The length of Ruben's rectangular living room is 9 meters and the distance between opposite
corners is 10 meters. What is the width of Ruben's living room. Use Pythagorean theorem.
Answers
We know c^2 is 10, the diagonal length, and one leg we will call a^2 is 9
10^2 - 9^2 = b^2 (width)
Width is 4.36
Related Questions
The functions f(x) and g(x) are described using the following equation and table:
f(x) = −4(1.09)x
x g(x)
−4 −10
−2 −7
0 −4
2 1
Which equation best compares the y-intercepts of f(x) and g(x)?
Answers
The value of the y-intercepts of f(x) and g(x) is f(0), g(0) which gives -4.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The y intercept of an equation is the value of the function when x = 0.
Given that f(x) = -4(1.09)ˣ
f(0) = -4(1.09)⁰ = -4
From the table of g(x), when x = 0, g(0) = -4
The value of the y-intercepts of f(x) and g(x) is f(0), g(0) which gives -4.
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What is 3 + 2 HELP then after add 3456 then subtract 45 and then divid 20
Answers
The simplify value of numeric expression, 3 + 2, after adding 3456 then subtracting 45 and then dividing by 20 is equals the 17.8.
We have an expression of numbers, 3 + 2 we have to apply some arithematic operations on it and determine the final simplfy value. Let the expression be x = 3 + 2, add 3456 in it
=> x = 3 + 2 + 3456
Substracts 45 from above expression
=> x = 3 + 2 + 3456 - 45
Dividing the above expression of x by 20
=>
\(\frac{ x } {20} = \frac{ 3 + 2 + 3456 - 45}{20}\)
\(= \frac{3416}{20}\)
= 17.8
Hence, required simplify value is 17.8.
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Pleas help me this is due today you will get points and I will mark you as brain list I promise please help me. I have a learning disability and I need help with this
The Rodriguez family and the Hernandez family ate dinner together at the Safari Restaurant. They are deciding which family is going to pay the bill. They flip a coin to decide. If it lands on heads the Rodriguezs have to pay and if it lands on tails the Hernandez family pays.
The coin landed on heads 40% of the time. If it landed on heads 4 times, how many times did they flip the coin?
A. 5
B. 400
C. 4
D. 10
Answers
The total number of times that the coin was flipped would be 10 times. Option D.
What is probabilityA probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable." Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.
In order to prove that the number of flips that was done by the families 10, we would have to solve for the probability of heads using total of 10 and 4 as the total for the Rodriguez.
4 / 10 * 100
= 40%
Hence the other family flipped the coin 60 percent of the time. Such that 10 - 4 = 6
6 + 4 = 10
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Calculate the injury probability p (rounded to 2 decimals) that makes the decision maker indifferent between entering now and waiting until next year, that is for what probability are the EMV of both alternatives equal
Answers
The injury probability p that makes the decision maker indifferent between entering now and waiting until next year is approximately 0.26.
To calculate this probability, we need to set the expected values of entering now and waiting until next year equal to each other and solve for p. Let EMV₁ be the expected value of entering now and EMV₂ be the expected value of waiting until next year. Then we have:
EMV₁ = -1000p + 5000(1-p)
EMV₂ = 0.9(-1000p) + 0.1(5000)
Setting EMV₁ equal to EMV₂, we get:
-1000p + 5000(1-p) = 0.9(-1000p) + 0.1(5000)
Solving for p, we get:
p ≈ 0.26
Therefore, if the probability of injury is greater than 0.26, the decision maker should wait until next year to enter the market, and if the probability of injury is less than 0.26, the decision maker should enter the market now.
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list and describe two specialized alternatives not often used as a continuity strategy. quizlet
Answers
1. P-adic Numbers:
P-adic numbers are a specialized alternative not commonly used as a continuity strategy in mathematics. They are an extension of the real numbers that provide a different way of measuring and analyzing numbers. P-adic numbers are based on a different concept of distance, known as the p-adic metric. This metric assigns a measure of closeness or distance between numbers based on their divisibility by a prime number, p. P-adic numbers have unique properties and can be useful in number theory, algebraic geometry, and other branches of mathematics. However, they are not typically employed as a continuity strategy in practical applications.
