What is the quotient of the rational expressions shown below? Make sure
your answer is in reduced form.
x2 + 5x +6/x-6/x^2-9/2x-12
Answers
Picture of the right answers
Hence, the quotient of the rational expression given below is x-3.
How to solve?
To solve the division we will use basic properties of rational numbers here.
The first step is to factor numerator/denominator if possible.
To divide the expressions follow the following steps
1.leave the first fraction as it is
2. Convert division to multiplication
3.Turn the second fraction upside down
([tex]x^{2}[/tex]+5x+6)/x-6 / ([tex]x^{2}[/tex]-9)/2x-12
=([tex]x^{2}[/tex]+5x+6)(2(x-6))/([tex]x^{2}[/tex]-9)(x-6)
=2([tex]x^{2}[/tex]+5x+6)/[tex]x^{2}[/tex]-9
By splitting the quadratic equation into factors we get,
[tex]x^{2}[/tex]+5x+6=(x+2)(x+3)
and using the formula [tex]a^{2}[/tex]-[tex]b^{2}[/tex]=(a-b)(a+b) we get [tex]x^{2}[/tex]-9=(x-3)(x+3)
=2(x+3)(x+2)/(x+3)(x-3)
=2(x+2)/(x-3)
hence, the quotient of the given ration expression is x-3.
Learn more about solving rational expressions
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Related Questions
Stephanie has three shirts for every two pairs of jeans that she owns. If she owns 14 pairs of jeans, then how many shirts does she own?
Answers
Answer:
21 shirts
Step-by-step explanation:
Ratio jeans to shirts: 2:3
Mutiply by the same
2 to get to 14 is 7
7 x 2 = 14
7 x 3 = 21
Answer: i think the answer is 21
Step-by-step explanation:
Two pounds of dried cranberries cost $5.04, 3 pounds of dried cranberries cost $7.56, and 7 pounds of dried cranberries cost $17.64. What equation gives the total cost y of x pounds of dried cranberries?
Answers
Answer:
y = 2.52x
y = cost, x = pounds of cranberries.
each pound costs 2.52
Step-by-step explanation:
5.04/2 = 2.52
Solve five ninths minus two sixths
options:
twelve fifty fourths
twenty fifty fourths
six thirds
three over one
Answers
26+5 i am in kinder pls help
Answers
31
you could just use a calculator yk
if you have a class with 32 students and 16 of them are boys how many girls are there in the class
Answers
Answer: if there are 32 students in the class and 16 are boys so the other half well be 16 girls. 16 + 16 = 32. Sooo the answer is 16 girls
Step-by-step explanation:
What is the value of x 39 (2x+1)
Answers
Answer:
2xx_{39}+x_{39}
Step-by-step explanation:
x 39 ( 2 x + 1 )
Use the distributive property to multiply x_{39} by 2x+1.
2x_{39}x+x_{39}
2xx_{39}+x_{39}
Angie divides the polynomial function f (x)+x3+3x2-7x-21 by (x+3) what can she conclude from the fact that the remainder is equal to 0
Answers
Answer:
Yes, and if you divide x^3+3x^2-7x-21 with x+3 you will result in x^2-7
Step-by-step explanation:
Hope this helps
And I like your profile pic
The given polynomial is divisible by x+3 because f(-3)=0
So , the remainder is equal to 0
Her conclusion is correct.
Given :
Angie divides the polynomial function
[tex]f (x)=x^3+3x^2-7x-21[/tex] by (x+3)
Apply remainder theorem to check whether the remainder is equal to 0
If a polynomial p(x) is divisible by (x-a), the remainder obtained is P(a)
x+3 is the divisor
Lets set the divisor =0 and solve for x
[tex]x+3=0\\x=-3[/tex]
Now we plug in -3 for x in given f(x) and see whether f(-3) =0
[tex]f (x)=x^3+3x^2-7x-21\\f (-3)=(-3)^3+3(-3)^2-7(-3)-21\\f(-3)=-27+27+21-21\\f(-3)=0[/tex]
So, f(-3)=0 and hence the remainder is 0
Her conclusion is correct
Learn more : brainly.com/question/19908280
Given the points (-1,1) and (-2,1) on the line find the equation of the line
Answers
slope: 2/-3
point slope form: y-1=2/-3(x-(-1))
slope intercept: y=-2/3x+1/3
A function is a relation in which the value of the domain (x-values) DO NOT repeat.
