(x-5) divided by (x^2+3x-40)
Answers
Answer:
1/ x +8
*The 1 over x + 8
Answer:
[tex]\frac{1}{x+8}[/tex]
Step-by-step explanation:
Here is your original equation:
[tex]\frac{x-5}{x^{2} +3x-40}[/tex]What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to [tex]x-5[/tex] later):
[tex]x^{2} +3x-40[/tex]
Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.
Let's begin building our expressions. We know that [tex]x^{2}[/tex] has an exponent of 2. When variables are multiplied, the exponents are added, meaning that [tex]x*x=x^{2}[/tex]. (Or [tex]x^{1} + x^{1} =x^{2}[/tex] , the 1s just don't show)
We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.
[tex]x^{2} +3x-40 = (x+)(x-)[/tex]
Next, let's look at the factors of 40:
1 and 40 2 and 20 4 and 10 5 and 8
Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!
[tex]8-5=3[/tex]In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in [tex]3x[/tex]. Therefore, [tex]8(-5)=-40[/tex].
[tex]x^{2} +3x-40 = (x+8)(x-5)[/tex]Now let's go back to our original equation and substitute our old expression with the new one:
[tex]\frac{x-5}{(x+8)(x-5)}[/tex]Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a [tex]\frac{1}{1}[/tex].
[tex]\frac{x-5}{(x+8)(x-5)}[/tex] = [tex]\frac{1}{x+8}[/tex]Therefore, your simplified answer is [tex]\frac{1}{x+8}[/tex] !
Here's the whole process:
[tex]\frac{x-5}{x^{2} +3x-40} \\\\(x+?)(x-?)\\\\40:\\1, 40\\2, 20\\4, 10\\5, 8\\\\8-5=3 \\(8x-5x=3x)\\\\(x+8)(x-5)\\\\\frac{x-5}{(x+8)(x-5)}=\frac{1}{x+8} \\\\\frac{1}{x+8}[/tex]
To check your answer, confirm your expressions using the box method attached.
I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!
Related Questions
I WILL GIVE YOU BRAINLIEST!!!!!!
Which of the following is equivalent to –(–5.25)?
–5
5
5.25
–5.25
Answers
Step-by-step explanation:
The decimal number 5.25 is equal to the fraction 21/4.
HELP PLEASE
in order!!!
Answers
Answer:
m<6=54 m<4=126
Step-by-step explanation:
Last month, Juan ate 6 apples, 7 bananas, 4 peaches, and
5 oranges. Write the ratio of Peaches to the total number
of pieces of fruit Juan ate last month as a fraction in
simplest form.
Answers
Answer:
4/18
Step-by-step explanation:
A cyclist travels 10 km from home to the park.
She leaves home at 12:20 and arrives at the park at 12:50.
What is her average speed in km/h?
Answers
Answer:
20 km/h
Step-by-step explanation:
the total time is 0.5 hours as the cyclist travels for 30 minutes
the formula for speed is distance travelled divided by time taken which gives us 20 km/hr
A local hamburger shop sold a combined total of 591 hamburgers and cheeseburgers on Tuesday. There were 59 fewer cheeseburgers sold than hamburgers
On tuesday how much did they sell
Answers
Answer:
On Tuesday
591 burgers are sold.
Some are hamburgers and some are cheeseburgers.
59 fewer cheeseburgers sold than hamburgers.
Number of cheeseburgers --> x
Number of hamburgers --> y
x+y= 591 --> x = 591-y
x = y-59
so
591-y = y-59
-2y = -650
y = 325
so
x = 325-59
x =266
The hamburger shop sold a combined total of 591 hamburgers and cheeseburgers on Tuesday.
Let's represent the number of hamburgers sold as "H" and the number of cheeseburgers sold as "C." From the information given, we have two equations:
1. H + C = 591 (The combined total of hamburgers and cheeseburgers sold on Tuesday was 591).
2. C = H - 59 (There were 59 fewer cheeseburgers sold than hamburgers).
Now, we can use substitution to solve for the number of hamburgers: Substitute the value of C from the second equation into the first equation:
H + (H - 59) = 591
Now, combine like terms:
2H - 59 = 591
Next, isolate the term with H:
2H = 591 + 59
2H = 650
Now, solve for H:
H = 650 / 2
H = 325
So, they sold 325 hamburgers on Tuesday. To find the number of cheeseburgers sold, use the second equation:
C = H - 59
C = 325 - 59
C = 266
They sold 266 cheeseburgers on Tuesday. To find the total sales, add the number of hamburgers and cheeseburgers: Total sales = 325 (hamburgers) + 266 (cheeseburgers) = 591.
