Answers
Answer:
[tex]\frac{3x+1}{x}, x\neq -1[/tex]
Step-by-step explanation:
We can start by combining the fractions in the numerator. We can multiply them by x/x and x + 1/x + 1 respectively to get a common denominator of x(x + 1).
[tex]\frac{4}{x+1}*\frac{x}{x} +\frac{2}{x} *\frac{x+1}{x+1}\\\\\frac{4x}{x(x+1)}+\frac{2x+2}{x(x+1)}\\\\\frac{6x+2}{x(x+1)}[/tex]
Now we can rewrite an simplify:
[tex]\frac{\frac{6x+2}{x(x+1)} }{\frac{2}{x+1} }\\\\\\\frac{6x+2}{x(x+1)}*\frac{x+1}{2} \\\\\frac{3x+1}{x}[/tex]
The domain would be x ≠ -1 because the starting domain is [tex]x\neq -1; x\neq 0[/tex] and it changed to [tex]x\neq 0[/tex], so for the two fractions to be equal, the domain would be [tex]x\neq -1[/tex].
Related Questions
What is the range of the function y=(x+2)(x-4)
Please explain how you got it as well
Answers
Answer:
The range is between -2 and +4.
Step-by-step explanation:
To find range you just need to get X ignoring the Y.
(X+2) is X= -2
(X-4) is X = +4
Y = x^2 -2x -8
Now we know that the range is from the minimum y-value to the maximum (if there is one)
In functions like this, they have the form y = ax^2 + bx + c, where c is the minimum or maximum for the given function
In this case, it's a minimum because there aren't any y points on the graph smaller than -8
That means the range is: y >= -8
3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.
Which inequality explains why these three segments cannot be used to construct a triangle?
EF + FD > DE
ED + EF < DF
ED + EF > DF
EF + FD < DE
Answers
Answer:
second option ED + EF < DF
Step-by-step explanation:
in order to build a triangle or of 3 lines, every pair of 2 of these lines must be longer together than the third line.
otherwise you could put them together and place them flat alongside the third line and still cannot connect to the endpoint of the third line => no triangle possible.
ED (or DE) is half of the third line (DF or FD).
FE (or EF) is a third of the third line.
1/2 + 1/3 < 1/1 (because 1/3 < 1/2)
Answer:
ED + EF < DF or b
Which option would prove that triangle ABC ~ triangle XYZ? Select two options.
Answers
Answer:
BA/YX=BC/YZ=AC/XZ
Step-by-step explanation:
SINCE,
ABC AND XYZ ARE EQUILATERAL TRIANGLE
ALL THREE SIDES ARE EQUAL
Solve for x.
5(x – 10) = 30 – 15x
Answers
Answer:
x=4Step-by-step explanation:
[tex]\sf 5(x - 10) = 30 - 15x[/tex]
[tex]\sf 5x-50=30-15x[/tex]
[tex]\sf 5x-50+50=30-15x+50[/tex]
[tex]\sf 5x=-15x+80[/tex]
[tex]\sf 5x+15x=-15x+80+15x[/tex]
[tex]\sf 20x=80[/tex]
[tex]\sf \frac{20x}{20}=\frac{80}{20}[/tex]
[tex]\sf x=4[/tex]
Express y in terms of x
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
Given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k\\}{x^2}[/tex] ← k is the constant of variation
To find k use any ordered pair from the table.
Using (1, 4 ) , then
4 = [tex]\frac{k}{1^2}[/tex] = [tex]\frac{k}{1}[/tex] ( multiply both sides by 1
4 = k
y = [tex]\frac{4}{x^2}[/tex] ← equation of variation
(b)
When y = 25 , then
25 = [tex]\frac{4}{x^2}[/tex] ( multiply both sides by x² )
25x² = 4 ( divide both sides by 25 )
x² = [tex]\frac{4}{25}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{4}{25} }[/tex] = ± [tex]\frac{2}{5}[/tex]
Since x > 0 then x = [tex]\frac{2}{5}[/tex]
Una pileta de natación tiene un desnivel en el fondo, de tal manera que su profundidad varía entre 1m y 4,3m. ¿Cuál es el cambio de presión al nadar por el fondo de la pileta, desde la zona más baja hacia la zona más profunda? (Aplique Teorema Fundamental de la Hidrostática). Peso específico agua: γ=1000kgf/m³
Answers
Answer:
dhhdf Hf fu vvvvvvvbbb jcjsjjsisydydhfb DJ
What is the value of the 30th percentile for the data set? 6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896
Answers
5896
Step-by-step explanation:Given data set:
6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896
To calculate the 30th percentile;
i. Rearrange the given data set in ascending order.
5581 5700 5700 5896 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381
ii. Use the following formula to get the index of the value at the 30th percentile.
N = p(n)
Where;
N = the number of data points at or below the intended percentile.
p = the intended percentile.
n = the number of points in the data.
In this case;
p = 30 percent = 0.3
n = 14
Substitute these values into the equation;
N = 0.3(14)
N = 4.2
iii. From the calculated index, find the value of the 30th percentile.
If the index is a whole number x, the desired percentile is the average of the values at index x and x+1.
For example if the index is 4, then the desired percentile is the average of the values at index 4 and 5. In our case, that will be;
[tex]\frac{5896+5896}{2}[/tex] = 5896
If the index is a decimal number, it is rounded up to the nearest integer. The value at the rounded index is the desired percentile.
For example, in our case, the index is 4.2 which when rounded up becomes 4.
Therefore, the data point or value at index 4 is the 30th percentile. From the arrangement in (ii) above, that will be 5896. i.e
5581 5700 5700 5896 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381
A man owes rs 4000 in 4 years and rs 3400 due in 6 years. His creditor agreed for him to pay debts with a payment of rs 3000 in 3 years and the remainder in 8 years. If money is worth 7% compounded quarterly, the amount of the second payment is?
Answers
Answer:
15000 loan
Step-by-step explanation:
Suppose comparison date = 8 years
Hope this answer helps you :)
Have a great day
Mark brainliest
what is the solution to the system of equations
Answers
Answer:
O A. [tex](-1,2)[/tex]
Step-by-step explanation:
[tex]y=x+3[/tex]
[tex]2=-1+3[/tex]
[tex]2=2[/tex]
[tex]y=-x+1[/tex]
[tex]2=-1+1[/tex] Since two -x's are being used, x becomes positive!
2 = 1 + 1
2 = 2
Solution: (-1, 2)
work out the average speed of 40 km in 2.5 hours
Answers
Answer:
19.20
Step-by-step explanation: used
a calc
What is the remainder when 4x^3+8x-32 is divided by x+10?
Answers
Answer:
The remainder is -4112.
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. According to the PRT, when we divide a polynomial P(x) by a binomial in the form of (x - a), then the remainder will be P(a).
We are dividing:
[tex](4x^3+8x-32)\text{ by } (x+10)[/tex]
We can rewrite the divisor as:
[tex]x+10=x-(-10)[/tex]
So, a = -10.
Then according to the PRT, the remainder of the operation will be:
[tex]R=P(-10)=4(-10)^3+8(-10)-32=-4112[/tex]
Find the surface area of the figure using its net
Answers
The three rectangles are 12m wide and 6 high. Area = 72 m^2
There are two triangle ends. Area = 2 x (1/2 x 3 x 4) = 12 m^2
Total surface area of prism = 72 + 12 = 84 m^2
Write an inequality that represents the graph.
Answers
m=(y2-y1)/(x2-x1)
m=(0+3)/(1-0)
m=3
b=-3
y=3x-3
y ≤ 3x-3
Andrea played dominos nonstop for 52 minutes in Little Havana. If each match lasted 13 minutes, how many matches did she play in that time?
Answers
Answer:
4 Matches
Step-by-step explanation:
According To the Question,
Given, Andrea played dominos nonstop for 52 minutes.And, each match lasted 13 minutes .Now, The Total Matches she plays in that time = [tex]\frac{(Total Time Played)}{(Time On Each Match)}[/tex]
Thus, Total Matches = 52 / 13 ⇔ 4 Matches
hey there, please help me. thank you
Answers
Answer:
S.S.S
Step-by-step explanation:
When three sides of a triangle are respectively equal to three corresponding sides of another triangle, they are said to be congruent .
hope it is helpful to you
Drag each label to the correct location on the image.
Here is a multiplication sentence:
(1 × 4) × 2 = 8
Drag the numbers and the parentheses to create an equivalent multiplication sentence that illustrates the associative property of multiplication.
Answers
Answer:
1 x (4 x 2) = 8
Step-by-step explanation:
1 x (4 x 2) = 8
I suck at math can someone help me
Answers
Answer:
x=22
Step-by-step explanation:
x+14=5x-74 (being corresponding angles and correcponding angles are always equal)
14+74=5x-x
88=4x
88/4=x
22=x
In, z = 4 cm, x=8cm, and m
Answers
Answer:
what do u want us to do pls be more clear!
how much square units of 50 units
Answers
Answer:
7.07106781187
Step-by-step explanation:
if its just asking [tex]\sqrt50[/tex]
:D
Jameson middle school give bottles of water to teachers and students who are going on a field trio. The school orders 500 bottles of water. They plan to give 35 bottles of water to teacher . They orderd at least 2 bottles of water for each student. How many students could be going on the field trip? Show your work
Answers
Answer: Almost 232 students going on the field trip.
Step-by-step explanation:
Let x be the number of students going on the field trip.
As per given,
[tex]2x+35 \leq500[/tex], where [tex]x\geq2[/tex].
To solve the inequality , subtract 35 from both sides
[tex]2x\leq465\\\\x\leq232.5[/tex] [divide both sides by 2]
i.e Almost 232 students going on the field trip.
To solve for the missing length, which operation should you perform?
Answers
Answer:
? = 15 yards
Step-by-step explanation:
h² + b² = ?²
9² + 12² = ?²
81 + 144
225
√225 = 15
Answer:
Pythagorean theorem
Step-by-step explanation:
You should use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
9^2+ 12^2 = ?^2
81 +144 = ?^2
225 = ?^2
Take the square root of each side
sqrt(225) = sqrt(?^2)
15 =?
can someone help me understand this, please? For some reason my answer is correct but I need to understand how did I found the correct answer
Answers
Answer with step-by-step explanation:
The way the question is worded, this actually shouldn't be correct. The correct answer should be [tex]3:4[/tex].
Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.
Why?
By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.
Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are [tex]\overline{RS}[/tex] and [tex]\overline{AB}[/tex].
The ratio of [tex]\overline{RS}:\overline{AB}[/tex] is [tex]18:24\implies \boxed{3:4}[/tex].
The reason why it ideally should be [tex]3:4[/tex] and not [tex]4:3[/tex] is because the question states [tex]RTSU\sim ABCD[/tex], which mentions [tex]RSTU[/tex] first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.
Mike works h hours in a week. To find his weekly pay he multiplies his hours by his pay of $30 per hour and adds $5 for his sales bonus. He's decided that he wanted to take one-fifth of his weekly pay and place it in his savings. Which simplified expression represents the amount that will go into his savings each week?
Answers
Answer:
6h + 1
Step-by-step explanation:
number of hours: h
pay per hour: 30
pay for the hours: 30h
add sales bonus: 30h + 5
1/5 of total above: (1/5)(30h + 5) = 6h + 1
Answer: 6h + 1
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π
Answers
Answer:
volume of a cone formula = V=πr²h/
3
V=3.14(5)²3/3
V≈78.54
Pleeeeeeease help meeee!!!!
Answers
Answer:
a = -7, b = -1, c = 1/3
Step-by-step explanation:
-x + 1/3 - 7x² ⇒ -7x² - x + 1/3
a = -7 b = -1 c = 1/3
Answer:
Step-by-step explanation:
[tex]ax^{2} + bx + c\\-7x^{2} - x + \frac{1}{3} \\a = -7\\b = -1\\c = \frac{1}{3}[/tex]
602.88 rounded to 2 decimal place is ?
Answers
Answer:
it will be 603.00
it will. e counted from the right to the left
a bucket contains 3 1/2 gallon of water. If Marie adds 5 gallons more, how many gallons of water will there be in all?
Answers
Answer:
8 1/2
because 3 + 5= 8+ 1/2= 8 1/2
Can anyone help with this?
Answers
Sexagesimal
measure of (2pie/3)^c
Answers
Answer:
Step-by-step explanation:
In Sexagesimal system we know that π=180°
[tex](2\times \frac{\pi}{3})^{\circ} = (2 \times \frac{180}{3})^{\circ} = (2 \times 60)^{\circ} = 120^{\circ}[/tex]
Answer:
120 ° is the correct ☑ answer.
Step-by-step explanation:
We know that in Sexagesimal measure the value of π is 180 ° .
( 2 π / 3 ) = 2 × 180 ° /3 = 360 °/ 3
= 120 °
factorize: 9x^2 - 24xy + 16y^2
Answers
9x²-24xy+16y²
(3x)²-2.(3x)(4y) +(4y)²
(3x-4y)²
(3x-4y)(3x-4y)
Answer:
[tex](3x -4y)^2[/tex]
Step-by-step explanation:
[tex]9x^2 - 24xy + 16y^2 = (3x)^2 - 24xy + (4y)^2[/tex]
[tex]=(3x)^2 -2(3x \times 4y) + (4y)^2\\[/tex]
a = 3x , b = 4y . The expression [tex]a^2 - 2ab + b^2 = (a-b)(a-b) =(a-b)^2[/tex]
[tex]=(3x -4y)(3x - 4y)[/tex]
[tex]9x^2 - 24xy + 16y^2 = (3x -4y)^2[/tex]