If f(x)=x²+5 and g(x)=3x, find
a. (f+ g)(x)
b. (f -g)(x)
c. (f . g)(x)
d. (f/g)(x)
a. (f + g)(x)= _____
(Simplify your answer.)
Answers
The value of the functions are:
a. (f + g)(x) = x² + 3x + 5
b. (f - g)(x) = x² - 3x + 5
c. (f * g)(x) = 3x³ + 15x
d. (f/g)(x) = (x² + 5)/(3x)
How to Solve Functions?If we are given an expression of functions, we need to plug in each of the given functions into the equation and solve as you would simplify an algebraic expression.
We have the functions:
f(x) = x² + 5
g(x) = 3x
a. (f + g)(x) means we are going to add the functions f(x) and g(x):
(f + g)(x) = x² + 5 + 3x = x² + 3x + 5
b. (f - g)(x) means we are going to find the difference of the functions f(x) and g(x):
(f - g)(x) = x² + 5 - 3x = x² - 3x + 5
c. (f * g)(x) means we are to find the product of the two functions f(x) and g(x):
(f * g)(x) = (x² + 5)(3x) = 3x³ + 15x
d. (f/g)(x) means we are to find the quotient of the two functions f(x) and g(x):
(f/g)(x) = (x² + 5)/(3x)
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Related Questions
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. cos 75° = ___
Answers
Answer:
0.26
Explanation
Given the expression
Cos 75°
According to the calculator
Cos 75° = 0.2588
Converting to the nearest hundredth
Cos 75 = 0.26
Hence the required answer is 0.26
Air pressure decreases exponentially with increases in elevation. The air pressure, y, (in atm units) at a given elevation, x, (in meters) can bemodeled using equation y = e where k is the decay constant.At an elevation of 5486 m where the air pressure is 0.5 atm, what is the value of k?O A k=In( 5486)0.5B. k =In(0.5)548654860.5D. k = - In ( 3956
Answers
Take natural log on both side of the equation to simplify it,
[tex]\begin{gathered} \ln y=\ln (e^{-kx}) \\ \ln y=(-kx)\ln e \\ \ln y=-kx \\ k=\frac{-\ln y}{x} \end{gathered}[/tex]S
What are two ways you can find 17-8? Explain.
Answers
The two ways to find solution of the expression (17-8) are by direct arithmetic method and indirect simplification method.
In arithmetic method, the first step is to determine whether the numbers are rational or irrational, so as to simplify the solution process. If numbers are rational, then they are checked for the sign determining their position on number line and then the calculations are performed. Here, 17 is positive rational number and -8 is negative rational number. Hence, 17-8 is equalized to 9. In indirect simplification method, the numbers to be subtracted are broken down to simpler terms which can be easily subtracted and reduced to get the answer. In the subtraction of 17-8, we break 8 in the form of (7+1). Then the expression becomes 17 - (7+1). Now, this expression can easily be solved to get the answer. Therefore, 17 - (7+1) = 10 - 1 = 9.
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Angles A and B are supplementary angles. If m
Answers
Answer:
138 degrees
Explanation:
Two angles are said to be Supplementary if they add up to 180 degrees.
Given that Angles A and B are supplementary and:
[tex]\begin{gathered} m\angle A=(2x-24)^0 \\ m\angle B=(5x-27)^0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m\angle A+m\angle B=180^0 \\ 2x-24+5x-27=180 \\ 7x=180+27+24 \\ 7x=231 \\ x=\frac{231}{7} \\ x=33^0 \end{gathered}[/tex]Therefore, the measure of angle B will be:
[tex]\begin{gathered} m\angle B=(5x-27)^0 \\ =5(33)-27 \\ =165^0-27^0 \\ =138^0 \end{gathered}[/tex]The measure of angle B is 138 degrees.
The question: Rounded to the nearest integer, what is the approximate surface area of this right triangular prism with an equilateral triangle for a base? I just need help solve it because I’m confused
Answers
Okay, here we have this:
Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:
Then we will substitute in the following formula:
Surface Area of Triangular Prism=(√3a^2)/2+3(a+h)
Replacing:
Surface Area of Triangular Prism=(√3*8^2)/2+3(8+6)
Surface Area of Triangular Prism=(√3*64)/2+3(14)
Surface Area of Triangular Prism=(√3*64)/2+42
Surface Area of Triangular Prism=(√3*32)+42
Surface Area of Triangular Prism=32√3+42
Surface Area of Triangular Prism=97 ft^2
Finally we obtain that the aproximately surface area is 97 ft^2.
