Answers
Answer:
[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}\\=\frac{x^2+(2-1)x-2}{x^2(x-1)+2(x-1)}\\=\frac{x^2+2x-x-2}{(x-1)(x^2+2)}\\=\frac{x(x+2)-1(x+2)}{(x-1)(x^2+2)}\\=\frac{(x-1)(x+2)}{(x-1)(x^2+2)} \\=\frac{x+2}{x^2+2}\\So, ~last~option~is~the~correct~answer.[/tex]
The simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm \dfrac{\left(x^2+x-2\right)}{x^3-x^2+2x-2}[/tex]
[tex]\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{x^3-x^2+2x-2}[/tex]
[tex]\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-1\right)\left(x^2+2\right)}[/tex]
= (x + 2)/(x² + 2)
Thus, the simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.
Learn more about the expression here:
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Related Questions
What multiplication equation is represented by this picture? Explain.
Answers
Answer:
Step-by-step explanation:
Each circle represents : [tex]\frac{3}{5}[/tex] and 5 circles
5 * [tex]\frac{3}{5}[/tex]
Answer
Step-by-step explanation:
is Each circle represents : 3/2 and 5 circles
Change 8.94 into a fraction
Answers
Answer:
447 / 50
Step-by-step explanation:
447 / 50 Because if you divide it you will get 8.94 same answer
Answer:
inproper fraction would be 447/50 but the proper fraction would be 8 47/50
Martha will build a pool in her backyard. She wants the pool to have a rectangular shape
and to be five meters long and three meters wide. What would the area in Martha's backyard that will be lost due to the construction of the pool? There are 3.28084 feet in
one meter.
A 15 square feet
B 80.729 square feet
C 161.459 square feet
D 322.918 square feet
Answers
9514 1404 393
Answer:
C. 161.459 square feet
Step-by-step explanation:
In feet, the dimensions of the pool are ...
(5 m)(3.28084 ft/m) = 16.4042 ft
(3 m)(3.28084 ft/m) = 9.84252 ft
Then the area of the pool is ...
(16.4042 ft)(9.84252 ft) = 161.458666584 square feet
about 161.459 square feet
_____
Additional comment
If you consider that a square meter is slightly less than 11 square feet, the pool area can be estimated to be (5 m)(3 m)(11 ft²/m²) = 165 ft². This is close enough to point you to the correct answer choice.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Answers
Answer: it's b on edge
Step-by-step explanation:
Elena is designing a paint can with thickness ttt millimeters and height hhh centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1, point, 1 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0.2 + t+ 0.5h)cents, must be at most 12.2, point, 2 cents. Which system of inequalities best models the relationship between height and thickness?
Answers
Answer:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Step-by-step explanation:
Given
[tex]t= thickness[/tex]
[tex]h =height[/tex]
From the first statement, we have that:
[tex]t\ mm \ge 0.1 * h\ cm[/tex]
Convert mm to cm
[tex]t\ * 0.1*cm \ge 0.1 * h\ cm[/tex]
[tex]t\ *0.1 \ge 0.1 * h[/tex]
Divide both sides by 0.1
[tex]t \ge h[/tex]
From the second statement, we have that:
[tex]Cost \le 12.2[/tex]
Substitute 0.2 + t + 0.5h for Cost
[tex]0.2 + t + 0.5h \le 12.2[/tex]
Collect Like Terms:
[tex]t + 0.5h \le 12.2-0.2[/tex]
[tex]t + 0.5h \le 12.0[/tex]
So, the inequalities are:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Answer: it's a, the answer
Step-by-step explanation:
Simplify the expression below.
5(7x+4y+1)+2(8x+3y+6)
help plz!
Answers
Answer:
51x+26y+17
Step-by-step explanation:
Answer:
51x + 26y + 17
Step-by-step explanation:
distribute
5(7x) + 5(4y) + 5(1) + 2(8x) + 2(3y) + 2(6)
35x + 20y + 5 + 16x + 6y + 12
51x + 26y + 17
Help with all 3 ASAP
Answers
Answer:
The second one is right
The third one is wrong.
Find two numbers whose sum is 8 and whose product is 17
Answers
Answer:
Step-by-step explanation:
x+y = 8
y = 8-x
xy = 17
x(8-x) = 17
8x - x² = 17
x² - 8x + 17 = 0
Quadratic formula
x = [8 ± √(8² – 4·1·17)] / [2·1]
= [8 ± √(-4)] / 2
= [8 ± 2i] /2
= 4±i
x = 4+i
y = 4-i
A quadratic equation is written in the form of ax²+bx+c. The two numbers whose sum is 8 and whose product is 17 are (4+i) and (4-i).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Let the first number be 'a' and the second number be 'b'. Therefore, the sum of the two numbers is,
a+b=8
The product of the two numbers is,
ab=17
b=17/a
now, the equation can be written as,
a+b=8
a+(17/a)=8
a² + 17 = 8a
a²-8a+17=0
a = 4±i
Hence, the two numbers whose sum is 8 and whose product is 17 are (4+i) and (4-i).
