Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!
Answers
Answer:
x = √17 and x = -√17
Step-by-step explanation:
We have the equation:
[tex]\frac{3}{x + 4} - \frac{1}{x + 3} = \frac{x + 9}{(x^2 + 7x + 12)}[/tex]
To solve this we need to remove the denominators.
Then we can first multiply both sides by (x + 4) to get:
[tex]\frac{3*(x + 4)}{x + 4} - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}[/tex]
[tex]3 - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}[/tex]
Now we can multiply both sides by (x + 3)
[tex]3*(x + 3) - \frac{(x + 4)*(x+3)}{x + 3} = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}[/tex]
[tex]3*(x + 3) - (x + 4) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}[/tex]
[tex](2*x + 5) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}[/tex]
Now we can multiply both sides by (x^2 + 7*x + 12)
[tex](2*x + 5)*(x^2 + 7x + 12) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)[/tex]
[tex](2*x + 5)*(x^2 + 7x + 12) = (x + 9)*(x + 4)*(x+3)[/tex]
Now we need to solve this:
we will get
[tex]2*x^3 + 19*x^2 + 59*x + 60 = (x^2 + 13*x + 3)*(x + 3)[/tex]
[tex]2*x^3 + 19*x^2 + 59*x + 60 = x^3 + 16*x^2 + 42*x + 9[/tex]
Then we get:
[tex]2*x^3 + 19*x^2 + 59*x + 60 - ( x^3 + 16*x^2 + 42*x + 9) = 0[/tex]
[tex]x^3 + 3x^2 + 17*x + 51 = 0[/tex]
So now we only need to solve this.
We can see that the constant is 51.
Then one root will be a factor of 51.
The factors of -51 are:
-3 and -17
Let's try -3
p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0
Then x = -3 is one solution of the equation.
But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.
This means that we can take a factor (x + 3) out, so we can rewrite our equation as:
[tex]x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0[/tex]
The other two solutions are when the other term is equal to zero.
Then the other two solutions are given by:
x = ±√17
And neither of these have problems in the denominators, so we can conclude that the solutions are:
x = √17 and x = -√17
Related Questions
how many are right handed??
Answers
Answer:
40
Step-by-step explanation:
8) Circle each statement that is true.
:5>-8
-7>-4
-15-6
-3>2
:3<-9
10 >8
No links
Answers
Answer:
5>-8
10>8
hope this helps
The election committee for a candidate running for mayor randomly selects 100 women to complete a telephone survey. The women are asked to identify which mayoral candidate they are most likely to vote for in the upcoming election. Of the 100 women polled, 21 women chose not to answer and 51% indicated they would vote for candidate Smith. Based on these results, what can be INFERRED (inference) about the outcome of the election?
Answers
Answer:
Step-by-step explanation:
Can you help me, please?
Answers
Answer:
(5,27)
Step-by-step explanation:
parabolas are symmetrical around the vertex. therefore x axis crossing points are equidistant from the vertex.
f(x) cross x axis when x=2 and x=8
the mid point of 2 and 8 is 5.
f(5)=-3(5-2)(5-8)
f(5)=27
vertex=(5,27)
The perimeter of a rectangle is 76cm.
Its longest side has a length of 29cm.
State the length of the shortest side.
Answers
Answer:
The length would be 9cm
Step-by-step explanation:
Because the perimeter is 76, you have to add 29 to 29 which equals 58, then you have to subtract 58 from 76, which is 18. The last episode is divide 18 by 2 because re are two sides remaining. So answer would be 9. To check the answer you can add 29+29+9+9
Drag each sequence to show whether it is a linear function, an exponential function, or
not a function.
I will give you 20 brainiest points!! Please help.
Answers
Answer:
Step-by-step explanation:
From the picture attached,
Option A
From the given table,
Ratio of the 2nd value and 1st value = [tex]\frac{8}{4}=2[/tex]
Ratio of 3rd value and 2nd value = [tex]\frac{16}{8}=2[/tex]
There is a common ratio of 2.
