What two rational expressions sum to 2x+3/x^2-5x+4
Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
Answers
Answer:
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]
Step-by-step explanation:
Given the rational expression: [tex] \frac{2x + 3}{x^2 - 5x + 4} [/tex], to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
[tex] x^2 - 5x + 4 [/tex]
[tex] x^2 - 4x - x + 4 [/tex]
[tex] (x^2 - 4x) - (x + 4) [/tex]
[tex] x(x - 4) - 1(x - 4) [/tex]
[tex] (x- 1)(x - 4) [/tex]
Thus, we now have: [tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex]
Step 2: Apply the concept of Partial Fraction
Let,
[tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex] = [tex] \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]
Multiply both sides by (x - 1)(x - 4)
[tex] \frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) [/tex] = [tex] (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4) [/tex]
[tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
Step 3:
Substituting x = 4 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
[tex] 2(4) + 3 = A(4 - 4) + B(4 - 1) [/tex]
[tex] 8 + 3 = A(0) + B(3) [/tex]
[tex] 11 = 3B [/tex]
[tex] \frac{11}{3} = B [/tex]
[tex] B = \frac{11}{3} [/tex]
Substituting x = 1 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
[tex] 2(1) + 3 = A(1 - 4) + B(1 - 1) [/tex]
[tex] 2 + 3 = A(-3) + B(0) [/tex]
[tex] 5 = -3A [/tex]
[tex] \frac{5}{-3} = \frac{-3A}{-3} [/tex]
[tex] A = -\frac{5}{3} [/tex]
Step 4: Plug in the values of A and B into the original equation in step 2
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]
Answer:
Step-by-step explanation:
Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
Thus, we now have:
Step 2: Apply the concept of Partial Fraction
Let,
=
Multiply both sides by (x - 1)(x - 4)
=
Step 3:
Substituting x = 4 in
Substituting x = 1 in
Step 4: Plug in the values of A and B into the original equation in step 2
Step-by-step explanation:
Related Questions
Maylin is mailing a package that has the
size shown below. What is the volume
of the package? Write the expression
you used to find the volume.
7 in.
Area of base:
54 in.2
Answers
Answer:
V=378 inch³
Step-by-step explanation:
The package is in the shape of a cuboid. The volume of a cuboid is given by :
V = lbh
l=length, b=breadth and h=height
Area of base = 54 inch²
Height of box, h = 7 in
It means that, volume of the package is :
V = 54 × 7
V=378 inch³
So, the volume of the package is 378 inch³.
what’s the square root of 5 times the square root of 5 ??
Answers
Answer:
5
Step-by-step explanation:
Whenever you multiply square roots that have the same number inside the radicand, you get the number under the radicand. For example, the square root of 4 squared will equal four. Similarly, you are simply squaring the square root of 5, so you should get 5 as your answer.
-5x+7x+8=1+3x im am looking for what makes this equation true
Answers
Answer:
x=7
Step-by-step explanation:
Start with the left side
-5x+7x+8
combine like terms
2x+8=1+3x
subtract 2x from both sides to get 8=1+x
subtract 1 from both sides to get 7
put the variable on the left
x=7
Hope this helps :-)
Given that f(n) = 8n – 3 and g(n) = 3n - 10, evaluate the following functions with the indicated
values.
1. f(5) = 2. g(5) =
4. g(-4) =
5. f(0) =
6. g(0)=
7. f(1) =
8. g(1) =
Answers
Answer:
1. 37
2. 5
4. -22
5. -3
6. -10
7. 5
8. -7
Step-by-step explanation:
Given the functions:
[tex]f(n) = 8n - 3 \\g(n) = 3n - 10[/tex]
To find:
[tex]1. f(5) = ?\\2. g(5) =?\\4. g(-4) =?\\5. f(0) =?\\6. g(0)=?\\7. f(1) =?\\8. g(1) =?\\[/tex]
Solution:
Let us put the given values one by one in the functions [tex]f(n), g(n)[/tex] to find the various values required.
