Answer to question. F(x) = 4x + 1 and g(x) = X to the 2nd power - 5, find (f - g)(x)
Answers
Given -
f(x) = 4x + 1
g(x) = x² - 5
To Find -
(f - g)(x) =?
Step-by-Step Explanation -
(f - g)(x) = f(x) - g(x)
Now,
Putting the values f(x) and g(x)
= 4x + 1 - (x² - 5)
= 4x + 1 - x² + 5
= -x² + 4x + 6
Final Answer -
A,
Related Questions
if F(x)=x-5 and G(x)=x2what is G(F(x))?
A. x^2 - 5
B.x^2(x-5)
C. (x-5)^2
D. x^2 + x - 5
Answers
Answer:
C. g(f(x)) = [tex](x - 5)^{2}[/tex]
Step-by-step explanation:
f(x) = x - 5
g(x) = [tex]x^{2}[/tex]
g(f(x)) = [tex](x - 5)^{2}[/tex]
Help me on #10 Please help on my homework assignment
Answers
A piecewise defined function is a function divided into branches by certain conditional rules. The conditions stand after the conditional "if". To evaluate a piecewise defined function for a particular value, we need to know first which condition it satisfies, and then, apply its corresponding rule.
Here, we have the function
[tex]f(x)=\begin{cases}x^2\text{ if }x<0 \\ x+2\text{ if }x\ge0\end{cases}\text{.}[/tex]Let's begin the evaluations with -4. Note that it's less than 0, that is, it satisfies the first condition (x<0). By what I said before,
[tex]f(-4)=(-4)^2=-4\cdot-4=16.[/tex]The next is f(-3). Again, -3<0. Thus
[tex]f(-3)=(-3)^2=-3\cdot-3=9.[/tex]Now, 0 satisfies the second condition,
[tex]0\ge0.[/tex]This means that we must apply the second rule (adding 2):
[tex]f(0)=0+2=2.[/tex]The next two numbers 3 and 4 satisfy the second condition as well (for they are positive). Then,
[tex]f(3)=3+2=5,\text{ and }f(4)=4+2=6.[/tex]Answer[tex]\begin{gathered} f(-4)=16, \\ f(-3)=9, \\ f(0)=2, \\ f(3)=5, \\ f(4)=6. \end{gathered}[/tex]Given SU = 10. VX = 44 and TW = 2x – 1, find the value of x and the length of the median TW in Trapezoid SUXV.
Answers
The Solution.
By Similarity Theorem, we have that Trapezoid SUTW is congruent to trapezoid TWVX.
So,
[tex]\begin{gathered} \frac{SU}{TW}=\frac{TW}{VX} \\ \text{Where SU=10} \\ VX=44\text{ , TW=2x-1} \end{gathered}[/tex]Substituting these values into the ratio above, we get
[tex]\frac{10}{2x-1}=\frac{2x-1}{44}[/tex]Cross multiplying, we get
[tex]\begin{gathered} (2x-1)^2=44\times10 \\ (2x-1)^2=440 \\ \text{Square rooting both sides, we get} \\ 2x-1=\sqrt[]{440} \\ 2x-1=\pm20.976 \end{gathered}[/tex][tex]\begin{gathered} 2x=1\pm20.976 \\ \text{Dividing both sides by 2, we get} \\ x=\frac{1\pm20.976}{2} \\ \\ x=\frac{1+20.976}{2}=\frac{21.976}{2}=10.988 \\ Or \\ x=\frac{1-20.976}{2}=-9.988\text{ but x cannot be negative.} \end{gathered}[/tex]So, the correct value of x is 10.988
To find the length TW:
We substitute 10.988 for x in 2x-1
[tex]\begin{gathered} TW=2(10.988)-1 \\ \text{ =21.976-1} \\ \text{ =20.976}\approx21 \end{gathered}[/tex]Thus, the correct answer is:
x = 10.988
TW = 20.976
find each of the following explain your reasoning 1. The length of segment BE 2. The coordinates of E
Answers
Given data:
The given triangle shown.
