inequality]
Since exams are graded on 100 points, David cannot score 109, so the upper limit is put at 89.
Thus, the exam grade in the fourth test must be at least 73 but less than or equal to 89 to get a B average.
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Which function has the greater average rate of change over the interval [0,3]?
If the interval is [0,3] then the second function whose graph is given has the greater average rate of change.
Given two functions, one is in the table and the other one is in the form of graph.
We are required to choose the function which has the greater average rate of change.
Function is basically the relationship between two or more variables that are expressed in equal to form. The values that we enter are known as part of domain and the values that we get from the function are known as part of codomain or range of the function.
If we observe the table then we will find that in the interval [0,3] there is not any change in the value of function, it is constant to be 4.
If we observe the graph then we will find that the value of function is continuously decreasing.
So, the second function has greater average rate of change over the interval [0,3].
Hence if the interval is [0,3] then the second function whose graph is given has the greater average rate of change.
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Find the domain and range of the function represented by the graph.
beinggreat78 is great
but that's literally her user so....♀️
anywayso
Answer:
1.2 × 10⁻⁵
Step-by-step explanation:
The exponent is negative, so the decimal was moved -5 places back, making the number a decimal.
Answer:
1.2 x 10^5
Step-by-step explanation:
All work is shown in the attached screenshot! :)
I really need help it’s due in 10 minutes
In the picture we have to solve the individual variables A=2πr²+2πrh. We got function with r as subject is[tex]\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }[/tex]
Given that,
In the picture we have to solve the individual variables
A=2πr²+2πrh
We have to find function with r as subject.
Taking A to left side we get
2πr²+2πrh-A=0
We can see the equation is in the form of quadratic equation with variable r.
So, The factor we find by using the formula
That is [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Here, a=2π,b=2πh and c=-A
r=[tex]\frac{-2\pi h\pm\sqrt{(2\pi h)^{2}-4(2\pi)(-a) } }{2(2\pi)}[/tex]
r=[tex]\frac{-2\pi h\pm\sqrt{(4\pi^{2}h^{2} +8\pi a) } }{4\pi}[/tex]
r=[tex]\frac{-h}{2} \pm\frac{\sqrt{(4\pi^{2}h^{2} +8\pi a )} }{4\pi}[/tex]
r=[tex]\frac{-h}{2} \pm\sqrt{\frac{4\pi^{2}h^{2}+8\pi a }{16\pi^{2} } }[/tex]
r=[tex]\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }[/tex]
Therefore, We got function with r as subject is[tex]\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }[/tex]
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If $5,000 had been invested in a certain investment fund on September 30, 2008, it would have been worth $23,125.59 on
September 30, 2018. What interest rate, compounded annually, did this investment earn? (Round your answer to two decimal
places.)
Interest rate compounded annually for the amount of $5,000 invested would have been worth $23,125.59 after 10 years is equal to 16.55% per year.
As given in the question,
Principal (P) = $5,000
Time (t) = 10 years
Amount = $23,125.59
[tex]r = n[(A/P)^{\frac{1}{nt}}-1]\\\\\implies r = 1[(23125.29/5000)^{\frac{1}{10} }-1]\\\\\implies r = 0.1655\\[/tex]
Convert r into percentage
r = 0.1655 × 100
= 16.55% compounded annually
Therefore, interest rate compounded annually for the amount of $5,000 invested would have been worth $23,125.59 after 10 years is equal to 16.55% per year.
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Samir measured a boarding school and made a scale drawing. He used the scale 10 millimeters = 2 meters. What is the scale factor of the drawing?
The scale factor of the drawing is 1 / 200 or 0.005.
What is scale factors?Scale factor is used to scale shapes in different dimensions.
In other words, Scale factor is described as the number or the conversion factor which is used to change the size of a figure without affecting its shape.
Therefore, scale factor can be represented mathematically as follows:
Scale factor = dimensions of the new shape ÷ dimensions of the original shape.
Hence he uses the scale 10 millimetres equals to 2 meters.
We have to convert metres to millimetres to get the scale.
10millimetres = 2meters
Therefore,
1 meter = 1000 millimetres.
2 meters = ?
cross multiply
length = 2 × 1000 = 2000 millimetres
Therefore, the scale factor of the drawing is as follows:
scale factor = 10 / 2000
scale factor = 1 / 200
scale factor = 0.005
Therefore, the scale factor of the drawing is 1 / 200 or 0.005.
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I need help with this
Answer:
1. He get get to school 10 minutes faster riding by hisself than ridding with Christina.
Step-by-step explanation:
Christina is 22 minutes - Luis 12 minutes = 10 minutes.
kevin found a deal on a computer that has been marked down by 30% to be $490. what was the original price of the computer?
Answer:
$700
Step-by-step explanation:
Since the deal is 30% off, that means that the price is now 70% of the original price.
70% of x = 490
0.7x = 490
x = 490/0.7
x = 700
Answer: $700
……………………………………………………………
same here 2383882828x7767=?
For her 1st birthday, Ruth's grandparents invested $1500 in an 18-year certificate for her that pays 12% compounded annually. How much will the certificate be worth on
Ruth's 19th birthday? (Round your answer to the nearest cent.)
The certificate will be worth of $11534.9 on Ruth's 19th birthday.
Compound Interest is calculated using the formula.
[tex]Amount=P*(1+\frac{r}{n} )^{nt}[/tex]
where , P=principal
r = rate of interest
n= number of times interest is compounded
t = no of years
In the given question ;
Principal = $1500
n=1 ...(as it is compounded annually)
t= 18 years ...(as on 19th birthday Ruth will complete 18 years)
r=12%=0.12
Substituting the values of P,n,t,r in the formula we get,
[tex]Amount=P*(1+\frac{r}{n} )^{nt}[/tex]
[tex]=1500*(1+\frac{0.12}{1} )^{1*18}[/tex]
On solving further we get
=[tex]1500*(1.12)^{18}[/tex]
=1500*7.6899
=11534.85
Therefore , On Ruth's 19th birthday the certificate will be of worth $11534.9 .
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What is the inverse of f(x)=(3x)2 for x≥0
The inverse of the function f(x) = (3x)^2 is f-1(x) = 1/3√x
How to determine the inverse of the function?The function is given as:
f(x) = (3x)^2
Remove the bracket in the above equation
So, we have:
f(x) = 9x^2
Express f(x) as y
So, we have
y = 9x^2
Swap the positions of x and y
So, we have
x = 9y^2
Make y the subject of the formula
y^2 = x/9
Take the square root of both sides
y = 1/3√x
Express as an inverse function
f-1(x) = 1/3√x
Hence, the inverse of the function f(x) = (3x)^2 is f-1(x) = 1/3√x
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An aspiring business owner is planning their college course of study and would like to know whether they should pursue a doctoral degree before they open their own business. Explain what you would recommend to them using two specific examples from the bar graph to support your response.
Answer:
Yes
Step-by-step explanation: