The simplification form of the expression "(z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12)" is = "1/(z+6)".
To add the two fractions, we need to have a common denominator. Since both fractions already have the same denominator of z^(2)+8z+12, we can simply add the numerators together and keep the same denominator.
So, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = (z+2)/(z^(2)+8z+12)
Now, we need to simplify the fraction as much as possible. We can do this by factoring the denominator and seeing if there are any common factors that can be canceled out.
The denominator can be factored as (z+6)(z+2).
So, (z+2)/(z^(2)+8z+12) = (z+2)/(z+6)(z+2)
Now, we can see that there is a common factor of (z+2) in both the numerator and denominator, so we can cancel them out.
So, the final simplified answer is 1/(z+6).
Therefore, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = 1/(z+6).
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Simplify the following expressicn using addition and subtraction. (x)/(3)+(2x)/(18)-(6x)/(3)
The answer is (-14x)/(9).
To simplify the given expression, we need to find a common denominator for all the fractions, which is 18. We can then multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions. Once we have the same denominator, we can combine the numerators using addition and subtraction. Finally, we can simplify the resulting fraction if possible.
The expression is: (x)/(3)+(2x)/(18)-(6x)/(3)
First, find a common denominator for all the fractions. The smallest common denominator is 18.
Next, multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions:
(x)/(3) * (6)/(6) = (6x)/(18)
(2x)/(18) * (1)/(1) = (2x)/(18)
(6x)/(3) * (6)/(6) = (36x)/(18)
Now, we can combine the numerators using addition and subtraction:
(6x)/(18) + (2x)/(18) - (36x)/(18) = (6x + 2x - 36x)/(18) = (-28x)/(18)
Finally, we can simplify the resulting fraction by dividing both the numerator and denominator by 2:
(-28x)/(18) = (-14x)/(9)
So the simplified expression is: (-14x)/(9)
Therefore, the answer is (-14x)/(9).
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23
b. Complete the double number line diagram that represents the situation.
Photos
0
0
Minutes!
:: 1
7
2
4
:: 4
:: 6
1
#15
21
8
3
28
:: 9
80
#20
# 10
35
12
:: 14
PLEASE HELP I NEEEDA LIKE FINISH IT RN HELP
Answer:
10mins for 35 photos
Step-by-step explanation:
If it takes 8mins to produce 28photos, that is ratio 1:3.5
For 7 photos, divide by 3.5, that is 2mins
For 4mins, multiply by 3.5, that will be 14photos
For 21 photos, divide by 3.5, that will be 6 mins
Ordering Fractions (A) Order each set of fractions using the number line. (1)/(2),(4)/(5),(1)/(5),1(3)/(10),1(9)/(10)
The correct order of the fractions is: (1)/(5), (1)/(2), (4)/(5), 1(3)/(10), 1(9)/(10).
To order the fractions using the number line, we need to compare each fraction and determine which one is smaller or larger. Here are the steps to do this:
1. Find the least common denominator (LCD) of all the fractions. In this case, the LCD is 10.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator. This means multiplying the numerator and denominator of each fraction by the same number to get the LCD as the new denominator.
- (1)/(2) = (1*5)/(2*5) = (5)/(10)
- (4)/(5) = (4*2)/(5*2) = (8)/(10)
- (1)/(5) = (1*2)/(5*2) = (2)/(10)
- 1(3)/(10) = (13)/(10)
- 1(9)/(10) = (19)/(10)
3. Now that all the fractions have the same denominator, we can compare the numerators to determine the order of the fractions.
4. Arrange the fractions from smallest to largest according to their numerators:
- (1)/(5) = (2)/(10)
- (1)/(2) = (5)/(10)
- (4)/(5) = (8)/(10)
- 1(3)/(10) = (13)/(10)
- 1(9)/(10) = (19)/(10)
In conclusion, to order the set of fractions (1)/(2),(4)/(5),(1)/(5),1(3)/(10),1(9)/(10) using the number line, we need to find the least common denominator, convert each fraction to an equivalent fraction with the LCD as the denominator, and then compare the numerators to determine the order of the fractions.
The correct order is (1)/(5), (1)/(2), (4)/(5), 1(3)/(10), 1(9)/(10).
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True; by the Invertible Matrix Theorem if the equation Ax^(0) has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the identity matrix.
The given statement, "by the Invertible Matrix Theorem if the equation [tex]Ax^{(0)}[/tex]has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the identity matrix," is true (T).
