Answer:
h(-3)=-1
Step-by-step explanation:
h(x)=-3x - 10
Let x = -3
h(-3)=-3(-3) - 10
= 9-10
=-1
hey guys please help me I'm lowkey confused on how to do this :)
Answer:
x = [tex]\frac{2}{7}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex](7x+2) = 2
7x+2 = 2÷[tex]\frac{1}{2}[/tex]
= 2×2
= 4
7x = 4-2
= 2
∴x = 2÷7
= [tex]\frac{2}{7}[/tex]
Answer:
[tex]\displaystyle \frac{2}{7} = x[/tex]
Step-by-step explanation:
[tex]\displaystyle 2 = \frac{1}{2}(7x + 2) \Rightarrow 2 = 3\frac{1}{2}x + 1 \hookrightarrow \frac{1}{3\frac{1}{2}} = \frac{3\frac{1}{2}x}{3\frac{1}{2}} \\ \\ \boxed{\frac{2}{7} = x}[/tex]
I am joyous to assist you at any time.
A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?
y=-x+1
y=1/√x+7
y=-2x-8
y = 2x + 16
Answer:
Correct answer not shown on the options.
y = -(1/2)+1
Step-by-step explanation:
Let's find an equation in the format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
The slope can be calculated as the Rise/Run of the line between the two given points (-6,4) and (-2,2):
Rise = (2 - 4) = -2
Run = (-2 - (-6)) = 4
Slope = Rise/Run = -2/4 or -(1/2)
In fact, the actual full equation is y= -(1/2)x+1 (See attached graph).
None of the options have a slope of -(1/2). Either the information on the two points or the options are incorrect.
Answer:
y=[tex]-\frac{1}{2}x[/tex]+1
Step-by-step explanation:
y = mx plus c,where m is the gradient.
∴m =[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{2-4}{-2-(-6)}[/tex]=[tex]\frac{-2}{4}[/tex]=[tex]-\frac{1}{2}[/tex]
Equation of a line equals
y-y1=m(x-x1) (Using point (-6, 4) for x1 and y1 values)
y-4=[tex]-\frac{1}{2}[/tex](x-(-6))
y-4=[tex]-\frac{1}{2}[/tex](x+6)
y-4=[tex]-\frac{1}{2}[/tex]x-3
2(y-4)=-x-3(2)(multiply through by 2)
2y-8=-x-6
2y=-x+2(divide through by 2)
y=[tex]-\frac{1}{2}x[/tex]+1
∴the equation of the line is y=[tex]-\frac{1}{2}x[/tex]+1
Writing Exercises
352. How do you decide which pattern to use?
Answer:
Hence if the square of binomials needs to be find then we use square of binomial pattern and if the product of conjugate pair needs to determine then we use product of conjugate pattern.
Step-by-step explanation:
Explanation
We have to explain how we decide which pattern to use.If we need to determine the squares of binomials then we use the binomial square pattern for example [tex]$(x-y)^{2}$[/tex] or [tex]$(x+y)^{2}$[/tex] wherease when we need to find the product of the pair of the binomials each have the same first term and the same last term, but one binomial is the sum and the other is a diference then we the the product of conjugate pattern for example [tex]$(x+y)(x-y)$.[/tex]A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet.
A) The outcome for Event X or Y is expressed as; X ∪ Y = {D, A, B, E}
B) The outcome of Event X and Y is; X ∩ Y = {A, B, E}
How to use the sets notation?We are given the events;
Event X; The letter selected is found in the word "BEAD"
Event Y; The letter selected comes after D
Thus;
A) The outcome for Event X or Y is expressed as;
X ∪ Y = {D, A, B, E}
B) The outcome of Event X and Y is;
X ∩ Y = {A, B, E}
C) Complement of Event Y is;
Y^(c) = {D}
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Brandon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Brandon scored a total of 16 points and made twice as many three point shots as two point shots. Write a system of equations that could be used to determine the number of two point shots Brandon made and the number of three point shots he made. Define the variables that you use to write the system
The system of equations are x+ y =16 and 2y=x.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions
let the two points shots be x
let the three points shots be y.
