Which of the following shows the correct simplification assuming the denominator is not equal to zero?
Answers
Answer:
[tex]=\frac{3x+2}{x\left(x+1\right)}[/tex]
or
[tex]\frac{(3x+2)}{x^2+x}[/tex]
Step-by-step explanation:
[tex]\frac{2}{x}+\frac{1}{x+1}\\\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x+1:\quad x\left(x+1\right)\\Adjust\:Fractions\:based\:on\:the\:LCM\\Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:x\left(x+1\right)\\\mathrm{For}\:\frac{2}{x}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x+1\\\frac{2}{x}=\frac{2\left(x+1\right)}{x\left(x+1\right)}\\[/tex]
[tex]\mathrm{For}\:\frac{1}{x+1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x\\\frac{1}{x+1}=\frac{1\cdot \:x}{\left(x+1\right)x}=\frac{x}{x\left(x+1\right)}\\=\frac{2\left(x+1\right)}{x\left(x+1\right)}+\frac{x}{x\left(x+1\right)}\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{2\left(x+1\right)+x}{x\left(x+1\right)}\\[/tex]
[tex]\mathrm{Expand}\:2\left(x+1\right)+x:\quad 3x+2\\2\left(x+1\right)+x\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=2,\:b=x,\:c=1\\=2x+2\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:1=2\\=2x+2\\\mathrm{Simplify}\:2x+2+x:\quad 3x+2\\2x+2+x\\\mathrm{Group\:like\:terms}\\=2x+x+2\\\\mathrm{Add\:similar\:elements:}\:2x+x=3x\\=3x+2\\=\frac{3x+2}{x\left(x+1\right)}[/tex]
Related Questions
Evaluate A^2 for A = -4. -16 -8 8 16
Answers
Answer:
The answer is 4^2 (-16)
Step-by-step explanation:
Declan says that for any number n, the product 4x n is greater than 4. Which value of n shows why Declan is incorrect
Answers
Answer:
[tex]n > 1[/tex]
Step-by-step explanation:
Given
Statement: 4x n is greater than 4
Required
Value of n
First we need to rewrite the statement in algebraic form;
Product 4 * n is represented by 4n
greater than 4 is represented by > 4
Bringing these two together, it gives the following
[tex]4n > 4[/tex]
Divide through by 4
[tex]\frac{4n}{4} > \frac{4}{4}[/tex]
[tex]n > 1[/tex]
We've arrive at solution;
This means that n is greater than 1
So, the values of n must start from 2 to show that the condition is true
The value of n = 7/8 makes the inequality 4n > 4 false because 7/8 is less than 1.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have n as a number.
4n > 4
Plug n = 5
20 > 4 (true)
Plug n = 9/5
36/4 > 4
9 > 4 (true)
Plug n = 3
12 > 4 (true)
Plug n = 7/8
28/8 > 4
3.5 > 4 (false)
Thus, the value of n = 7/8 makes the inequality 4n > 4 false because 7/8 is less than 1.
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Solve by completing the square:
x2 + 3x – 9 = 0
Answers
Answer:
Step-by-step explanation:
x = 9/5
The solution of the equation [tex]x^2 + 3x - 9 = 0[/tex] by completing the square would be [tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex].
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that the equation is,
[tex]x^2 + 3x - 9 = 0[/tex]
Now completing the square as
[tex]x^2 + 3x - 9 = 0[/tex]
Add and subtract by 9/4,
[tex]x^2 + 3x + \dfrac{9}{4} - \dfrac{9}{4} - 9 = 0[/tex]
[tex]x^2 + 3x + ( \dfrac{3}{2})^2 - \dfrac{9}{4} - 9 = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{9}{4}+ 9) = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{45}{4}) = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 = ( \dfrac{45}{4})[/tex]
Taking square root on both sides,
[tex](x + \dfrac{3}{2} ) = \pm ( \dfrac{\sqrt{45}}{2})[/tex]
Therefore, the solution of an equation is,
[tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex]
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Maria bought an SUV for 21,000 dollars. Nancy bought a sedan for 2/3 as much. How much less did Nancy spend on her sedan?
Answers
Answer:
7000
Step-by-step explanation:
21,000*(2/3)=14000
21,000-14,000=7000
Answer:
7,000 dollars
Step-by-step explanation:
21,000 divided by 3 is 7,000 = 1/3
So 2/3 = 7,000 x 2 = 14,000
To find how much less Nancy spent on her sedan you do 21,000 - 14,000 = 7,000
The volume of the giant beach ball is approximately 267.95 feet^3 . Find the diameter of the ball. Use 3.14 for pie.
Answers
Answer:
8 feet
Step-by-step explanation:
Hello, I can help you with this.
the volume of a sphere is given by.