2. Nonstandard Analysis:
Nonstandard analysis is a mathematical framework that provides an alternative approach to calculus and analysis. It introduces new types of numbers called "infinitesimals" and "infinite numbers" that lie between the standard real numbers but are infinitely smaller or larger than any real number. Nonstandard analysis allows for more rigorous treatment of infinitesimal quantities and provides a different perspective on limits, continuity, and differentiation. While nonstandard analysis has theoretical implications and can provide valuable insights in mathematical research, it is not commonly used as a continuity strategy in practical applications where standard analysis and calculus are more prevalent.
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A large orange weighs 11/16 pound. A small orange weighs 2/8 pound. How much more does the large orange weigh?
Answers
Answer:
7/16 pounds
Step-by-step explanation:
Change the small orange to have the same denominator by multiplying by a magic 1 or \(\frac{2}{2}\).
1. \(\frac{2}{8}\)·\(\frac{2}{2}\)\(=\frac{4}{16}\)
2. Subtract Fractions
\(\frac{11}{16}\)-\(\frac{4}{16}\)=\(\frac{7}{16}\)
If 1 serving of stir fry use 3/5 cup of rice how many cups are in 11 servings?
Answers
Answer:
11 servings include 11(3/5), or 33/5, or 6 3/5, cups of rice.
Step-by-step explanation:
If 1 serving includes 3/5 cup of rice, then multiplying both numerals here by 11 produces a similar statement for 11 servings:
11 servings include 11(3/5), or 33/5, or 6 3/5, cups of rice.
convert n = (2.80∠–29.9°) to rectangular form, (a + jb)
Answers
The rectangular form of n = (2.80∠–29.9°) is n = 2.45 – 1.38j.
To convert the polar form of n = (2.80∠–29.9°) to rectangular form, we can use the following equations:
a = r*cos(θ)
b = r*sin(θ)
where r is the magnitude of the complex number and θ is its angle in polar form.
Using the given values, we have:
r = 2.80
θ = –29.9°
Converting θ to radians:
θ = –29.9° * π/180 = –0.522 radians
Substituting the values in the equations, we get:
a = 2.80*cos(–0.522) = 2.45
b = 2.80*sin(–0.522) = –1.38
Therefore, the rectangular form of n = (2.80∠–29.9°) is:
n = 2.45 – 1.38j
So, The rectangular form of n = (2.80∠–29.9°) is n = 2.45 – 1.38j.
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solve and check for -3x + 12= -7x -20
Answers
Answer:
x=8
Step-by-step explanation:
Make sure variables are on one side of the equation and numbers are on the other
-3x+7x=-20-12
-4x=-32
4x=32
x=8
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The lengths of the sides of a triangle are 15cm, 20cm, 30cm. What are the lengths of the sides of a similar triangle that has a perimeter of 26cm?
Answers
second triangle:
a+b+c=26cm
those 3 nombers have 5 in common
so 3x+4x+6x=26(divided each by 5)
13x=26
x=2
so: 6+8+12=26cm. (plug the value of x)
any questions?
The lengths of the sides of a similar triangle that has a perimeter of 26 cm are 6 cm, 8 cm and 12 cm.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, the lengths of the sides of a triangle are 15cm, 20cm, 30cm.
Now, perimeter =15+20+30
= 65 cm
The lengths of the sides of a similar triangle that has a perimeter of 26cm
The ratio of the perimeters of two similar figures is equal to the ratio of their corresponding side lengths.
So, 65/26 =2.5
Now, sides of similar triangle are
15/2.5 =6 cm
20/2.5 =8 cm
30/2.5 =12 cm
Therefore, the lengths of the sides of a similar triangle that has a perimeter of 26 cm are 6 cm, 8 cm and 12 cm.
