The auxiliary function used in the composition between the two functions f(x) and g(x) is equal to linear function g(x) = x + 3.
How to derive the auxiliary function in a composition function
Herein we find the result of a composition between two functions, where the variable x of the parent function f(x) is substituted by the auxiliary function g(x). The composition between the two functions is defined below:
h(x) = f ° g (x) = f [g (x)]
If we know that the parent function f(x) = x⁵, then the auxiliary function within the composition is the linear function g(x) = x + 3.
Remark
The statement is poorly formatted, the correct form is shown below: The function h(x) = (x + 3)⁵ can be expressed in the form f[g(x)] where f(x) = x⁵ and g(x) is defined below.
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NO LINKS!! State the Domain and Range for each graph
Both end points are represented by closed circles, it means both points are included.
The graph is restricted between the end points from left to right and between the end point and the highest point from bottom to top.
Domain, the set of possible x- coordinates:
x ∈ [- 2, 6]Range, the set of possible y- coordinates:
y ∈ [- 3, 7]The graph on the rightBoth end points are represented by arrows directed to left and right, it means both ends are indefinite but lines are parallel to the x-axis.
It makes x-values infinite but y-values restricted between the two lines.
Domain, the set of possible x- coordinates:
x ∈ (- ∞, + ∞)Range, the set of possible y- coordinates:
y ∈ [1, 5]Answer:
1. Domain: [-2, 6]
Range: [-3, 7]
2. Domain: (-∞, ∞)
Range: [1, 5]
Step-by-step explanation:
Definitions
Domain: The set of all possible input values (x-values).Range: The set of all possible output values (y-values).Open circle: The value is not included in the interval.Closed circle: The value is included in the interval.Arrow: The function continues indefinitely in that direction.Note: Assume that each square on the given graphs is 1 unit.
Question 1The domain of the function is restricted since the curve has two distince endpoints. As each endpoint is marked by a closed circle, the x-value of the endpoints is included in the domain.
Domain: [-2, 6]The function has a maximum point at (-1, 7) and a minimum point at (6, -3).
Therefore, the range of the function is restricted.
Range: [-3, 7]Question 2As there are arrows at both endpoints of the function, and the function is continuous between the arrowheads, the domain is unrestricted.
Domain: (-∞, ∞)The maximum y-value is y = 5. When x < 1, the line continues indefinitely at y = 5.
The minimum value is y = 1. When x > 1, the line continues indefinitely at y = 1.
Therefore, the range of the function is restricted.
Range: [1, 5]Anya has a change jar that contains $1.06 in pennies and dimes. The number of pennies is 10 more than two times the number of dimes. How many of each type of coin does she have?
The number of pennies that Anya has is equal to 15.6 pennies.
The number of dimes that Anya has is equal to 2.8 dimes.
How to determine the number of coins?In order to solve this word problem, we would assign variables to the number of pennies and dimes, the total number of coins, and then translate the word problem into algebraic equation as follows:
Let d represent the number of dimes.Let p represent the number of pennies.Let T represent the total number of coins.Note: 1 penny is equal to 0.05 dollar and 1 dime is equal to 0.10 dollar.
Therefore, translating the word problem into an algebraic equation, we have the following;
p = 10 + 2d ......equation 1.
0.05p + 0.1d = 1.06 .......equation 2.
Substituting equation 1 into equation 2, we have:
0.05(10 + 2d) + 0.1d = 1.06
0.5 + 0.1d + 0.1d = 1.06
0.5 + 0.2d = 1.06
0.2d = 1.06 - 0.5
0.2d = 0.56
Dimes, d = 0.56/0.2
Dimes, d = 2.8 dimes.
For the number of pennies, we have:
p = 10 + 2d
p = 10 + 2(2.8)
p = 10 + 5.6
p = 15.6 pennies.
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See question in screenshot below:
Answer:
1440/17 degrees (approximately 84.7059 degrees)
19π/9 radians ---> or π * 19/9 radians
Step-by-step explanation:
The conversion factor for radians to degrees is 180/π
8π/17 * 180/π = 1440/17 degrees (approximately 84.7059 degrees)
The conversion factor for degrees to radians is π/180
380 * π/180 = 380π/180 = 19π/9 radians
x- (3/2)y=-2 find five solutions and plot
Five solutions of the given equation x- (3/2)y = -2 is given by as follow:
( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).
Plotted graph of the given function is attached.
As given in the question,
Given equation is equal to :
x- (3/2)y = -2
Simplify the given equation we get,
2x - 3y = -4
⇒ y = ( 1 / 3) ( 2x + 4 )
Now , five solutions of the given function to be plotted on the graph.
When x = 0
⇒ y = 4/3
When x = 1
⇒ y = (1/3)(2 +4)
⇒ y = 2
When x = 4
⇒ y = (1/3)( 8 + 4)
⇒y = 4
When x = -2
⇒y = (1/3)(-4 +4)
⇒y=0
When x = -5
⇒y = (1/3)(-10 +4)
⇒y= -2
Five solutions are ( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).
Plotted graph of the given function is attached.
Therefore, five solutions of the given equation x- (3/2)y = -2 is given by as follow:
( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).
Plotted graph of the given function is attached
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7=3 + h over 6
solving 2 step equations
Answer:
h=24
Step-by-step explanation:
7=3+h/6
-3 -3
4=h/6
x6. x6
24=h
hopes this helps please mark brainliest
Evaluate for A(12). Round your answer to the nearest hundredth.
The value the function A(12) is 2960.94
How to evaluate the function?From the question, we have the following function definition that can be used in our computation:
A(t) = 710e⁰°¹¹⁹⁺
To calculate the function A(12), we set t to 12
i.e. calculate A(t) when t = 12
This equation becomes
A(12) = 710e⁰°¹¹⁹ˣ¹²
Evaluate the products
A(12) = 710e¹°⁴²⁸
Evaluate the exponents
A(12) = 2960.94
Hence, the solution is 2960.94
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An intravenous (IV) solution of 8% D/W (Dextrose in water) is infusing at a rate of 2.15 milliliters (mL) per minute. How many mL would infuse in 5.25 hours?
By evaluating a linear equation, we can see that 677.25 mL will be infused in 5.25 hours.
How many mL would infuse in 5.25 hours?We know that the solution is being infused at a rate of 2.15 mL per minute.
So, t minutes after the infusion starts, the volume infused is given by the linear equation:
V(t) = 2.15mL*t
Here we want to see how many mL would infuse in 5.25 hours, to do that, we need to write that time in hours:
We know that one hour = 60 min, then:
5.25 h = 5.25*60 min = 315 min
Then the volume infused is:
V(315) = 2.15mL*315 = 677.25 mL
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3) Bill is a freshman attending a 4-year college. He has been approved for a $5,000 with an APR of 6.75%.
He is not required to make any payment for 10 years since his payment will be deferred while his enroll
in school. How much interest will he pay in 10 years?
Interest will he pay in 10 years is $3375.
Given:
Bill is a freshman attending a 4-year college. He has been approved for a $5,000 with an APR of 6.75%.
He is not required to make any payment for 10 years since his payment will be deferred while his enroll in school.
1 year interest = 5000*6.75%
= 5000*6.75/100
= 50*6.75
= 50*675/100
= 1*675/2
= 337.5
10 years interest = 10 * 337.5
= 10 * 3375/10
= $3375.
Therefore Interest will he pay in 10 years is $3375.
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Clayton's mortgage payment was originally $2,460 per month. Now, after refinancing his home loan, Clayton's mortgage payment is $1,968. What is the percent of decrease in Clayton's mortgage payment?
please
Answer:
20%
Step-by-step explanation:
2460-1968=492
492/2460=0.20
Check answer2460 x 0.20 = 492
Katrina buys a 66-ft roll of fencing to make a rectangular play area for her dogs. Use 2(l+w) = 66 to write a function. for the length, given the width. Graph the function. What is a reasonable domain for the situation? Explain. The function f(w) = gives the length as a function of the width. (Simplify your answer.)
The function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted
The total length of the roll = 66 feet
The perimeter of the rectangular paly area = 66
The perimeter of the rectangle = 2(l + w)
Then the equation will be
2(l + w) = 66
l + w = 66/2
l + w = 33
The function for length when the width is given
l = 33 - w
Therefore the domain of the function is 0 < w < 33
When w = 1
l = 33 - 1
l = 32
The first point is (1, 32)
When w = 32
l = 33 - 32
l = 1
The second point is (32, 1)
Draw the graph of the function
Hence, the function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted
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In a water park, there is a swimming pool of dimensions 40 m × 20 m × 2 m. The management wants to repaint it, if the cost of painting an area of 1 m 2 is ₹13, then how much amount of money is required to paint the swimming pool?
The cost of repainting the swimming pool is 15,600 pounds
The swimming pool forms a three-dimensional object. Three-dimensional space is a geometric setting in which three values are required to determine the position of an element or its area.
The area of the object is the space the swimming pool occupies
How to find the area of the swimming pool?
Mathematically represented as: A =lbh metres square
A=areal =lengthb=breadthA=40x20x2
A=1200m²
The cost of im² is 13 pounds
Therefore, multiplying the area by cost of 1m per square
Cost=1200x13
Cost=15,600 pounds
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10. Your family decides to construct a below ground swimming pool in the backyard. The
pool will be:
.8 feet deep,
20 feet long, and
• 14 feet wide.
The local fire department will fill the pool with water for a $50 fee plus $12.60 for the
first 1,000 gallons and then $27.20 for each 1,000 gallons after that.
The amount of water will be rounded up to the nearest 1,000 gallons. In other words,
7,280 gallons is rounded up to 8,000 gallons.
How much will the water cost to fill the swimming pool?
Answer:
$497.8
Step-by-step explanation:
1. get the pool volume
volume = 8 x 20 x 14 = 2240 ft3
2. convert ft3 to gallons
2240 x 7.481 = 16757.44
3. You need 17000 gallons
4. Fee you have to pay fee + first 1000 gallon + the rest of the gallon
50 + 12.60 + 16 x 27.20 = 497.8
Chandler buys a mattress priced at $975.90.If the sales tax is are 10%, how much tax will Chandler pay?
Answer:
97.59
Step-by-step explanation:
975.90*0.10
97.59
Hope this Helps!!!
What is the true solution to 2 In en 5x = 2 In 15?
x= 0
x= 3
x= 9
x= 15
The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.
Given,
2 ln e^ ln (5x) = 2 ln (15)
Apply log rule;
logₐ (aᵇ) = b
ln (e^ln (5x)) = ln (5x)
2 ln (5x) = 2 ln (15)
Divide both sides by 2;
2 ln (5x) / 2 = 2 ln (15)/ 2
ln (5x) = ln (15)
For ln (5x) = ln (15), solve for 5x = 15;
That is,
5x = 15
Then,
x = 15/5
So,
x = 3
Check this by substituting it to 2 ln (5x) = 2 ln (15);
x = 3
2 ln (5 × 3) = 2 ln (15)
x = 3 makes this true.
Therefore,
The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.
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Please explain how you get your answer so i get a better understanding of this...
Using the image below, if I is parallel to M, find the value of y.
(im really struggling with this question so please do explain your answering.)
Answer:
16.11 (appx.)
Step-by-step explanation:
since l and m are parallel and a line intersects them, so we can say that the line is the transversal. from the figure we see that
7x + 12 = 12x - 28 [they are internal alternate angles and alternate angles are always equal to one another]
now, we can find the value of x from the equation
12x - 7x = 28 + 12
⇒ 5x = 40
⇒ x = 8
so the angle (7x+12)° is ((7*8)+12) = 68°
so (12x-28)° is also equal to 68° [cause of being alternate angles]
now, look at the figure,
angle (9y-77)° & (12x-28)° add upto a straight line as in 180°
and we know (12x-28)° = 68°
so now,
9y-77 = 68
⇒9y = 68+77
⇒9y = 145
⇒y = 16.11 (appx.)
Please help me !!!!!
Answer: [tex]2\frac{19}{36}[/tex]
Step-by-step explanation:
You subtract the woman's height from her son:
Woman's height: [tex]60\frac{5}{18} =\frac{(60*18)+5}{18} =\frac{1085}{18}[/tex]Son's height: [tex]57\frac{3}{4} =\frac{(57*4)+3}{4} =\frac{231}{4}[/tex][tex]60\frac{5}{18} -57\frac{3}{4} =\frac{1085}{18} -\frac{231}{4} =\frac{1085*2}{18*2} -\frac{231*9}{4*9} =\frac{2170-2079}{36} =\frac{91}{36} =2\frac{19}{36}[/tex]
$4.25,$6.71,$3.24,$5.06,$4.94 what is the average ?
The average of the number given is $4.84.
The average can be calculated as follows:
Sum up all the numbersGiven X
X =$4.25+$6.71+$3.24+$5.06+$4.94
X =$24.2
To find the average, you need to divide the X by n or the amount of numbers, where n=5= X ÷ n
= $24.2 ÷ 5
= $4.84
Hence, the average is $4.84
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If (n factorial) is equal to 720, what is n? n! Select the correct response:
A216
B 343
C125
D 64
Answer: B
Step-by-step explanation:
What is the coefficient of the first term in this expression
8c³+3+b³
Answer:
8c³
Step-by-step explanation:
What is a coefficient?
A coefficient is a number that does not stand alone. For example, 3w means 3 times w, and "w" is a variable, so 3 is a coefficient.
How do we find the first term?
We can find the first term by putting the numbers from greatest to least. For example, if we had the numbers: 3x+7p+2 we would rearrange the series to this: 7p+3x+2. The number that comes first in the series would be the first term.
Jillian sells handmade t- Shirts and large purses; each tea shirt costs $15. Each Large purse goes for $59 and the cost of small purses is $32 each. In the first week she sold 4 t-shirts and 3 large purses and 9 small. In the second week she sold another 5 t-shirts, 7 large bags and 4 small ones. Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses. What was the exact amount she made in 3 weeks?
Jillian made the exact amount was $1598 in 3 weeks.
Each t-shirt costs $15.
Each Large purse goes for $59
And the cost of small purses is $32 each.
In the first week, she sold 4 t-shirts and 3 large purses, and 9 small ones.
Her earning in the first week = 4 × $15 + 3 × $59 + 9 × $32 = $525
In the second week, she sold another 5 t-shirts, 7 large bags, and 4 small ones.
Her earning in the second week = 5 × $15 + 7 × $59 + 4 × $32 = $616
Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses.
Her earning in the Last week = 8 × $15 + 3 × $59 + 5 × $32 = $457
The exact amount she made in 3 weeks = $525 + $616 + $457 = $1598
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What is the sum of: 1 + x + x2 + x3 + x4 + x5 + ⋯ + x100?
The Sum is 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)
What is Series?A finite series is one that has a finite number of terms.
If the series [tex]a_1[/tex]+ [tex]a_2[/tex] + [tex]a_3[/tex] +... + a has n terms and is a finite series with n terms.
As a result, [tex]S_n[/tex] is used to represent the series' sum as follows:
[tex]S_n[/tex]=∑ [tex]a_n[/tex]
Given:
1 + x + x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex]
let P= 1/ 1-x
P - Px= 1
P= 1+ Px
= 1 + (P)x
= 1 + (1+ Px) x
= 1+ x + Px²
= 1+ x + (1+ Px)x²
= 1+ x + x² + Px³ and so on
So, 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)
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Find the slope of this line.make it a fraction.
Answer:
[tex]\frac{-2}{3}[/tex]
Step-by-step explanation:
to find the slope of linear line, you need two points. It does not matter which pints you use. I am going to use (0,5) and (3,3) The slope is the change in y over the change is x. Our y values are 3 and 5. Our x values are 3 and 0
[tex]\frac{3-5}{3-0}[/tex] = [tex]\frac{-2}{3}[/tex]
The point N lies on the segment MP
Find the coordinates of N so that MN is 3/7
of MP.
M(-4,6)
N (?,?
P (17,-22)
The coordinates of N are (5,-6) so that segment MN is 3/7 of MP.
Given the coordinates of M is (-4,6) and the coordinates of P is (17,-22).
now we have to find the coordinates of N such that the MN : NP is 3:4 .
We will use the section formula:
The section formula states that:
[tex]{\displaystyle N=\left({\frac {mx_{2}+nx_{1}}{m+n}},{\frac {my_{2}+ny_{1}}{m+n}}\right)}[/tex]
Where the coordinates of the points are given and the ratio in which the points are divided is given.
Now we will substitute the values:
[tex]{\displaystyle N=\left({\frac {17\times 3+4\times -4}{3+4}},{\frac {3\times-22+4\times 6}{3+4}}\right)}[/tex]
Solving we get:
N=(5,-6)
The Section formula is used to determine the coordinates of things like the point that separates a line segment (internally or externally) into a particular ratio.
Both physics and mathematics regularly employ this formula. In mathematics, it is used to find the centroid and incenters of a triangle, but in physics, it is used to find the center of mass, equilibrium points, etc. The section formula is often used to find the midpoint of a line segment.
Therefore coordinates of N are (5,-6) so that MN is 3/7 of MP.
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Which is bigger 21.17 or 2.117
Answer:
21.17
Step-by-step explanation:
If you were to round each number to the nearest whole number you would get :
21.17 ⇒ 21
2.117 ⇒ 2
Now the question is , which is bigger 21 or 2?
Now that is a very straightforward answer (21 in case your still lost)
Hope this helped and have a good day
Which number is divisible by 5 and 10? I NEED HELP FAST
Answer: Many even numbers are divisible by ten. A simple answer to that is 20. 30 is also, and so is 40. Any number going up by 10 will be divisible by 10 and 5. 10 is also divisible by 10 and 5.
NO LINKS!! Use the diagram below to answer the following questions Part 4
Answer:
Parallel LinesCoplanar lines that do not intersect.Arrows are used to indicate the lines are parallel.[tex]\textbf{Symbolic Notation:} \quad \overleftrightarrow{AB} \parallel \overleftrightarrow{CD}[/tex]Parallel PlanesPlanes that do not intersect.[tex]\textbf{Symbolic Notation:} \quad \mathcal{J} \parallel \mathcal{K}[/tex]Skew LinesNon-coplanar lines that do not intersect.[tex]\textbf{Examples:} \quad \overline{PS} \; \& \; \overline{QU}[/tex][tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]
Step-by-step explanation:
Coplanar: In the same plane.
Parallel LinesCoplanar lines that do not intersect.Arrows are used to indicate the lines are parallel.[tex]\textbf{Symbolic Notation:} \quad \overleftrightarrow{AB} \parallel \overleftrightarrow{CD}[/tex]The notation for a line is a double-ended arrow placed above two points contained on the line.
The symbol denotating two objects are parallel is a vertical double line.
Parallel PlanesPlanes that do not intersect.[tex]\textbf{Symbolic Notation:} \quad \mathcal{J} \parallel \mathcal{K}[/tex]A plane can be named by a capital letter (often written in script), or by the letters naming three non-collinear points in the plane.
The symbol denotating two objects are parallel is a vertical double line.
Skew LinesNon-coplanar lines that do not intersect.[tex]\textbf{Examples:} \quad \overline{PS} \; \& \; \overline{QU}[/tex][tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]
The notation for a line segment is a bar placed above the endpoints of the line segment.
Find an explicit formula for the arithmetic sequence 10,-10,-30,-50,...10,−10,−30,−50,...10, comma, minus, 10, comma, minus, 30, comma, minus, 50, comma, point, point, point. Note: the first term should be \textit{c(1)}c(1)start text, c, left parenthesis, 1, right parenthesis, end text. c(n)=c(n)=c, left parenthesis, n, right parenthesis, equals
An explicit formula for the arithmetic sequence is aₙ = 10 - 20(n - 1).
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 10
Second term, a₂ = -10
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = -10 - 10
Common difference, d = -20
Substituting the parameters into the mathematical expression, we have;
aₙ = 10 + (n - 1)(-20)
aₙ = 10 - 20(n - 1).
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+83--95 x + 7+72÷-9 what is the answer
Answer:
7.4
Step-by-step explanation:
Not completely sure because that equation is really hard to read. You might have put it in wrong.
Answer:
-95x + 91
Step-by-step explanation:
72/9 = 8
83 - 95x + 8
91 - 95x or -95x + 91
Determine the vertex of the graph of the following parabola. f(x)=−(x+1)2−6
The vertex of the graph of the parabola is at the point (-1, -6)
How to find the vertex of the parabola?We know that for any parabola with a vertex at the point (h, k) and a leading coefficient a, can be written in vertex form as:
y = a*(x - h)^2 + k
In this case the parabola is:
f(x) = (-1)*(x + 1)^2 - 6
Comparing this with the general form, we can see that:
h = -1
k = -6
Then the vertex of the parabola is (-1, -6)
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What expression represents the verbal phrase?
one-half times a number m plus twenty-five
The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
According to the question,
We have the following information,
The given verbal phrase is one-half times a number m plus twenty-five.
Now, we will solve it step by step.
Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:
m/2
Now, adding 25 to this term, we have the following final expression:
m/2+25
Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
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