To know more about combined total:
https://brainly.com/question/31657570
#SPJ2
Can someone plz help really quickly!? Thank you! Marking brainlyest to to the first and correct answer!! Worth a lot of points to!!
Answers
Answer:
I believe its A. 7/16 inches per hour
Step-by-step explanation:
This is wrong don't put this
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
Answers
Answer:
Step-by-step explanation:
y=1/2-5x
Answer:
y = -1/3x - 5Step-by-step explanation:
Using points on the graph to get the equation
Slope intercept form:
y = mx + bFrom the graph, point (0, -5) we can see y-intercept is b = -5
An calculating the slope using two points (-6, -3) and (6, -7):
m = (-7 - (-3)) / (6 - (-6)) = -4 / 12 = -1/3So the line is:
y = -1/3x - 5Please help me I will really appreciate it!!!
Answers
U would subtract a^2 then square both sides to isolate the variable
Which answer choice shows 12.444 rounded to the nearest half?
A. 11
B. 11.5
C. 12
D. 12.5
Answers
Answer:
C. 12
Step-by-step explanation:
Remember 0 to 4 turn it back
5 or above give it a shove.
Since 12.444 is around 0 to 4.
We can round that to 12.
Answer:
C.12
Step-by-step explanation:
Rounding a number involves replacing the number with an approximation of the number that results in a shorter, simpler, or more explicit representation of said number based on specific rounding definitions. For example, if rounding the number 2.7 to the nearest integer, 2.7 would be rounded to 3.
I participated in a math competition but I did not do very good. Does anybody have some tips?
Answers
18- 8x = 8 + 3(1 - 3x)
Work shown please!
Answers
Answer
7 = -x
Step-by-step explanation:
18- 8x = 8 + 3(1 - 3x)
18- 8x = 8 +3-9x
18- 8x = 11 - 9x
7- 8x = -9x
7 = -x
Answer:
x=-7
Step-by-step explanation:
step by step in picture.
What is the inverse of the function f(x) = 2x - 10?
Answers
Answer:
[tex]\huge\boxed{f^{-1}(x)=\dfrac{1}{2}x+5}[/tex]
Step-by-step explanation:
[tex]f(x)=2x-10\to y=2x-10\\\\\text{exchange x to y and vice versa}\\\\x=2y-10\\\\\text{solve for}\ y\\\\2y-10=x\qquad|\text{add 10 to both sides}\\\\2y-10+10=x+10\\\\2y=x+10\qquad|\text{divide both sides by 2}\\\\\dfrac{2y}{2}=\dfrac{x}{2}+\dfrac{10}{2}\\\\y=\dfrac{1}{2}x+5[/tex]
HELP PLEASEEEEEEE ASP!!
WILL GIVE BRAINLIEST ❤️
Find the slope of the line passing through the given
points using the slope formula. Describe the slope as
positive, negative, zero, or undefined.
(-7, -18) and (-7,-4)
Answers
Answer:
Step-by-step explanation:
Slope formula= rise over run, or y2-y1 over x2-x1
y2=-4 y1=-18 x2=-7 x1=-7
-4-(-18)/-7-(7)
-22/-14 negative
Answer:
7/11
Step-by-step explanation:
the slope is positive. tell me what happens
Sahil has a fish tank in the shape of a cuboid, as shown in the diagram
Answers
Answer:
12
bcz he can't put a 0.725 fish so it will be rounded up back to 12
The greatest number of neon tetra fish he puts in the tank is 12.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
Sahil has a fish tank in the shape of a cuboid, as shown in the diagram.
The tank is 55 cm wide, 28 cm long and height is 33 cm.
And the surface of the water in the tank is 3 cm below the top of the tank.
That means,
to determine the volume,
So, the volume of cuboid
= 55 x 28 x 33
= 50820 cubic centimeters.
And we know 1000 cubic centimeters is 1 liter of water.
So, 50820 = 50.820
And divide by 4
We get the greatest number of neon tetra fish he puts in the tank.
50.820 / 4
= 12.705
≈ 12
Therefore, 12 is the required number for neon tetra fish.
To learn more about the cuboid;
https://brainly.com/question/29568631
#SPJ2
PLEASE ANSWER QUICKLY
Find the value of f(-142) for the function below.
f(x) = -0.2(x + 223)
A.
251.4
B.
-186.6
C.
81
D.
