f as a function of x is equal to the square root of quantity 4 x plus 6, g as a function of x is equal to the square root of quantity 4 x minus 6
Find (f + g)(x). (5 points)
Answers
The sum (f + g)(x) of two functions f(x) = √(4x + 6) and g(x) = √(4x - 6) is determined by simply adding the two functions together, hence (f + g)(x) = √(4x + 6) + √(4x - 6).
Explanation:The functions provided are f(x) = √(4x + 6) and g(x) = √(4x - 6). The question asks for the value of (f + g)(x), which is the sum of f(x) and g(x).
To find (f + g)(x), you simply add the two functions together. Hence, (f + g)(x) = f(x) + g(x) = √(4x + 6) + √(4x - 6).
This indicates that the function (f + g)(x) is the addition of the values of f(x) and g(x) at any given value of 'x'.
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Related Questions
Evelyn evaluated 1 and 6/7 - 3/4. Each statement below is a way for Evelyn to check her answer.
Use the drop down menus to complete each statement.
If the sum of her anwser is 3/4 is 1, Evelyn's answer is A. Too high , B. Too low, C. Correct?
If the sum of her answer and 3/4 is 1 and 6/7 , Evelyn's answer is A. Too high , B. Too low, Or C. Correct?
If her answer is minus 3/4 is 1 and 6/7, Evelyn's answer is A. Too high , B.Too low , C.Correct?
Answers
if the sum of her answer and 3/4 is 1, evelyn's answer is too low
if the sum of her answer and 3/4 is 1 and 6/7, evelyn's answer is correct
if her answer is -3/4 and 1 and 6/7, her answer is too high
The required solutions are as follows,
(a) Evelyn's answer is Too low, Option B is correct.
(b) Evelyn's answer is correct, and Option C is correct.
(c) Evelyn's answer is Too high, Option A is correct.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
According to the question,
Evelyn evaluated 1 and 6/7 - 3/4 as,
= 1 6/7 - 3/4 and add 3/4 later,
= 1 6/7 -3/4 + 3/4
= 1 6/7
So,
If the sum of her answers is 3/4 is 1,
Evelyn's answer is Too low, Option B is correct.
If the sum of her answer and 3/4 is 1 and 6/7
Evelyn's answer is correct, and Option C is correct.
If her answer is minus 3/4 is 1 and 6/7,
Evelyn's answer is Too high, Option A is correct.
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How do you interpret algebraic expressions in terms of their context?
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Final answer:
To interpret algebraic expressions contextually, students should grasp the meaning behind each symbol and the relationships within equations rather than just substituting numbers. Understanding the conceptual basis for equations and checking the reasonableness of solutions aids in developing a deeper comprehension and ability to solve complex problems.
Explanation:
Interpreting Algebraic Expressions
To interpret algebraic expressions in terms of their context, it's essential to understand what each symbol represents within a given problem. Instead of rushing to substitute numerical values for symbols, students should focus on understanding the underlying concepts and relationships that the equation models. For example, consider the equation w = A/h, which relates the width of a rectangle to its area (A) and height (h). Instead of viewing it as a mere formula, recognizing it as a rearranged version of A = wh allows one to comprehend that if the height (h) decreases while the area (A) remains constant, the width (w) must increase. This understanding is crucial when working with equations, as it transforms them from abstract symbols to meaningful representations of physical quantities or logical relationships.
To further contextualize equations, students are encouraged to eliminate unnecessary terms to simplify the algebra, and upon finding a solution, to check if the results are reasonable within the context of the problem. This not only aids in solving the problem correctly but also in developing a deeper intuitive understanding of the subject matter.
In sum, interpreting algebraic equations requires a balance between the abstract manipulation of symbols and the practical reasoning about what these symbols represent in the real world. This applied understanding forms the basis of problem-solving in many scientific and engineering fields and empowers students to tackle more complex problems with confidence.
which of the following best represents the average rate at which infants can grow in height during the first four years after birth.
*3 inches per month
*3 inches per year
*3 feet per month
*3 feet per year
Answers
I'm pretty sure that the answer is three inches PER YEAR because think, there is 12 months in a year so if he grows 3 inches per month for 4 year he/she would be taller than an 8 year old, so per year makes more sense.
162 water bottles in 9 cases =
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Adam travels 248 miles on Monday and 167 miles on Tuesday. Estimate the total number of miles Adam travels
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Answer:
Adam travels total 415 miles.
Step-by-step explanation:
The distance Adam travels on Monday = 248 miles
The distance Adam travels on Tuesday = 167 miles
We have to calculate the total number of miles Adam travels.