O True
O False
Answers
Answer:
true
Step-by-step explanation:
josephin is going on a run around the lake. she knows the distance around the lake. but she would like to complete her run in a certain amount of time. josephine knows she can use the formula d= rt.
which equation correctly rearranges the formula to find the time it will take her to run around the lake?
look at picture and tell me if it is a, b, c, or d.
Answers
Answer:
A. [tex]t = \frac{d}{r}[/tex]
Step-by-step explanation:
Given
[tex]d = rt[/tex]
Required
Determine the time
From the question, we understand that:
[tex]d = distance[/tex]
[tex]r = rate[/tex]
[tex]t = time[/tex]
This question implies that we make t the subject of formula.
[tex]d = rt[/tex]
Divide both sides by r
[tex]\frac{d}{r} = \frac{rt}{r}[/tex]
The equation becomes:
[tex]\frac{d}{r} = t[/tex]
Reorder the equation.
[tex]t = \frac{d}{r}[/tex]
The correct option is (a) [tex]t = \frac{d}{r}[/tex]
give example of a monotone subsequence of the sequence Sn=cos(n.π/3)
Answers
A monotone subsequence is a subsequence that is either increasing or decreasing, which we define as follows:
A sequence (S) is increasing if [tex]S_n \geq S_m[/tex] whenever n>m.A sequence (S) is decreasing if [tex]S_n \leq S_m[/tex] whenever n>m.Here, we can create a subsequence by taking every sixth term:
• When n = 6, [tex]S_n = \cos(6\pi /3) = \cos(2\pi) = 1[/tex]
• When n = 12, [tex]S_n = \cos(12 \pi /3) = \cos(4\pi) = 1[/tex],
and so on, and every such element will have a value of 1. This is a monotone subsequence.
Christopher is deciding between two landscaping companies for his place of business. Company A charges $30 per hour and a $200 equipment fee. Company B charges $50 per hour and a $100 equipment fee. Let
A
A represent the amount Company A would charge for
t
t hours of landscaping, and let
B
B represent the amount Company B would charge for
t
t hours of landscaping. Write an equation for each situation, in terms of
t
,
t, and determine the number hours,
t
,
t, that would make the cost of each company the same.
Answers
Answer:
A=30t+200
B=50t+100
The number of hours,t, that would make the cost of each company the same is 5.
30(5)+200= A
150+200=350
50(5)+100= B
250+100=350
6 minutes to 16 minutes
Answers
Answer:
um im not sure if you need to simplify but then the answer would be 3 minutes to 8 minutes.
NEED HELP WITH THIS PLEASE
Answers
Answer:
-25 + 75 = 50
Step-by-step explanation:
Since we don't know the value of the bar, we will call it x.
-25 + x = 50
Add 25 to both sides to find the value of x.
x = 75
You can also double check this answer by doing simple math.
-25 + 75 = 50
Please help this is for a grade I don’t know the answer will give brainlest
Answers
Answer:
The answer is d
Step-by-step explanation:
Answer: d
Step-by-step explanation:
Rewrite
8
as
2
3
.
x
3
−
2
3
=
0
Since both terms are perfect cubes, factor using the difference of cubes formula,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
x
and
b
=
2
.
(
x
−
2
)
(
x
2
+
x
⋅
2
+
2
2
)
=
0
Simplify.
Tap for more steps...