Therefore, the given table will represent an exponential function.
Option B
Given recursive formula of the sequence is,
[tex]A_1=3[/tex]
[tex]A_n=5.A_{n-1}[/tex]
From this recursive formula sequence will be,
3, 15, 75, 375,.......
Therefore, it's an exponential function.
Option C
[tex]F_n=3n+17[/tex]
Given function is in the form of a linear function (y = mx + b),
Therefore, it's a linear function.
Option D
From the given table,
Difference between 2nd value to the 1st value = 8 - 4 = 4
Difference between 3rd value to the 2nd value = 12 - 8 = 4
Therefore, there is a common difference of 4 in each successive term to the previous term.
Hence, the given table represents a linear function.
Answer:
above me will also work for problems in the photo below
Step-by-step explanation:
I did the problem
I will give BRAINLIEST to WHOEVER GETS IT RIGHT and can you please tell me how you solve your answer!!!!!!!!!!!!!!
Find the output, k, when the input, x, is -5. k = 6x + 100
y=?
Answers
What does reduce mean and which scale factor could be an example of a reduction?
Answers
Answer:
The scale factor describes the size of an enlargement or reduction. For example, a scale factor of means that the new shape is twice the size of the original. Reduce means to make smaller, to lessen a amount.
Step-by-step explanation:
An example of a scale factor of reduction is 1:25
Enlarging scale means that the drawing is larger than the actual object. Hence the representative fraction will be greater than unity. For reducing scale the representative fraction is less than unity.
So now looking at 1:25, we see it's a reduction scaling because it's fraction is less than unity.
And what 1:25 means is that 1 on paper while the actual size of the object is 25
Drag tiles to match each fraction, decimal, or percent to an equivalent number
Answers
3/5= 0.60
9/50= 0.18
26%= 13/50
0.35= 7/20
how do i solve this?
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: x = 110
Explanation:
We can see that both the sides are equal because of the lines on the sides of the triangle. That means that the angle on the other side is also 35, we also know that the total amount of degrees in a triangle is 180
So now we can do this equation:
35 + 35 + x = 180
70 + x = 180
x = 110
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Step-by-step explanation:
[tex]180 - (35 \times 2) = \\ = 180 - 70 = \\ = 110[/tex]
The sum of internal angles of a triangle is 180 and we have a triangle with 2 lengths that are the same. We can say that also the other angle is 35,so the result is 110
HELPPP ASAP!!!
How many cubes are in this set?
Answers
Answer:
7
Step-by-step explanation:
7 because it's not asking for squares it asking for cubes
what is algbra
plz help me
Answers
Answer:
Algebra is math, like X, Y and all that.
Step-by-step explanation:
Answer:
algebra basically study of mathematical symbols and the rules governing the manipulation of these symbols as well.
find the missing measurement round your answer to the nearest tenth
Answers
Answer:
5
Step-by-step explanation:
Let, the unknown side be x.
1/2 × 6.6m × xm = 16.5m²
or, x= 33/6.6
x= 5
Which expression is equivalent to:1/2(x-8)+3x
Answers
Answer:
Step-by-step explanation:
1/2*(x-8)+3x=x/2-4+3x=3.5x-4
Hope this helps!
How many integers are greater than -6 and less than 10?
Answers
Answer:
15 integers
Step-by-step explanation:
To find the number of integers count from -6 to 10
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,9
that is 15 integers
if a bakery offers, tuna, and vegetable sandwiches on a plain or onion bagel how many possible sandwiches are there?
Answers
Answer:6
6
66
66
6
6
66
6
6
6
6
6
Step-by-step explanation:
6 sandies sir/ma'am have fun
This trapezoid-based right pyramid has a volume of 48m3 .What is the area of the base of the pyramid?
