Simplify the expression given below x^2+x-2/x^3-x^2+2x-2
Answers
Answer:
The simplest form is [tex]\frac{x+2}{x^2+2}[/tex]
Explanation:
The given is: [tex]\frac{x^2 + x-2}{x^3-x^2+2x+2}[/tex]
1- For the numerator:
[tex]x^2+x-2[/tex] can be factorized to give (x-1)(x+2)
2- For the denominator:
[tex]x^3-x^2+2x-2[/tex]
We will factor this using grouping
Take [tex]x^2[/tex] as a common factor from the first two terms and [tex]2[/tex] as a common factor from the last two terms
This will give us:
[tex]x^3-x^2+2x-2[/tex] [tex]=x^2(x-1) + 2(x-1)[/tex]
Now, take (x-1) as a common factor:
[tex]x^3-x^2+2x-2[/tex] = (x-1)(x²+2)
3- Finally, getting the simplest form:
[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}=\frac{(x-1)(x+2)}{(x-1)(x^2+2)}=\frac{x+2}{x^2+2}[/tex]
Hope this helps :)
The solution is [tex]\frac{x+2}{x^2+2}[/tex]
Step-by-step explanation:See the image attached
Related Questions
Point W(5, -6) is reflected across the line y = -x. Which of the following is the location of its image, W’.
(-5, -6)
(5, 6)
(-6, 5)
(6, -5)
Answers
(6, -5)
Key Concepts for Reflections:if (a, b) is reflected on the x-axis, the image is the point (a, -b)if (a, b) is reflected on the y-axis, the image is the point (-a, b)if (a, b) is reflected on the line y = x, the image is the point (b, a)if (a, b) is reflected on the line y = -x, the image is the point (-b, -a)(5, -6) --> (-5, 6)
Hope this helps!!
I'd right the key concepts for future reference!
:D
Answer:
(6,-5)
Step-by-step explanation:
Solve for x 34=-2x solve for x
Answers
Answer:
x = -17
Step-by-step explanation:
Divide both sides by two and get:
x = -17
Answer:
x=-17
Step-by-step explanation:
-2x=34
-2x/-2=34/-2
x=-17
I NEED HELP REALLY BAD!
Answers
The area is 168 yd²
Step-by-step explanation:The area of Trapezoid is given by
A= (a+b)/2 * h
Putting the values
A = (5+23)/2 * 12
A = 168 yd²
Answer:
A = 168 Square Yards
recognizing the no-solution case algebraically
need geometry help!!
Answers
Answer:
"The values for y are square roots of negative numbers"
Step-by-step explanation:
The steps shown are correct. But at the end we can see that we have to "take the negative square roots".
This means we have to take the square root of -1. In the real number system, we CANNOT take the square root of any negative number. Hence, there is NO SOLUTION to the system.
2nd answer choice, "The values for y are square roots of negative numbers", is right.
The following expression represents the density of an object that has a mass of m and a volume of V.
M/V
If a laptop has a volume of 2,850 cubic centimeters and a mass of 2,300 grams, what is the density of the laptop in G/cm3
A. 1 5/23
B.15/19
C. 1 11/46
D. 46/57
Answers
Final answer:
The density of the laptop is calculated by dividing the mass (2,300 grams) by the volume (2,850 cubic centimeters), resulting in a density of 0.807 g/cm³, which is approximately 46/57.
Explanation:
To find the density of the laptop in grams per cubic centimeter (g/cm³), we use the formula density = mass/volume. The mass of the laptop is given as 2,300 grams and the volume is given as 2,850 cubic centimeters. By substituting into the formula:
Density = Mass / Volume = 2,300g / 2,850cm³ = 0.807 g/cm³.
When expressed as a fraction in simplest form, this is approximately 46/57 (since 0.807 ≈ 46/57). Hence, the answer is D. 46/57.
Y=f(x) = -1x find f(x) when x= 0
Answers
f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.
To find the value of f(x) when x=0 for the function f(x) = -1x, substitute 0 for x:
f(0) = -1(0) = 0.
Therefore, f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.
Is 6(4x-5) equivalent to 3+22x-33-2x?
YES or NO?????
Show your work!
6(4x-5) 3+22x-33-2x
Answers
Answer:
NO
Step-by-step explanation:
To find if they are equivalent, we need to simplify them first.
Using the distributive property we get:
6(4x-5) = 24x - 30
In this case we need to combine like terms.
3 + 22x - 33 - 2x = 20x - 30
So now we can compare.
24x - 30 ≠ 20x - 30
So we can conclude that the two expressions are not equal because 24x - 30 and 20x - 30 are obviously not equal.