Answer:
199FT
Step-by-step explanation:
I took the quiz
Simplify the expression below by applying the zero exponent rule. (5-8)^0 = Answer
Answers
Zero Exponent Rule:
[tex]\begin{gathered} a^0=1 \\ a\neq0 \end{gathered}[/tex]Thus, anything to the power of 0 is "1", except 0.
Let's simplify the expression shown:
[tex]\begin{gathered} (5-8)^0 \\ =(-3)^0 \\ =1 \end{gathered}[/tex]Answer1PLEASEE HELPP THIS IS DUE 2DAY!!!!!!
Create and solve a word problem using the equation 2x+12>2(x+6).include steps and strategies on how to solve the word problem.
Answers
A word problem of the scenario is "twelve more than twice a number is greater than double the sum of the number and six"
It has no solution
How to create a word problem?The inequality expression is given as
2x + 12 > 2(x + 6)
To create the word problem, we represent the variable with a real world concept
Take for instance, we can set the variable to "a number"
So, the representation of x is "a number"
This means that the word problem can be:
Twelve more than twice a number is greater than double the sum of the number and six
The solution of the word problemIn (a), we have
Twelve more than twice a number is greater than double the sum of the number and six
When represented as an inequality, we have
2x + 12 > 2(x + 6)
Open the bracket
2x + 12 > 2x + 12
Both sides of the inequality are the same and the inequality symbol is greater than
This means that the inequality has no solution
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Solve the equation algebraically
-3(h+6)-7=5
Write your answer as an internet or reduced fraction.
H=
Answers
Answer:
h = -10
Step-by-step explanation:
-3(h+6) - 7 = 5
-3h - 18 - 7 = 5
-3h - 25 = 5
+25 +25
-----------------------
-3h = 30
÷-3 ÷-3
-----------------------
h = -10
I hope this helps!
Simplify 7-0.65r+3 to the lowest
Answers
for each problem find the instantaneous rate of change of the function at the given value ...Thank you and God Bless
Answers
Answer:
The instantaneous rate of change of the function at the given value is -2.
[tex]f^{\prime}(0)=-2[/tex]Explanation:
The instantaneous rate of change of the function at point x=a can be written as;
[tex]f^{\prime}(a)=\frac{df(a)}{dx}[/tex]For the given function;
[tex]y=2x^2-2x+2[/tex]Then the derivative of the function is;
[tex]f^{\prime}(x)=y^{\prime}=4x-2[/tex]substituting x=0, we have;
[tex]\begin{gathered} f^{\prime}(0)=4(0)-2 \\ f^{\prime}(0)=-2 \end{gathered}[/tex]Therefore, the instantaneous rate of change of the function at the given value is -2.
[tex]f^{\prime}(0)=-2[/tex]Shavon and Jesiah are having a race. Shavon can run 100 meters in 30 seconds. Jesiah can run 120 meters in 40 seconds. Who is running faster in meters per second, and by how much?
Answers
Shavon is running faster by 0.33 meter.
How to calculate the value?From the information, Shavon and Jesiah are having a race and Shavon can run 100 meters in 30 seconds. The speed will be:
= Distance / Time
= 100 / 30
= 3.33 meter per second
Jesiah can run 120 meters in 40 seconds. The speed will be:
= Distance / Time
= 120 / 40
= 3 meters per second.
Shavon runs faster. This is illustrated as:
= 3.33 - 3
= 0.33 meter
She's 0.33 meters faster.
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The teacher is handing out note cards to her students. She gave 84 note cards to the first
student, 76 note cards to the second student, 68 note cards to the third student, and 60 note
cards to the fourth student. What kind of sequence is this?
arithmetic
geometric
both
neither
Answers
Answer: Arithmetic
Step-by-step explanation: Because its decreasing at a constant rate of the same number 8
Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1. The factors of the expression are______and_____
Answers
The factors of the expression are 2.5 and 11/5.
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions. Similar to this, we are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3.
Given Data
Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1.
Algebraic expression:
The factors of the expression are:
10 = 5y -1
11 = 5y
y = 11/5
y = 2.5
The factors of the expression are 2.5 and 11/5.
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Solve for X.
X =?]
5X - 16 x + 10
Answers
5x-16x+10
calculate the difference
= -11x+10
-11x + 10
Find the solution set for y = 4x - 3,
given the replacement set
{(-3, 9), (-2, -11), (0, -2), (2,5)}
Answers
The solution set for y = 4x-3 is {(2,5)} from the replacement set {(-3, 9), (-2, -11), (0, -2), (2,5)}.
The provided function is an equation of line in slope-intercept form of line.