Answers
Answer
Explaination
Answer:
18
Step-by-step explanation:
i did my khan
What is the area of this triangle m2
19 m
22m
Answers
explain the steps needed to determine the value of the expression below. 3(y-4)-7y+3/4
Answers
Answer:
3(y-4)-7y+3/4=3y-(3)(4)-7y+3/4=-4y-12/1+3/4=-4y+(-12×4+3)/4=-4y-45/3
Sue knitted a scarf for her friend June that was also 4 feet long. After a month, the length of June's scarf could be represented by the expression 3/3 x 4. How did the length of June's scarf change? Explain.
Answers
Answer:
There was no change in the length of June's scarf, that is, the length of it remained the same.
Step-by-step explanation:
Since Sue knitted a scarf for her friend June that was also 4 feet long and, after a month, the length of June's scarf could be represented by the expression 3/3 x 4, to determine how did the length of June's scarf change you must perform the following calculation:
Month 1 = 4
Month 2 = 3/3 x 4 = 1 x 4 = 4
Therefore, as can be seen, there was no change in the length of June's scarf, that is, the length of it remained the same.
Joann decides to paint one wall in her room with blackboard paint. The wall has the dimensions shown. A can of paint covers 25 square feet. How many cans of blackboard paint does Joann need for the wall?
Answers
Answer:
6 cans of paint
Step-by-step explanation:
Help me please I need this ?!!!!!!
Answers
Answer:
16x^4 y^2
Step-by-step explanation:
GIVING BRAINLIEST!!!!
Which expression represents the following statement? Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2.
A) 7 x (6 + 3) − 4 ÷ 2
B) 7 + 6 − (3 ÷ 4) x 2
C) 7 + 6 ÷ 3 − (4 + 2)
D) 7 x (6 + 3) + 4 − 2
Answers
Answer:
B
Step-by-step explanation:
Answer:
I'm gonna say the answer should be A
Write an expression for “seven less than three halves of z”
Answers
Answer:
7- 3/2Z
thank for points and pick me brainliest pls!
how many solutions does this have -3x+3y=12
Answers
Answer:
infinite number of solutions
Step-by-step explanation:
graph y = x + 4 to see all the solutions
How can we eliminate the fraction?
y = - - 2
Answers
Answer:
multiply each term on both sides by 4
Step-by-step explanation:
PLZ HELP ME!!
I QILL GIVE BRAINLIEST
What is your best estimation for the number
of Trucks? How did you come up with that estimation?
no links
just answer and explain plzz
Answers
Answer:
200 trucks
Step-by-step explanation:
There's about 15 trucks in the 2nd row from the right. It looks to be about 1/2 the size of the rows to the left of it.
So based on that, I can assume, there are about 30 trucks in each of the 5 long rows, and both of the short rows would make up about another 30 trucks total. There are various trucks parked along the perimeter or between rows, so I estimated there would be about 20 of those based on 3 per row.
30 x 5 = 150 +30 = 180 + 20 = 200
How to multiple and divided fractions
Answers
Answer:
Search up on youtub.e "How to multiply and divide fractions"
Step-by-step explanation:
Answer:
Step-by-step explanation:
To multiply fractions, all you have to do is multiply the numerators and denominators and simplify the result. To divide fractions, you simply have to flip the numerator and denominator of one of the fractions, multiply the result by the other fraction, and simplify.
What type of triangle can an equilateral be?
Answers
Answer:
An acute triangle.
Step-by-step explanation:
There is a rule that if a triangle is equilateral, then it also must be acute. A right and obtuse triangle will always have a scenario where one of the sides is longer both of the other sides. And, if the triangle has at least one side longer than the other, it cannot be a equilateral triangle. Therefore, an equilateral triangle can also be an acute triangle. Hope this helps!
The Green family went camping one summer. The campsite charges $65.00 a day for the space and provides food for $8.00 a person per day. If the Green family went camping for 5 days and spent $525, how many people are there in the Green family?
Answers
Answer:
5 people
Step-by-step explanation: