Answers
Answer:
B (1/x^2 - 4x + 3)
Step-by-step explanation:
You can first write the second equation as multiplication by multiplying by the reciprocal and then expand.
The result of the given division expression is [tex]\frac{1}{(x-3)(x-1)}[/tex]
Given the expression;
[tex]\frac{x+3}{x^2-2x-3} + \frac{x^2+2x-3}{x+1}[/tex]Factorize the quadratic function in the expression to have:
[tex]=\frac{x+3}{x^2-3x+x-3} \div \frac{x^2+3x-x-3}{x+1} \\=\frac{x+3}{x(x-3)+1(x-3)} \div \frac{x(x+3)-1(x+3)}{x+1} \\=\frac{x+3}{(x-3)(x+1)} \div \frac{(x+3)(x-1)}{x+1} \\=\frac{x+3}{(x-3)(x+1)} \times \frac{x+1}{(x+3)(x-1)} \\=\frac{1}{(x-3)(x-1)}[/tex]
Hence the result of the given division expression is [tex]\frac{1}{(x-3)(x-1)}[/tex]
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Related Questions
A rectangular plot of land is represented on a map by the vertices (10,10), (10, 90), (70.5, 90), and (70.5, 10), where the x- and y-coordinates are measured in yards. What is the area of the plot of land?
Answers
Answer:
Area of the plot of the land is 4840 square units.
Step-by-step explanation:
Let's draw the rectangle approximately on an x y plane. That would help us to find the length and width of the rectangle.
Answer: 4,480yd^2
Step-by-step explanation:
You have the x and y coordinates of the vertices (10, 10), (10,90), (70.5,90), and (70.5, 10) you have the coordinates: x and y as the first two which are the ones in bold. From that you do 70.5-10= 60.5.
Then you subtract the x and y coordinates again, which are underlined. From that do 90-10=80
Last you do 60.5x80=4,840 yards squared
Mark me brainliest!!!
Hope this Helps!!!
((will give brainliest)) What is the output of the function y = 12 + 3x if the input is 5.
Answers
Answer:
y = 27
Step-by-step explanation:
The output is the value of y when x = 5
Substitute x = 5 into the function , that is
y = 12 + 3(5) = 12 + 15 = 27 ← output
to solve you plug in the input into x and rewrite the equation as y=12+3(5) then you add 12+15 and get y=27
plz help me I only have 5 minutes left winner gets brainliest
In what year did the Apartheid Laws in South Africa end?
1990
1972
1994
1958
Answers
Answer:1994.
Step-by-step explanation:I need brainliest I helped with your other questions in comments pls
The local movie theater charges $13 for adult tickets and $7 for children’s tickets. Yesterday they sold 115 tickets and made $943. How many adult and children tickets did they sell?
Answers
Answer:
i need more info
Step-by-step explanation:
help please !!!! (will give brainliest)
Answers
Montana has a temperature of -0.7 so to get to 0 degrees you need to add 0.7. Once you get to zero you need to add 18.1 (Florida’s temperature) and then add 18.1 + 0.7 to get 18.8
Help, Help, Please
[tex] \sf find \: the \: value \: of \: \theta \: when \: \theta \: is \: acute\: angle[/tex]
[tex] \sf \cos^{2}(\theta) - \sin^{2}(\theta) =2-5 \cos(\theta) [/tex]
[tex]\text{note:explanation is a must}[/tex]
Answers
Answer:
θ = [tex]\frac{\pi }{3}[/tex] (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = [tex]\frac{1}{2}[/tex] , so
θ = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex] ( or 60° )
Answer:
[tex] \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:[tex] \sf \: rewrite \: \sin ^{2} ( \theta) \: as \: 1 - \cos ^{2} ( \theta) : \\ \sf \implies \: \cos ^{2} ( \theta) - (1 - \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: remove \: parentheses \: and \: change \: its \: sign : \\ \sf \implies \: \cos ^{2} ( \theta) - 1 + \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: add : \\ \sf \implies \: 2\cos ^{2} ( \theta) - 1 = 2 - 5 \cos( \theta) [/tex][tex] \sf \: move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \: : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 5 \cos( \theta) - 1 -2 = 0[/tex][tex] \sf \: rewrite \: 5\cos( \theta) \: as \: 6 \cos( \theta) - \cos( \theta) : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 6 \cos( \theta) - \cos( \theta) - 3 = 0[/tex][tex] \sf \:factor \: out \: 2 \cos( \theta) \: and \: - 1 : \\ \sf \implies \: 2\cos ( \theta)( \cos( \theta) + 3 ) -1( \cos( \theta) + 3) = 0[/tex][tex] \sf \: group: \\ \sf \implies \: (2\cos( \theta) - 1) ( \cos( \theta) + 3 ) = 0[/tex][tex] \sf \: rewrite \: as \: two \: seperate \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) - 1 = 0\\ \cos( \theta) + 3 = 0 \end{cases} [/tex][tex]\sf add \: 1 \: to \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) = 1\\ \cos( \theta) = - 3 \end{cases} [/tex][tex] \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation[/tex]
[tex] \sf substract \: both \: sides \: by \: 2 : \\ \implies\frac{ 2\cos( \theta) }{2} = \frac{1}{2} \\ \implies\cos( \theta) = \frac{1}{2} \\ \therefore \: \theta \: = {60}^{ \circ} [/tex]Carlos has 2.6 meters of wire. He has 3 projects for which he needs 0.9 meters each. Does carlos have enough wires?