According to which, if a line has slope m and it has the Y-intercept c, then the equation of line will be,
y = mx+c,
One thing to be noted here is, if the line passes through (a,b) then it will satisfy the equation and also, it will be called a solution of the equation.
The equation is y = 4x-3,
The given replacement sets is, {(-3, 9), (-2, -11), (0, -2), (2,5)}.
We will check for each and every element of the set,
1. For (-3,9)
Putting values in,
y = 4x-3
9 = 4(-3)-3
9 ≠ -15
Not a solution.
2. For (-2,11)
Putting values in,
y = 4x-3
11 = 4(-2)-3
11 ≠ -11
Not a solution.
3. For (0,-2)
Putting values in,
y = 4x-3
-2 = 4(0)-3
-2 ≠ -3
Not a solution.
4. For (2,5)
Putting values in,
y = 4x-3
5 = 4(2)-3
5 = 5
It is a solution for the equation y = 4x -3.
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Consider the figure. If <7 and <11 are supplementary then lines
Answers
Solution
- The two angles, <7 and <11 are supplementary. This implies that the line q is a transversal line upon which angles <7 and <11 are drawn.
- In order for line q to be the transversal and <7 and <7 to be supplementary, it implies that the lines r and s are parallel.
Final Answer
The answer is "r and s"
Kelly bought a soda for three dollars and 7 candy barswent to the movies. She spent a total of $21. How much did eachcandy bar cost?Write equation and solve. Show work
Answers
She spent a total of $21 dollars.
The soda cost $3
Then, she bought 7 candy bars for x dollars
We set x because we don't know the price
3 + 7x = 21
Solve the equation for x
Subtract both sides by 3
3-3 + 7x = 21 -3
7x = 18
Divide both sides by 7
7x/7 = 18/7
x= 2.571
Each candy bar cost 2.57 aprox
Help 40 points
Two questions!
Answers
The resultant of the product of 7 and 6 added to the quotient of 121 and 11 is 53.
The point (3,9) satisfies the equation y = 8x - 15 thus it will be the solution of the equation.
What is a number system?Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
01)
The quotient of 121 and 11 is 11.
As per the given,
Product of 7 and 6 ⇒
7 × 6 + 11 = 53
Hence "The resultant of the product of 7 and 6 added to the quotient of 121 and 11 is 53".
02)
As per the given equation,
y = 8x - 15
Substitute,(3,9)
9 = 8(3) - 15
9 = 9
Since it is satisfying thus it will be the solution.
Hence "The point (3,9) satisfies the equation y = 8x - 15 thus it will be the solution of the equation".
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Simplify.3(x + 4)12 x3 x + 127x3(x+4)
Answers
We need to apply "Distributive Property" in order to get rid of the grouping symbols in the algebraic expression.
Such means to multiply 3 by each of the terms inside the parenthesis. That is:
3 times x and then 3 time 4:
3 times x remains as "3 x" since we don't know the value of "x", and 3 times 4 becomes 12:
3 (x+4) = 3 x + 12
Which seems to be the second option you listed.
helpppp me out please will give brainiest to first right answer
Answers
Answer:
-490
Step-by-step explanation:
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We want to buy special tile for the shaded area. The tile costs $4.39 per square foot. How much does it cost to tile the shaded area?
Answers
If the area of the rectangle is 800 square feet. Then the cost to tile the shaded area will be $3,512.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The area of the rectangle is given below.
A = 20 x 40
A = 800 square ft
Then the cost to tile the shaded area will be given as,
C = 4.39 x 800
C = $3,512
If the area of the rectangle is 800 square feet. Then the cost to tile the shaded area will be $3,512.
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The missing diagram is attached below.
Which is closest to X, the distance between the base of the lighthouse and the boat
Answers
we have
then, we use the trigonometric tangent identity:
[tex]\begin{gathered} \tan 25=\frac{22}{x} \\ x=\frac{22}{\tan 25} \\ x=47.2 \end{gathered}[/tex]answer: x = 47.2
what is the means proportional between 4 and 81
Answers
Given
4
18
Procedure
The mean proportional, or geometric mean, of two positive The mean proportional, or geometric mean, of two positive
[tex]\frac{a}{x}=\frac{x}{b}[/tex]When solving
[tex]\begin{gathered} x=\sqrt[]{a\cdot b} \\ x=\sqrt[]{4\cdot81} \\ x=\sqrt[]{324} \\ x=18 \end{gathered}[/tex]The answer would be 18
10. The value of the 8th term is 78.The sequence is increasing by 10 at each step.Explicit equation: y = 10x - 2Recursive: now = previous term + 10Find the 9th term.Explanation:
Answers
We have the explicit equatiion:
[tex]\text{ y = 10x - 2}[/tex]The 8th term is 78
y = 10 * 8 - 2
y = 80 - 2
We replaced x by 8
Therefore, for finding the 9th term, we calculate the value this way:
y = 10 * 9 - 2
y = 90 - 2
y = 88
The 9th term of the series is 88
Write the equation of a line that is parallel to the line whose equation is y = 1/3x +6 and passes through the point(-3,5).