[tex]Volume= \frac{4}{3} \ \pi\ radius^{3}\\\\[/tex]
Step one
isolate radius
[tex]\frac{3}{4}* volume= \pi\ radius^{3}\\\\\\\ \frac{3}{4 \pi }* volume=radius^{3}\\radius=\sqrt[3]{\frac{3}{4 \pi }* volume}[/tex]
According to the question the volume is 267.95 cubic feet , and pi= 3.14
put this values into the equation
let
volume =267.95
pi=3.14
[tex]volume=radius^{3}\\radius=\sqrt[3]{\frac{3}{4 \pi }* volume}\\radius=\sqrt[3]{\frac{3}{(4 *3.14) }*267.95}\\radius=\sqrt[3]{64}\\\\radius=4[/tex]
so the radius of the beach ball is 4 feet, but we need its diameter
Diameter=2* radius
radius=4 feet
Diameter= 4 feet*2
Diameter=8 feet
what a big ball¡¡
I hope it helps, have a great day.
PLEASE HELP ASAP worth alot
Answers
Answer:
I believe it is C
Step-by-step explanation:
Hope this helps
and if it at all possible and you mark me brainlyest please
Answer:
5 pts isnt a lot but ok.. and yes it is c
Step-by-step explanation:
13. A circle with radius x is shown below. The diagram is not drawn to scale. (1 point)
What is the value of x? Round the answer to the nearest tenth.
Answers
Answer: 16.1
Step-by-step explanation:
x^2 = 8^2 + (28/2)^2
x^2=64 + 196
x^2= 260
Take the square root of 260 and get 16.1!
The value of x is x=16.1
Chord
The perpendicular from the center of a circle bisects the chord
RadiusA line from the center of the circle to the circumference of the circle is the radius of the circle
Lets connect the center of the circle to the other end of the chord that is at the circumference of circle
The diagram attached below
The line OA from the center bisects the chord
AB= half of 28 = 14
the triangle AOB forms a right angle triangle
apply Pythagorean theorem to find out the value of x
[tex]x^2=8^2+14^2\\x^2= 64+196\\x^2=260\\\sqrt{x^2}=\sqrt{260} \\ x=16.1[/tex]
The value of x is 16.1
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The amounts of Cathy’s last six clothing purchases were $109, $72, $99, $15, $99, and $89. For each question, choose the mean, median, or mode and give its value.
C.) Which value would Cathy NOT tell her parents to convince them that she needs an increase in her allowance?
{I only need help on part C}
Answers
Answer:
The mean value = $80.5
Step-by-step explanation:
The value of her last six spendings are $109, $72, $99, $15, $99, and $89.
For the mean.
Mean = Total spendings/number
Mean =483/6
Mean = $80.5
For the median.
Lets arrange it in ascending order
$15 ,$72, $89, $99, $99, $109
The middle values are two.
Median = (89+99)/2
Median = 188/2
Median = $94
For the mode
$15 ,$72, $89, $99, $99, $109
Highest occuring is $99 with two frequencies.
To convince her parents that she needs an increase in allowance she would show them the bigger spendings .
So the least value on the list it's mean value which is $80.5.
What is the sum of 1-2 and V-18?
Answers
Answer:
v-19
Step-by-step explanation:
Answer:
It depends on what you mean.
Step-by-step explanation:
If its to separate questions,
1-2= 1
V-18= -13
If its one whole question then
1-2 - V-18= 14
1-2 / V-18= -0.07692307692
1-2 * V-18= -13
1-2 + V-18= -12
Hope this helps! :D
Write a quadratic function with a vertex at (-9,13).
Answers
Answer:
y = x² + 18x + 94
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 9, 13) and letting a = 1, then
y = (x + 9)² + 13 ← expand (x + 9)² using FOIL
= x² + 18x + 81 + 13
= x² + 18x + 94
Hope that helps.
how to i find b in y=my+b if the slope is undefined?
Answers
Answer:
By finding the y- intercept in the graph.
Step-by-step explanation:
This is the only point in the graph that is on the y axis.
1. which is greater value 0.4 3/4 0.15
2. which is least value 2 and 2/3, 2.45, 2 and 2/5
3.which is the greater value 3.95, 3 and 5/6, 3 and 4/5
ANSWER THEM ALLL
Answers
If each quadrilateral below is a rectangle find the missing measure in #5
Answers
Answer:
What do you mean by #5?
Step-by-step explanation:
The graph of Y = COS X+ż is the graph of the y = cos(x) shifted in which direction?
T
2 units to the left
2
units to the right
units up
2 units down
Answers
Answer:
2 units up
Step-by-step explanation:
You're just taking the entire graph of cos(x) and then adding 2 so it moves everything up. If you added 2 to x BEFORE taking the cosine
(like y = cos (x+2) ), then you would shift it left 2. Adding and subtracting from the x moves everything left or right. Adding or subtracting at the end just moves it up and down.
The graph of y = cos x + 2 is the graph of the y = cos(x) shifted in ''2 units up.''
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
To find the graph of y = cos x + 2 is the graph of the y = cos(x) shifted in which direction.
Here, The function is,
⇒ y = cos x
Now, After translate 2 units up, we get;
⇒ y = cos x + 2
Thus, The graph of y = cos x + 2 is the graph of the y = cos(x) shifted in ''2 units up.''
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What is the value of x? Leave answer in simplest radical form.
8
60°
Answers
Answer:
Your answer is A . 8
Step-by-step explanation:
hope it helps !
Complete 4 A,B 9 for points.
Answers
Answer:
R = (1/t) (A/P - 1)
T = (1/r) (A/P - 1)
I need help nothing is working for the answer p÷3> 2
Answers
Answer:
p > 6
Step-by-step explanation:
Given
[tex]\frac{p}{3}[/tex] > 2 ( in fractional form )
Multiply both sides by 3 to clear the fraction
p > 6
Answer:
honestly idk
Step-by-step explanation:
it may be p (1/3)
hope this is right:000
Which number sentence is true?
A. 78 = 68
B. 78 < 69
C. 78 = 75
D. 78 < 81
E. 78 > 84
Answers
Answer: the answer choice “d” is correct
Step-by-step explanation:
because the different symbols mean different things and yeah
Answer:
D
Step-by-step explanation:
lesser value ------- < --------This side bigger value {open mouth}
78 < 81
81 is bigger than 78
PLEASE ANSWERRRRR! EASY!!!!!!!!!!!!!
People use water to cook, clean, and drink every day. An estimate of 17.2% of the water used each day is for drinking. If a family uses 68.8 gallons of water a day for drinking, how many gallons do they use every day?
Answers
What if the value of x?
Answers
Answer:
x = 5
Step-by-step explanation:
This is a right triangle with hypotenuse x
We can use the Pythagorean theorem
a^2+b^2 = c^2
3^2+4^2 = x^2
9+16= x^2
25=x^2
Take the square root of each side
sqrt(25) = sqrt(x^2)
5 = x
How to change miles per hour to feet per second?
Answers
Answer:
1 mph = 1.46666667 fps
What is the value of x in the figure? Enter your answer in the box.
HELP IMMEDIATELY!
Answers
Answer:
Step-by-step explanation:
145 = 2x + 15
2x = 130
x = 65 (ANS)
Answer:
65º
Step-by-step explanation:
145º = (2x + 15)º
145º = (2x + 15)º
145º - 15º = 2xº + 15º - 15º
130º = (2x)º
x = 65º
Yehudy invested $19.250 in a simple interest account. After 6 years and no additional deposits or withdrawals, the account balance was
$22.957.55. Find the interest rate for the account. Round to the nearest hundredth of a percent if needed
Answers
Answer: 3.21%
Step-by-step explanation:
Interest = (1/t)(A/P - 1)
How many servings of
cups are in 33 cups of ice cream?
Answers
Answer:
I am 99% sure its 33 servings
Step-by-step explanation:
because the question says that "how many servings of cups are in 33 cups".
(hopefully im right) and HOPEFULLY THIS HELPS. : )
What is the value of b? -8/5b = 8
Answers
Answer:
-0.2 or -2/10
Step-by-step explanation:
hope this helps
Find an explicit formula for the geometric sequence 3, 15, 75, 375...
Answers
Answer:
3 * 5 ^ (n-1)
Step-by-step explanation:
3 is the first term and it multiplies by 5
The explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]
The standard explicit formula for a geometric sequence is expressed as:
[tex]T_n = ar^{n-1}\\[/tex]
a is the first term
r is the common ratio
n is the number of terms
Given the sequence of numbers 3, 15, 75, 375...
r = 15/3 = 75/15 = 5
a = 3
Substitute the given parameters into the formula to have:
[tex]T_n = ar^{n-1}\\T_n=3(5)^{n-1}[/tex]
Hence the explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]
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I need help finding the length of GH.
Answers
Answer:
length of arc=2r+teete ×2πr
360
2×13+155°×2×22×13
360. 7
26+155°×572
360. 7
26+88660
2520
88686
2520
35.404
What is the surface area of this design?
Answers
Answer:
440 inches squared - the last option
Step-by-step explanation:
Step 1. Surface area of top square.
5 x 5 = 25 inches sq
Step 2. Surface area of the 4 sides of the cuboid.
5 x 8 = 40 inches sq
40 x 4 = 160 inches sq
Step 3. Surface area of the large square.
10 x 10 = 100 inches sq
100 - 25 (because it's being covered) = 75 inches sq
Step 4. Surface area of the 4 sides of the large flat cuboid.
2 x 10 = 20 inches sq
20 x 4 = 80 inches sq
Step 5. (OPTIONAL) Surface area of the bottom
10 x 10 = 100 inches sq
Step 6. Add up all.
25 + 160 + 75 + 80 (+ 100 if including the base) = 340
We can conclude that we have to include the base as well because 340 inches sq is not an option listed.
340 + 100 = 440 inches sq
440 inches sq is the last option
Hope this helps :)
What type of function is represented?
Answers
Answer:
b
Step-by-step explanation:
ITS B NOT C ITS B ITS B ITS B.
A plane intersects a pentagonal pyramid horizontally as shown. Describe the cross-section.
A)
pentagon
B)
rectangle
C)
trapezoid
D)
triangle
Answers
Answer:
The answer is A I JUST DID it
The cross section of the figure is Pentagon.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A plane intersects a pentagonal pyramid horizontally as shown.
Now, By the given figure,
The plane slices through the pentagonal pyramid horizontally and forms a pentagon shaped cross-section.
Hence, It represent the Pentagon.
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