1. [tex]f(5)[/tex] means to replace the value of [tex]n[/tex] with 5 in [tex]f(n)[/tex]:
[tex]f(5) = 8\times 5 - 3 = \bold{37}[/tex]
2. [tex]g(5)[/tex] means to replace the value of [tex]n[/tex] with 5 in [tex]g(n)[/tex]:
[tex]g(5) = 3\times 5 - 10 = \bold{5}[/tex]
4. [tex]g(-4)[/tex] means to replace the value of [tex]n[/tex] with -4 in [tex]g(n)[/tex]:
[tex]g(-4) = 3\times -4 - 10 = \bold{-22}[/tex]
5. [tex]f(0)[/tex] means to replace the value of [tex]n[/tex] with 0 in [tex]f(n)[/tex]:
[tex]f(0) = 8\times 0 - 3 = \bold{-3}[/tex]
6. [tex]g(0)[/tex] means to replace the value of [tex]n[/tex] with 0 in [tex]g(n)[/tex]:
[tex]g(0) = 3\times 0 - 10 = \bold{-10}[/tex]
7. [tex]f(1)[/tex] means to replace the value of [tex]n[/tex] with 1 in [tex]f(n)[/tex]:
[tex]f(1) = 8\times 1 - 3 = \bold{5}[/tex]
8. [tex]g(1)[/tex] means to replace the value of [tex]n[/tex] with 1 in [tex]g(n)[/tex]:
[tex]g(1) = 3\times 1 - 10 = \bold{-7}[/tex]
1. A standard dice has 6 sides with the numbers 1-6 on it. What is the probability of rolling a 4 on a
standard dice?
Answers
Answer:
1/6
Step-by-step explanation:
There are six sides on a die and only one of them has a 4
P( 4) = number of sides with a 4/ total number of sides
= 1/6
Answer:
P (4) = 1/6
Step-by-step explanation:
The probability can be found by creating a fraction. The numerator is the number of favorable outcomes and the denominator is the total number of outcomes.
P (4) = sides with a 4 / total sides
The standard dice has 6 sides numbered 1 through 6.
P (4) = sides with a 4/ 6
Only one side on the cube has a 4.
P (4) = 1/6
This fraction cannot be simplified further, so it is our final answer.
The probability of rolling a 4 on a standard dice is 1/6
PLEASE ANSWER ASAP!!! THIS IS MY LAST OF POINTS PLEASEEE!!! Solve for X. 15=7x+3-5x X=_(simplify your answer)
Answers
15= 7x-5x + 3
15 = 2x + 3
-3 + 15 = 2x
12=2x
12/2 = 2x/2
6=x
hi pls help urgent <3
Answers
Answer:
-548
Step-by-step explanation:
Let x be the number
Plug x in: x - -150 = -398Simplify: x + 150 = -398Subtract 150 from each side, so it now looks like this: x = -548I hope this helps!
A bakery the price of the cake is nine dollars more than the price of a pie. One day the bakery sold 8 cakes and 14 pies for a total of $402. The system of equations below can be used to find c the cost in dollars of a cake and P the cost in dollars of a pie. What is the price of a cake?
Answers
Answer:
The price of the cake is $24 and the price of the Pie is $15
Step-by-step explanation:
Given
Represent price of Cake with C and Price of Pie with P
[tex]C = 9 + P[/tex]
Cakes sold = 8
Pies sold = 14
[tex]Total = \$402[/tex]
Required
Determine C and P
To represent the cakes and pies sold, we have the following expression
[tex]8C + 14P = 402[/tex]
Substitute 9 + P for C
[tex]8(9+P) + 14P = 402[/tex]
Open the bracket
[tex]72 + 8P + 14P = 402[/tex]
Collect Like Terms
[tex]8P + 14P = 402 - 72[/tex]
[tex]22P= 330[/tex]
Divide both sides by 22
[tex]P = \frac{330}{22}[/tex]
[tex]P = 15[/tex]
Recall that
[tex]C = 9 + P[/tex]
[tex]C = 9 + 15[/tex]
[tex]C = 24[/tex]
Hence, the price of the cake is $24 and the price of the Pie is $15
WILL MARK BRAINLIEST
NEED HELP ASAP
Solve for x: 3/ 4 x+ 1 /4 =2x
Answers
Answer:
X=1/5
Step-by-step explanation:
Please see the attachment.
Answer:
Maybe? kinda confused
Step-by-step explanation:
3/4x+1/4=2x
-3/4 -3/4
x+1/4=1 1/4
-1/4 -1/4
x=1
How would I create a graph for this equation? The equation is c=4.95+3.99b
Answers
Answer:
plot two points and draw a line through them
Step-by-step explanation:
The graph is created for this the same way it is for any function: find some points on the graph, plot them, and draw an appropriate curve through them.
Since this is a linear equation, the graph is a straight line. Only two points are needed to allow you to plot the entire line.
For b=0, the point is (b, C) = (0, 4.95)
For b=5, the point is (b, C) = (5, 24.90)
The graph might look like the attached.
_____
For b=5, the equation gives ...
C = 4.95 +3.99(5) = 4.95 +19.95 = 24.90
Subtract 10x + 7y from -15x+6y
Answers
Step-by-step explanation:
= -15x+6y-(10x+7y)
= -15x+6y-10x-7y
= -25x-y.