Answers
Answer: Carlos does not have enough wires by 0.1 meters
Step-by-step explanation:
To determine if Carlos has enough wires, you need to find out the total amount of wires needed and then compare this to the amount of wires that Carlos has already.
= 0.9 + 0.9 + 0.9
= 2.7 meters
Carlos has 2.6 meters of wire but needs 2.7 meters.
Carlos therefore, does not have enough wires.
5 1 point > 키 Angles x and y are complementary in the diagram shown. 1 2 Z X 3 35° у 4 What is the measure, in degrees, of angle z? 5 Type your answer... 5
Answers
Answer:
∠z = 55°
Step-by-step explanation:
90° - 35° = 55°
Please look at the picture and answer my question I need help!
Answers
Answer:
64oz=4lb
Step-by-step explanation:
When converting ounces to pounds there is a 16:1 ratio, or there is 16 ounces in every pound.
To solve this, simply do 64/16 and you'll get your answer of 64oz=4lb.
64/16=4
64oz=4lb
May someone please help me with this :)
Answers
Answer:
14.3 yd
Step-by-step explanation:
apply the pythagorean Theorem formula:
= sqrt(14^2 +3^2)
= sqrt(205)
roughly 14.3 yd
Add or Subtract to simplify
Answers
Answer:
3. - 8n² -8n + 3
Step-by-step explanation:
(4n^4 - 8n +4) - (8n² + 4n^4 +1)
Firstly, open the brackets.
= 4n^4 - 8n +4 - 8n² - 4n^4 - 1
Now, group like terms.
= 4n^4 - 4n^4 - 8n² -8n - 1 + 4
4n^4 - 4n^4 cancel out with each other since one is negative and the other is positive. So we're left with - 8n² -8n - 1 + 4
= - 8n² -8n - 1 + 4
= - 8n² -8n + 3
How many equal sections divide a directed line segment if it is to be partitioned with a 2:7 ratio? 2, the least number given in the ratio
2, the least number given in the ratio
14, the least common multiple of the numbers given in the ratio
9, the sum of the numbers given in the ratio
5, the difference of the numbers given in the ratio
7, the greatest number given in the ratio
Answers
9514 1404 393
Answer:
9, the sum of the numbers given in the ratio
Step-by-step explanation:
The reduced ratio 2 : 7 means that two parts correspond to one length and 7 parts correspond to the other length. That is, there are a total of 2+7 = 9 parts in the full length of the segment.
It is convenient to think of the line segment as being divided into 9 equal parts.
_____
Additional comments
It is often helpful to consider the total number of "ratio units" in a given ratio. For example, in this problem, the shorter segment is 2/9 of the whole, and the longer one is 7/9 of the whole.
It can also be useful to consider what a "ratio unit" represents. If the whole segment is 27 inches long, then each of the 9 ratio units will represent 3 inches, for example. This means the division 2:7 is 2(3 in):7(3 in) = 6 in : 21 in.
Ab and cd intersects at e, aec=5x+12 and deb=8x-3
Answers
Answer:
x = 5
Step-by-step explanation:
Angles DEB and AEC are vertical angles, so they are congruent, and their measures are equal.
8x - 3 = 5x + 12
3x = 15
Write an inequality for the statement the temperature is greater than 100°F
Answers
T > 100 oF
SIMPLE 7TH GRADE MATH PROBLEM?!?!
Answers
Answer:
I'm sure it is 25 hope this helps!!!
Answer:
Should be 25
Step-by-step explanation:
Lol is that pearson realize? i hate that buddy good luck
If I have 14 neutrons and 11 electrons, what is my mass number?
A.25
B.3
C.11
D.14
Answers
Answer:
A : 25
Step-by-step explanation:
In a neutral atom, the number of electrons is equal to the number of protons. The atomic number indicates the number of protons.
The mass number is the sum of the number of neutrons and the number of protons.
mass number=protons+neutrons
As we know from the atomic number, the number of neutrons is 14 and the number of electrons is 11.
mass number = 14 + 11
Is parallelogram BCDE a rectangle?
Answers
Can someone help me with this??