According to question,
x+ y =16
and,
2y=x
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Use the image to answer the question.
A rectangle with length 15 inches and width 4 thirds feet.
© 2018 StrongMind. Created using GeoGebra.
What is the area, in square inches, of the rectangle?
Enter your answer as a number, like this: 42
The area of the rectangle is 240 square inches
How to determine the area?The dimensions are given as:
Length = 15 inches
Width = 4/3 feet
Start by converting feet to inches
Width = 4/3 * 12 inches
Width = 16 inches
The area is then calculated as:
Area = Length * Width
This gives
Area = 15 * 16
Evaluate
Area = 240
Hence, the area of the rectangle is 240 square inches
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Many electronic devices use disposable batteries, which eventually have to be replaced. Assume that for one particular brand and type of battery, the distribution of the hours of useful power can be approximated well by a Normal model. The mean is 140 hours, and the stand deviation is 4 hours. The marketing department wants to write a guarantee for battery life. What lifespan should they quote so that they can expect 98% of the batteries to meet the guarantee
They should quote 150 hours so that they can get 98% of the batteries to meet the guarantee.
Given mean of 140 hours and standard deviation of 4 hours with confidence level=98%.
We have to find the lifespan which they should quote to get 98% confident that their batteries meet the guarantee.
We have to use z test for this .
μ=140 hours and σ=4 hours
Z=X-μ/σ
When p value is 0.98 then from z table z value will be 2.58.
Z=X-140/4
2.58=X-140/4
2.58*4=X-140
10.32=X-140
X=150.32
after rounding off we will get 150 hours.
Hence they should quote 150 hours of lifetime on batteries.
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Answer:
132
Step-by-step explanation:
help asap!!!!!
Select the correct answer from each drop-down menu.
Consider polygon JKLMNO on the coordinate grid.
first: 12.5, 25, 17,07
second: 20, 30, 50
third: 47, 37, 61, 68.5
Answer:
12.5
30
68.5
Step-by-step explanation:
The graph of f(x) = x² is shown.
Compare the graph of f(x) with the graph of d(x) = x² - 27.
Answer:
The graph of [tex]d(x)[/tex] is [tex]f(x)[/tex] shifted right by [tex]27[/tex] units.
Expand (x – 2)5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.
Answer:
[tex](x-2)^5 = x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32[/tex]
Step-by-step explanation:
Binomial Theorem
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
Given expression:
[tex](x-2)^5[/tex]
Compare with the Binomial Theorem:
[tex]a=x, \quad b=-2, \quad n=5[/tex]
Substitute the values into the formula:
[tex]\begin{aligned}(x-2)^5 & = x^5+\dfrac{5!}{1!4!}x^{4}(-2)+\dfrac{5!}{2!3!}x^{3}(-2)^2+\dfrac{5!}{3!2!}x^{2}(-2)^3+\dfrac{5!}{4!1!}x^{1}(-2)^4+(-2)^5\\\\& =x^5+\dfrac{120}{24}x^{4}(-2)+\dfrac{120}{12}x^{3}(4)+\dfrac{120}{12}x^{2}(-8)+\dfrac{120}{24}x(16)-32\\\\& =x^5-\dfrac{240}{24}x^{4}+\dfrac{480}{12}x^{3}-\dfrac{960}{12}x^{2}+\dfrac{1920}{24}x-32\\\\& =x^5-10x^{4}+40x^{3}-80x^{2}+80x-32\end{aligned}[/tex]
Pascal's Triangle
Pascal's triangle is an arrangement of binomial coefficients in triangular form. Each row has 1 at both ends, and each remaining number in the row is found by adding together the two numbers directly above it.