Answer: 4
Step-by-step explanation:
10 + 7 = 17
15 + 6 = 21
21 - 17 = 4
I don’t know but wanted to try it might not be right
If n represents a number, then write an
expression for two less than one fourth of n.
Answers
Answer:
n = n/4 - 2
Step-by-step explanation:
n = 1/4 * n - 2
= n/4 - 2
answer this 2(3^2 + 4^2) = ?
Answers
Answer:
50
Step-by-step explanation:
2(3^2+4^2)=
3^2/(3x3) = 9
4^2/(4x4) = 16
9+16=25
so.... rewritten it is
2(25)= or 2 x 25= 50
what is 1.5g - 10 + 6.5g - 3 simplified?
Answers
The simplified expression of 1.5g - 10 + 6.5g - 3 is 8g - 13.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers with each other called subtraction.
As per the given,
1.5g - 10 + 6.5g - 3
Bring near of likely terms,
1.5g + 6.5g - 10 - 3 = 8g - 13
Hence "The simplified expression of 1.5g - 10 + 6.5g - 3 is 8g - 13".
To learn more about the arithmetic operators,
brainly.com/question/25834626
#SPJ2
-2x + 4x = -4 + 0
What is the answer?
Answers
Answer:
x = -2
Step-by-step explanation:
-2x + 4x = -4 + 0
2x = -4
2x/2 = -4/2
x = -2
Hope this helps.
Answer:
The answer is -2
Step-by-step explanation:
You add the 4x to the -2x to get 2x, then you add -4 to zero to get -4. You are then left with 2x=-4 meaning that x would be -2
Please help me qwq In a reflection, what are corresponding angles?!
Answers
Answer: When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. Example: a and e are corresponding angles. When the two lines are parallel Corresponding Angles are equal.
30 seconds of 2.5 mins in percentage
Answers
Answer:
20%
Step-by-step explanation:
2.5 min =(60×2.5)sec=150 sec
30sec to 150sec=30×100/150=20%
Answer:
20 %
Step-by-step explanation:
2.5 mins = 150 sec
30 sec of 150 sec in % = 30/150 × 100
= 20 %
On Novenber 4, your bank statement shows a balance of $2,253.18. Your checkbook shows a balance of $2,324.34. If there are outstanding checks in the amounts of $105.50 and $158.10, deposits in transit amount to $605.27, account earnings of $68.51 and there is a service charge of $5.00. Determine the Adjusted Checkbook Balance and the Adjusted Statement Balance.
Answers
Answer:
The final answer is "$2387.85 and $2594.85".
Step-by-step explanation:
Given values:
The bank statement balance= $2,253.18
The checkbook balance = $2,324.34
outstanding check amounts= $105.50 and $158.10
transit amount= $605.27
account earnin(credits)= $68.51
service charge= $5.00
Adjusted Checkbook Balance =?
Adjusted Statement Balance=?
Adjusted the Checkbook Balance:
checkbook balance = $2,324.34
[tex]\text{total checkbook balance = checkbook balance+ credits}\\[/tex]
[tex]= \$ 2,324.34+ \$ 68.51\\\\= \$ 2392.85[/tex]
[tex]\text{ Adjust check book balance= total checkbook balance - servicec charge}[/tex]
[tex]= \$2392.85 - \$5.00\\\\= \$ 2387.85[/tex]
Adjusted the Statement Balance:
bank statement balance= $2,253.18
[tex]\text{total Statement balance = bank Statement balance+ transit amount}\\[/tex]
[tex]= \$ 2,253.18+ \$ 605.27\\\\= $ 2,858.45[/tex]
[tex]\text{outstanding check amounts = $105.50+ $158.10}[/tex]
[tex]= \$263.60[/tex]
[tex]\text{ Adjust statement balance= total statement balance - outstanding check amount }[/tex] [tex]= \$ 2,858.45 - \$263.60\\\\= $ 2,594.85[/tex]
¿Cuál es la intersección con el eje y de la gráfica de la ecuación? y = X 2 - 2 X + 3?
Answers
Answer:
1
Step-by-step explanation:
la respuesta sería un por que si multiplicas el 2 y luego más tres te da un resultado como uno
Answer:
Step-by-step explanation:
One positive number is 6 times another number. The difference between the two numbers is 205. Find the numbers. (Enter your answers as a comma-separated list.)
Answers
Answer:
Hence the positive numbers are 246, and 41
(246, 41)
Step-by-step explanation:
From the question,
One positive number is 6 times another numberLet the first positve number be [tex]x[/tex]
and the other number be [tex]y[/tex]
Hence,
[tex]x = 6y[/tex] ....... (1)
Also,
The difference between the two numbers is 205That is,
[tex]x - y =205[/tex] ........(2).