(
x
−
2
)
(
x
2
+
2
x
+
4
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
−
2
=
0
x
2
+
2
x
+
4
=
0
Set the first factor equal to
0
and solve.
Tap for more steps...
x
=
2
Set the next factor equal to
0
and solve.
Tap for more steps...
x
=
−
1
+
i
√
3
,
−
1
−
i
√
3
The final solution is all the values that make
(
x
−
2
)
(
x
2
+
2
x
+
4
)
=
0
true.
x
=
2
,
−
1
+
i
√
3
,
−
1
−
i
√
3Rewrite
8
as
2
3
.
x
3
−
2
3
=
0
Since both terms are perfect cubes, factor using the difference of cubes formula,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
x
and
b
=
2
.
(
x
−
2
)
(
x
2
+
x
⋅
2
+
2
2
)
=
0
Simplify.
Tap for more steps...
(
x
−
2
)
(
x
2
+
2
x
+
4
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
−
2
=
0
x
2
+
2
x
+
4
=
0
Set the first factor equal to
0
and solve.
Tap for more steps...
x
=
2
Set the next factor equal to
0
and solve.
Tap for more steps...
x
=
−
1
+
i
√
3
,
−
1
−
i
√
3
The final solution is all the values that make
(
x
−
2
)
(
x
2
+
2
x
+
4
)
=
0
true.
x
=
2
,
−
1
+
i
√
3
,
−
1
−
i
√
3
what is 98.704 in expanded using powers of ten
Answers
Answer:
[tex]9.8704 * 10^1[/tex]
Step-by-step explanation:
The standard form is called the scientific notation expressed generally as;
[tex]A * 10^n[/tex]
A is an integer between 1 and 10
n is ant integer or fraction
Given the decimal value 98.704, we ill shift the decimal point to the back once to have;
98.704 = [tex]9.8704 * 10^1[/tex]
Note the when the decimal point is shifted backwards the value of n is always positive. Hence the expansion in power of 10 is [tex]9.8704 * 10^1[/tex]
What is the solution to the inequality -6+12p+31 > 71
Answers
Step-by-step explanation:
-6 + 12p + 31 > 71
12p + 25 > 71
12p > 46
p > 23/6.
Answer:
Step-by-step explanation:
12p>71+6-31
12p>46
p>23/6
Here are three symbols.
<
>
=
Write one of these symbols in each box to make four true state
Answers
Step-by-step explanation:
4 + 9 = 3 ^ {2}
13=3^{2}
13=9
Answer:
a. <
b. =
c. =
d. >
these are correct I guess
A 14-ounce energy drink contains 42 teaspoons of sugar. How much sugar is one ounce of the drink?
Answers
Answer:
3 teaspoonsStep-by-step explanation:
14-ounce ⇒ 42 teaspoons of sugar14/14 ounce ⇒ 42/14 = 3 teaspoons of sugar1-ounce ⇒ 3 teaspoons of sugarScenario: Does the age at which babies learn to crawl depend on the time of the year that the babies were born? Data were collected from parents who brought their babies into the University of Denver’s Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age in which their child first began to crawl. The resulting data were grouped by month of birth: January, May, and September.
Answers
The age for when babies learn to crawl is different for Januar,May, and September.. so I guess yes?
In a particular triathlon the athletes cover 1/24 of the total distance by
swimming, 1/3 of it by running, and the rest by bike. What is the ratio of
the distance covered by bike to the distance covered by running?