-16.2
Answers
you replace X with -142 and get -0.2 (142 + 223)
20 – 3n > 7n show work
Answers
Answer:
n>5
Step-by-step explanation:
move the 20 onto the other side of the > by subtracting 20 on the left side and adding 20 on the right side
now you have
-3n>7n-20
move the 7n onto the other side the same way. subtract 7n from one side and add it to -3n. now you have
4n>20
this is called adding similar terms or inverse operations what ever you wanna call it. Now you divide N by 4. This is because 4n can be simplified to 4×N and the opposite of multiplication is division. you do the same on the other side.
n/4>20/4.
you are left with n>5
Answer:
n<2
Step-by-step explanation:
Subtract 20 from both sides 20-3n-20>7n-20
Simplify -3n>7n-20
Subtract 7n from both sides -3n-7n>7n-20-7n
Simplify again -10n>-20
multiply both sides by -1 (-10n)(-1) < (-20)(-1)
Simplify 10n<20
Divide both sides by 10 Then you get your answer
Graph the linear equation x=4.
Answers
A linear equation has only more than one additional, that may be expressed as [tex]\bold{ax + by = c}[/tex], and the further discussion can be defined as follows:
In this, No factor has been raised the power which is greater than one or utilized as the denominator of a fraction. When we discover pairs of values that satisfy a linear model and plot them on a coordinate grid, all the points fall on the same line.Please find the attached file of the graph.
Learn more:
brainly.com/question/576841
5 to the 2 power
help
Answers
Answer:
25
Step-by-step explanation:
5²=25
Answer:
25
Step-by-step explanation:
it is like 5 times 5
PLEASEEEE HELPPPPPP WIll add extra pointtss
Answers
Explanation :-
As B is midpoint of SR :- SB = BR and if. SR = 6x then SB = 3x
AC parallel SR ( MID POINT THEOREM )
Hence AC parallel SB
Similarly , AB parallel CS (MID POINT THEOREM)
So ABCS is a parallelogram
And we know that in parallelogram opposite sides are equal so AC = SB
So now we have AC = 5x - 8 and SB = 3x
So, 5x - 8 = 3x
5x - 3x = 8
2x = 8
x = 4
Which of the following equations is written in factored form?
O y= 2x² + 3x – 8
o y= 3 (2 + 5) (2 – 2)
o y=-2(1 + 5)2 – 2
O y = 3.2 - 5
Need help please!!
Answers
Answer:
Option B is correct option.
Step-by-step explanation:
We need to identify equations written in factored form.
Factored form: A factored form of expression is an expression broken down into a product of its factors.
In the given options A, C and D we don't have product of factors.
Only option B consists of product of factors.
So, Option B is correct option.
HURRY PLEASE HELP ME!!!This graph shows a bicyclist moving at a constant rate. Write and equation for bicycle rider A.
Answers
Answer:
y= 30x
tep-by-step explanation:
HELPPPPPPP ASAPPPPPP PLEASEEEE
Answers
70
f(-4)=5(2-3(-4)
f(-4)=10+60
f(-4)=70
qual é 33⅓% de 108?
Answers
= 36 (esta é a resposta final, eu não sei se você realmente precisa dela)
What is the Zero of f ?
Answers
Answer:
(-1, 0)
Step-by-step explanation:
Hi... can you tell me is this formula is right or wrong??
Answers
Answer:
this formula is right
The diagram below represents which percent?
An area model with 32 shaded sections and 68 unshaded sections.
3.2%
8%
32%
42%
Answers
Answer:
32 percent
Step-by-step explanation:
32 plus 68 =100
32 divided by 100 equals .32 or 32 percent
Answer:
Your answer is C, 32%
Step-by-step explanation:
It is 32% because if there is 32 shaded and 68 unshaded you would count the ones that are shaded which would be 32%.
5) y=-2
4x – 3y = 18
This
Answers
Answer:
x=3
Step-by-step explanation:
if y is -2, 3*-2 =-6, 4x-(-6) = 4x+6=18
18-6=12
12/4=3
x=3 I hope you learned something
Find two consecutive integers whose sum is 73. Which of the following equations could be used to solve the problem?
A. 2x = 73
B. 2 x + 2 = 73
C. x^2 + 1= 73
D. 2x + 1 = 73
Answers
For which equations is the solution for x the same number?
i. 15 - X = -3
ii. x/2 + 6 = 15
iii. -1/3x - 5.7 = 0.3
O A. i and ii
O B. i and iii
O C. ii and iii
O D. i, ii and iii
O E. none of the questions
Answers
Answer:
A. i and ii
Step-by-step explanation:
i) 15 - x = -3
x=18
ii) x/2 + 6 = 15
x/2 = 9
x= 18
iii) -1/3x -5.7 = 0.3
-1/3x = 6
x = -18
Charles shooting basketballs during recess he made 30 baskets and miss 10 for a total of 40 shots at this rate how many baskets would he miss if he shot a total of eight times?
Please help
Answers
Answer:he would miss three times
Step-by-step explanation:because he missed once every 3 times so which would equal 2.5 which i will round up to 3 to get my answer.