The value of the composite function (f o g)(x) is 8x - 17
How to evaluate the function?The definition of the functions are given as
f(x) = 4x - 1
g(x) = 2x - 4
The composite function definition is given as
(f o g)(x)
This composite function is calculated using the following composite function formula
(f o g)(x)= f(g(x))
Substitute the known values in the above equation
So, we have the following equation
(f o g)(x) = 4(g(x)) - 1
So, we have the following equation
(f o g)(x) = 4(2x - 4) - 1
Open the brackets
(f o g)(x) = 8x - 16 - 1
Evaluate
(f o g)(x) = 8x - 17
Hence, the composite function is (f o g)(x) = 8x - 17
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x - 0.1x = 54solve for x
The equation to solve:
[tex]x-0.1x=54[/tex]We can subtract the like terms on the left hand side:
[tex]\begin{gathered} (1-0.1)x=54 \\ 0.9x=54 \end{gathered}[/tex]Now, we can divide both sides by 0.9 and solve for x. Shown below:
[tex]\begin{gathered} \frac{0.9x}{0.9}=\frac{54}{0.9} \\ x=60 \end{gathered}[/tex]The answer is
[tex]x=60[/tex]Answer: x = 60
Step-by-step explanation:
To solve for x, we will isolate the variable with simplifying and reverse operations.
Given:
x - 0.1x = 54
Subtract 0.1 from 1:
0.9x = 54
Divide both sides of the equation by 0.9:
x = 60
Determine whether the graph represents a function.
The tallest man living is Sultan Kosen from Turkey. He measures 2510 mm. How many meters tall is he?
Given:
The height of tallest man is 2510 mm.
Explanation:
The conversion unit for mm to meter is,
[tex]1\text{ mm=}\frac{1}{1000}\text{ meter}[/tex]Determine the height in meters.
[tex]\begin{gathered} 2510\text{ mm=2510 mm}\cdot\frac{1\text{ m}}{1000\text{ mm}} \\ =2.510\text{ m} \end{gathered}[/tex]So height of tallest man Sultan Kosen is 2.510 meters.
Answer: 2.510 meters
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y = 3900(0.937)
ANSWER
This function represents a decay. The rate of decrease is 6.3%
EXPLANATION
When the growth/decay factor is less than 1, the function represents a decay:
[tex]y=a(b)^x[/tex]b is the growth/decay factor.
For a function that represents decay, the decrease factor is:
[tex]b=1-r[/tex]where r is the rate of decrease. In this case, b = 0.937. We can find r:
[tex]\begin{gathered} 0.937=1-r \\ r=1-0.937 \\ r=0.063 \end{gathered}[/tex]To know the rate as a percentage, we have to multiply it by 100:
[tex]r=0.063\times100=6.3\text{ \%}[/tex]Jim graduated in the top 6% of his class. If the mean was 585 and the standard deviation was 134, and the distribution was normal, what was Jim's Z-score?
Answer:
see below
Step-by-step explanation:
From a z-score table look for the value .9400 this would represent the top 6% From my table this is a z-score +1.56
Consider the function f(x) = 4 - 2x ^ 2 on the interval \ -6,6] Find the average or mean slope of the function on this interval , i.e. (f(6) - f(- 6))/(6 - (- 6)) =
f(x) = 4 -2x^2
First we need to find f(6)
f(6) = 4 - 2( 6) ^2 = 4 - 2(36) = 4 - 72 = -68
Then we need to find
f(-6) = 4 - 2( -6) ^2 = 4 -2( 36) = 4 - 72 = -68
Now we find the average or mean slope
The mean slope is zero
Now f'(c) must equal 0
The derivative is -4x and evaluated at c
-4c
This must be equal to 0
-4c =0
Solving for c
c=0
How many ways can twelve jurors be assigned seats in the courtroom?
The number of ways to arrange 12 jurors willbe given as,
[tex]\begin{gathered} n!=(n-1)(n-2)! \\ W\text{here n is the number of jurors } \\ n=12 \end{gathered}[/tex]Therefore,
For 12 jurors we will have the number of ways as
[tex]\begin{gathered} 12!=12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1 \\ =479,001,600\text{ ways} \end{gathered}[/tex]Therefore,
12 jurors can be assigned seats in a courtroom in 479,001,600 ways
[20 points]Practice analyzing stretches and shrinks of exponential
functions.
Consider the exponential function f(x) = 2(3¹) and its
graph.
ty
8
The initial value of the function is
The base of the function is
The function shows exponential
The function's initial value is 2, its base value is 3, and it exhibits exponential growth.
What is meant by initial value?An initial value of a function denotes the function's y-intercept. The constant of an equation can also be used to find initial values. Understanding the y-intercept will help you with graph functions. Substitute 0 0 for x x and solve for y y to confirm the initial value. A differential equation with some initial conditions is used to solve an initial value problem. For instance, with initial conditions y(0)=1, dy/dx = x. An initial value problem (IVP) in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.To learn more about initial value, refer to:
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A teacher gives pens and pencils to elementary students at an equal rate.
Pencils Pens
21 63
33 A
45 135
B 153
Determine the missing value for the letter B.
The missing value for the letter B is 51.
Given,
A teacher gives pens and pencils to elementary students at an equal rate.
Pencil ; 21 33 45 B
Pen ; 63 A 135 153
We have to determine the missing value of B.
Here,
Ratio of pencil to pen for each student.
Student 1; Pencil/pen = 21/63Each student get pencil and pen in the same ratio as 1/3
Then,
Student 2 gets;33/A = 1/3
33 × 3 = A
A = 99
Ratio = 33/99 = 1/3
Student 3 gets;45/135 = 1/3
Student 4 gets;B/153 = 1/3
3B = 153
B = 153/3 = 51
Ratio = 51/153
That is,
The missing value for the letter B is 51.
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g(x)=26÷x-7 how do I find the domain
The domain of a function, are the values for which the function is defined on the x-axis,
Let the function:
[tex]\frac{26}{x\text{ - 7}}[/tex]denominator can't be
For the polynomial below, 2 is a zero.f(x) = x^3– 8x² + 18x – 124 –Express f (x) as a product of linear factors, F(x)=
The polynomial can be factorized in linear factors:
[tex]\begin{gathered} f(x)=x^3-8x^2+18x-12 \\ f(x)=(x-2)(\frac{x^3-8x^2+18x-12}{x-2}) \\ f(x)=(x-2)(x^2-6x+6) \end{gathered}[/tex]For (x^2) - 6x - 6 we use the general equation:
[tex]\begin{gathered} x^2-6x+6 \\ x_{1,2}=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\mleft(6\mright)}}{2} \\ x_{1,2}=3\pm\frac{\sqrt[]{8}}{2}=3\pm\frac{\sqrt[]{2^3}}{2}=3\pm2^{\frac{3}{2}-1}=3\pm\sqrt[]{2}^{} \\ x_1=3+\sqrt[]{2} \\ x_2=3-\sqrt[]{2} \end{gathered}[/tex]Then, our factors are:
[tex]f(x)=(x-2)\cdot(x-(3+\sqrt[]{2}))\cdot(x-(3-\sqrt[]{2}))[/tex]A pattern has 12 red squares to every 84 blue circles. What is the ratio of red squares to bluecircles?Saleet
A pattern has 12 red squares to every 84 blue circles
The ratio is shown below;
[tex]\begin{gathered} \text{Ratio}=\frac{12}{84} \\ \text{Divide all through and reduce to the simplest form and you now have;} \\ \text{Ratio}=\frac{1}{7} \end{gathered}[/tex]Solve: - 3 < 2x – 7 < 1 State your solution as a compound inequality:
-3 < 2x - 7 < 1
we can solve the inequality if we split the inequalities
-3 < 2x - 7
-3 + 7 < 2x
4< 2x
divide both sides by 2
2 < x
x> 2
also
2x - 7 < 1
2x < 1 + 7
2x < 8
divide both sides by 2
x < 4
so upon combining x> 2 and x < 4
2 < x < 4
The value of x is greater than 2 but less than 4
Matt has five times as many stickers as David. How many stickers must Matt give David so that they will each have 180 stickers?