Total number of miles Adam travels = distance traveled on Monday + distance traveled on Tuesday
= 248 + 167
= 415 miles
Adam travels total 415 miles.
Seven less than one-third of a number is 5
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the environmental club is having a trash pick up day.there are 130 people signed up to help.for trash pickup day,they will work in groups of 4.no more than 4 people can join a group.how many groups are there?explain how you interpreted the remainder
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There are 32 full groups and another group that is not full.
There are 33 groups.
8 x ( 14 + 7) = ____ + ( 8 x 7)
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8 x 21=168
8 x 7= 56
224
because
add 14 and 7 which is 21 then multiply 8 by 21 which is 168 then multiply 8 and 7 which is 56 then finally add both 168 and 56 and you get 224
the larger of two numbers is 10 less than twice the smaller number. If the sum of the two numbers is 38, find the two numbers. Show how you got your answer?
Answers
x + y = 38...because the sum of the numbers is 38
x = 2y - 10....larger one is 10 less then twice the smaller
now we will sub in 2y - 10 for x back into the first equation
x + y = 38
2y - 10 + y = 38
3y - 10 = 38...add 10 to both sides
3y = 38 + 10
3y = 48 ...divide both sides by 3
y = 48/3
y = 16
now sub 16 in for y back into either of the original equations and find x
x = 2y - 10
x = 2(16) - 10
x = 32 - 10
x = 22
so ur numbers are 16 and 22
The larger number will be 22 and the smaller number will be 16.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say the larger number is L and the smaller number is s
Given the larger of the two numbers is 10 less than twice the smaller number
So,
L = 2s - 10
And
The Sum of the two numbers is 38
So,
L + s = 38
By substitution
38 - s = 2s - 10
s = 16
By again substitution
L = 2(16) - 10
L = 22
Hence "The larger number will be 22 and the smaller number will be 16".
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the table shows how far four students walked in 5 minutes. how far did they walk together. 3/4, 1/2,2/3,3/4.
Answers
To find the total distance walked by the four students, add their individual distances together.
Explanation:To find the total distance walked together, you need to add up the distances each student walked. The distances given are represented as fractions. To add fractions, first make sure the denominators are the same. In this case, the denominators are already the same, so you can add the numerators together. So, 3/4 + 1/2 + 2/3 + 3/4 = 15/12.
Simplify the resulting fraction by finding the greatest common divisor of the numerator and the denominator, which is 3. Divide both the numerator and denominator by 3 to get the final answer: 15/12 ÷ 3/3 = 5/4.
Therefore, the students walked a total distance of 5/4 or 1 1/4.
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help wit the last 2... pic
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What is the value of x2y , when x = 10 and y = 1?
A.1/10
B.1/5
C.5
D.10
Answers
Answer:
The answer is 5
Step-by-step explanation:
x/2y = 10/2*1 = 10/2 =5
So basically you do the 10 on top and on the bottom you do 2*1 which equals 2 then you got 10/2 then you would see how many times 2 goes into 10 which is 5 so 5 is your answer hoped this helped! :)
what is the difference between the commutative distributive and associative properties when multiplying?
Answers
For addition: (a + b) + c = a + (b + c)
For multiplication: (ab)c = a(bc)
The commutative property is about which operations you can do backward and forward. You can remember this by thinking of people commuting to work: they go to work every morning, then they repeat the same operation backward when they commute home. It looks like this:
For addition: a + b = b + a
For multiplication: ab = ba
Finally, the distributive property tells you what happens when you distribute one operation against another kind in parentheses. It looks like this:
a * (b + c) = ab + ac
In other words, the a is "distributed" over the b and c.
Of course, you can make these work together:
a * (b + (c + d))
= a * ((b + c) + d) (by the associative property)
= a * (d + (b + c)) (by the commutative property)
= ad + a (b + c) (by the distributive property)
= ad + ab + ac (by the distributive property again).
Hope this helps.
Which of these are NOT examples of the four essential parts of natural selection? Question 2 options: A One offspring of an organism has green fur, and the other has blue fur. This variation in fur color is passed down to their offspring as well. B All offspring of lions will always survive because Earth can always support new organisms. C Cats’ sharp teeth helped them to consume other organisms and survive in their environment. D Jaguars with large jaws made it easier for them to eat certain animals and survive long enough to reproduce.
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simplify 8(7-1)+4(x+5).
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48 + 4x +20
68 + 4x is your answer
hope this helps
I need help with (b) plz help me
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What is the best estimate of (-3/5)(17 5/6)
Answers
[tex]\text{Hey there!}[/tex]
[tex]17\dfrac{5}{6}=17\times6 + 5 =17\times6 \rightarrow102+5 = 107\\\\\text{107 would be your numerator \& 6 would be your denominator.}[/tex]
[tex]17\dfrac{5}{6} = \dfrac{107}{6}[/tex]
[tex]-\dfrac{3}{5}\times\dfrac{107}{6}\\\\5 + 6 = 10\\\\\text{Your new equation is: }\dfrac{-107}{10}\text{Which the mixed number fraction is: }-10\dfrac{7}{10}[/tex]
[tex]\boxed{\boxed{\bf{Answer(s): -10\dfrac{7}{10} \ or \dfrac{-107}{10}}}}\checkmark\\\\\text{Good luck on your assignment and enjoy your day!}\\\\\frak{LoveYourselfFirst:)}[/tex]
Considering the one time deposit and monthly rent, the equation y=1200 + 400x can be used to represent y
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Answer: $1200
Step-by-step explanation:
Why is 39 rational ????????????????????
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All whole numbers are rational
What is the value of the 8 in 381,697?
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"10.000"
Hope this helps, Pal
Solve the equation for y. Leave your answer in terms of π.
π=7x−2y
Answers
7x - π =2y
y = (7x - π) / 2
Answer:
The value of the equation for y is [tex]y=\frac{-\pi+7x}{2}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex] \pi=7x-2y[/tex]
We need to solve the equation for y.
Subtract 7x to both sides of the equation.
[tex] \pi-7x=7x-7x-2y[/tex]
[tex] \pi-7x=-2y[/tex]
Divide both the sides by -2.
[tex] \frac{\pi-7x}{-2}=\frac{-2y}{-2}[/tex]
[tex]y= \frac{\pi-7x}{-2}[/tex]
[tex]y=\frac{-\pi+7x}{2}[/tex]
Hence, the value of the equation for y is [tex]y=\frac{-\pi+7x}{2}[/tex].
eight less than the quotient of a number and 3 is 18
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Hope this helps
Which name correctly classifies this triangle?
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The name of Triangle is Isosceles Triangle.
What is an Isosceles Triangle?Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles.
Given:
From the figure we can see that the triangle is have two of its line segment is equal.
As, we know that the triangle which have two of its sides and angles are equal is an Isosceles Triangle.
Thus, the Triangle is Isosceles Triangle.
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how many even numbers are between 32 and 60. (not including 32 & 60)
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13.
Hope this helps!
I hope this helped
4.30 makeup;40% discount;6% tax equals
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THANKS IN ADVANCE!
Jenna multiplied four numbers together and then divided by -2. The result was a positive value.
Which of the following statements MUST be true?
None of the factors were negative.
All of the factors were negative.
An odd number of factors were negative.
An even number of factors were negative.
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(1)negative x (2)negative = positive x (3)negative = negative x (4)positive = negative
negative divided by negative = positive
odd number were negative
Jed made 2 free throws in 5 second how many would he make in one minute
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Sarah splits five cookies evenly among her 6 friends. Write a fraction to represent the amount of cookies each friend received.
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hope this helps
5 cookies = 30/6
divide (30/6 )/ 5
each friend recieved 5/6 of a cookie
In geometry, how do defined terms and undefined terms relate to each other
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In geometry, how do defined terms and undefined terms relate to each other?
Ask for details Follow Report by Da5ncing4bearnelogi 05.08.2016AnswersHussain514 AmbitiousIn geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These three undefined terms are point, line and plane.
POINT (an undefined term)
In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x,y).
LINE (an undefined term)
In geometry, a line has no thickness but its length extends in one dimension and goes on forever in both directions. A line is depicted to be a straight line with two arrowheads indicating that the line extends without end in two directions. A line is named by a single lowercase written letter or by two points on the line with an arrow drawn above them.
PLANE (an undefined term)
In geometry, a plane has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or wall. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC).
Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the end point, and all points extending infinitely to one side of the end point.
Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single end point. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them.
Everything else builds on these and adds more information to this base. Those added things include all the theorems and other "defined" terms like parallelogram or acute angle.
a chinchilla weighs 2 pounds its weight is 1/8 the weight of a koala write an expression and solve it to show how much the koala weights
Answers
So x * 1/8 = 2
2 being the chinchilla's weight and the 1/8 coming from the fact that the chinchilla weighs 1/8 of the weight of the koala.
So you can just divide both sides by 1/8 first.
x * 1/8 = 2
/ 1/8 / 1/8
Or,
x *1/8 * 8/1 = 2 * 8/1
x = 16
So the koala weighs 16 pounds.