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(08.01)
Given the arithmetic sequence an = 4 + 8(n - 1), what is the domain for n? (1
point)
All integers
All integers where n > 1
All integers where n > 0
All integers where n > 1
Answers
N must be greater than one so it doesn’t equal zero when you subtract
Question 1: How much fabric is needed for a round table cloth?
Assume the radius is 10 inches. How much fabric would you need?
Answers
Answer:
50 yards because of the roundness of the table
A= π•r^2
r=10in
A= π•10^2
A=3.14 • 100
A=314 in^2
Which expression is equivalent to the given expression? (+2+6)-(- 2+3) x +9 O A I O B. - } +3 O C. x+3 OD. - *+9
Answers
Answer:
The equivalent expression is;
\(\frac{5}{7}x+3\)Explanation:
We want to simplify the expression;
\((\frac{1}{7}x+6)-(-\frac{4}{7}x+3)\)we will first multiply the negative by every term in the bracket, then simplify by collecting the like terms.
\(\begin{gathered} \frac{1}{7}x+6-(-\frac{4}{7}x)-(+3) \\ \frac{1}{7}x+6+\frac{4}{7}x-3 \\ \text{collecting the like terms we have;} \\ \frac{1}{7}x+\frac{4}{7}x+6-3 \\ \frac{5}{7}x+3 \end{gathered}\)Therefore, the equivalent expression is;
\(\frac{5}{7}x+3\)The leading brand of cosmetics in the US had about 20% of the total sales in the industry. The total sales were $ 200,000. What was the leading brands sales? Show your work.
Answers
Answer: $40000
Step-by-step explanation:
200000(0.2) = $40000
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Write an addition problem that has a sum of -2 4/5 and the two addends have different signs.
Answers
Answer:
-3+1/5
Step-by-step explanation:
Mr. Brutry ordered 78 pencils for the students in his class. He ordered enough pencils for each student to have exactly 3
pencils.
How many students are in Mr. Bruno's class?
Use a letter to represent the number of students in Mr. Bruno's class.
Write an equation and use it to solve the word problem.
Answers
Answer:
He has 26 students
Step-by-step explanation:
78/3=26
1. y = (x - 5)(x + 1), Find y if x = - 3.
2. v= u + at
(a)
YEAR 7 HOME WORK
Work out v when u = 23, a = 4, and t = 3
(b)
Work out u when v= 30, a = 2 and t = 8
(c) Work out t when v = 40, u = 12 and a = 4
3. The circumference of a circle can be found using the formula C = 2nr or C = nd
Find the circumference of a circle with radius 8 cm.
Leave your answer to one decimal place.
4. Speed is calculated using the formula S=
Find the speed at which a car travelled if it took 2 hours to travel a distance of 100 km
D
T
where D is distance and T is time.
Answers
Answer:
1) y=-2, y=-8
2a) v=35
b) u=12
c) t=7
3) c=50.3
4) s=50
1 ]
Given:-
\( \tt{y = ( x - 5 ) ( x + 1 ) }\)\( \: \)
\( \tt{x = - 3}\)\( \: \)
To find:-
\( \tt \: y = ?\)\( \: \)
Solution:-
\( \tt{y = ( x - 5 ) ( x + 1 )}\)\( \: \)
now , put the value of x = -3 in equation
\( \tt \: y = ( -3 - 5 ) ( -3 + 1 )\)\( \: \)
\( \tt \: y = ( - 8 ) ( - 2 )\)\( \: \)
or
\( \tt \: y = 16 \)\( \: \)
\( \texttt{The value of \boxed{ \tt \red{ y = ( -8 ) ( -2 )} } \: or \boxed{ \tt \red{ 16}} !}\)
\( \: \)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