Answers
Answer:
15/8
Step-by-step explanation:
Let "d" be the total distance, that is, the distance for swimming (s), running (r) and going by bike (b).
d = s + r + b [1]
1/24 of the total distance is covered by swimming.
s = 1/24 d [2]
1/3 of the distance is covered by running.
r = 1/3 d [3]
If we replace [2] and [3] in [1], we get
d = 1/24 d + 1/3 d + b
b = d - 1/24 d - 1/3 d
b = 24/24 d - 1/24 d - 8/24 d
b = 15/24 d = 5/8 d
The ratio of the distance covered by bike to the distance covered by running is:
b/r = (5/8 d)/(1/3 d) = 15/8
In a recent News, it was reported that light trucks, which include SUV’s , pick-up trucks and minivans, accounted for 40% of all personal vehicles on the road in 2012. Assume the rest are cars. Of every 100,000 cars accidents, 20 involve a fatality; of every 100,000 light trucks accidents, 25 involve a fatality. If a fatal accident is chosen at random, what is the probability the accident involved a light truck?
Answers
Answer:
45.45%Step-by-step explanation:
Light tracks = 40% = 0.4Cars = 60% = 0.6Fatal accidents involving light tracks:
25/100000 = 0.00025Fatal accidents involving cars:
20/100000 = 0.0002Probability of a fatal accident involving a light track:
p = involving light tracks /involving both cars and light tracksp = 0.4*0.00025/(0.4*0.00025 + 0.6*0.0002) = 0.4545 p = 45.45%Four boxes of cookies cost $18 how much does one box of cookies cost
Answers
Answer:
$5.50
Step-by-step explanation:
Answer:
You would get 4.5 as your answer or 4 1/2
Step-by-step explanation:
You literally just do 18/4
And you get your answer
Jovie’s boss tells her to make 6 inch ribbon curls. If she makes 60 ribbon curls per hour, how many hours would it take her to make 480 ribbon curls? Write an equation and then solve.
Answers
Answer:
To make 480 ribbon curls, it would take 8 hours.
Step-by-step explanation:
x=480/60
x=8
Love the Elf reference btw. Hope this helped! :D (Sorry if I'm wrong)
A plant has a height of 8 1/4 inches. What is the height of the plant after it grows 1 7/8 inches?
Answers
Answer: 10 1/8 inches
1. Name the two-dimensional shapes that when rotated around the vertical axis form the following three-dimensional solids?
Cone:
Cylinder:
Sphere:
2. Name four, three-dimensional solid objects found in your home, workplace, etc. , and tell what geometric solid each most closely represents.
Object 1:
Object 2:
Object 3:
Object 4:
3. State the volume formulas for a cylinder, sphere, pyramid, and cone.
a. Volume formula for a cylinder:
b. Volume formula for a sphere:
c. Volume formula for a pyramid:
d. Volume formula for a cone:
Answers
Problem 1
Answers:
Cone: TriangleCylinder: RectangleSphere: Circle------------------------
Explanation:
Imagine a fan blade rotating. As it rotates really quickly, it occupies a 3D space. Or perhaps imagining rotating eggbeaters is a better thing to have in mind. Those blades spin really fast to form a 3D shape. So that's what's going on with this problem. If you spin a triangle around an axis, a cone will form. The base of the triangle forms the base of the cone. Half the base of the triangle is the radius of the cone. The height of the triangle is the height of the cone.
Similarly, a rectangle rotated around its center axis forms a cylinder. Think of a revolving door. That's often a classic example. Finally, a circle spun around any of its diameters will form a sphere.
========================================================
Problem 2
Answers:
Object 1: Cup = CylinderObject 2: Ball = SphereObject 3: Funnel = ConeObject 4: Paper towel roll = Cylinder-------------------------------
Explanation:
Pick objects around your house that are fairly simple in design and resemble either a cylinder, sphere, or cone. A cup resembles a cylinder just it doesn't have a top to it. A ball is a 3D sphere that has an interior to it, unless the ball is filled with air. A funnel resembles a cone due to its triangular shape of sorts. A paper towel roll (the card board piece or the cardboard plus the actual paper towels) resemble a cylinder as well. You can pick any four other objects you have around your house such as a cylindrical speaker, batteries (shaped as a cylinder), soup cans (also cylinders), and so on.
