If x > 3,, which of the following is equivalent to
1
1
1
+
x+ 2 x+3
?
I
Answers
If (x > 3), then the simplified form of the expression \([\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\) will be equivalent to \([\frac{x^{2}+5x+6 }{2x+5}]\).
As per the question statement, we are provided with a mathematical expression in the form of a fraction which goes as \([\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\).
We are required to calculate an equivalent simplified form of the above mentioned expression.
To solve this question, we simply have to add the fractions in the denominator part and then perform a reciprocal of the overall fraction, and simplify it further in that format only, to obtain our final desired answer. The process is shown below as:
\([\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\\=\frac{1}{\frac{(x+3)+(x+2)}{(x+2)(x+3)} } \\=\frac{1}{\frac{(2x+5)}{(x+2)(x+3)} }\\=\frac{(x+2)(x+3)}{(2x+5)} \\=\frac{x^{2}+3x+2x+6 }{2x+5} \\=\frac{x^{2}+5x+6 }{2x+5}\)
Hence, If (x > 3), then the simplified form of the expression \([\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\) will be equivalent to \([\frac{x^{2}+5x+6 }{2x+5}]\).
Expression: In Mathematics, expressions are mathematical statements that have at least two terms, comprising of numbers or variables, or both, and being connected by an operator in between.To learn more about Expressions, click on the link below.
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Related Questions
pls help me hepl me
Answers
Answer:
b at most 199
Step-by-step explanation:so the total was 121 and there is a flat fee of 21.50 so you subtract that out and gat 99.5 since its .5 per mile its going to be divided giving 199 and that is the most she could have driven.
PLZZZ HELP MEEEeeeeeeeeeeeeeeeeeee
Answers
Answer:
I am a professional, worry not
-1.6 < -1.55 < -0.4 < 1.35 < 1.7
What is the total weight of the bags that weighed /8 pound each?
Answers
The total weight of Rice that Mark buys is given as follows:
2.5 pounds.
How to obtain the total weight?The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.
The weight of each bag is given as follows:
5/8 pounds = 0.625 pounds.
The number of bags is given as follows:
4 bags.
Hence the total weight of Rice that Mark buys is given as follows:
4 x 0.625 = 2.5 pounds.
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Use the function f(x) to answer the questions: f(x) = 2x^2 − x − 10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Answers
(1/4,f(1/4)) = (1/4,-81/8)
Three friends got the prize money worth $105,000. The first friend would get twice the amount of the third friend's portion. The third friend would get twice the amount of the second friend's portion. Determine the amount that each friend would receive.
Answers
Answer:
Step-by-step explanation:
The first friend would get $60,000
The second friend would get $15,000
The third friend would get $30,000
jackson hikes 220.2 meters up a mountain, if he is 60% of the way up, how tall is the mountain?
Answers
Answer:
132.12
Step-by-step explanation:
Please give me the answer to this problem!!
Answers
Answer:
2nd option
Step-by-step explanation:
x is left and right
y is up and down
just look at the y coordinate for any point and translate 5 points down.
Answer:
Step-by-step explanation:
second answer
-3 times b is smaller than -33
Answers
Answer:
l think so because -3 if you add a 0 (-30) its smaller than -33
HELP FAST FAST FAST pls
Answers
The number of the nonfiction hardcover books (49), and the total number of the hardcover books sold (72), indicates that the percentage of the hardcover books sold that are nonfiction is the option;
D. 68%
What is a percentage?A percentage is a ratio of quantities presented as a fraction of with a denominator of 100.
The result of the tracking information of the number of books sold by the presented in the summary table indicates;
The number of hardcover notebooks in the table = 72
The number of fiction hardcover notebooks in the table = 49
The percentage of fiction hardcover books = (49/72) × 100 ≈ 68%
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The amount of a same le remaining after T days is giving by the equation p(f)=a(1/2) T/h
Answers
Answer:
6
Step-by-step explanation:
Makeeya only has $25 to spend on a custom T-shirt. It costs $10 for a plain T-shirt, and there is a charge of $$1.50 for each square inch of design added to the T-shirt. Which solution represents the number of square inches of design,x , Makeeya can put on her T-shirt?