Learn more about Quadratic Equations:
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if you have 60 G of fluorescent powder and 124 cups of medium base paint, and the ratio is one part powder to five parts paint how many cups of paint can I make with fluorescent powder
Answers
Answer:
1.268 cups
Step-by-step explanation:
60 G=0.2536 cups (I found a G to cup converter on the internet)
0.2536x5=1.268 cups of paint it would mix with at a 1 to 5 ratio
descrease £250 by 15%
Answers
Hope this helps c:
Answer:
£212.5
Step-by-step explanation:
15% of 250 = 37.5
250 - 37.5 = 212.5
Write the percent as a fraction and as a decimal.
5% tax
Answers
Answer:
The answer would be 0.05
Step-by-step explanation:
This is because it is PER Cent so 5% is 0.05 of 1
Answer:
1/20 and 0.05
Step-by-step explanation:
The Maine Public Health Department reported that there have been 90 flu cases requiring hospitalization in Portland, ME (population of 70,000) since the beginning of 2018 - today is July 4th, 2018. On February 1st, 2018, 43 of those cases were hospitalized. What was the prevalence rate of flu cases requiring hospitalization thus far in 2018?
Answers
Answer:
The prevalence rate of flu cases requiring hospitalization thus far in 2018 is:
= 0.13%
Step-by-step explanation:
a) Data and Calculations:
Population of Portland, ME = 70,000
Number of flu cases requiring hospitalization on February 1st, 2018 = 43
Number of flu cases requiring hospitalization on July 4th, 2018 = 90
The prevalence rate of flu cases requiring hospitalization thus far in 2018 = 90/70,000 * 100 = 0.13%
b) The prevalence rate represents the proportion of the population of Portland, ME, who have the flu at the time that the Maine Public Health Department reported the number of flu cases requiring hospitalization on July 4th, 2018.
According to the Oxnard College Student Success Committee report in the previous year, we believe that 25% of students struggle in their classes because they don't spend more than 8 hours studying independently outside of a 4-unit class. For this year, you would like to obtain a new sample to estimate the proportiton of all Oxnard students who struggle in their classes because they don't study enough outside of the classrooms. You would like to be 99% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required? Do not round mid-calculation
Answers
Answer:
sdfghj
Step-by-step explanation:
9) Linda and Maria share £200. Linda has 4 times as much money as Maria.
How much money does Maria have?
Answers
Answer:
40
Step-by-step explanation:
maria is x
linda is 4x
x+ 4x = 200
5x = 200
x= 40
What is the difference between the greatest and the smallest rational numbers
given below?
7/15,11/20,2/5,12/25
Answers
Answer:
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
Step-by-step explanation:
Step(i):-
Given that the rational numbers
[tex]\frac{7}{15} , \frac{11}{20} ,\frac{2}{5} ,\frac{12}{25}[/tex]
we have to find that the difference between the greatest and the smallest rational numbers
solution:-
The greatest rational number = [tex]\frac{11}{20}[/tex]
Convert into decimal = 0.55
The smallest rational number = [tex]\frac{2}{5}[/tex]
Convert into decimal = 0.4
The difference between the greatest and smallest rational number
[tex]= \frac{11}{20} - \frac{2}{5}[/tex]
= [tex]\frac{11-8}{20}[/tex]
[tex]=\frac{3}{20}[/tex]
Final answer:-
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
I need the answers ASAP
Answers
Answer:
Image attached
Step-by-step explanation:
Just wandering, no hate, you can post answers on brainly but can't read an analog clock.
BTW I've got one in my house
Write the equation of the line in fully simplified slope-intercept form???
Answers
Answer:
[tex]y = - \frac{4}{5} x + 3[/tex]
Step-by-step explanation:
[tex]b = 3[/tex]
[tex] - 2 = 4a + 3[/tex]
[tex]a = - \frac{4}{5} [/tex]
If m∠4 = 101.9°, find each of the following in degrees.
(a) m∠5
(b) m∠8
Answers
Answer:
m<5=101.9 m<8=101.9
Step-by-step explanation:
alternate interior and vertical angles
Answer:
(a) m∠5=<4[alternate angle]=101.9°,
(b) m∠8=<5[vertically opposite angle]=101.9°,
The distance from the ground to where the ladder is touching the wall is 7
feet. The distance from the wall to the base of the ladder is 4 feet. What is
the length of the ladder?
wall
ladder
Answers
Answer:
L=8.062 feet
Step-by-step explanation:
wall=7
distance=4
Pythagorean theorem
7^2+4^2=L^2
49+16=L^2
65=L^2
L=8.062 feet
The required length of the ladder is given as 8.06 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
here,
As mentioned in the question,
perpendicular length = 7, base length = 4 feet,
Let the length of the ladder be x,
Following the Pythagoras theorem,
x² = 7 ² + 4²
x ² = 49 + 16
x² = 65
x = √65
x = 8.06
Thus, the required length of the ladder is given as 8.06 feet.