To solve for the two unknowns, substitute the value of [tex]x[/tex] in equation (1) into equation (2).
Since,
[tex]x = 6y[/tex]
Then
[tex]x - y =205[/tex] becomes
[tex](6y) - y =205\\[/tex]
Then,
[tex]6y - y = 205\\5y = 205\\[/tex]
Divide both sides by 5
[tex]\frac{5y}{5} = \frac{205}{5} \\ y = 41\\[/tex]
∴ the value of [tex]y[/tex] is 41
Now, substitute the value of y into equation (1) to find [tex]x[/tex]
Then,
[tex]x = 6y[/tex] becomes
[tex]x = 6(41)\\x = 246\\[/tex]
∴ the value of [tex]x[/tex] is 246
Hence the positive numbers are 246, and 41
(246, 41)
mZAOB = 6x- 12°
mZBOC = 3x+ 30°
Find mZAOB:
Answers
Answer:
36°
Step-by-step explanation:
I’m assuming <AOC is a right angle.
6x-12+3x+30=90
9x+18=90
9x=90-18
9x=72
x=8
<AOB=6x-12=6*8-12=48-12=36°
A lot is 50 m by 32 m. A house 27 m by 9 m is built on the lot. How much area is left over?
Answers
Answer:
1357 sq.m
Step-by-step explanation:
50*32= 1600
27*9= 243
Area left = 1600 - 243 = 1357
A student has these scores on their assignments. The teacher is considering dropping
a lowest score. What effect does eliminating the lowest value, 0, from the data set have
on the mean and median?
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
(A)What is the five-number summary for the data 2,2,4,4,5,5,6,7,9,15?
(B)When the maximum, 15, is removed from the data set,what is the five-number summary?
this is one of my math questions i need help on!
Answers
dude google works search it up sorry bro just needs some points you get it raight
Step-by-step explanation:
The number of books Jason reads each week is inversely proportional to the number of hours he spends with his friends if Jason read three books and spent four hours with his friends one week how many books does he read during the week in which he spent six hours with his friends
Answers
Answer:
Number of books= 2 books
Step-by-step explanation:
number of books Jason reads each week is inversely proportional to the number of hours
Let books be x
Let hours be y
X= k/y
Where k is constant of proportionality
Jason read three books and spent four hours
3= k/4
3*4= k
12= k
So
X= 12/y
If he spent six hours
Number of books x
X= 12/6
X= 2 books
Enter the sum of numbers as a product of their GCF. 75 + 30 The sum of the numbers as a product of their GCF is
Answers
Answer: 75+30 = 15 x 7
Step-by-step explanation:
The given expression is 75+30 (=105) which defines the sum of 75 and 30.
Prime factorization of 75 and 30 are as below:
75 = 5 x 5 x 3
30 = 5 x 3 x 2
GCD (75,30) = 5x 3 = 15 [Note: GCD = Greatest common divisor]
Consider 75+30 = (15 x 5) + (15 x 2) [75 = 15 x 5 and 30= 15 x 2]
= 15 (5+2) [taking 15 as common ]
= 15 x (7)
(=105)
So, 75+30 which is sum of the numbers and it is expressed as 15 x 7 which a product of their GCF.
the tripled product of 12 and a number is 102. what is the number
Answers
Answer:
Another number is 28
Step-by-step explanation:
Given:
Number = 12
Another number = x
The tripled product = 120
Find:
Number
Computation:
3(x + 12) = 120
x + 12 = 40
x = 40 - 12
x = 28
Another number is 28
*PLEASE ANSWER, DIFFICULT QUESTION, ASAP* An ice cream machine offers three flavors: vanilla, chocolate, and strawberry. Each flavor can be served as a milkshake, in a cone, or in a cup. This is a tree diagram that represents the probability of customers choosing the different ice cream options.
What is the value of Z?
a.)0.2
b.)0.45
c.)0.4
d.)0.35
Answers
Answer:
What was it?
Step-by-step explanation:
I NEED HELP WITH THESE RNNNN!!!!!!!
Answers
Answer:
Step-by-step explanation:
Given: -3(2x + 7) = -29 – 4x; Prove: x = 4
Answers
Answer:
See steps below
Step-by-step explanation:
-3(2x+7)=-29-4x
Use the distributive property
-6x-21=-29-4x
Add 21 to each side
-6x=-8-4x
Add 4x to both sides
-2x=-8
Divide by -2
x=4
Write the sentence as an equation. A number added to -6 is -33
Answers
Answer:
x+(-6)= -33
hope that helps : )
Answer: x+-6=-33
Step-by-step explanation: The x is a variable which is added to -6 which equals -33.