Answers
Answer:
10 square inches
Step-by-step explanation:
cost of a plain t-shirt = $10
cost of 1 square inch of design addition = $1.50
let there be x square inches of design
then cost of x square inches of design = x*cost of 1 square inch of design
= 1.50*x = 1.5x
Total cost for t-shirt with x square inches of design = cost of a plain t-shirt + cost of x square inches of design = 10 + 1.5 x
It is given that Makeeya has only $25, then total cost which can be afforded by him will be $25 only
Thus,
10 + 1.5 x = 25
=> 1.5x = 25-10 = 15
=> x = 15/1.5 = 10
Thus, Makeeya can put 10 square inches of design on her T-shirt.
Which of the following illustrates the truth value of the given conjunction?
The number -343/9
is an integer, and a rational number.
Answers
Answer:
an integer is a rational number sometimes(eg.17=17/1) but not always.
a rational number can be written in the form p/q where p and q are integers.
Step-by-step explanation:
A store pay $120 for a bicycle. The store has a 60% markup policy. What is the selling price of the bicycle? (answer $192)
Use your answer from the above question to help answer this question!! The store is now going out of business and is selling all of the bicycles at a 30% discount. What is the sale price of the bicycle? (answer $134.4)
Use the information from the last two questions to help you answer this question. Will the store make money or lose money on the bicycle? How much?
Answers
Answer:
The store will make money for each option/event. For the first option, the store will earn extra $72. For the second option, the store will earn extra $14.4.
Step-by-step explanation:
120 x 1.6 = 192
192 x 0.7 = 134.4
For problem 1, the answer is $192
For problem 2, the answer is $134.4
The store will make money for each option/event.
192-120=72
134.4-120=14.4
The cash register subtracts $2.00 from a $10 Coffee Cafe gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation.
Answers
The equation of the line in the slope-intercept form is: y = -2.00 x + 10.
The slope and provided point are both in the equation for the straight line.
The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.
y-y₁ = m(x-x₁)
It is the necessary equation for a line in the form of a point-slope.
That gift card to the Coffee Café has been provided. = $10
Medium coffee = $2.00
customers
The quantity of coffees a consumer can purchase can be represented using a linear equation.
Slope formula
m = (8 - 10)/(1 - 0)
m = -2
Now consider the line's point-slope shape.
y-y₁ = m(x-x₁)
( y - 10) = -2.00 ( x - 0)
y = -2.00 x + 10
The slope: m = - 2.00
The equation of the line: y = -2.00 x + 10
The y-intercept is 10
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Simplify (4x³y + 5xy² - 2xy) + (6x³y - 9xy² + 3xy).
O 10x³y - 4xy² + xy
O 10x³y + 4xy² + xy
O 10x³y - 4xy² + 5xy
O10x³y + 4xy² + 5xy
Answers
Answer:
So, the answer is (A) The First Option.
Which number has a 3 that is 1/10 the value of the 3 in 14.37 ?
Answers
Answer:
0.3
Step-by-step explanation:
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answers
Answer: 4.12 km
Step-by-step explanation:
Use the Pythagorean theorem. Name the hypotenuse (longest side) c and the bottom side b. Then, simplify and solve for a.
a^2 + b^2 = c^2
a^2 + 8^2 = 9^2
a^2 + 64 = 81
a^2 = 17
a = square root of 17 or approx. 4.12
Please give brainliest!
f(x)=x^7/9
Show the work steps of the function above to find the inverse of the function algebraically using rational exponents notation. Do not use radical notation.
Answers
Answer:
x^(9/7)
Step-by-step explanation:
inverse function f(x) = (x^(1/9))^7 = x^(9/7)
Which is an INCORRECT name for this angle?
Answers
Answer:
<FH
Step-by-step explanation:
The reason why is because FH is a line and everything else includes G, this answer does not.
The ratio of pizza to nachos sold during A-lunch is 4 to 3. There were 48 nachos sold. What is the number of pizzas sold during A-
lunch?
Answers
Answer:
The number of pizzas sold during A- lunch is 64
Step-by-step explanation:
Let us solve the question using the ratio method
∵ The ratio of pizza to nachos sold during A-lunch is 4 to 3
∵ There were 48 nachos sold
→ By using the ratio method
→ Pizza : Nachos
→ 4 : 3
→ x : 48
→ use the cross multiplication
∵ x × 3 = 4 × 48
∴ 3x = 192
→ Divide both sides by 3
∵ \(\frac{3x}{3}\) = \(\frac{192}{3}\)
∴ x = 64
∴ The number of pizzas sold during A- lunch is 64
The graph shows the distribution of the number of text messages young adults send per day. The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
What percentage of young adults send more than 158 text messages per day?
16%
34%
68%
84%
Answers
Answer:
16%
Step-by-step explanation:
From the graph of distribution of the number of text messages
Young adults send more than 158 text messages per day is 16%
Given :
The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
Given 158 text messages . so x is 168
Now we find out z -score
\(z=\frac{x-mean}{standard\; deviation }\)
Replace the values and find out z
\(z=\frac{158-128}{30} =1\)
the value of z=1
Lets use the standard deviation table that gives area on the left
the table gives the percentage of adults less than 158
z-score value for z=1 is 0.8413
Now, percentage of young adults send more than 158 text messages
Percent (more than 158)=1- P(less than 158)=\(1-0.8413=0.1587\)
To get percentage we multiply by 100
\(0.1587 \cdot 100= 15.87= 16\)
Young adults send more than 158 text messages per day is 16%
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6th grade ratios 50 pts
Answers
Answer:
13 milliliters
Step-by-step explanation:
it is 13
What is the coefficient in the expression 10x+8
Answers
Answer:
In the given expression, 10x + 8, the numerical coefficient is 10 and the literal coefficient is x. The number 8 is not considered as a coefficient since the value is a constant.
Answer: 10 + 8
Step-by-step explanation: If you want to find a coefficient you need to only remove the variable from the expression. For example what is the coefficient of 4x its 4. Please mark as the brainliest!
Find f(g(x)) for the functions f(x)=5sqrt(x+1)-2 and g(x)=x^2-1
Answers
The value of the composite function f(g(x)) is 5x + 2
Composite functionsComposite functions are functions inside another function. Given the following functions:
f(x) = 5√x+1 - 2
g(x) = x² - 1
Determine the composite function f(g(x))
f(g(x)) = f(x² - 1)
f(x² - 1) = 5√x² - 1+1 - 2
f(x² - 1) = 5√x² + 2
f(x² - 1) = 5x + 2
Hence the value of the composite function f(g(x)) is 5x + 2
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26. My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CAN- NOT be the correct combination of my brother's lock? (A) 8560 (B) 3015 (C) 4906 (D) 1893 (E) 6348 0782 Activate Windows
Answers
Answer:
A
Step-by-step explanation:
The answer is option (A) 8560. This combination cannot be the correct combination for your brother's lock because it contains the digit '6' in the same position as the correct combination (6348), but the other digits do not match.
f f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g
Answers
The value of the function operation f - g(x) is 3x² + x
What is Function OperationsFunction operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.
Addition and subtraction of functions:
A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.
Multiplication of functions:
Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.
Composition of functions:
Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.
In this problem, we have two functions which are;
f(x) = 3x² + 1g(x) = 1 - xThe value of (f - g)(x) = 3x² + x
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Solve for x. Below is the equation.
Answers
x = 110
Angle 4 is a vertical angle to the 115 degrees angle. Therefore, it must be the same in degree measure. So, we know angle 4 is 115 degrees.
Additionally, angle 4 and angle (x+5) are co-interior angles. This means that they should add up to 180 degrees.
Applying these concepts, we can create an equation:
115 + (x+5) = 180.
When we solve, we end up with x = 110
If your car gets 34 miles per gallon, how much does it cost to drive 370 miles when gasoline costs $3.30 per gallon?
The cost is $
nothing.
(Simplify your answer. Round to the nearest cent as needed.)
Answers
Answer:
Cost = 2.5*(380/33) = $28.79
Step-by-step explanation:
20c - 8d? need help kinda hard
Answers
Answer:
the answer is 4(5c-2d)
Answer:
20c-8d
Step-by-step explanation:
As long as you weren't any values for c or d, this expression cannot be simplified any further.
HTH :)
what is equal to 12/10
Answers
Answer:
6/5, or 1.2
Step-by-step explanation:
The right answer is 6/5
Look at the attached picture
Hope it will help you
Good luck on your assignment