Answers
Answer:
A
Step-by-step explanation:
When dilating an object, you multiply the x and y values by whatever scale you want to dilate the object by. It cannot be C because 2/5 is less than 1, which means that the object would shrink. So the answer must be A
help! parallel, perpendicular, or neither?
Answers
Answer:
parallel
Step-by-step explanation:
Because a is pependicular to k
Hope that’s helpful :)
The equation shown has an unknown number ⍰÷3/4=4/9
Answers
Answer:
9
Step-by-step explanation:
Analyze: 30 + 11 when c=4
Answers
Answer:
23
Step-by-step explanation:
3c + 11
3(4) + 11
12 + 11
23
how do you find the range of 0.3 0.9 0.2 0 0.7 0.9 0.4
Answers
The base of a 14-foot ladder is 2 feet from a building. If the ladder reaches the flat roof , how tall is the building
Answers
a^2 + b^2 = c^2
14^2 + 2^2 = 200
squareroot 200 is abt 14.14
Answer:
Step-by-step explanation:
The height of the building is 8 rad 3
Approximately 13.9 ft
If these four countries trade only with each other, what is the difference between the highest balance of trade and the lowest
balance of trade within this group?
a €4,378,000,000
€2,797,000,000
€1,928,000,000
d €738,000,000
Answers
Answer:
€4,378,000,000
Step-by-step explanation: just took the test :)
Answer:
A
Step-by-step explanation:
Took the test
QUESTION 6 / 10
Which of the following is not a source of income?
A. Your monthly student loan payment.
B. The stipend you receive for doing an internship.
C. Your annual salary for doing your job.
D. The wages you receive after a work shift.
Answers
Answer:
b. The stipend you receive.
Step-by-step explanation:
It would say paid intern if they were paid.
What is the image of the point (-7,-8)(−7,−8) after a rotation of 270^{\circ}270 ∘ counterclockwise about the origin?
Answers
The image of the point (-7, -8) after a rotation of 270 degrees counterclockwise about the origin is (8, -7).
What is counterclockwise ?
Counterclockwise is a direction of rotation that is opposite to the direction of the hands on a clock. It is also known as anticlockwise in some parts of the world. When viewed from above, counterclockwise rotation goes in the direction of a left-handed spiral, while clockwise rotation goes in the direction of a right-handed spiral. In mathematics, physics, and other fields, counterclockwise is often used as a standard convention for the positive direction or orientation of angles, planes, and other geometric objects. In graphical user interfaces, counterclockwise rotation is often used to indicate an undo or reverse action, while clockwise rotation is used to indicate a redo or repeat action.
According to the question:
When a point is rotated by 270 degrees counterclockwise about the origin, the new point is found by switching the x and y-coordinates of the original point, and negating the new x-coordinate. So, to find the image of the point (-7, -8) after a rotation of 270 degrees counterclockwise about the origin, we can use the following formula:
(x', y') = (-y, x)
where (x, y) is the original point and (x', y') is the new point after the rotation
Plugging in the values from the given point, we get:
(x', y') = (-(-8), -7)
Simplifying this expression, we get:
(x', y') = (8, -7)
Therefore, the image of the point (-7, -8) after a rotation of 270 degrees counterclockwise about the origin is (8, -7).
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Which expressions are equivalent to this exponential expression?
6-10
6-4
06-6
0 66
0
1
0
O
1
36
Answers
Answer:
6*6=36
Step-by-step explanation:
6*6. 6 with exponent of 2=36
[AB] is a diameter of center C(O, 3cm). M is a point on (C) such that MA=MB. D is the symmetric of A with respect to M.
What is the nature of triangle AMB? Justify.
Answers
Answer: I dont know AZ
ESCRIBE LA EXPRESION ALGEBRAICA : Paul tenía S/ e. Compró un libro y recibió S/ 3 de vuelto. ¿Cuánto costó el libro en términos de e? *
Answers
Answer:
p(e)=e-3
Step-by-step explanation:
De acuerdo a la información proporcionada, sabes que Paul tenía una determinada cantidad e y al comprar el libro recibió 3 de vuelto, lo que significa que el precio del libro sería igual a restar 3 de la cantidad que tenía al inicio, lo cual se puede expresar de la siguiente forma:
p(e)=e-3, donde
p es el precio del libro
e es la cantidad que Paul tenía al inicio
A survey was conducted on 800 students regarding the number of automobiles in their household. The population mean is 2.7 automobiles with a standard deviation of 0.7.
Which statement is true?
A.
There is a 95% certainty that the sample mean will fall within the interval 2.68 to 2.72.
B.
There is a 95% certainty that the sample mean will fall within the interval 2.67 to 2.73.
C.
There is a 95% certainty that the sample mean will fall within the interval 2.62 to 2.77.
D.
There is a 95% certainty that the sample mean will fall within the interval 2.65 to 2.75.