Matt must give David 120 stickers
Explanation:Let the number of stickers that Matt has be m
Let the number of stickers that David has be d
If each of them ends up with 180 stickers each:
the total number of stickers available = 2(180)
the total number of stickers available = 360
Matt has 5 times has many stickers has David
m = 5d
Note that:
Matt's stickers + David's stickers = 360
m + d = 360
5d + d = 360
6d = 360
d = 360/6
d = 60
David has 60 stickers
m = 5d
m = 5(60)
m = 300
Matt has 300 stickers
The number of stickers Matt must give David so that they will each have 180 stickers = 300 - 180 = 120
Matt must give David 120 stickers so that they will each have 180 stickers
Complete the proof below that utilizes the Triangle Inequality Theorom.
1. Firstly, statement 1 is given in the question.
[tex]\bar{PL}\left|\right|\bar{MT}\text{ }\rightarrow\text{ 1. Given}[/tex]2. When two lines cut through two parallel lines, the alternate interior angles are congruent(equal)
So;
[tex]\measuredangle P\cong\measuredangle T\text{ }\rightarrow\text{ Alternate interior angles are equal}[/tex]3. Given
4. PK = KT
Since K is the mid point of PT as stated in the question, then PK will be of equal length as KT.
[tex]PK=KT\text{ }\rightarrow\text{ Since K is the midpoint of }\bar{PT}[/tex]5. Vertically opposite angles are equal.
So;
[tex]\measuredangle PKL=\measuredangle TKM\text{ }\rightarrow\text{ Vertical angles Theorem}[/tex]6. when two corresponding angles and the included side are respectively equal, a triangle is said to be congruent.
[tex]\Delta PKL\cong\Delta TKM\text{ }\rightarrow\text{ Congruent triangles (SAS- two sides and one including side are equal)}[/tex]7. The Triangle Inequality theorem states that the sum of two sides of a triangle is greater than the third side.
[tex]PK+KL>PL\text{ }\rightarrow\text{ Triangle Inequality Theorem}[/tex]8. CPCTC means that Corresponding Parts of Congruent Triangles are Congruent.
The corresponding sides of the two congruent triangles are;
[tex]\begin{gathered} \bar{KL}=\bar{KM} \\ \bar{PK}=\bar{KT} \\ \bar{PL}=\bar{MT} \end{gathered}[/tex]So;
[tex]\begin{gathered} \bar{KL}=\bar{KM}\text{ .} \\ \bar{PK}=\bar{KT}\text{ }\rightarrow\text{ CPCTC} \\ \bar{PL}=\bar{MT}\text{ .} \end{gathered}[/tex]9. The final one is a conbination of CPCTC and Triangle Inequality theorem
[tex]\bar{PK}+\bar{KM}>\bar{PL}\text{ }\rightarrow\text{ since }PK+KL>PL\text{ and }\bar{KL}=\bar{KM}[/tex]Simplify the expression.2.7 - 5.2n - 4n + 6= ? Help me solve this
To simplify the expression, we need to operate the like terms, then:
[tex]2.7-5.2n-4n+6[/tex][tex]2.7+6-5.2n-4n[/tex]Therefore:
[tex]8.7-9.2n[/tex]Solve in simplest form
-6x(-4/3)
Answer:
-6x(-4/3) in simplest form is 8x :)
−6x(−4/3)
=(−6/1)(−4/3)
=(−6)(−4)/(1)(3)
=24/3
=8x
Answer:
8x
Step-by-step explanation:
So, you have -6x(-4/3)
-4/3 could be written as a division problem, or we could just call it a fraction. And -6x is the same thing as -6x/1, so we can write that as a fraction as well. So, we multiply.
Numerators: -4 times -6=24, and we throw the x on, so we have 24x
Denominators: 3 times 1 = 3, so the denominator is 3
So, we have 24x/3, which simplifies to 8x
A demand function for a certain product is given by the equation q = 1200 - 5p, where p is the price in
dollars, and q is the quantity demanded. Find a function to represent the revenue generated by producing
and selling q items. Use this function to determine the quantity that maximizes revenue. What price
should be charged in order to maximize revenue?
A function to represent the relation is f = q × p, the quantity that maximizes value could only be when q = p, therefore p = 200 so, q = 200 too according to demand function q = 1200 - 5p.
What is demand function?In mathematics, the relationship between demand and its factors is represented by a demand function. The function demonstrates how elements like a product's own price, buyer income, and the cost of related products affect demand for a given good (substitutes and complements).
We can deduce from the equation how they influence a product's demand, whether positively or negatively, and how much.
A function for generated revenue is simply f = q × p
where f is the generated revenue and
q is the quantity and
p is the price.
The quantity that maximizes value could only be when q = p
Lets substitute the value of q in q = 1200 - 5p,
q + 5p = 1200
But q = p so
p + 5p = 1200
6p = 1200
p = 1200/6
p = 200
So when price is 200 the revenue will be maximized as the quantity is equal to as price.
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Adults ate 3 1/2 pizzas and kids ate 7 1/8 pizzas. How many pizza eaten in total?
Answer:
10 5/8
Step-by-step explanation:
First, we want to convert the mixed fraction to an improper fraction.
3 1/2 = 7/2
7 1/8 = 57/8
Now, we have to find the Least Common Denominator (LCD).
The LCD is 8.
We multiply the top and bottom by 4 because the denominator is 2, which multiplied by 4 is 8.
7 x 4 = 28
_ _
2 x 4 = 8
Now we have 28/8.
We add.
28/8 + 57/8 = 85/8.
85/8 simplified is 10 5/8.
Answer = 10 5/8
Hope this helps!
Btw, if this is correct, can I have Brainliest?
Thanks!
I would really appreciate if you helped me on all of these
33. For this problem you have to sole the following system of equations.
x+y=531
5.75x+1.25y=2013.75
After you solve the system of equations you get that
x=300, y=231
Therefore 300 full-price tickets were sold.
34. Since water is not acid, you have to solve the following equation
0*Water + 0.40*50 = 0.30*(Water+50)
After you solve the equation you get
Water = 16.67
So, you have to add 16.67 ML of water.
and that's the solution for 34.
35.
The next problem is very easy, notice that 12/6 = 2 and 4/6 = 0.666666=0.67 , therefore the scale factor would be 6. And that would be it.
The number of tiles needed for a bathroom floor is proportional to the area of the bathroom floor. Five tiles cover an area of 90 square inches. The bathroom floor has a total area of 3,024 square inches. Let n be equal to the total number of tiles needed for the floor. Set up and solve a proportion to find the value of n.( Show your work)
Given:
5 tiels cover the area 90square inch.
bathroom floor area is 3024
[tex]\begin{gathered} 5\text{ tiles covers the area = 90} \\ 1\text{ tiles cover the area = }\frac{90}{5} \\ \text{ =18} \end{gathered}[/tex]1 tiles cover the area is 18 square inch.
Let n tiles cover 3,024 square inch then:
[tex]\begin{gathered} n\times18=3024 \\ n=\frac{3024}{18} \\ n=168 \end{gathered}[/tex]So 168 tiels required for cover the bathroom floor.
Find the value of x in each case.
The variable x has a value of 22.5 degrees
What are angles?Angles are the measure of space when two or more lines intersect.
How to determine the value of x?The figure represents the given parameter
On the figure, we have the following angle measures
AED = 2x
BEF = 4x
EBC = 6x
Using the above as a guide, we have the following angle measures
BAE = AED = 2x ---- Corresponding angles
BEA = 180 - BEF ---- Angle on a straight line
BEA = 180 - 4x
ABE = 180 - EBC ---- Angle on a straight line
ABE = 180 - 6x
The sum of angles in a triangle is 180
So, we have
BAE + BEA + ABE = 180
This gives
2x + 180 - 4x + 180 - 6x = 180
Evaluate the like terms
-8x = -180
Divide both sides by -8
x = 22.5
Hence, the measure of x is 22.5
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y = (x - 2)² -6
What is the vertex?
Whats the answer to 2^3 A) 2 x 2 x 2 ???
ANSWER:
A) 2 x 2 x 2
STEP-BY-STEP EXPLANATION:
The exponent indicates the number of times the base is multiplied. If in this case, the exponent is 3 and the base is two, the equivalent expression would be:
2 x 2 x 2
So the correct answer is:
A) 2 x 2 x 2
Consider the system of equations.x + 2y = 8-3x – 2y = 12How do you solve the system of equations with Cramer's rule? Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.
The solution to the system of equations using Cramer's rule is given by the image at the end of the answer.