t
Which figure is similar to Figure A? (The triangles are not drawn to scale)
HELP ASAP
Answers
The figure similar to triangle in figure A is figure C
What are similar triangles ?This a term in geometry used to compare triangles. The comparison is done by considering
The ratio of corresponding dimensionssize of corresponding anglesCorresponding as used refers to same position as the other
How to find the similar triangleThe given triangle shows angle
59 degrees85 degreesThe third angle is soled using some of angles of a triangle as follows
59 + 85 + third angle = 180
third angle = 80 - 85 - 59
third angle = 36 degrees
similar triangles has equal size of angles and figure C meets this criteria and hence the answer
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Before you can multiply two matrices together, the number of ___ in the first matrix must equal the number of rows in the second matrix.
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Before you can multiply two matrices together, the number of columns in the first matrix must equal the number of rows in the second matrix.
What is the short definition of the Matrix?
Matrix, a collection of numbers lined up in rows and columns to create a rectangular array. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.It is called so because it has only one row, and the order of a row matrix will hence be 1 × n.The number of rows in the second matrix must be equal to the number of columns in the first matrix for matrix multiplication to be defined.
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A and B are subsets of a universal set U in which,n (U)=80, n(A)=50, n(B)=30 and n(A∩B)= 10, the find the value of n(A∪B)
Answers
Solution
We are given
[tex]\begin{gathered} n(U)=80 \\ n(A)=50 \\ n(B)=30 \\ n(A\cap B)=10 \\ n(A\cup B)?? \end{gathered}[/tex]Note:
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]Solving
[tex]\begin{gathered} n(A\cup B)=n(A)+n(B)-n(A\cap B) \\ n(A\cup B)=50+30-10 \\ n(A\cup B)=70 \end{gathered}[/tex]Therefore,
[tex]n(A\cup B)=70[/tex]The revenue for selling a units of a product is R = 40x. The cost of producing x units is C = 20 + 7700.In order to obtain a profit, the revenue must be higher than the cost, so we want to know, for what values of a will this product return a profit.To obtain a profit, the number of units must be greater than _____
Answers
EXPLANATION:
We are given the revenue function and the cost function for x units of a product as follows;
[tex]\begin{gathered} Revenue=40x \\ Cost=20x+7700 \end{gathered}[/tex]We are also told that to obtain a profit, the revenue must be higher than the cost. This means;
[tex]\begin{gathered} Profit: \\ R(x)>C(x) \end{gathered}[/tex]To determine which unit(s) of x will yield a profit, we can now substitute the values into the equation above;
[tex]\begin{gathered} Profit: \\ 40x>20x+7700 \end{gathered}[/tex][tex]\begin{gathered} Profit: \\ 40x-20x>7700 \end{gathered}[/tex][tex]\begin{gathered} Profit: \\ 20x>7700 \end{gathered}[/tex]Divide both sides by 20;
[tex]\frac{20x}{20}>\frac{7700}{20}[/tex][tex]x>385[/tex]For this answer, we know that to make a profit, the units produced must be greater than 385 units.
ANSWER:
To obtain a profit the number of units must be greater than 385
One month Ravi rented4 movies and8video games for a total of $57 The next month he rented2 movies and3 video games for a total of$ 23 Find the rental cost for each movie and each video game. One month Ravi rented4 movies and8 video games for a total of$ 57 The next month he rented2 movies and 3 video games for a total of$23 Find the rental cost for each movie and each video game. Rental cost for each movies $??Rental cost for each vidéo games $ ??
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to get the rental cost for each movie and each video game.
Step 1: Write the representation for the two rentals
Let m represents movies
Let v represent video games
Step 2: Write the statements in form of a mathematical equation
[tex]\begin{gathered} \text{Month 1: }4m+8v=57 \\ \text{Month 2: }2m+3v=23 \end{gathered}[/tex]Step 3: Solve the equations above simultaneously using elimination method to get the values of m and v
[tex]\begin{gathered} 4m+8v=57----(1) \\ 2m+3v=23----(2) \\ \text{ multiply equation 1 by 2 and equation 2 by }4 \\ 8m+16v=114----(3) \\ 8m+12v=92----(4) \\ \text{subtract equation (4) from equation (3)} \\ 4v=22 \\ v=\frac{22}{4}=5.5 \\ \text{Substitute 5.5 for v in equation 1 to get the value of m} \\ 4m+8v=57 \\ 4m+8(5.5)=57 \\ 4m+44=57 \\ 4m=57-44=13 \\ m=\frac{13}{4}=3.25 \\ m=\text{\$}3.25,v=\text{\$}5.50 \end{gathered}[/tex]Rental cost for each movies is $3.25
Rental cost for each video games $5.50
If concrete was selling for $55.5 per cubic yard, how much did you spend to pave the sidewalk? (See 162 cubic feet.)
Answers
Given:
The volume of the sidewalk is 162 cubic feet.
In yards,
[tex]\frac{162}{3\times3\times3}=6\text{ cubic yards}[/tex]The selling price of concrete is $55.5 per cubic yard.
To find the amount that I spend to pave the sidewalk:
So,
[tex]6\times55.5=\text{ \$}333[/tex]Hence, the amount that I spend to pave the sidewalk is $333.
Using the form 0.00 what is 17% as a decimal.
Answers
0.17
Explanation
Step 1
the percentage is a ratio , between a number and 100
for example:
if you know that 56 % of the students are boys, it means that 56 of every 100 students are boys.
[tex]x\text{ percent=x of every 100=}\frac{x}{100}[/tex]then.
Step 2
[tex]\begin{gathered} 17\text{ percent=}\frac{x}{100} \\ \text{then} \\ 17\text{ percent=17 of every 100=}\frac{17}{100} \\ 17\text{ percent=0.17} \end{gathered}[/tex]I hope this helps you
Define three equivalence relations on the set of buildings on a college campus. determine the equivalence classes for each of these equivalence relations.
Answers
If a relationship R fulfills the three conditions of being transitive, symmetric, and reflexive, then R is said to be an equivalence relation.
When (a, a) € R for any element a € A, we say that R is reflexive on A.
When (b, a) €R for every (a, b) €R, we say that the relation R on A is symmetric.
If (a.b) € R and (b, c) € R implies (a, c) € R, then R is transitive on A.
If you have an a, you may think of all the components that are equivalent to it as its equivalence class.
A=College buildings
We need to define three sets of things that are the same. For instance:
R1 = "(a, b) Both a and b have the same number of rooms."
R2=(a,b): Both a and b have the same number of floors.
R3=(a,b), which means that both a and b have the same number of windows.
Note: If the statement says that a and b have the same property, the relation is probably an equivalence relation.
The set of all elements that are related to an is its equivalence class.
[a]R1,= {b|b has the same number of rooms as a}
[a]R2 = {b|b has the same number of floors as a}
[a]R3= {b|b has the same number of windows as a}
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how much is the hourly median income for a male with a high school diploma but no college assuming a 40-hour work week
Answers
Solution
7 days ----> 1 week
24 hours -----> 1 day
[tex]\frac{819}{7\times24}=4.875[/tex]please help ASAP!!!!
Answers
can't you see my messages?
then the answers are 3 and 4
A(n) blank is a quotient in which the numerator and denominator are both polynomialsA) linear expressionB) quadratic expressionC) exponential expressionD) rational expression
Answers
A(n) blank is a quotient in which the numerator and denominator are both polynomials
A) linear expression
B) quadratic expression
C) exponential expression
D) rational expression
The answer is
option D) rational expressionWhat is the slope of the line that passes through the points (4,0) and (3,1)
Answers
The slope of the line passing through the two given points would be:
[tex]m = -1[/tex]
Hope this helps!
What is the vertical shift of y = 5 + 8 sin(56+ ³T)?4A. 5OB. 8OC. 320D. noneReset Selection
Answers
Given,
The equation of the function is,
[tex]y=5+8sin(5\theta+\frac{3\pi}{4})[/tex]Required
The vertical shhift of the function.
The standard form of the function is,
[tex]\begin{gathered} y=Asin(Bx+C)+D \\ Here\text{ A = amplitude} \\ B=period \\ C\text{ = phase shift} \\ D=vertical\text{ shift} \end{gathered}[/tex]Comapring the given function with standard form then it obtain that the vertical shift is of 5 units.
Hence, the vertical shift of the curve is 5 units.
How you identify radius, diameter, chord, arc, and circumference. If a circle has a radius of 2 centimeters, what is the diameters?
Answers
In order to identify these mentioned terms, it is important that each of them is defined.
Diameter: It is a line that passes through the center of the circle from one endpoint to another. It is two times the radius of the circle
Radius: It is a line drawn from the center of the circle to one endpoint of the circle.
It is half of the diameter.
Chord: It is a line drawn from one endpoint of the circle to another but does not necessarily pass through the center. Diameter is an example of a chord, but a chord does not have to be a diameter
Arc: It is a segment of the circumference of a circle
Circumference: is the total distance around the circle
From the diagram above:
|AB| is a diameter
|OA| or |OB| is the radius
|CD| is the chord
Arc CD is indicated on the diagram
If a circle has a radius of 2 cm:
Diameter = 2 x radius
Diameter = 2 x 2
Diameter = 4 cm
Therefore, if a circle has a radius of 2 cm, the diameter is 4 cm
I need help solving this math problem any help ?
Answers
We know that m and n are parallel.
Then, x is supplementary of 145 degrees.
This is because the adyacent (and supplementary) angle of x is, with the angle of measure 145 deg, alternate exterior angles and have the same measure.
Therefore, x and the angle of 145 degrees are also supplementary.
If they are supplementary, they add 180 degrees, so we can write:
[tex]\begin{gathered} x+145=180 \\ x=180-145 \\ x=35 \end{gathered}[/tex]x = 35 degrees
2+8-15x34 i need help on this question
Answers
Answer:
-500
Step-by-step explanation:
Using the order of operations, you first multiply the 15 by 34, to get 510. This turns the equation to 2+8-510, which can be simplified to 10-510. This equals 500.
Do y’all know the answer of (3 ^ 4) ^ 5 in exponential form
Answers
Answer:
[tex]3^{20}[/tex]
Step-by-step explanation:
Answer: Hi that would be 3^9, but since it has a parantheses it becomes 3^20, hope this helps.
I do not understand this problem does this mean I choose all of the ratios lower than 9:1 ??
Answers
Less generous, means that the value is less than 9:1 or 9/1
[tex]9\colon1\Rightarrow\frac{9}{1}=9[/tex]for the other values we have
[tex]\begin{gathered} 4\colon1\Rightarrow\frac{4}{1}=4 \\ 18\colon1\Rightarrow\frac{18}{1}=18 \\ 15\colon1\Rightarrow\frac{15}{1}=15 \\ 2\colon1\Rightarrow\frac{2}{1}=2 \end{gathered}[/tex]now, let's find the values that are less than 9
4 < 9
2 < 9
then, the odds that are less generous are
[tex]\begin{gathered} 4\colon1 \\ 2\colon1 \end{gathered}[/tex]Find the amplitude, period, phase shift, and midline of this function. [tex]y = \sin( \frac{\pi}{6}x + \pi) - 3 [/tex]
Answers
Standard form of a function is
[tex]a\sin (bx+c)\pm d[/tex][tex]y=\sin (\frac{\pi}{6}x+\pi)-3[/tex]So by comparing the given equation to the standard form, we get
a=1, b=pi/6, c=pi, d=3
amplitude can be written as mod a or
[tex]\lvert a\rvert=\lvert1\rvert=1[/tex]So the amplitude is 1
Now for the period, we use generalization as
[tex]\frac{2\pi}{\lvert b\rvert}\text{radians}[/tex][tex]=\frac{2\pi}{\lvert\frac{\pi}{6}\rvert}=\frac{2\pi}{\frac{\pi}{6}}=2\times6\times\frac{\pi}{\pi}=12[/tex]So the period is 12
Here, c is the phase shift, so c=pi
Hence phase shift is pi
Midline is the line that runs between maximum and minimum values
Since, the amplitude is 1 and the phase shift is -pi, the minimum and maximum values are
[tex]\min =\text{ 1-}\pi\text{ }=1-\pi_{}[/tex][tex]\max =1+\pi[/tex]Midline will be the centre of region (1+pi, 1-pi)
So the midline will be
[tex]\frac{1+\pi-(1-\pi)}{2}=\frac{2\pi}{2}=\pi[/tex]americans drink an average of 23.3 gallons of bottled water per capita per year. if the standard deviation is 2.7 gallons and the variable is normally distributed, find the probability that a randomly selected american drinks more than 25 gallons of bottled water. what is the probability that the selected person drank between 18 and 26 gallons?