Answer:
Not equivalent
Step-by-step explanation:
We are given an expression [tex] 6 ( 4 x - 5 ) [/tex] and we are to check if it is equal to [tex] 3 + 22 x - 33 - 2 x [/tex] or not.
Evaluation the given expression first:
[tex] 6 ( 4 x - 5 ) = 24 x - 30 [/tex]
While adding the terms in [tex] 3 + 22 x - 33 - 2 x [/tex], we get:
[tex] 22 x - 2 x - 33 + 3 = 20 x - 30 [/tex]
[tex] 24 x - 30 \neq 20 x - 30 [/tex]
Therefore, [tex] 6 ( 4 x - 5 ) [/tex] is not equivalent to [tex] 3 + 22 x - 33 - 2 x [/tex].
During the spring and summer months, the Happy Home Motel sees a rise in travelers. The manager of the motel turned in this report of how many travelers stayed at the Happy Home Motel. Month Number of Travelers March 217 April 232 May 252 June 277 July 307 August ? If the Happy Home Motel continues to follow this pattern, how many travelers will stay during August?
Answers
Answer:
342
Step-by-step explanation:
Let's see the difference is each successive values:
232 - 217 = 15
252 - 232 = 20
277 - 252 = 25
307 - 277 = 30
As we can see, each month the increase is 5 more than previous months' increase. Clearly from the pattern we can surmise that the next month (August), it will increase by 35 from the value of July.
Number of visitors in August = Number of Visitors in July + 35 = 307 + 35 = 342
Answer:
342
Step-by-step explanation:
Kelsey is hiking from the woods to the lodge. She hikes past tree A (3 Miles) and B (4 Miles) in order to get to the lodge. How much distance should she have saved by going straight to the lodge from tree A ?
Answers
Answer:
1 mile
Step-by-step explanation:
The manager of a store that specializes in selling tea decides to experiment with a new blend.She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 600 pounds of the new blend. the selling price of the new blend is $4.50 per pound and there was something to be no difference in revenue from selling the new blend versus selling the other types. how many pounds of the Earl Grey tea and orange Pekoe tea are required?
Answers
Answer:
Earl Grey: 150 poundsOrange Pekoe: 450 poundsStep-by-step explanation:
Let "e" represent the number of pounds of Earl Grey tea required for the mix. Then (600-e) is the number of pounds of Orange Pekoe tea required. The total cost of the mix is ...
6·e + 4·(600 -e) = 4.50·600
2e = 600·(4.50 -4.00) . . . . . simplify, subtract 4·600
e = 300/2 = 150 . . . . . . . . . . divide by the coefficient of x
Required are 150 pounds of Earl Grey and 450 pounds of Orange Pekoe.
The amount of Earl Grey and Pekoe tea required for the new blend is :
150 pounds of Earl450 pounds of PekoePrice of new blend per pound = $4.50
Price per pound of Earl tea = $6
Price per pound of Pekoe tea = $4
Let :
Pound of Earl tea = a
Pound of Pekoe tea = b
Converting the information to Mathematical expressions :
a + b = 600 - - - (1)6a + 4b = 600(4.50)6a + 4b = 2700 - - - (2)From (1):
a = 600 - b
Put a = 600 in (2)
6(600 - b) + 4b = 2700
3600 - 6b + 4b = 2700
Collect like terms :
-6b + 4b = 2700 - 3600
-2b = -900
b = 900 ÷ 2
b = 450
Recall :
a = 600 - b
a = 600 - 450
a = 150
Therefore,
Pound of Earl tea required = 150Pound of Pekoe tea required = 450Learn more : https://brainly.com/question/11335251
find the height, round to the nearest hundredth
Area is 72units squared
Answers
Answer:
[tex]\large\boxed{h=10\dfrac{2}{7}}[/tex]
Step-by-step explanation:
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
We ahve b = 14 and A = 72. Substitute:
[tex]72=\dfrac{14h}{2}[/tex] multiply both sides by 2
[tex]144=14h[/tex] divide both sides by 14
[tex]h=\dfrac{144}{14}\\\\h=\dfrac{144:2}{14:2}\\\\h=\dfrac{72}{7}\\\\h=10\dfrac{2}{7}[/tex]
Factor the polynomial: x^3+x^2+x+1
Answers
Answer:
(x+1)(x2+1)
Step-by-step explanation:
Factor x3+x2+x+1
x3+x2+x+1
=(x+1)(x2+1)
also a great website for your problems is called mathpapa-algebra calculator
I need help plz show steps
Answers
Answer:
D
Step-by-step explanation:
We will solve the equation by using quadratic formula.
x= (-b ± √(b^2-4ac))/2a
The standard form of quadratic equation is:
ax^2+bx+c=0
So by comparing with the standard form, we get:
a=1
b= -4
c=18
Putting the values in the formula
x= (-(-4)± √((-4)^2-4(1)(18)))/2(1)
x = (4± √(16-72))/2
x = (4± √(-56))/2
The minus sign in square root will introduce the imaginary symbol.
x = (4± √(14*4*(-1)))/2
The minus 1 can be replace by the imaginary i => i^2 = -1
x = (4± √(14*2^2*i^2 ))/2
The terms with squares can be brought out of the square root
So,
x = (4± 2i√14)/2
Taking 2 as common
x = (2(2± i√(14)))/2
x = 2± i√14
how do I find the x value of this triangle? thank youuuu
Answers
answer = 42
if you look at the triangle you see a small square in the corner indicating that the triangle is a 90 degree angle, therefore all the sides add up to 90. With this knowledge just add the values of the two known sides, 18 and 30, which is 48 and then subtract 48 from 90 which gives you the value of x, 42
x ^2 + 18 ^2 = 30 ^ 2
x^2 = 30^2-18^2
x^2 = 900-324
x^2 = 576
x = 24 Answer
Fill in the blank so that the ordered pair is a solution of y=8x+3.
Answers
Answer:
11
Step-by-step explanation:
8 plus 3 i dunno know if it is forsure but yeah.
Find the value of y. Round answer to the nearest tenth if needed
Answers
Answer:
y = 54.1
Step-by-step explanation:
The big triangle is divided in two: one on the left and one on the right. Lets start working with the right one.
We know the right triangle is a right triangle with legs 24 and 36, so we can use Pitagoras to find the hypotenuse (h), in a way that:
24^2 + 36^2 = h^2
1872 = h^2
Applying sqr root in both sides:
h = 43.27
So, the hypotenuse measures 43.27 or 43.3.
Now lets do the same with the triangle of the right which legs are 36 and y, lets find it hypotenuse (g):
36^2 + y^2 = g^2
1296 + y^2 = g^2
Now we will pass to the large triangle, which is composed by the left and the right triangles and has legs of 43.3 and g, and the hypotenuse is 24+y. Lets apply Pitagoras:
43.3^2 + g^2 = (24+y)^2
1875 + 1296 + y^2 = 24^2 + 48y + y^2
3171 + y^2 = 576 + 48y + y^2
As we have y^2 in both sides we can eliminate them
3171 + = 576 + 48y
Now subtract 576 in both sides:
3171 -576 = 576 + 48y - 576
2595 = 48y
Divide both sides by 48:
2595/48 = 48y/48
54.1 = y
So, the large hypotenuse measures 54.1+24 = 78.1. Lets verify:
43.3 ^2 + 1296 + 54.2^2 = 6,108.53
And the sqrd root of 6,108.53 is approximately 78.1. Verified!!!!
So, we can confirm: y = 54.1
a fruit drink is made by mixing lemon juice, orange juice and lime juice in the ratio 5:2:3 james makes 400ml of the fruit drink how much lemon juice is used
Answers
Answer:
200ml
Step-by-step explanation:
5+2+3=10
400/10=40
Since lemon's ratio is 5, you multiply 40 by 5 to get 200.
What is the product of (2x^2+5x-3) and (3x+7)
Answers
Answer: option D.
Step-by-step explanation:
To solve this exercise you must apply the proccedure shown below:
- Apply the Distributive property (Remember that when you multiply two powers with the same base, you must add the exponents).
[tex]b^m*b^n=b^{(m+n)}[/tex]
- Add the like terms.
Therefore, you obtain that the product is:
[tex](2x^2+5x-3)(3x+7)=6x^3+14x^2+15x^2+35x-9x-21\\=6x^3+29x^2+26x-21[/tex]
An expression is defined as a set of numbers, variables, and mathematical operations. The product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The product of (2x²+5x-3) and (3x+7) can be done as,
(2x²+5x-3) × (3x+7)
= 3x(2x²+5x-3) + 7(2x²+5x-3)
= 6x³ + 15x² - 9x + 14x² + 35x - 21
= 6x³ + 29x² + 26x - 21
Hence, the product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ2
What is the slope of the line?
Answers
The slope is
[tex] - \frac{1}{3} [/tex]
What’s the standard form of the following polynomial?
(3x-2)(x-1)+2(x-5)^2-25
Answers
Answer
x^2 + 4x - 49
Step-by-step explanation:
you have to do PEMDAS first then add all the like-terms
hope this helps
p.s. you're pretty
How do I solve? (10y+9)-(4y-8)=
Answers
Answer:
(6y+17)
Step-by-step explanation:
1. Subtract 4y from 10y to get 6y
2. 9 is positive and 8 is negative but to subtract a negative is basically adding so you would add 9 to 8
3. You final equation would be (6y+17)
4. (10y+9)-(4y-8)= (6y+17)
Answer:
(10y + 9) - (4y - 8) = 6y + 17Step-by-step explanation:
[tex](10y+9)-(4y-8)\\\\=10y+9-4y-(-8)\\\\=10y+9-4y+8\qquad\text{combine like terms}\\\\=(10y-4y)+(9+8)\\\\=6y+17[/tex]
Gina has 400 records. If Johnny were to double the number of records that he now owns, he would still have fewer than Gina has.