This is because the theorem states that a square matrix is invertible if and only if it can be transformed into the identity matrix by a sequence of elementary row operations. And if the equation [tex]Ax^{(0)}[/tex] only has the trivial solution, then the matrix must be row equivalent to the identity matrix, implying that it is invertible.
The Invertible Matrix Theorem is a powerful result in linear algebra that allows us to determine whether a square matrix is invertible or not. It states that a square matrix is invertible if and only if its determinant is nonzero, which is equivalent to saying that the matrix can be transformed into the identity matrix by a sequence of elementary row operations.
If the matrix is not invertible, then its determinant is zero, and it is said to be singular. In this case, the equation [tex]Ax^{(0)}[/tex] will have infinitely many solutions or no solutions at all, depending on the specific values of the right-hand side vector.
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Use a calculator to find the trigonometric value to 4 decimal places. sin 14° = __________
The trigonometric value of sin 14° to 4 decimal places is sin 14° = 0.241.
Step 1: Enter the value of 14 into the calculatorStep 2: Press the sin button on the calculatorStep 3: The calculator will display the value of sin 14°Step 4: Round the value to 4 decimal places
The value of sin 14° to 4 decimal places is 0.2419.
An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.
The unit of measurement associated with angles is degrees.
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A second year mathematics unit at a university in a foreign country has unpredictable patterns of administering weekly tests. There will be either no test, or one test, and if there is one, it is either a 15 minute minor test or a 30 minute major test. For any given week, if there was no test in the previous week, the probability that there will be a minor test is 0.6, and the probability that there will be a major test is 0.3. For a week where there was a minor test in the previous week, the probability of minor and major tests are 0.4 and 0.2 respectively. If there was a major test in the previous week, this week there will be a minor test with probability 0.3 and no test with probability 0.7. Let Xn be the Markov chain for the situation described above, with state space {0, 1, 2}, where 0 indicates no test, 1 stands for a minor test, and 2 indicating a major test. a) Write down the transition matrix for the Markov chain. b) Find the two-step transition probability matrix for the Markov chain. c) Given that there was no test this week, find the probability that there is a test in two weeks time. d) Compute P(X5 = 2|X3 = 1, X1 = 0).
Given that there was no test this week (X0 = 0), the probability that there is a test in two weeks time (X2 = 1 or X2 = 2) is given by the sum of the probabilities of the two possible states in the two-step transition probability matrix:
P(X2 = 1 or X2 = 2|X0 = 0) = P^2[0][1] + P^2[0][2] = 0.36 + 0.12 = 0.48
To compute P(X5 = 2|X3 = 1, X1 = 0), we can use the formula for conditional probability:
P(X5 = 2|X3 = 1, X1 = 0) = P(X5 = 2, X3 = 1, X1 = 0)/P(X3 = 1, X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)*P(X1 = 0)/P(X3 = 1|X1 = 0)*P(X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)/P(X3 = 1|X1 = 0)
= P(X5 = 2|X3 = 1)
= P²[1][2]
= 0.12
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Designing an Addition A 40-ft-wide house has a roof with a
6-12 pitch (the roof rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will have a 3-12 pitch to its roof. Find the lengths of AB and BC in the accompanying figure.
We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
What is sine formula in trigonometry?Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.
Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof
rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will
have a 3-12 pitch to its roof.
We can write the measure of length AB as -
AB = 6 + √(9 + 296)
AB = 6 + 17.46
AB = 23.46 ft
We can write the measure of length BC as -
BC = 6 + 1/4 x 12
BC = 6 + 3
BC = 9 ft
Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
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Question 3 of 12 , Step 1 of 1 Find three consecutive integers whose sum is 360.
The three consecutive integers whose sum is 360 are 119, 120, and 121.
To find three consecutive integers whose sum is 360, we can use algebra to set up an equation and solve for the first integer. Let x be the first integer, then the next two consecutive integers will be x+1 and x+2. The sum of these three integers is 360, so we can write the equation:
x + (x+1) + (x+2) = 360
Simplifying the equation gives us:
3x + 3 = 360
Subtracting 3 from both sides gives us:
3x = 357
Dividing both sides by 3 gives us:
x = 119
So the first integer is 119. The next two consecutive integers are 120 and 121. Therefore, the three consecutive integers whose sum is 360 are 119, 120, and 121.
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The selling price of each cup of lemon juice is 3/2 times as much as the selling price of a cup of apple juice. For every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. He earns $12 more from apple juice than from lemon juice. How much does Mr Tan earn altogether?
He makes $8/49 for every 7 cups of juice, so his overall profits will be some multiple of $8/49.
what is unitary method ?Finding the worth of one unit of a quantity, then using this value to determine the value of a specified number of units of the quantity, is known as the unitary technique. When solving issues involving rates, ratios, and proportions, this approach is helpful. The fundamental tenet of the unitary technique is that we can use the value of one unit of a quantity to determine the value of any number of additional units of the same quantity.
given
Let's symbolise the cost of a cup of apple juice by the variable x.
So, a cup of lemon juice is sold for 3/2 times x, or (3/2)x.
Mr. Tan offers 5 cups of apple juice for every 2 cups of lemon juice. This indicates that there are 2.5 sales of lemon juice for every 1 sales of apple juice.
Assume Mr. Tan sells 5y cups of apple juice and 2y cups of lemon juice.
Based on the information provided, we can conclude that apple juice generates $12 more revenue than lemon juice.
in order to create an equation:
5yx = 2(3/2)x + 12
Simplifying:
5yx = 3x + 12
adding two to both sides:
10yx = 6x + 24
x(10y - 3) = 12
x = 12 / (10y - 3) (10y - 3)
We can now re-use this number of x to represent the revenue from apple juice in the equation:
5yx = 3x + 12
5y(12 / (10y - 3)) = 3(12 / (10y - 3)) + 12
Therefore, Mr. Tan charges $1/7 for each cup of apple juice and (3/2)($1/7) Equals $3/14 for each cup of lemon juice.
He charges (5/7)($1/7) = $5/49 for 5y = 5(1/7) = 5/7 glasses of apple juice.
For a sum of (2/7)($3/14) = $3/49, he sells 2y = 2(1/7) = 2/7 cups of lemon juice.
For each 7 cups of juice sold, Mr. Tan makes a sum of $5/49 + $3/49 = $8/49.
Consider that he offers 2n cups of lemon juice and 5n glasses of apple juice. (2n)($3/14) + (5n)($1/7) = $6n/49 + $5n/49 = $11n/49
He makes $8/49 for every 7 cups of juice sold, so his overall profits will be some multiple of $8/49.
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cindy bought 7/8 yard of ribbon jacob bought 4/5 more than cindy how much did he buy
In linear equation, 7/10 did he buy .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
multiply the fractions by each other.
7/8*4/5
7*4=28
8*5=40
28/40
"B" would be the correct answer but, it the fraction should be reduced to 7/10.
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The length and width of two rectangular gardens are shown. Find the sum of the
areas of the two gardens in simplest form.
Answer:
13.1y
Step-by-step explanation:
Normally in questions like this, you would be given the total area and asked to find the value of y. In this case, the area is not given, so it can be assumed the question requires you to give your answer in terms of y.
The area of a rectangle is found by multiplying the length by the width. In this case, we want to add two areas together to find the total area of the two gardens:
(3.3 * 2y) + (1.3y * 5)
We can simplify both sides of the expression:
3.3 * 2y = 6.6y
1.3y * 5 = 6.5y
Now we can add these together to find the total area, in terms of y:
6.6y + 6.5y = 13.1y
I need some help please
Someone please help me on this
Answer:
x=6
Step-by-step explanation:
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A pool is filled with 270 cubic meters of water. The base of the pool is 15 meters long and 9 meters wide. What is the height of the water in the pool?
pool = length x width x height
pool = 15 x 9 x ?
270 = 135x
x = 2
the height is 2 meters.
pls help with this math
[tex]\overline {BC}[/tex] corresponds to [tex]\overline {FG}[/tex] statement is true for the given question.
What is a rectangle?
A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.
Here, we have
Given: Rectangle ABCD is translated to produce image EFGH.
We have to determine the true statement that satisfies the given rectangle.
We concluded from the rectangle that BC will correspond to FG
Polygons' matching sides and corresponding angles are compared in tests for congruence and resemblance. In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Hence, BC corresponds to FG.
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The perimeter of a rectangular field is 294 m. If the length of the field is 96 m, what is its width?
The width of the rectangular field is 51 m. To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Given:
P = 294 m
L = 96 m
Substituting the given values into the formula, we get:
294 = 2(96) + 2W
Simplifying the equation, we get:
294 = 192 + 2W
Subtracting 192 from both sides of the equation, we get:
102 = 2W
Dividing both sides of the equation by 2, we get:
W = 51
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Suppose the total length of the guitar is given by the expression 8 147. Which radical expression represents the length of the body if the neck measures 8 48 ?
The length of the body of the guitar is represented by the radical expression 24√3.
We can start by simplifying 8√147.
8√147 = 8√(49 × 3) (since 49 is a perfect square)
= 8 × 7√3
= 56√3
Next, we need to find the length of the body of the guitar, given that the neck measures 8√48. We know that the total length of the guitar is 56√3, so we can set up an equation:
total length = length of neck + length of body
56√3 = 8√48 + length of body
To solve for the length of the body, we can start by simplifying 8√48:
8√48 = 8√(16 × 3) (since 16 is a perfect square)
= 8 × 4√3
= 32√3
Substituting this back into the equation:
56√3 = 32√3 + length of body
Simplifying:
length of the body = 24√3
Therefore, the answer is A) 24√3.
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The question is -
Suppose the total length of the guitar is given by the expression 8√147. Which radical expression represents the length of the body if the neck measures 8√48? A) 24√3 B) 12√3 C) 8√3 D) 9√9
plssss helppp this mathematics
Answer:
y = x+5
x+2y=16
x+2(x+5)=16
x+2x+10=16
3x+10=16
16. 3x + 10 = 16
3x+10=16
-10 -10
3x=6
Divide 3 from both sides
x=2
y=x+5
y=2+5
y=7
17. (2,7)
Andy has been saving his pocket money. He began the month with $44 and ended with $110. He said the end of the month amount was 250% of his original amount. Is the statement CORRECT? Justify your thinking
The Andy's statement is correct because the end of the month amount is indeed 250% of his original amount.
To determine if Andy's statement is correct, we need to verify if the end of the month amount is indeed 250% of his original amount.
Let original amount of money that Andy had at beginning of month be = x ;
According to the problem, he began with $44, so x = $44.
Let amount of money that Andy had at the end of the month be = y;
According to the problem, he ended with $110, so y = $110.
Andy's statement is that the end of the month amount of $110 is 250 percent of his original amount of $44;
⇒ y = 2.5x
Substituting the values,
We get,
⇒ $110 = 2.5 × $44;
Simplifying,
We get,
⇒ $110 = $110.
Therefore, Andy's statement is correct.
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Find the measure of pkt
Answer:
32°
Step-by-step explanation:
You want the measure of the smaller angle of the linear pair marked (3g+23) and (7g+127).
Linear pairThe angles of a linear pair total 180°, so we have ...
(3g +23) +(7g +127) = 180
10g = 30 . . . . . . . . . subtract 150
g = 3 . . . . . . . . . divide by 10
The smaller angle is ...
∠PKT = (3·3 +23)°
∠PKT = 32°
What is the probability of picking a purple marble and spinning green?
Answer:
two out of how many there is.
Step-by-step explanation:
Graph the inequality y+4<-2(x-4) on the set of axes below
Answer:
y < 2x + 4
Step-by-step explanation:
y+4<-2(x-4)
y + 4 < -2x +8
y < 2x + 4
extra points for help (dont guess please)
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
What exactly are exponential functions?
Exponential functions are functions that involve a variable exponent. They are of the form f(x) = aˣ, where "a" is a positive constant base and "x" is the variable exponent.
Exponential functions exhibit rapid growth or decay, depending on the value of "a" and the sign of "x". For example, if "a" is greater than 1, the function grows rapidly as "x" increases, while if "a" is between 0 and 1, the function decays rapidly as "x" increases.
Now,
As stated above that for exponential function y=aˣ
when a>1 it shows exponential growth
and when a<1 it shows decay.
hence,
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
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Two integers between 60 where the square root lies
It is answer choice (C). 7 and 8!
Really hope this helped! brainliest would be very appreciated!
~HAPPY DAYZ~
solve equation . show or explain your method
5(y+2/5)=−13
Answer:
Step-by-step explanation:
You can use simple algebraic principles for this. First we distribute:
5(y + 2/5) = -13
5y + 10/5 = -13
5y + 2 = -13
Now we isolate the variable term:
5y + 2 = -13
5y = -15
Now we divide to isolate the variable itself:
5y = -15
y = -3
Hope this helps!