Answers
a) A random American has a 0.25249 probability of drinking over 25 gallons of bottled water.
b) The chance that a random person consumed around 18 and 26 gallons is 0.66575.
Using the z score formula, z = (x-μ) ÷ σ, where x is the raw score, the population mean = 23.2 gallons, and the population standard deviation = 2.7 gallons.
a) The probability that a randomly chosen American consumes over 25 gallons of water bottles in a year.
For x = 25 gallons
z = 25 - (23.2 ÷ 2.7)
z = 0.66667
Z-Table probability value:
P(x<25) = 0.74751
P(x>25) = 1 - P(x<25)
1 - 0.74751
= 0.25249
A random American has a 0.25249 chance of drinking over 25 gallons of mineral water in a year.
2) The possibility that the chosen individual consumes between 18 and 26 liters of water
For x = 18 gallons
z = 18 - (23.2 ÷ 2.7)
z = 9.407
Z-Table probability value:
P(x = 18) = 0.32836
For x = 26 gallons
z = 26 - (23.2 ÷ 2.7)
z = 17.407
Z-Table probability value:
P(x<25) = 0.74751
P(x>25) = 1 - P(x<25)
1 - 0.74751
= 0.25249
The selected person is going to consume between 18 and 26 liters of alcohol.
P(x = 26) - P(x = 18)
= 0.99411 - 0.32836
= 0.66575
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List the integers in each solution set. 2 ≤2x <x+5
how to do this step by step ?
Answers
Answer:
Step-by-step explanation:
By subtracting 2 from both sides, we get the equivalent inequality
x>−5 .
So, the solution set is
{x | x>−5} .
==========================================================
Explanation:
The tri-inequality A < B < C breaks up into A < B and B < C
Use this idea to break up 2 ≤ 2x < x+5 into these two pieces
2 ≤ 2x2x < x+5We'll solve each inequality individually.
Let's start with the first one.
2 ≤ 2x
2/2 ≤ 2x/2
1 ≤ x
Now onto the second inequality
2x < x+5
2x-x < x+5-x
x < 5
-------------------------
From here recombine 1 ≤ x and x < 5 to get 1 ≤ x < 5
If x is an integer only, then the roster set of solutions that satisfy this inequality is {1, 2, 3, 4}. Notice 5 is not part of the solution set, but 1 is.
We can replace x with any of those items in bold to get a true statement.
For instance, let's replace x with 3.
1 ≤ x < 5 updates to 1 ≤ 3 < 5 which is true
Let's go back to the original tri-inequality and replace each x with 3. Then simplify each side.
2 ≤ 2x < x+5
2 ≤ 2*3 < 3+5
2 ≤ 6 < 8
We end up with a true statement, which verifies that x = 3 is one of the integer solutions. I'll let you verify the other values 1,2, and 4.
Compare the probability that a randomly selected student is in grade 10 at each school. Move options to the blanks to complete thesentences.
Answers
From the question
The probability a student at school A is in grade 10 is
From the table
Number of students in grade 10 at school A = 25
Total number of students in School A = 120
Therefore
The probability a student at school A is in grade 10 is
[tex]\frac{25}{120}=\frac{5}{24}[/tex]Hence, The probability a student at school A is in grade 10 is 5/24
The probability a student at school B is in grade 10 is
From the table
Number of students in grade 10 at school B = 20
Total number of students in School A = 80
Therefore
The probability a student at school B is in grade 10 is
[tex]\frac{20}{80}=\frac{1}{4}[/tex]Hence, The probability a student at school B is in grade 10 is 1/4
Since, the probability a student at school B is in grade 10 is greater than the probability a tudent at school A is in grade 10 then
It is less like
A figure is made up of two triangles. The triangles have thesame base of 12 inches. One triangle has a height of 7 inchesand one has a height of 13 inches. What is the total area of thefigure?
Answers
We need to find the area of each triangle and then do a sum of both
[tex]\begin{gathered} A_1=\frac{12\cdot7}{2}=\frac{84}{2}=42\text{ and } \\ A_2=\frac{12\cdot13}{2}=\frac{156}{2}=78\text{ } \end{gathered}[/tex]Then the total area of the figure is 120 inches^2
[tex]42+78=120[/tex]The triangle in Quadrant III is the image of the triangle in Quadrant IV after a counterclockwise rotation about the origin. What is the angle of rotation?
Answers
As per given by the question,
There are given that the triangle in quadrant III.
Now,
From the quadrant III, there are given a triangle.
Then,
If we wiil rotate the triangle on counterclockwise or anticlockwise direction , then it will be matched with given triangle on fourth quadrant at angle of 90 degree.
Hence, the option A is correct.
The answer is "A" 90 Degrees
Find the missing value. Round your answer to the nearest cent Principal: 5850, Rate: 9.72%, time 4 1/2 years. missing value are Amount and Interest
Answers
SOLUTION
Given the following parameters
[tex]\text{ Principal=\$5850,Rate=9.72\%, time = 4}\frac{\text{1}}{2}=\frac{9}{2}years[/tex]The missing value are
[tex]\text{Amount and Interest}[/tex]Where
[tex]\begin{gathered} \text{Interest,I}=\frac{\text{PRT}}{100} \\ \text{And } \\ \text{Amount A=P +I} \end{gathered}[/tex]Obtain the interest, we have
[tex]\begin{gathered} I=\frac{P\times R\times T}{100} \\ I=\frac{5850\times9.72\times\frac{9}{2}}{100}=\frac{5850\times9.72\times9}{2\times100}=\frac{511758}{100}=2558.79 \end{gathered}[/tex]Therefore
The Interest I = 2558.79
The Amount will be obtain by using the formula
[tex]\begin{gathered} \text{Amount, A=Principal +Interest} \\ A=5850+2558.79=8408.79 \end{gathered}[/tex]Hence
The Amount, A is 8408.79
Quadnlateral ABCD is graphed on the set of axes below. When ABCD is rotated 90 in a counterclockwise direction about the origin, its image is quadrilateral A'B'C'D' Is distance preserved under this rotation, and whuch coordinates are correct for the given vertex"? 1) no and C (1,2) 2) no and D' (24) 3) yes and A'(6,2) 4) yes and B'(-24) Option 1 Option 2 Option 3
Answers
The rotation operation preserves the distance of the figure. We just change its orientation but the distance stays the same.
Rotation about 90 degrees will change the coordinates of the quadrilateral via the equation
[tex]R_{(0,0),90}(x,y)=(-y,x)[/tex]Hence, for the vertices of the given quadrilateral on the figure, the following will be the new vertices upon rotation of the quadrilateral about 90 degrees counterclockwise.
[tex]\begin{gathered} A(-2,6)\rightarrow\rightarrow A^{\prime}(-6,-2) \\ B(4,3)\rightarrow\rightarrow B^{\prime}(-3,4) \\ C(2,-1)\rightarrow\rightarrow C^{\prime}(1,2) \\ D(-4,2)\rightarrow\rightarrow D^{\prime}(-2,-4) \end{gathered}[/tex]Based on the provided solution above, the answer to this problem would be yes and B'(-3,4), which is option 4.
Answer: Option 4