[tex]\phantom{-b)))))))}1\\\phantom{-b)))))}1 \:\quad 1\\\phantom{-b)))}1 \:\quad 2\: \quad 1\\\phantom{-b)}1 \:\quad 3\: \quad 3\: \quad 1\\\phantom{))}1 \quad 4 \:\: \quad 6 \quad \;4 \: \quad 1\\1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1[/tex]
(Note: The initial row with the single number 1 is row zero)
Each term in the binomial expansion using Pascal's triangle is the product of a coefficient, a with an exponent, and b with an exponent.
As we move through each term from left to right, the exponent of a decreases from the exponent of the expression down to zero, and the exponent of b increases from zero up to the exponent of the expression.
The coefficients of each term are the numbers which appear in the number of the row that corresponds with the exponent of the expression.
From the given expression, the power that we are expanding the bracket to is 5, so we need to look at line 5 of Pascal's triangle, which is:
1 5 10 10 5 1
Therefore, the expansion using Pascal's triangle to the power 5 of is:
[tex](a+b)^5=1a^5b^0+5a^4b^1+10a^3b^2+10a^2b^3+5a^1b^4+1a^0b^5[/tex]
Substituting the values of a and b:
[tex]\begin{aligned}(x-2)^5 & = 1x^5(-2)^0 + 5x^4(-2)^1 + 10x^3(-2)^2 + 10x^2(-2)^3 + 5x^1(-2)^4 + 1x^0(-2)^5\\\\ & = x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32\end{aligned}[/tex]
What is the equation of the following line?
The equation of the given line is y=2/3x-6
We have given the graph of the line and also the equation of the line
[tex]y=-6x+\frac{2}{3}[/tex]
[tex]y=\frac{2}{3}x-6[/tex]
[tex]y=-6x+\frac{3}{2}[/tex]
[tex]y=\frac{3}{2}x-6[/tex]
We have to determine which equations graph is given here
We have to draw a graph of the given equation of the line
To find the coordinate of the given line
The equation of the line second is
x=0 then y=-6
and when y=0 then x=9
We get the points (0,-6) and (9,0)
plot this point and we get the given graph of the line.
Therefore the second option is correct.
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Write the following linear equations into the standard form Ax+ By=c DETERMINE the values of A, B and C
Answer:
[tex] < 25 = 56. < { \times 4 \div hwh3 \times }^{?} [/tex]
Answer:
Attached
Step-by-step explanation:
See attached image
The letters $A, B$ and $C$ are used to form every possible three letter ``word.'' When these ``words'' are arranged in alphabetical order and numbered so that $AAA$ is Word $1$ and $CCC$ is Word $27$, what number will correspond to the position of word $BAB$ on the list?
The number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.
What number will correspond to the position of word $BAB$ on the list?As evident in the task content, by observation, if follows that since; $AAA$ is Word $1 and $CCC$ is Word $27$.
Then, it can be inferred that A = 1 , B = 2 and C = 3.
On this note, the number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.
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Efraín es un vendedor de celulares, cada equipo cuesta 7500 pesos, el cuenta con su propia línea telefonica y tiene dos métodos de pago, una que es de contado y otra que es a creditó.
Si un cliente compra un celular a crédito aumenta un 20% a su costó inicial.
Samara quiere comprar un celular a crédito y otro de contado dando un total de 11 veces el 20%
¿Cuánto costará cada celular?
¿Cuanto es el valor de el 20%?
El celular de contado costará 7500 pesos, mientras que el celular a crédito tendrá un costo de 9000 pesos.
¿Cuál es el 20% de 7500?7500 / 100 = 75 (valor del 1%)
75 x 20 = 1500 pesos
¿Cuánto cuesta cada celular?Celular a contado: El precio no aumenta por lo que el valor sería de 7500 pesos.
Celular a crédito: 7500 + 1500 = 9000 pesos
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Ted borrowed $5,600 from his bank for 4 months with interest at 9%. ted paid the note in full on its due date. how much was the check he gave to the bank for payment?
Ten gave the check of $5768 to the bank for payment.
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a borrower will never have to pay interest on the interest already accumulated because a creditor will only pay interest on the principal amount.
Formula for simple interest is;-
Simple interest = (principal amount×rate of interest×time duration in years)/100
S.I = (P×R×T)/100
Calculation of the total amount paid by Ted to the bank-
The principal amount is $5,600.
The rate of interest is 9%.
Time duration is 4 months equals 4/12 = 1/3 years.
S.I = (5,600×9×1)/(3×100)
S.I = 168
The simple interest on amount is $168.
Thus, the total amount is S.I + principal amount
Total amount = 168 + 5600
= 5768
Therefore, the total amount paid by the Ted to the bank is $5768.
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A population has a standard deviation of 7.89. what is the approximate standard error of the mean for a sample size of 300?
Answer:
Below.
Step-by-step explanation:
Standard error =
standard deviation / √n
= 7.89 / √300
= 0.456 approx.
Intervals of increasing and decreasing are written in terms of the_____value, and you will use the symbol for_______with the____–coordinate from the vertex.
The Intervals of increasing and decreasing are written in terms of the 'x' value, and you will use the symbol for 'x' with the 'y' coordinate from the vertex.
How to denote the termsThe increasing and decreasing intervals are written in the terms of the 'x' value of the function
They are represented thus;
Increasing interval = f (x) ≤ f (y)
Decreasing interval = f (x) ≥ f (y)
Thus, the Intervals of increasing and decreasing are written in terms of the 'x' value, and you will use the symbol for 'x' with the 'y' coordinate from the vertex.
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Use the given information to prove that
A line segment can be made up of the addition of different fractions of the line on a straight path i.e a given line segment can be broken into smaller parts.
Therefore, the required proof that EG = HK is shown below:
Given that: EF = JK
FG = HJ
But,
EG = EF + FG .............. 1
and
HK = HJ + JK ............. 2
From equation 1, we have:
EG = EF + FG
= JK + HJ (since EF = JK, and FG = HJ)
So that,
EG = JK + HJ ........... 3
Also from equation 2, we have:
HK = HJ + JK
= FG + EF (since EF = JK, and FG = HJ)
So that,
HK = FG + JK ........... 4
Therefore, comparing equations 1, 2, 3, and 4, it can be concluded that;
EG = HK
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e) Explain the approach you would take to verify that the following equation is an identity and why you would choose that approach. Do not actually verify that the equation is an identity.
(sin(x) + cos(x))² / sin(2x)= csc (2x) + 1
See below for the proof of the trigonometry identity
The approach to takeThe identity is given as:
(sin(x) + cos(x))² / sin(2x)= csc (2x) + 1
Start by expanding the numerator
(sin²(x) + cos²(x) + sin(2x)) / sin(2x)= csc (2x) + 1
Express sin²(x) + cos²(x) as 1
(1 + sin(2x)) / sin(2x)= csc (2x) + 1
Expand the fraction
1/sin(2x) + sin(2x)/sin(2x) = csc(2x) + 1
Evaluate the quotient
csc(2x) + 1 = csc(2x) + 1
Hence, the trigonometry identity has been proved
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Help me please I need a hand
The statements that are true are
The sum of A and C is negativeA + D = BThe quotient of D and B is -10/3 The product of A and B > the product of A and CNumber lineFrom the question, we are to determine the statements that are true
In the given number line,
A = -2 1/6
B = - 1/2
C = 1/3
D = 1 2/3
B - C = 1/6B - C = -1/2 - 1/3
B - C = -5/6
∴ B - C ≠ 1/6
The sum of A and C is negativeA + C = -2 1/6 + 1/3
A + C = -1 5/6
∴ The sum of A and C is negative
A + D = BA + D = -2 1/6 + 1 2/3
A + D = -1/2
B = -1/2
∴ A + D = B
Quotient of D and B1 2/3 ÷ - 1/2 = -10/3
∴ The quotient of D and B is -10/3
Product of A and B
A×B = -2 1/6 × -1/2
A×B = 13/12
Product of A and C
A×C = -2 1/6 × 1/3
A×C = -13/18
∴ The product of A and B > the product of A and C
|B| < |C||B| = 1/2
|C| = 1/3
|B| > |C|
|B| is NOT less than |C|
Hence, the statements that are true are
The sum of A and C is negativeA + D = BThe quotient of D and B is -10/3 The product of A and B > the product of A and CLearn more on Number line here: https://brainly.com/question/1545224
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On january 1, 2020, gators corp. acquired a machine at a cost of $900,000. it is to be depreciated on the straight-line method over a five-year period with no residual value. because of a bookkeeping error, no depreciation was recognized in gators' 2020 financial statements. the oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be:
Option b. The oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be $372,000.
The yearly straight-line devaluation cost for the machine would be $186,000 ($930,000/5). In any case, since no deterioration was perceived in 2020, the collected devaluation toward the start of 2021 would be $0 rather than $186,000. In this manner, the complete devaluation cost for 2021 would be the yearly deterioration of $186,000 in addition to the get up to speed devaluation for 2020 of $186,000, for a sum of $372,000. This make up for lost time devaluation is important to address the blunder made in the earlier year and guarantee that the resource is appropriately recorded on the asset report. Accordingly, the right response is $372,000.
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The complete question is:
On January 1, 2020, Oriole Corp. acquired a machine at a cost of $930000. It is to be depreciated on the straight-line method over a 5-year period with no residual value. Because of a bookkeeping error, no depreciation was recognized in Oriole's 2020 financial statements. The oversight was discovered during the preparation of Oriole's 2021 financial statements. Depreciation expense on this machine for 2021 should be
$232500.
$372000.
$186000.
$0.
Find the image of (-1, 2) reflected across the y-axis.
Answer: (1,2)
Step-by-step explanation:
Reflecting across the y-axis means [tex](x,y) \longrightarrow (-x,y)[/tex]
So, [tex](-1,2) \longrightarrow \boxed{(1,2)}[/tex]
Geometry question I need help finding the x, MB, CM, and CB
Answer:
x=10, MB=19 CM=16 CB=35
Step-by-step explanation:
Since M is the midpoint of line CB
CM=MB
x+6=2x-4
6+4=2x-x
10=x
The rest is pretty simple, plug 10 in for x
Which function has the given properties below?
The domain is the set of all real numbers.
One x-intercept is (2 pi, 0).
The amplitude is 4.
The point (StartFraction pi over 2 EndFraction, negative 4 EndFraction) is on the graph.
The y-intercept is (0, 0).
The function that has the given properties below is y = -4sin(x).
How to illustrate the function?It should be noted that a function can be used to illustrate the relationship between variables.
In this case, the domain is the set of all real numbers, the amplitude is 4, and one x-intercept is (2 pi, 0).
The appropriate function is y = -4sin(x).
The graph is attached.
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help me solve this pls ?
Answer:
x = 2
Step-by-step explanation:
divide both sides by 2
then simplify
Apply exponent rule and vowla theirs your final answer of x = 2
From the triangle below, if AD = 5 and CD = 20, find the length of side BD.
Select one:
a.
10
b.
28
c.
7
d.
25
Answer: 10
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{BD}{5}=\frac{20}{BD}\\\\(BD)^2 = 100\\\\BD=10[/tex]
The length of side BD, given that AD = 5 and CD = 20 is 10 (Option A)
Data obtained from the questionLength of side AD = 5 Length of side CD = 20Length of side BD =?How to determine the length of side BDSince the triangles are similar, we can obtain the length of side BD as illustrated below:
CD / BD = BD / AD
20 / BD = BD / 5
Cross multiply
BD × BD = 20 × 5
BD² = 100
Take the square root of both sides
BD = √100
BD = 10
Thus, the length of side BD is 10
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Find the distance between the points (-9,0) and (2,5)
A. 12.08
B. 14.6
C. 8.6
D. 74
A. 12.08
9 + 2 = 11
(So, 11 across on our x - axis from - 9 to 2)
Then, up 5 from 2 on our x-axis
Join the 2 dots of coordinates, & creating a triangle. Base 11, height 5
Use Pythagoras Theorem, to find that distance between the coordinates (the hypotenuse)
Root 11^2 + 5^2 = 12.083056...
(root means square root)
Hope this helps!
Answer:
Hello! The answer to this question is A. 12.08.
Step-by-step explanation:
The distance formula is:
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2 }[/tex]
With the distance formula, we can now substitute the values from the points provided:
[tex]\sqrt{(2 - (-9))^2 + (5 - 0)^2} \\= \sqrt{11^2 + 5^2\\\\\\\\= \sqrt{121 + 25} \\=\sqrt{146} \\= 12.08[/tex]
The distance between the points is 12.08.
The expressionx^2-9/x2+6x+8 is equal to zero when x = .
Hello !
Answer:
When x = -3 or x = 3
Step-by-step explanation:
[tex] \frac{ {x}^{2} - 9}{ {x}^{2} + 6x + 8} = 0[/tex]
[tex]\Leftrightarrow \frac{ {x}^{2} - 9 }{ {x}^{2} + 6x + 8} \times ( {x}^{2} + 6x + 8) = 0 \times ( {x}^{2} + 6x + 8)[/tex]
[tex]\Leftrightarrow {x}^{2} - 9 = 0[/tex]
[tex]\Leftrightarrow(x - 3)(x + 3) = 0[/tex]
[tex]\Leftrightarrow \: x - 3= 0 \: or \: x + 3 = 0[/tex]
[tex]\Leftrightarrow \: x = 3 \: or \: x = - 3[/tex]
[tex]\boxed{S = {-3 \: \: or \: \: 3}}[/tex]
what is the volume of the regular pyramid below?
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
This question is incomplete, the missing image is uploaded along this answer below.
What is the volume of the regular pyramid?The volume of pyramid is expressed as;
V = ( 1/3 ) × l × w × h
Given that;
Length l = 8Width W = 8Height h = 6We substitute our given values into the equation above.
V = ( 1/3 ) × 8 × 8 × 6
V = 128 unit³
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
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F(x) = x^2 + 4x. G(x) = 1 + e^2x. As a single logarithm find fg(x) = 21
Answer:
1/2 log2
Step-by-step explanation:
I hope you understand
Answer:
[tex]x & = \dfrac{1}{2} \ln 2[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x^2+4x\\g(x)=1+e^{2x}\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
Therefore, the given composite function fg(x) means to substitute the function g(x) in place of the x in function f(x):
[tex]\begin{aligned}f[g(x)] & = [g(x)]^2 + 4[g(x)]\\& = \left(1+e^{2x}\right)^2+4\left(1+e^{2x}\right)\\& = 1+2e^{2x}+(e^{2x})^2+4+4e^{2x}\\& = e^{4x}+6e^{2x}+5\end{aligned}[/tex]
[tex]\textsf{Let }u=e^{2x}[/tex]
[tex]\implies e^{4x}+6x^{2x}+5=u^2+6u+5[/tex]
Set the composite function to 21 and factor:
[tex]\begin{aligned}f[g(x)] & = 21\\\implies u^2+6u+5 & = 21\\u^2+6u-16 & = 0\\u^2+8u-2u-16 & = 0\\u(u+8)-2(u+8) & = 0\\(u-2)(u+8) & = 0\\\end{aligned}[/tex]
Apply the zero-product property:
[tex]\implies (u-2)=0 \implies u=2[/tex]
[tex]\implies (u+8)=0 \implies u=-8[/tex]
[tex]\textsf{Substitute back in }u=e^{2x}:[/tex]
[tex]\implies e^{2x}=2[/tex]
[tex]\implies e^{2x}=-8[/tex]
As we cannot take logs of negative numbers, the only solution is:
[tex]\begin{aligned}e^{2x} & = 2\\\ln e^{2x} & = \ln 2\\2x \ln e & = \ln 2\\2x(1) & = \ln 2\\2x & = \ln 2\\\implies x & = \dfrac{1}{2} \ln 2\end{aligned}[/tex]
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