How to solve a system of equations using Cramer's rule?The solution of a system of equations using Cramer's rule is based on the use of determinants of matrices.
In the context of this problem, the system is:
x + 2y = 8.-3x - 2y = 12.The matrix for the system is:
M =
[1 2]
[-3 - 2]
The determinant of the matrix M of the system is given as follows:
|M| = -2 + 6 = 4.
(using the standard procedure to obtain the determinant of a 2 x 2 matrix).
To find the matrix for x, the x-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:
Mx =
[8 2]
[12 - 2]
Then the determinant is:
|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.
The solution for x is:
x = -40/4 = -10.
To find the matrix for y, the y-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:
My =
[1 8]
[-3 12]
The determinant is:
|My| = 12 - (-3)(8) = 12 + 24 = 36.
Hence the solution is:
y = 36/4 = 9.
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hola me puede ayudar
La expresión dada es
[tex](a+b)+(-c+e)^2[/tex]Primero, desarollamos el producto notable a la derecha
[tex](a+b)+(e-c)^2=(a+b)+e^2-2ec+c^2[/tex]Por tanto, la expresión final es
[tex]e^2+a+b-2ec+c^2[/tex]Usando los valores a = 2, b = -1, c = 3, d = 1, y e = 5, tenemos
[tex]\begin{gathered} 5^2+2-1-2\cdot5\cdot3+3^2 \\ 25+1-30+9 \\ 35-30=5 \end{gathered}[/tex]Por tanto, la respuesta es 5.
Which represents the inverse of the function f(x) = 4x?Oh(x) = x + 4O h(x) = x - 4Oh(x) =O h(x) = x
Let y=f(x). To find the inverse of f, isolate x:
[tex]\begin{gathered} f(x)=4x \\ \Rightarrow y=4x \\ \Rightarrow x=\frac{1}{4}y \end{gathered}[/tex]Let x=f^{-1](y). Then:
[tex]f^{-1}(y)=\frac{1}{4}y[/tex]Evaluate the inverse of f at y=x:
[tex]f^{-1}(x)=\frac{1}{4}x[/tex]Therefore, the rule of correspondence of the inverse of f is given by the expression:
[tex]\frac{1}{4}x[/tex]All changes saved 5. Harry is purchasing bananas at the grocery store. The table below shows how many he can purchase and the cost. What is Harry's total cost if he wishes to purchase 7 bananas? Note: The table represents a proportional relationship of bananas per dollar. Number of Bananas
Let's determine the cost of each banana based on the given data.
Number of Bananas Total Cost Price per Banana
4 $2.48 $0.62
8 $4.96 $0.62
12 $7.44 $0.62
lt appears that each banana cost $0.62.
Thus, buying 7 bananas, it'll cost:
7 x 0.62 = $4.34
The answer is letter C.
Walmart buys shoes from a factory in China for $8.50. Walmart then marks up the price of the shoes by 65% to sell to their customers. If the shoes aremarked up 65%, how much do they cost at Walmart? *
Answer
The shoes cost $14.03 at Walmart.
Explanation
The markup, the selling price and the cost price are all related through the relation
[tex]\text{Markup percent = }\frac{(Selling\text{ Price) - (Cost Price)}}{(Cost\text{ Price)}}\times100[/tex]For this question,
Markup percent = 65%
Selling Price = x = ?
Cost Price = $8.50
[tex]\begin{gathered} \text{Markup percent = }\frac{(Selling\text{ Price) - (Cost Price)}}{(Cost\text{ Price)}}\times100 \\ 65=\frac{x-8.5}{8.5}\times100 \\ \text{Divide both sides by 100} \\ 0.65=\frac{x-8.5}{8.5} \\ \text{Cross multiply} \end{gathered}[/tex]x - 8.5 = (0.65) (8.5)
x - 8.5 = 5.525
x = 8.5 + 5.525
x = $14.025
x = $14.03
Hope this Helps!!!
I need the answer for x
Answer:
x=-1
Step-by-step explanation:
make equation
-2x-3=x
-3=3x
-1=x
Answer:
x=-1
Step-by-step explanation:
-x+-x-1-1-1 = x
-2x-3=x
3x=-3
x=-1
