Answer:
[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]
Step-by-step explanation:
[tex]Domain:\\x+2\neq0\ \wedge\ 3x\neq0\\\\x\neq-2\ \wedge\ x\neq0[/tex]
[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{(4x+1)(3x)}{(x+2)(3x)}+\dfrac{(x-1)(x+2)}{(3x)(x+2)}\\\\=\dfrac{(4x)(3x)+(1)(3x)+(x)(x)+(x)(2)+(-1)(x)+(-1)(2)}{(3x)(x+2)}\\\\=\dfrac{12x^2+3x+x^2+2x-x-2}{(3x)(x)+(3x)(2)}\\\\=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]
what is 75% increase followed by a 33 1/3% decrease
a. greater than original
B. Same as the original
c. Less than the original
I believe it is “C”
X/9 × 4 what is the number of X? Im very confused.
Answer:
Step-by-step explanation:
If f(x)= 6x+7, determine the value of f(-5)
Determine which line is steeper. Explain your answer. What does it represent in this situation?
Which of the following sets contain all roots of the polynomial
All these given roots are contained in option C.
The given equation is :
[tex]9x^{3}+9x^{2}-4x-4=0[/tex]
[tex]9x^{2}(x+1)-4(x+1)=0[/tex]
[tex](9x^{2}-4)(x+1)=0[/tex]
[tex]9x^{2}-4=0,x+1=0[/tex]
[tex]x^{2}=\frac{4}{9},x=-1[/tex]
[tex]x=\frac{2}{3},x=-1[/tex]
Roots = [tex]-1,\frac{-2}{3} ,\frac{2}{3}[/tex]
Hence these lie in between [tex](\frac{-3}{2} ,\frac{3}{2})[/tex]
What is larger .475 or .44
.475 because .4 and .4 are equal but then you get too .47 and .44 which would make .475 larger.
The answer to your question is .44
Hopes this helps.
; P
The diagram shows a hexagon drawn inside a rectangle.
What is the area of the hexagon?
A. 21 cm²
B. 24 cm²
C. 30 cm²
D. 54 cm²
Answer is "C" 30 sq cm
which of the following demonstrates a proper application of the division property of exponents
Which of the following is equal to (the sqrt of) √-12 ?
A: 2t√3
B: 2√3
C: -2√3
D: 2√3t
what is the word form and standard form
Answer:
Step-by-step explanation:
The second 1 is eight hundred and ninedey seven then it’s 899+90+70
Natalie went to the shoe store and bought two pairs of sneakers. One pair was $35.60, and the other was $49.95. If she has $100.00, how much will she have left after buying sneakers?
First you need to add the prices to get 85.55. Then 100 - 85.55 is 14.45.
She will have $14.45 leftover
members of a comuntiy center have decided to paint a lrge circuler mural in the middle of the parking lot. The radius of the mural is to be 11 yards. Before they begin painting the mural,thay use rope to form the outline. How much rope will they need?
They will need 11 yards of rope
Please answer Correctly for brainly
√70 = 8.37
It would be between 8 and 9.
90 is 37.5% of what number?
what are the critical points for g(θ) = 20θ − 5 tan θ
g(θ) = 20θ − 5 tan θ
To find out critical points we take first derivative and set it =0
g(θ) = 20θ − 5 tan θ
g'(θ) = 20 − 5 sec^2(θ)
Now we set derivative =0
20 − 5 sec^2(θ)=0
Subtract 20 from both sides
− 5 sec^2(θ)=0 -20
Divide both sides by 5
sec^2(θ)= 4
Take square root on both sides
sec(θ)= -2 and sec(θ)= +2
sec can be written as 1/cos
so sec(θ)= -2 can be written as cos(θ)= -1/2
Using unit circle the value of θ is [tex]\frac{2\pi}{3} and\frac{4\pi}{3}[/tex]
sec(θ)= 2 can be written as cos(θ)=1/2
Using unit circle the value of θ is [tex]\frac{\pi}{3}and\frac{5\pi}{3}[/tex]
For general solution we add 2npi
So critical points are
[tex]\frac{2\pi}{3} + 2n\pi,\frac{4\pi}{3} + 2n\pi , \frac{\pi}{3} + 2n\pi, \frac{5\pi}{3} + 2n\pi[/tex]
The critical points of a function are where its derivative is zero or undefined. The critical points for the function g(θ) = 20θ − 5 tan θ can be found by taking its derivative, setting it to zero, and solving for θ. Additional critical points may occur when the derivative does not exist.