Learn more about Pythagorean triplets here:
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Find the difference.
4-(-8)=
Answers
Answer:
4
Step-by-step explanation:
subtract negative 4 by negative 8
After lunch, you see the bumper cars and want to ride them. Here’s what the sign says:
Bumper Cars:
6 minutes: 8 tickets
8 minutes:12 tickets
Which one gives you more time for your money?
Answers
This probability distribution shows the typical grade distribution for a Geometry course with 35 students. HELLLPPP PLSSS
Answers
Answer:
P(A, B or C) = 6/7 or 0.8571
Step-by-step explanation:
From the image, we have the frequency for each grade as;
Grade A = 5
Grade B = 10
Grade C = 15
Grade D = 3
Grade F = 2
We want to find the probability that a student earns a grade of A, B or C.
Total frequency for A, B & C = 5 + 10 + 15 = 30
There are a total of 35 students overall for the geometry course.
Thus;
P(A, B or C) = 30/35
P(A, B or C) = 6/7 or 0.8571
Answer:
0.86Step-by-step explanation:
Total frequency for A, B & C = 5 + 10 + 15 = 30
There are a total of 35 students overall for the geometry course.
P(A, B or C) = 30/35
P(A, B or C) = 6/7 or 0.8571
now we round to the hundredths place
0.8571 ⇒ 0.86
Children 4 years old or younger can ride the train for free. Write an inequality that expresses who can ride the train for free.
Answers
x<=4
x is less than or equal to four
children less than or equal to four can ride the train for free
5 (a) Write the ratio 15:35 in its simplest form.
Answers
Answer:
Step-by-step explanation:
5 is a factor of 15 and 35
15:35 = 3:7
Plz tell me if I’m wrong
How are these three numbers related. 50 1/2, 1/4, 202
Answers
Answer: If you divide 202/4=50.5 or 50 1/2
Step-by-step explanation:
3/4 divided by 1/5 PLEASE ANSWER
Answers
Answer:
3.75
Step-by-step explanation:
To make it a fraction form answer, you multiply the dividend numerator by the divisor denominator to make a new numerator.
Furthermore, you multiply the dividend denominator by the divisor numerator to make a new denominator:
To make the answer to 3/4 divided by 1/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
15/4 = 3.75
The answer is rounded to the nearest four decimal points if necessary.
15/4 is an improper fraction and should be written as 3 3/4.
Answer:
3.75
Step-by-step explanation:
A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a degree?
Answers
Answer:
56.7°
Step-by-step explanation:
A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a degree?
We solve this question using the Trigonometric function of Sine
From the question, we are told that:
A rectangle is 5.1 cm wide
and each diagonal is 9.3 cm long.
Since we have a diagonal, this means the shape is transformed to a triangle.
The width of the rectangle = Adjacent side of a triangle = 5.1cm
The diagonal of the rectangle = Hypotenuse = 9.3cm
Hence,
cosθ = Adjacent/Hypotenuse
cosθ = 5.1/9.3
cosθ = 0.5483870968
θ = arccos(0.5483870968)
θ = 56.743568714°
Approximately = 56.7°
The measure of the angle is 56.7°
Solve the equation x² = 5. (must show equality properties in work so I can earn full credit)
A. x = 5
B. x = 25
C. x = √5
D. x = ±√5
Answers
take root to both side to clear the square
√x² = ±√5
X = ±√5
please help, I'll give the correct answer brainliest.
find c and d. show your work.
Answers
9514 1404 393
Answer:
c = 6√2
d = 12
Step-by-step explanation:
The sides of any isosceles triangle (opposite the congruent angles) are congruent. Hence c = 6√2.
The hypotenuse of an isosceles right triangle is √2 times the side length, so ...
d = c√2 = (6√2)(√2) = 6·2
d = 12
__
If you don't believe that, you can always use the Pythagorean theorem to find d:
d^2 = (6√2)^2 +c^2
d^2 = 72 +72 . . . . . . . . . since c=6√2
d = √144
d = 12
If the exchange rate of US dollar to Naira is 1:70, what's the value of $1.50 in Naira?
Answers
Answer:
$1.50 is 105 Naira
Step-by-step explanation:
If the exchange rate is 1:70, that means that in order to get the amount of Naira equal to some amount of US dollars, you would multiply the number of US dollars by 70. And so we get...
1.5 x 70 = 105 (Naira)
Answer:
105 Naira
Step-by-step explanation:
Please see the attached image.
I hope this helps!