Answers
Johnny currently owns fewer than 200 records.
Let's denote:
- \( x \) as the number of records Johnny currently owns.
Given:
- Gina has 400 records.
- Johnny would still have fewer than Gina has if he were to double the number of records he owns.
We can set up the following inequality:
[tex]\[ 2x < 400 \][/tex]
To find the maximum value of \( x \), we solve for it:
[tex]\[ x < \frac{400}{2} \]\[ x < 200 \][/tex]
So, Johnny currently owns fewer than 200 records.
The parallel lines on top of each other confuse me,any help?
Answers
Set it up.
Make the equations equal to 180° because they are on a straight line. And a straight line adds up to 180°
PERFORM THE MULTIPLICATION
(x–3)^2(x+3)^2
SOMEONE PLZZZ HELP
Answers
Answer:
81 is the answer
Step-by-step explanation:
Answer:
Hold up im solving it
Step-by-step explanation:
Is this answer ok, please help?
Answers
Answer:
Step-by-step explanation:
Unfortunately not...
The shape is a triangle, and the area formula is A=[tex]\frac{1}{2}[/tex]bh.
b = 5 ft.
h = 4 ft.
Therefore:
A = [tex]\frac{1}{2}[/tex](5)(4)=10ft
The area is a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than twice x. Round to the nearest whole number.
Answers
Answer:
The solution is [tex]x=6\ cm[/tex]
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]A=56\ cm^{2}[/tex]
so
[tex]56=LW[/tex] ------> equation A
[tex]L=x+2[/tex] -----> equation B
[tex]W=2x-5[/tex] -----> equation C
Substitute equation B and equation C in equation A
[tex]56=(x+2)(2x-5)[/tex]
solve for x
[tex]56=(x+2)(2x-5)\\56=2x^{2}-5x+4x-10\\2x^{2}-x-66=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2}-x-66=0[/tex]
so
[tex]a=2\\b=-1\\c=-66[/tex]
substitute in the formula
[tex]x=\frac{1(+/-)\sqrt{-1^{2}-4(2)(-66)}} {2(2)}[/tex]
[tex]x=\frac{1(+/-)\sqrt{529}} {4}[/tex]
[tex]x1=\frac{1(+)23} {4}=6[/tex]
[tex]x2=\frac{1(-)23} {4}=-5.5[/tex]
The solution is [tex]x=6\ cm[/tex]
[tex]L=6+2=8\ cm[/tex]
[tex]W=2(6)-5=7\ cm[/tex]
Please please please please PLEASE answer
Answers
Yea it’s the second one
what does trace of matrix mean explain with examples
Answers
Trace of a matrix is defined only for a square matrix . It is the sum of the elements on the main diagonal, from the upper left to the lower right, of the matrix
There are 5 red pens,3 blue pens and 2 green pens in a box. Gary takes at random a pen from the box and gives the pen to his friend. Gary then takes at random another pen from the box . work out the probability that both pens are the same colour.
please help
Answers
➷ Find the total number of pens:
5 + 3 + 2 = 10
The probability of taking a red the first time is 5/10
The probability of taking a blue the first time is 3/10
The probability of taking a green the first time is 2/10
If you want to take the same colored pen again, there would be 1 less of the total pen (as it hasn't been replaced) and there would be one less of that color (as one has already been taken)
Therefore:
The probability of taking a red again is 4/9
The probability of taking a blue again is 2/9
The probability of taking a green again is 1/9
Multiply the values for the same color together:
5/10 x 4/9 = 20/90
3/10 x 2/9 = 6/90
2/10 x 1/9 = 2/90
Add these values together:
20/90 + 6/90 + 2/90 = 28/90
Your answer is 28/90
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
how do I simplify 15x+42-8y+20-4x
Answers
Answer:
[tex]\large\boxed{15x+42-8y+20-4x=11x-8y+62}[/tex]
Step-by-step explanation:
[tex]15x+42-8y+20-4x\\\\\text{combine like terms}\\\\=(15x-4x)-8y+(42+20)\\\\=11x-8y+62[/tex]
You add like terms together.
Ex. You would add 15x and(-4x) together, giving you 11x
So to simplify it, you need to do 15x-4x, 42+20, and 8y would be left by itself since there are no like terms for 8y.
So the simplified version would be: 11x+62+8y