Explanation:In mathematics, the critical points of a function are those where its derivative is zero or undefined. We can find the critical points for the function g(θ) = 20θ − 5 tan θ by taking its derivative and setting it equal to zero.
To find these points, we differentiate the function g(θ) to obtain g'(θ) = 20 - 5/(cos^2 θ). Setting this equal to zero and solving for θ will provide the critical points. In this case, the function is undefined whenever cos θ=0 , providing additional potential critical points. Thus, with trigonometric functions like the tangent function in this question, the critical points occur when the derivative is zero or the derivative does not exist.
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Please help i will mark brainly
It would be positive. The minus sign makes the negative a positive and adds the two. Just remember keep, change, change.
Simplify this algebraic expression, please!
Using the Division Property of Equality you need to divide.
How to get answer:
Reduce the expression by cancelling the common factors.
Factor 3 out of 3y^6.
Cancel the common factor.
Rewrite the expression.
Reduce the expression by cancelling the common factors.
−1⋅14
Last step: Multiply −1 by 14.
Answer: −14
the product of a number and 4 increased by 16 is -2
Let n = the unknown number
"The product of a number and 4" = 4 * n = 4n
"increased by 16" = + 16
Set it all equal to - 2.
4n + 16 = - 2
Subtract 16 from both sides to get constants on one side and variables on the other.
4n = - 2 - 16
Combine like terms:
4n = - 18
Divide both sides by 4 to isolate variable n.
n = - 18 / 4
= - 4 and 2/4 = - 4 and 1/2
write this number in expanded form 283,980
2/3x - 1 = -3/5, but what is x?
The perimeter of a rectangular garden is 132 meters. The length is 6 meters longer than twice the width. Find the dimensions of the garden.
The dimensions of the garden, based on the given condition and the total perimeter of 132 meters, are determined to be 46 meters in length and 20 meters in width.
Explanation:In order to find the dimensions of the garden, you have to solve two equations. The first equation comes from the definition of the perimeter of a rectangle, which is 2*length + 2*width = perimeter, so 2*length + 2*width = 132 meters. The second equation comes from the given information that the length is 6 meters longer than twice the width so length = 2*width + 6.
Now you can use substitution to solve these equations. Plug (2*width + 6) in for length in the perimeter equation and get: 2*(2*width + 6) + 2*width = 132. Simplifying this gives 4*width +12 + 2*width = 132, which further simplifies to 6*width + 12 = 132. Solving for width gives width = 20 meters.
Substituting width = 20 meters into the equation for length gives length = 2*20 + 6 = 46 meters. So the dimension of the garden is 46 meters by 20 meters.
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Lana got a tip of 16%, or 0.16For delivering pizzas for the party if the total bill for the pizza was $98.19 about how much was Lana’s tip
You can answer this question by writing and solving an equation to model the calculation of the total bill.
[tex]1.16x=98.19[/tex]
[tex]x=84.65[/tex]
$84.65
The tip Lana received corresponds to 16% of the bill total which amounts to about $15.71.
Explanation:In this question, we are asked to calculate Lana's tip from her pizza delivery. As it's described that the tip was 16% of the total bill, we use the percentage formula to find out how much Lana got. The formula for finding a percentage of a number is Percent% x Total Amount.