2 ]
\( \texttt{v = u + at} \: - - - \texttt{given \: formula \: or \: eqn}\)
a ) ----»
Given:-
\( \tt \: u = 23 \)\( \: \)
\( \tt \: a = 4\)\( \: \)
\( \tt \: t = 3\)\( \: \)
To find:-
\( \tt \: v = ?\)\( \: \)
Solution:-
\( \tt \: v = u + at\)\( \: \)
now , put the given value in equation
\( \tt \: v = 23 + 4×3\)\( \: \)
\( \tt \: v = 23 + 12\)\( \: \)
\( \boxed{\tt \purple{ v = 35}}\)\( \: \)
____________________________________
b )
Given:-
\( \tt \: v = 30\)\( \: \)
\( \tt \: a = 2 \)\( \: \)
\( \tt \: t = 8\)\( \: \)
To find:-
\( \tt \: u = ?\)\( \: \)
Solution:-
\( \tt \: v = u + at\)\( \: \)
put the given value in equation
\( \tt \: 30 = u + 2×8\)\( \: \)
\( \tt \: 30 = u + 16\)\( \: \)
\( \tt \: 30 - 16 = u\)\( \: \)
\( \tt \: 14 = u\)\( \: \)
\( \boxed{ \tt \pink{ u = 14}}\)\( \: \)
____________________________________
c )
Given:-
\( \tt \: v = 40\)\( \: \)
\( \tt \: u = 12\)\( \: \)
\( \tt \: a = 4\)\( \: \)
To find:-
\( \tt \: t = ?\)\( \: \)
Solution:-
\( \tt \: v = u + at\)\( \: \)
now , put the given value in equation
\( \tt \: 40 = 12 + 4t\)\( \: \)
\( \tt \: 40 - 12 = 4t\)\( \: \)
\( \tt \: 28 = 4t\)\( \: \)
\( \tt \cancel \frac{28}{4} = t\)\( \: \)
\( \tt \: 7 = t\)\( \: \)
\( \boxed{\texttt{ \green{t = 7}}}\)\( \: \)
━━━━━━━━━━━━━━━━━━━━━━━━━━━
3 ]
Given:-
\( \tt \: radius = 8\)\( \: \)
To find:-
\( \texttt{circumference of circle = ?}\)\( \: \)
By using given formula:-
\( \underline{ \tt \: \: C = 2πr \: \: }\)\( \: \)
Solution:-
\( \tt \: C = 2πr \)\( \: \)
\( \texttt{C = 2× 3.14× 8 [ as we know that the value of π = 3.14 constant ]}\)\( \: \)
\( \tt{C = 16 × 3.14}\)\( \: \)
\( \tt{C = 50.24}\)\( \: \)
\( \texttt{The Circumference of the circle is { \blue{50.24}} !}\)
\( \: \)
━━━━━━━━━━━━━━━━━━━━━━━━━━━
4 ]
Given:-
\( \texttt{Time ( T ) = 2h}\)\( \: \)
\( \texttt{Distance ( D ) = 100km}\)\( \: \)
To find:-
\( \texttt{Speed ( S ) = ?}\)\( \: \)
By using formula:-
\( \underline{\tt{ \: \: Speed= \frac{Distance}{Time} \: \: }}\)\( \: \)
Solution:-
\( \tt \: S = \frac{D}{T} \)\( \: \)
\( \tt \: S = \cancel\frac{100}{2} \)\( \: \)
\( \tt \: S = 50\)\( \: \)
\( \texttt{The Speed of the car is \color{green}50.}\)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps⸙
Please, if anyone knows help me, I need a lot of help in this activity.
Answers
Answer:
Step-by-step explanation:
Perimeter of the given polygon = n + 2 + 3 + 4 + n + 2 + 3 + 4
= 2(n + 2 + 3 + 4)
= 2(n + 9) units
Area of the composite figure = Area of rectangle A + Area of rectangle B + Area of rectangle C
= (3 × 4) + (n ×2) + (2 × 3)
= 12 + 2n + 6
= 2n + 18
= 2(n + 9) units²
Therefore, perimeter of the given figure = Area of the figure
what is 2+4x6 in math and english
Answers
Answer:
Step-by-step explanation:
4 x 6= 24
24+2=26
24+2=26
Si the answer is 26
Five regular six-sided dice are rolled. How many ways are there to roll the dice so that the total of the numbers on the five dice is 14
Answers
If five regular six sided dice are rolled then there are 540 ways through which sum of numbers coming after rolling will be 14.