Answers
Answer:
y = 1/3 x + 6
Explanation:
The slope of two parallel lines is the same; thereofre the equation of the line we are seeking looks like
[tex]y=\frac{1}{3}x+b[/tex]where b is a constant hitherto unknown.
Now, we know from point (-3, 5) that when when x = -3, y = 5; therefore,
[tex]5=\frac{1}{3}(-3)+b[/tex]the above simplifies to
[tex]5=-1+b[/tex][tex]\therefore b=6[/tex]Hence, the equation of the line is
[tex]y=\frac{1}{3}x+6[/tex]True or False. 8 (12 + 3) is equivalent to 120
Answers
Use the order of operations and the distributive property to solve this expression. Work starting from the parenthesis.
8(12 + 3) = 120
8(15) = 120
120 = 120
The equation is true.
Answer:
True because you must do parentheses first so 12+3=15x8=120 so it is equivalent
This composite figure is made up of three simpler shapes. What is the area of the figure? 3 cm 2 cm 8 cm 3 cm 12 cm A. 37 square cm B. 39 square cm C. 58 square cm D. 55 square cm
Answers
Consider the equation below.
log4(x+3)= log2 (2+x)
Which system of equations can represent the equation?
Answers
Answer:
x=2log(2)−3log(4)log(4)−log(2)
Step-by-step explanation:
I hope this matches one of your answers
The decimal form is -4
A new social media site is increasing its user base by approximately 6% per month.Ir the site currently has 21,740 users, what will the approximate user base be 8 months from now?
Answers
Data
• Increase: 6% per month
,• Current users: 21,740
,• Users after 8 months: ?
Procedure
As we are increasing 6%, we have to multiply the original quantity, which represents the 100%, times 100% plus the increase (6%). However, this must be done in decimals:
[tex]\frac{100\%+6\%}{100\%}=\frac{106\%}{100\%}=1.06[/tex]Then, for the first month the user base will be:
[tex]21,740\times1.06=23,044.4[/tex]Then, for the second month the user base will be:
[tex]23,044.4\times1.06=24,427.06[/tex]The third month would be:
[tex]24,427.06\times1.06=25,892.70[/tex]We could do this for eight months or we can take a shortcut:
[tex]U=U_0\times i^n[/tex]where U represents the user, U0 is the initial users, i is the increase rate, and n is the number of months.
Replacing the data we have we get:
[tex]U=21,740\times1.06^8[/tex][tex]U=34,650.26[/tex]Answer: 34,650.26 users after 8 months with a 6% increase per month.
Which sequences are geometric? Select three options.
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4, –4, –12, –20, ..
Answers
(i) –2.7, –9, –30, –100, ... case of a geometric sequence
(ii) –1, 2.5, –6.25, 15.625, ... case of a geometric sequence
(iii) 9.1, 9.2, 9.3, 9.4, ... not a case of a geometric sequence
(iv) 8, 0.8, 0.08, 0.008, ... case of a geometric sequence
(v) 4, –4, –12, –20, .. not a case of a geometric sequence
What is a geometric sequence?
A geometric sequence is one in which the ratio of two succeeding terms is fixed. The common ratio is what's known as this ratio.
Checking each sequence one by one right now.
(i) –2.7, –9, –30, –100, ...
r=(-9/2.7)=3.33
=(-30/9)=3.33
=(-100/9)=3.33
⇒This is a case of a geometric sequence
(ii) –1, 2.5, –6.25, 15.625, ...
r=(2.5/-1)=2.5
=(-6.25/2.5)=2.5
=(15.625/-6.25)= 2.5
⇒This is a case of a geometric sequence
(iii) 9.1, 9.2, 9.3, 9.4, ...
since the ratio between terms is not the same.
⇒This is not a case of a geometric sequence
(iv) 8, 0.8, 0.08, 0.008, ...
since the ratio between terms is the same.
⇒This is a case of a geometric sequence
(v) 4, –4, –12, –20, ..
since the ratio between terms is not the same.
⇒This is not a case of a geometric sequence
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Answer:
option 1,2,4,5 are correct answers
Step-by-step explanation: