g(x) = 3√(x-5) -1
The process of altering a graph to produce a different version of the preceding graph is known as graph transformation. The graphs can be moved about the x-y plane or translated. They may also be stretched, or they may undergo a mix of these changes.
Horizontal stretching: It means the graph is elongated or shrink in x direction.
Vertical stretching : It means the graph is elongated or shrink in y direction
Vertical translation : It means moving the base of the graph in y direction
Horizontal translation : It means moving the base of the graph in x direction
According to rules of transformation f(x)+c shift c units up and f(x)-c shift c units down.
Therefore, in order to move the graph down 1 units, we need to subtract given function by 1 , we get
g(x) = 3√x -1
According to rules of transformation f(x+c) shift c units left and f(x-c ) shift c units right.
Therefore, in order to move the graph left by 5 units, we need to add given function by 5 , we get
g(x) = 3√(x-5) -1
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[tex] \boxed{\begin{gathered} \rm Let \: \psi_1 : [0, \infty ) \to \mathbb{R} , \psi_2 : [0, \infty ) \to \mathbb{R},f :[0, \infty )\to \mathbb{R} \: and \: g :[0, \infty) \to \mathbb{R} \: be \\ \rm functions \: such \: that \: f(0) = g(0) = 0, \\\\ \rm \psi_{1}(x) = {e}^{ - x} + x, \: \: x \geq0, \\ \rm \psi_{2}(x) = {x}^{2} - 2x - 2 {e}^{ - x} + 2, \: \: x > 0, \\ \rm f(x) = \int_{ - x}^{x} ( |t| - {t}^{2} ) {e}^{ - {t}^{2} } \: dt, \: \: x > 0 \\\\ \rm g(x) = \int_0^{ {x}^{2} } \sqrt{t} \: {e}^{ - t} \: dt, \: \: x > 0 \end{gathered}}[/tex]
Which of the following is True?
[tex] \rm (A) \: \rm \: f ( \sqrt{ \ln 3 } )+ g( \sqrt{ \ln3} ) = \dfrac{1}{3} [/tex]
(B) For every x>1, there exists an α ∈ (1,x) such that ψ₁(x)=1+ax
(C) For every x>0, there exists a β ∈ (0,x) such that ψ₂(x)=2x(ψ₁(β)-1)
(D) f is an increasing function on the interval [tex] \bigg [0 , \dfrac{3}{2} \bigg][/tex]
(A) is false. By symmetry,
[tex]\displaystyle f(x) = \int_{-x}^x (|t|_t^2) e^{-t^2} \, dt = 2 \int_0^x (t-t^2) e^{-t^2} \, dt[/tex]
where [tex]|t|=t[/tex] since [tex]x>0[/tex]. Substitute [tex]s=t^2[/tex] to get the equivalent integral,
[tex]\displaystyle f(x) = \int_0^{x^2} (1 - \sqrt s) e^{-s} \, ds[/tex]
Then
[tex]\displaystyle f(x) + g(x) = \int_0^{x^2} e^{-s} \, ds[/tex]
[tex]\displaystyle f(\sqrt{\ln(3)}) + g(\sqrt{\ln(3)}) = \int_0^{\ln(3)} e^{-s} \, ds = \frac23 \neq \frac13[/tex]
(B) is false. Note that [tex]1+\alpha x[/tex] is linear so its derivative is the constant [tex]\alpha[/tex] at every point. We then have
[tex]{\psi_1}'(\alpha) = -e^{-\alpha}+1 = \alpha \implies 1-\alpha = e^{-\alpha}[/tex]
But this has no solutions, since the left side is negative for [tex]\alpha>1[/tex] and the right side is positive for all [tex]\alpha[/tex].
(C) is true. By the same reasoning as in (B), the line [tex]2x(\psi_1(\beta)-1)[/tex] has constant derivative, [tex]2\psi_1(\beta)-2 = 2e^{-\beta+2\beta-2[/tex]. Then
[tex]{\psi_2}'(\beta) = 2\beta-2+2e^{-\beta} = 2e^{-\beta}+2\beta-2[/tex]
holds for all values of [tex]\beta[/tex].
(D) is false. We use the first derivative test. By the fundamental theorem of calculus,
[tex]\displaystyle f(x) = 2 \int_0^x (t-t^2)e^{-t^2}\,dt \implies f'(x) = 2(x-x^2)e^{-x^2}[/tex]
Solve for the critical points.
[tex]f'(x) = 0 \implies x-x^2 = 0 \implies x = 0 \text{ or } x = 1[/tex]
[tex]e^{-x^2}>0[/tex] for all [tex]x[/tex], so the sign of [tex]f'[/tex] depends on the sign of [tex]x-x^2[/tex]. It's easy to see [tex]f'>0[/tex] for [tex]x\in(0,1)[/tex] and [tex]f'<0[/tex] for [tex]x\in\left(0,\frac32\right)[/tex]
Write the ratio as a fraction in lowest terms.
48 minutes to 3 hours
Answer: 4/15
Step-by-step explanation:
3 hours=
3*60 minutes=180 minutes
48:180=
(24*2):(90*2)=
(12*2*2):(45*2*2)=
(4*3*2*2):(15*3*2*2)=4/15
what is the slope of a line parallel line whose equation is 5x-2y=2
By which angle measures can the regular pentagon be rotated so it maps onto itself? Select each correct answer. 72° 72° 90° 90° 135° 135° 144° 144° 216° 216° 300°
The regular pentagon can be rotated through at angles of 72, 144°, 216°, and 288° to map it onto itself.
What is a regular polygon?A polygon is a two-dimensional geometric shape having a finite number of sides. Single-direction segments are connected end to end to make a closed shape on the sides or edges of polygons. The locations where two line segments converge to construct an angle are referred to as vertices or corners.
It is given that:
The pentagon has five sides.
As we know, the standard pentagon has five vertices and internal angles that are each 72 degrees. A regular pentagon also possesses rotational symmetry.
The angles are 72°.144°,216°, and 288°.
Thus, the regular pentagon can be rotated through at angles of 72, 144°, 216°, and 288° to map it onto itself.
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Write an equation letting
x
be the unknown number.
two subtracted from a number is 2.
Answer: x-2=2 (x=4)
Step-by-step explanation:
4 minus 2 equals 2
Determine whether the equation defines y as a function of x. y equals = 8 Over x Does the equation define y as a function of x?
Yes , the equation y =8ˣ defines y as a function of x.
An mathematical function could be a function within the kind f (x) = aˣ, wherever “x” could be a variable and “a” could be a constant that is termed the bottom of the perform and it ought to be bigger than zero.An mathematical function is outlined by the formula f(x) = aˣ, wherever the input variable x happens as a fan. The graph depends on the mathematical function and it depends on the worth of the x.Yes, because to fulfill the condition of an equation to be a function, a particular value of x must produce only one value of y and y =8ˣ fulfills the condition. This can be also tested using horizontal line test, which only cuts the graph at one point only,
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Estimate the quotient of
68)6080
Express any remainder beginning with an R.
35) A family is planning an annual picnic in Arizona. Rain is forecast for 45 days of the year, but when
rain is forecast, the prediction is correct only 90% of the time. What is the probability that it will rain on
the day of the picnic? Note that it is not a leap year.
Answer:
81/730
Step-by-step explanation:
The chance of picking a day forecasted to have no rain is 45/365.
There is a 90% chance it actually rains on this day, so the probability is
[tex](45/365)(0.9)=81/730[/tex]
What is the slope of a line parallel to the line whose equation is 2x - 5y = 30. Fully simplify your answer.
Answer: [tex]\boxed{y=\frac{2}{5} x-7}\ as\ an\ example[/tex]
Step-by-step explanation:
Find the slope-intercept form:
[tex]2x-5y=30\\\\-5y=-2x+30\\\\y=\frac{-2x+30}{-5} \\\\y=\frac{2}{5} x-6[/tex]
Therefore the slope is 2/5
An example of a line parallel to this line is
[tex]y=\frac{2}{5} x-7[/tex]
Why do banks charge a fee when clients transact on their accounts?
Answer:
Banks charge fees to help make a profit.
Step-by-step explanation:
Bank fees allow financial institutions to recoup operating expenses. Banks also make money on loans, via interest and other fees.
If it is given that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S , then concluding that m ∠ J K L = m ∠ Q R S is an example of:
Concluding that m∠ J K L = m ∠ Q R S is an example of: substitution property of equality
What is Substitution Property of Equality?The substitution property of equality states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.
Now, we are told that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S.
Thus, concluding that m ∠ J K L = m ∠ Q R S is an example of: substitution property of equality
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An 8-ounce cup of juice costs $1.20. A 12-ounce cup of the same juice costs
$1.44. Can the relationship between cost and ounces of juice be described
by a constant rate? Explain.
Answer: It can.
Step-by-step explanation:
If an 8 oz. cup of juice cost $1.20 and a 12 oz. cup of juice cost $1.44, there is a $0.24 difference between the money and cups of juice in ounces. If there were to be a constant rate of change, a 16 oz. cup of juice MUST cost $1.68
No, the relationship between cost and ounces of juice cannot be described by a constant rate.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Cost of 8 ounce juice= $1.20
Cost of 12 ounce juice= $1.44
Now,
If the relationship between cost and ounces of juice was described by a constant rate, then the cost per ounce would be the same for both the 8-ounce cup and the 12-ounce cup. However, we can see that the cost per ounce is different for each cup:
For the 8-ounce cup: cost per ounce = $1.20 / 8 ounces = $0.15 per ounce
For the 12-ounce cup: cost per ounce = $1.44 / 12 ounces = $0.12 per ounce
Therefore, by algebra the cost per ounce is different for each cup, the relationship between cost and ounces of juice cannot be described by a constant rate.
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(33) MOVIES Chaz has a collection of 15 movies downloaded on his media player. He decides to download 3 more movies each month. The function M(t) = 15 + 3t counts
the number of movies M(t) he has after t months. How many movies will he have after
8 months?
Answer: 39
Step-by-step explanation: 15 is the number of movies he has already. The t in the formula stands for months. So simply plug in 8 for t because we want to know how much has has after 8 months
15+3(8)
15+24
=39
Sterling already owes his parents $40. He asks to borrow money from them to purchase candy bars for his friends that cost $1.50 each. The rule in Sterling's house is that he can owe his parents no more than $50. How many candy bars can he purchase and still stay within the maximum borrowing amount?
Answer: 6
Step-by-step explanation: 6 because then he would owe his parents 49 dollars
The reading on a mercury manometer at 25 C ( open to the atmosphere at one end ) is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa what is the absolute pressure in kpa being measured? The density of mercury at 25 C is 13.534 g.cm^-3
If the reading on a mercury manometer at 25 C is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa The absolute pressure in kpa being measured is: 176.803kPa.
Absolute pressureUsing this formula
Pabs=Pg+Patm
Where:
Pabs= Absolute pressure.
Patm=Atmospheric pressure
ρm=Density of mercury
g=Acceleration of gravity
h=Reading on a mercury manometer
Let plug in the formula
Pabs=101.78×10³Pa+( 13.534×10³kg/m×9.832 m/s²×0.5638 m.
Pabs=101.78×10³Pa+75.023×10³kg/m.s²
Pabs=101.78×10³Pa+75.023×10³Pa
Pabs=176.803×10³Pa
Pabs=176.803kPa
Therefore If the reading on a mercury manometer at 25 C is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa The absolute pressure in kpa being measured is: 176.803kPa.
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The perimeter of the pentagon below is 63 units. Find the length of side AB.
Write your answer without variables.
Answer:
15
Step-by-step explanation:
The sides add to 63, so:
[tex]11+3x+11+x+2+2x+3=63 \\ \\ 6x+27=63 \\ \\ 6x=36 \\ \\ x=6 \\ \\ \implies AB=2(6)+3=15[/tex]
The point N lies on the segment MP.
Find the coordinates of N so that the ratio of MN to NP is 6 to 1.
M(-13, 20)
N (?, ?)
P(1-1)
If the point N lying on the Line segment MP, divides MP such that the ratio of MN to NP is 6 to 1, and the coordinates of M(-13, 20) and P(1-1), then the coordinates of "N" is
As per the question statement, N lying on the Line segment MP, divides MP such that the ratio of MN to NP is 6 to 1.
We are required to find out the coordinates of "N".
To solve this question, we need to know the formula to calculate the coordinates of a point (Say "c") that divides a line segment AB in the ratio of (m:n).
The formula goes as:
Abscissa of c [tex](x_{3})=\frac{mx_{2}-nx_{1} }{m-n}[/tex]
and, Ordinate of c [tex](y_{3})=\frac{my_{2}-ny_{1} }{m-n}[/tex]
where, [tex](x_{1}, y_{1})[/tex] are the coordinates of point A, while
[tex](x_{2}, y_{2})[/tex] are the coordinates of point B.
Using our given data in the above formulae, we get
Abscissa of N = [tex]\frac{(6*1)-[1*(-13)]}{6-1} =\frac{6-(-13)}{5}=\frac{6+13}{5}=\frac{19}{5}[/tex]
And, Ordinate of N = [tex]\frac{[6*(-1)-(1*20)}{6-1} =\frac{(-6)-20}{5}=\frac{-(20+6)}{5}=\frac{-26}{5}[/tex].
Hence, our concerned point N = [tex](\frac{19}{5}, \frac{-26}{5})\\[/tex].
Line Segment: In Euclidean geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints and it's length is given by the Euclidean distance between its endpoints.To learn more about Line Segments, click on the link below.
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-4 + (-19) = ? I need a answer
Answer: - 23
Step-by-step explanation:
Hope this helps!
Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive
integer value.
x²=8(x-5)
Answer:
See below
Step-by-step explanation:
Expand to get x^2 - 8x + 40 = 0
a = 1 b = -8 c = 40
Find the smallest value of k if 360k is a perfect square
Answer:
k = 1
Step-by-step explanation:
since 360 = 60² , a perfect square , then
360 × 1 ← is a perfect square
that is 360k with k = 1 is a perfect square
A bowl weighs 11/40 pound express this weight as a decimal
Answer:
0.275 lb
Step-by-step explanation:
Use a calculator to divide 11 by 40.
11/40 = 0.275
Answer:
0.275 pounds
Step-by-step explanation:
divide 11 (numerator) by 40 (denominator).
Which is bigger, 16\frac{1}{6}
6
1
or 0.16? Explain your reasoning.
Answer:
1/6 is greater than 0.16
Step-by-step explanation:
0.16 as a fraction is 4/25
4/25 < 1/6
26.
12/2(x+6)=2x-9
21
[tex]\frac{12}{2} (x+6)=2x-9[/tex]
[tex]6x+36=2x-9[/tex]
[tex]6x - 2x = -9 + 36[/tex][tex]4x = -45[/tex]
[tex]x = -\frac{45}{4}[/tex]
Hope that I helped you!
PACKS
(MP) Attend to Precision Write the numbers 108,567;
107,658; and 107,568 in order from least to greatest.
The arrangement is as follows 107,568 ; 107,658 ; 108,567
What is ascending order?Ascending order is an arrangement from smallest to largest value.
Given:
108,567; 107,658; and 107,568
We have to arrange these numbers from least to greatest
smallest number = 107,568
largest number = 108,567
Hence, the arrangement is 107,568 ; 107,658 ; 108,567
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2(x-1)+5(x-9) Show your work please!
Step-by-step explanation:
2(x-1) + 5(x-9)
2x - 2 + 5x - 45
2x + 5x - 2 - 45
7x - 47
Answer:
2x -2 + 5x -45 7x -47
Step-by-step explanation:
2*x = 2x
2*-1 = -2
5*x =5x
5*-9 = -45
a 42 inch string is to be cut so that one piece is 7 inches longer than the other. what is the length of the shorter piece?
Answer:
17.5 inches
Step-by-step explanation:
Let the length of the shorter piece be x
Shorter piece + Longer piece = Whole string
x + (x + 7) = 42
x + x + 7 = 42
Both sides minus 7 to remove the 7 from the left side of the equation.
2x + 7 - 7 = 42 - 7
2x = 35
x = 17.5 inches
Hope this helped! ^^
6 less the quantity 9 times a number
hi
with " x' a number then :
6 -9X
What is the number of combinations on a lock. (for a 40-number lock, no successive repeating numbers)
(permutations or combinations).
Alonso's family rented a car when they flew to
Orlando for a 4-day vacation. They paid $39
per day and $0.09 for each mile driven. How
much did it cost to rent the car for 4 days and
drive 350 miles, not including tax?
Answer:
$187.5
Step-by-step explanation:
39 (4) + 0.09 (350)
156 + 31.5
$187.5
⭐ Please consider brainliest! ⭐
Answer:
$187.5
Step-by-step explanation:
You need to multiply the daily cost by the days. In this case, 39*4 = 156. Then, we can get the cost for the miles driven, being 0.09*350 = 31.5.
We can now add the two numbers together:
156 + 31.5 = $187.5
Please help!! It’s due today!!
Answer:
A to B: 4
B to A: 1/4