Given Five regular six sided dices are rolled.
From stars and bars the number of n tuples of natural numbers summing up to k is given by
\((k-1\\n-1)\)
For k=14 and n=5
\((14-1 \\5-1)\)
=\((13\\4)\)
=715
Some of these will contains a number greater than 6.To get the number of 5 tuples that correspond to 5 rolls of a six sided dice we need to subtract from 715.
Total 5 tuples summing up to 14 for which no element is greater the 6 is given as under:
N=\((13/4)-5(6/3)-5(5/3)-5(4/3)-5(3/3)\)
where last term comes from the 5 tuples containing one 10 and fours'
=715-100-50-20-5
=540
Hence there are 540 such ways which sum to 14 when five six sided dices are rolled.
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find the value of x. A.12 B.30 C.9 D. 21.75
Answers
Answer:
i need help my self keep trying
Step-by-step explanation:
Lisa bought 4 feet of gold braid at a price of 5.75 per yard. what was the total price of the amount of gold braid she bought
Answers
Quincy uses 2 cups of vinegar in his salad dressing recipe. How much vinegar would Quincy use to make 1/2 of a recipe?
Answers
Can somebody answer this short word problem but show the steps when u get answer thanks!
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDDD
Answers
Answer:
8 dozen gingerbread men
Step-by-step explanation:
2 + 3 = 5
120 ÷ 5 = 24
24 x 4 = 96
96 ÷ 12 = 8
Information:
-5 raisins for each gingerbread man
-Buys 4(120) raisins= 480 raisins
-Dozens
Steps:
Use the equation: 480=5x, where x=number of gingerbread man
Divide both sides by 5 to eliminate x
= x=96
Next, divide that by 12 because the question is asking how many DOZENS.
96/12 = 8
An identity.[hint.multiply through by (3x-1)(x2+1) and equate the corresponding coef-ficiens of the polynomials on each side of the resulting equation.]
Answers
Answer:
Step-by-step explanation:
To prove an identity, let's start with the given equation:
(3x - 1) / (x^2 + 1) = (2x + 3) / (x^2 + x)
To prove the identity, we'll multiply through by (3x - 1)(x^2 + 1) on both sides of the equation:
(3x - 1)(x^2 + 1) * (3x - 1) / (x^2 + 1) = (3x - 1)(x^2 + 1) * (2x + 3) / (x^2 + x)
Simplifying the equation:
(3x - 1)(x^2 + 1) = (2x + 3)(3x - 1)
Now, we can expand both sides of the equation:
3x^3 - x^2 + 3x - 1 = 6x^2 + 5x - 3
Rearranging the terms:
3x^3 - x^2 - 6x^2 + 3x - 5x - 1 + 3 = 0
Combining like terms:
3x^3 - 7x^2 - 2x + 2 = 0
Now, we equate the corresponding coefficients of the polynomials on each side of the resulting equation:
Coefficient of x^3: 3 = 3 (same on both sides)
Coefficient of x^2: -7 = -7 (same on both sides)
Coefficient of x: -2 = -2 (same on both sides)
Constant term: 2 = 2 (same on both sides)
Since the coefficients on both sides of the equation are equal for all terms, we have proved the identity:
(3x - 1) / (x^2 + 1) = (2x + 3) / (x^2 + x)
Hope this answer your question
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560Steve can paint his greenhouse in four hours working alone; his ten-year-old son can paint the greenhouse alone in nine hours. Working together, how long, to the nearest minute, would it take them
Answers
By working together, they can make the work done in two hours and forty-six minutes.
How do you calculate work done together?The equation below may be used to compute work: Work is equal to force times distance. The Newton metre is the SI unit of work (N m). When an item is moved across a distance of 1 m with 1 N of force, one joule is equal to the amount of work that is accomplished.Every time a force pushes anything over a distance, work is done. By multiplying the force by the distance travelled in the direction of the force, you may determine the amount of energy transferred, or work done.Therefore, the formula for work is W = F d s, which stands for work done equal to force times displacement.Given data :
Think of these work rates as "greenhouses per hour", not "hours per greenhouse". Then Steve's work rate is one fourth of a greenhouse per hour, and his son's is one ninth of a greenhouse per hour. Now, multiply each rate by the time t to get the portion of the greenhouse each paints, and add the products up to get one greenhouse. The work equation becomes:
1 / 4 t + 1 / 9 t = 1
9 / 36 . t + 4 / 36 t = 1
13 / 36 t = 1
36 / 13. 13 / 36 t = 36 / 13 .1
t = 36 / 13 hrs
or 36 / 13. 60 = 166 min
This is two hours and forty-six minutes.
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Calculate the concentrations of all species present in 0.72 M
NH3 (Kb=1.8×10−5).
Express your answers using two significant figures separated by
commas. Enter the concentrations of the species in t
Answers
To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.
NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:
NH3 + H2O ⇌ NH4+ + OH-
Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.
To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:
1.8×10−5 = x * x / (0.72 - x)
Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.
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the yellow cab company charges a flat fee of $3.50 and an additional $2.50 per mile. the relaxicab company charge $2.30 per mile and a $4.54 fee. at how many miles do the two companies charege the same amount? write a system of equations that computes the cost of the cabs. use for the miles, and for the cost.
Answers
Step-by-step explanation:
Since the initial fee is fixed, we can assume it is a constant and the succeeding mile fee is the variable as it changes for every mile covered.
Let x = distance (mile)
let y = total charge (dollars)
Yellowcab company equation for cost calculation; 3.50 + 2.5x = y
laxicab company equation for cost calculation; 4.54+2.3x = z
the two companies charge the same amount when y = z
; 3.50 + 2.5x = 4.54+2.3x
x = 5.2 miles
COST CALCULATION
;3.50 + 2.5x = ?
if x = 5.2;
; 3.50 + 2.5(5.2) =$16.50
OR
; 4.54+2.3x = ?
; 4.54 + 2.3(5.2) = $16.50
P=-3 4 1. Find a basis {U1, U2, U3} for R3 such that P is the change-of-coordinates matrix from {U1, U2, U3} to the basis {V1, V2, V3}. 2. Find a basis {W1, W2, W3} for R3 such that P is the change-of-coordinates matrix from {V1, V2, V3} to {W1, W2, W3}.
Answers
To answer this question, you must first find the change-of-coordinates matrix from the basis U1, U2, U3 to the basis V1, V2, V3. This can be done by using the given matrix P, and setting it equal to the change-of-coordinates matrix:
P = [U1 U2 U3]-1 [V1 V2 V3]
Therefore, the basis {U1, U2, U3} is:
U1 = [-3 2 1]
U2 = [4 2 -3]
U3 = [1 -2 4]
To find the basis {W1, W2, W3}, use the same process as before, but setting P equal to the change-of-coordinates matrix from {V1, V2, V3} to {W1, W2, W3}:
P = [V1 V2 V3]-1 [W1 W2 W3]
Therefore, the basis {W1, W2, W3} is:
W1 = [-3 2 1]
W2 = [4 2 -3]
W3 = [1 -2 4]
To summarize, the change-of-coordinates matrix from {U1, U2, U3} to {V1, V2, V3}, and from {V1, V2, V3} to {W1, W2, W3}, is given by the matrix P = [-3 4 1].
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PLS PLS i need step by step please and undefined numbers to be shown please THANK YOU!
Answers
1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.
x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.
2) The given expression is:
(5-2x)/(x+2) + x^2/(x^2-4) - 5
To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:
[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]
Expanding the brackets and simplifying, we get:
(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]
This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.
(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.
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