========================================================
Problem 3
Answers:
a) volume of cylinder = pi*r^2*hb) volume of sphere = (4/3)*pi*r^3c) volume of pyramid = (1/3)*L*W*Hd) volume of cone = (1/3)*pi*r^2*h-------------------------------
Explanation:
These formulas are what you should memorize or have handy on a flashcard. It is possible to derive them, but it would require calculus to do so. Also, such a process is quite length. So memorization or flashcards are the better way to go.
For the cylinder and cone, r is the radius and h is the height. Note how the formulas are nearly identical except the cone has the (1/3) term. This shows that the cone's volume is 1/3 that of the cylinder's volume where they both have the same radius r and height h.
The sphere also deals with the radius r, but we don't have to worry about the height of the sphere (it's really just 2r).
For the pyramid, L,W,H represent the length width and height respectively. The length and width form the base of the pyramid. Recall that L*W*H is the volume of a rectangular block. The volume of a pyramid is 1/3 of that rectangular block's volume.
If all of a 2D object's sides and angles have different lengths, such shape is said to be irregular.
What is 2D shape?In geometry, a form or figure having length and breadth is referred to as a "2D shape." Due to the lack of a thickness, a third dimension, such as the case of a prism or a cube, two-dimensional or 2D objects are often measured in terms of their two faces.
'2D' refers for 2-dimensional. A 2D shape is any form that has two dimensions. Consider for a moment what it means to have two dimensions. We could only move backwards or forwards in a straight line if we only had one dimension to work with. One dimension is a line.
Cone: Triangle
Cylinder: Rectangle
Sphere: Circle
Therefore, if all of a 2D object's sides and angles have different lengths, such shape is said to be irregular.
To know more about 2D shape, here:
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Rachel’s penny bank is 1/2 full. After she adds 120 pennies, it is 7/10 full. How many pennies can Rachel’s bank hold?
Answers
Answer:
600 pennies
Step-by-step explanation:
to start you need to understand that 1/2=5/10 so if we start with the bank 5/10 full and she adds 120 pennies that goes up 2/10. so that means 1/10 of the bank holds 60 pennies. so to find the answer you need to multiply the 60 pennies by 10, because 10*60 would be equal to the entire bank.
Plz answer will mark brainliest
Answers
Answer:
3cm
It would be 3.35, but rounded it is 3cm
Step-by-step explanation:
268/80 = 3.35
Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 15 ft high? (Round your answer to two decimal places.)
Answers
Answer:
The height of the pile is increasing at a rate of 1.78 ft/min
Step-by-step explanation:
As we can see, we have the rate at which the volume is increasing
Mathematically, the volume of a cone can be calculated by the formula;
1/3 * π * r^2 * h
but here, we are dealing with base diameter which is d
and r is d/2
So we have the formula as;
1/3 * π * (d/2)^2 * h
since h is same as d for this particular cone, we can replace d with h so that we now have;
1/3 * π * h^3/4
= πh^3/12
what we have in the question is dv/dt
what we want to calculate is dh/dt
Mathematically;
dh/dt = dh/dv * dv/dt
dh/dv is 1/dv/dh
dv/dh = πh^2/36 where h = 15
dv/dh = 225 π/36
dh/dv is now;
36/225π
So, finally;
dh/dt = 36/225 π * 35
dh/dt = 1.78 ft/min
Solve for points....
Answers
Answer:
Step-by-step explanation:
For Mr Rowley,
Ratio of Number of home works to the number of exit tickets = [tex]\frac{12}{14}[/tex]
= [tex]\frac{6}{7}[/tex]
= 6:7
For Ms Rivera,
Ratio of Number of home works to the number of exit tickets = [tex]\frac{36}{42}[/tex]
= [tex]\frac{6}{7}[/tex]
= 6:7
Since, both the ratios are same, fractions will be proportional.
[tex]\frac{12}{14}=\frac{36}{42}[/tex]