To apply this formula here, we'll multiply the total bill amount ($98.19) by 0.16 (which represents the 16% tip as a decimal). This will give us Lana's tip. The calculation will look like this: $98.19 * 0.16 = $15.71. So Lana's tip for the pizza delivery was approximately $15.71.
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The sum of two consecutive numbers is -105. What are the numbers?
In a conference room, the number of small tables,s, is twice the number of large tables, t. Which equation matches the information ?
The equation that matches the information provided is:
s = 2tHow to determine the equation matches the informationIn this equation, we have two variables: s represents the number of small tables, and t represents the number of large tables.
The equation states that the number of small tables (s) is equal to two times the number of large tables (t). In other words, for every large table, there are two small tables.
For example, if there are 3 large tables (t = 3), then according to the equation, there would be 2 times 3 small tables, which is 6 small tables (s = 6).
This equation captures the relationship between the number of small tables and large tables in the conference room, where the number of small tables is always double the number of large tables.
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Suppose that in 2008, 860,800 citizens died of a certain disease. assuming the population of the country is 228 million, what was the mortality rate in units of deaths per 100,00 people?
The answer is 8.608 because you would just divide 860800 by 100k to get this answer
business paid utilities for $180.? which t account would it go in
It would go under Utilities Expense (right column, second from the bottom) as a Debit
A flower bed is in the shape of a rectangular prism. It’s dimensions are 3 feet wide by 16 feet long by 6 inches deep.
A: how many cubic feet of topsoil do you need to fill the flower bed?
B: you can spread topsoil at a rate of 4 cubic feet per minute. How long will it take you to spread all the top top soil?
If Martha had 154 stamps and then her sister at 248 stamps if they combined it I want to put 8 stamps on each page how many would they have
so 50 pages and 2 stamps in one page
Ana and chuyen are exploring underground caves anas location is -30 feet below the cave entrance and chuyen's patience is -12 feet below the cave entrance which girl is located farther from the cave entrance
Ana is located farther from the cave entrance than Chuyen. She is at -30 feet below the entrance, while Chuyen is at -12 feet, and the absolute value of Ana's depth is greater.
Explanation:The comparison of depths below the cave entrance for Ana and Chuyen is essentially a basic math problem involving negative numbers. In this case, we are looking at distances relative to a reference point, which is the entrance of the cave.
Ana's location is -30 feet below the cave entrance, while Chuyen's location is -12 feet below the cave entrance. To determine which girl is located farther from the cave entrance, we need to compare the absolute value of these numbers because depths below ground are considered negative.
Absolute value of Ana's depth: |-30| = 30Absolute value of Chuyen's depth: |-12| = 12Because Ana's absolute depth is greater than Chuyen's, Ana is located farther from the cave entrance.
Dakota read 130 pages over the weekend. Dajuan read 165 pages over the weekend. Which prime number do the prime factorization of 130 and 165 have in common?
In order to find the common prime factors of 130 and 165, let us first find prime factors of 130 and 165 individually and then we can compare.
Prime factors of 130 can be found as:
130 is a composite number because it has factors other than 1 and itself.
It is not a prime number. The 8 factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130. The factor pairs of 130 are 1 x 130, 2 x 65, 5 x 26, and 10 x 13.
The proper factors of 130 are 1, 2, 5, 10, 13, 26, and 65.
The prime factors of 130 are 2, 5, and 13.
Prime factors of 165 can be found as:
165 is a composite number because it has factors other than 1 and itself. It is not a prime number.
The 8 factors of 165 are 1, 3, 5, 11, 15, 33, 55, and 165. The factor pairs of 165 are 1 x 165, 3 x 55, 5 x 33, and 11 x 15.
The proper factors of 165 are 1, 3, 5, 11, 15, 33, and 55.
The prime factors of 165 are 3, 5, and 11.
Answer: On comparing the two, we can see that 5 is the common prime factor of both 130 and 165.