PLEASE? ILL GIVE BRAINLIEST AND PUT THE MOST AMOUNT OF POINTS
The value οf x is 1000 kg/m³ and the cοrrespοnding value οf y in lb/ft³ is 62.0 lb/ft³. The value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.
What is Quantities and measurements?Quantities and measurements are essential cοmpοnents οf the study οf mathematics and the physical sciences. A quantity is any prοperty οr characteristic that can be measured οr expressed in numerical terms, such as length, mass, time, temperature, and vοlume.
Frοm the prοject research part 2: Densities in lb/ft3 (pοunds per cubic fοοt). Cοnvert the densities as belοw,
Cοnvert kilοgrams per cubic meter tο the pοunds per cubic fοοt by multiplying by 0.062:
(x kg/m³) (0.062) = y lb/ft³
If we have a value οf x, we can multiply it by 0.062 tο get the cοrrespοnding value οf y in lb/ft³.
Let's say we have x = 1000 kg/m³. We can find y in lb/ft³ as fοllοws:
y lb/ft3 = (1000 kg/m3) (0.062) = 62.0 lb/ft3
Therefοre, the value οf x is 1000 kg/m3 and the cοrrespοnding value οf y in lb/ft3 is 62.0 lb/ft³.
Anοther questiοn is, Cοnvert pοunds per cubic yard tο pοunds per cubic fοοt by multiplying by 0.037:
(x lbs/yard³) (0.037) = y lb/ft³
Let's say we have x = 2000 lbs/yard³. We can find y in lb/ft³ as fοllοws:
y lb/ft³ = (2000 lbs/yard³) (0.037) = 74 lb/ft³
Therefοre, the value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.
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I KNOW PART OF THE ANSWER BUT HELP
The unknown measures are given as follows:
BC = 2.52, AB = 1.28, m < C = 27º.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle C is given as follows:
63 + 90 + m < C = 180
m < C = 27.
Side BC is opposite to the angle of 63º, while the hypotenuse is the square root of 8, hence it is obtained as follows:
sin(63º) = BC/sqrt(8)
BC = square root of 8 x sine of 63 degrees
BC = 2.52.
Side AB is opposite to the angle of 27º, hence it's length is given as follows:
sin(27º) = AB/sqrt(8)
AB = square root of 8 x sine of 27 degrees
AB = 1.28.
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NEED HELP DUE FRIDAY!!!!!!!!!!!
Find cos(A), sin(A), and tan(A) for triangle ABC.
Answer:
It’s a right triangle
Step-by-step explanation:
15 squared plus 8 squared equals 17 squared which 289=289
the form Q+bar (D) where the degree of R is less than the degree of (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4)
In this expression, Q+bar (D) is a polynomial, and we are asked to compare the degree of R with that of the polynomial (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4).
The degree of a polynomial is determined by the highest power of the variable. The highest power of c in (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4) is 3, so this polynomial has a degree of 3.
To compare it to the degree of R, we need to know the highest power of R in our expression. If the degree of R is less than the degree of (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4), then the expression Q+bar (D) will have a degree of 3.
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Current Attempt in Progress Which system of equations does not have a solution? {(x-2y=-3),(-2x+4y=6):} {(4x+6y=12),(6x+9y=12):} {(x+y=-1),(4x-3y=24):} eTextbook and Media
The system of equations that does not have a solution is {(x-2y=-3),(-2x+4y=6):}.
To see why, let's first look at the other two systems of equations:
{(4x+6y=12),(6x+9y=12):}
If we divide the first equation by 2, we get:
{(2x+3y=6),(6x+9y=12):}
If we then multiply the first equation by -3, we get:
{(-6x-9y=-18),(6x+9y=12):}
If we add these two equations together, we get:
{0= -6}
This is a false statement, so there is no solution for this system of equations.
Similarly, for the system of equations {(x+y=-1),(4x-3y=24):}, we can multiply the first equation by -4 and add the two equations together to get:
{-4x-4y=4, (4x-3y=24):}
{-7y=28}
This equation has a solution, so this system of equations does have a solution.
However, for the system of equations {(x-2y=-3),(-2x+4y=6):}, if we multiply the first equation by -2 and add the two equations together, we get:
{-2x+4y=6, (-2x+4y=6):}
{0=0}
This equation is always true, so there are an infinite number of solutions for this system of equations. Therefore, this system of equations does not have a unique solution.
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