The general solution of a linear second order homogeneous equation is represented as the combination of two particular solutions.
This is because the linear second order homogeneous equation is of the form ax2+bx+c=0 and has two distinct roots, i.e. x1 and x2. The general solution of the equation can be written as y=C1y1+C2y2, where C1 and C2 are constants and y1 and y2 are the two particular solutions. The particular solutions can be derived from the two distinct roots of the equation using the formula y1=e^(x1*t) and y2=e^(x2*t). The constants C1 and C2 can be found by solving the linear combination of the two particular solutions for the given initial conditions of the equation. This gives the general solution of the linear second order homogeneous equation as a combination of the two particular solutions.
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help on 4 and 6 please!!
The measures of the angles are Z = 146 degrees, X and W = 34 degrees and B = 119 degrees
How to determine the measure of the anglesQuestion 4
From the question, we have
<Y = 146 degrees
Because the lines XY and WZ are equal, it means that
<Z = 146
So, we have
X = W = (180 - 146)
Evaluate
X = W = 34
Question 6
Here, we have
Sum of the angles = 180 degrees
This gives
9x + 2 + 5x - 4 = 180
Evaluate the like terms
14x = 182
Divide by 14
x = 13
So, we have
B = 9 * 13 + 2
B = 119 degrees
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Problem Gregory forms two different numbers with the digits 1, 2, 3, 4, 5, and 6. Both numbers have 3 digits, and each digit is used only once. If he adds these two numbers, what is the greatest sum Gregory can get? Show your work.
The numeric value of the greatest sum that can be obtained by Greg is given as follows:
1173.
How to obtain the greatest sum?When two n digit numbers are added, the numbers in the equivalent positions are added with each other, that is, starting from the end of the number to the begining.
The first digit is added with the other first digits.The second digit is added with the other second digits.For example, 21 + 32:
1 + 2 = 3.2 + 1 = 5.Hence the sum is of 54.
Hence the greatest sum would be obtained as follows:
The first digits would be of 5 and 6.The second digits would be of 3 and 4. The third digits would be of 1 and 2.Hence the sum would be given as follows:
642 + 531 = 1173.
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NO LINKS!!
Please help me with #14.
Answer:
a) Domain: (-∞, 10)
b) k⁻¹(8) = 6
c) CBD
d) Range: (-∞, 7)
e) k⁻¹(0) = 4
f) x = -5
Step-by-step explanation:
Part aThe domain of the inverse of a function is the same as the range of the original function.
Therefore, the domain of the inverse function is:
(-∞, 10)Part bThe inverse of a function is its reflection in the line y = x.
Therefore, given that function k(6) = 8 then:
k⁻¹(8) = 6Part cThe inverse of a function is its reflection in the line y = x.
We cannot find k⁻¹(-9) since we have not been given the value of x when k(x) = -9.
Part dThe range of the inverse of a function is the same as the domain of the original function.
Therefore, the range of the inverse function is:
(-∞, 7)Part eThe inverse of a function is its reflection in the line y = x.
Therefore, given that function k(4) = 0 then:
k⁻¹(0) = 4Part fThe zero of the inverse function is the y-intercept of the original function. Therefore, given that k(0) = -5 then:
k⁻¹(-5) = 0Therefore, x = -5 is a zero of k⁻¹(x).
What is the value of 3h(2) + 4g(1)
The value of 3h(2) + 4g(1) is 39
How to evaluate a given mathematical expression with variables if values of the variables are known?You can simply replace those variables in function with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.
Given;
h(x)= 3x x<2
= 4x+1 x>2
g(x)= x^2+2 x<3
= x^3 x>3
Now, substituting the values;
3h(2)= 3*(4*2+1)
=3*9
=27
4g(1)= 4(1^2 + 2)
=4(3)
=12
3h(2)+4g(1)=27+12
=39
Therefore, the answer of the function will be 39
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what’s the geometric mean of 6 and 1/2
Answer:
1.7320508075689
Analyze the diagram below and complete the instructions that follow.
C
A
B
Given that
A. 10
B. 10.5
C. 11
D. 11.5
6
CB
CA
DE
DF'
find BA.
D
4
E
7
F
Save and Exit
Next
Submit
Analyze the diagram of the trapezoid gives BA = 10.5 units
How to find the side BA of the trapezoid the analyzing the diagram?A trapezoid (also known as a trapezium) is a four-sided geometric shape that has two parallel sides (the bases) and two non-parallel sides (the legs). The bases of a trapezoid can have different lengths, but the legs must be congruent and parallel to each other.
Let's analyze the diagram below and complete the instructions:
Since CB / CA = DE / DF
where CB = 6, DE = 4, EF = 7
We can say:
DF = DE + EF = 4 + 7 = 11
CA = CB + BA = 6 + BA
CB / CA = DE / DF
6/(6 + BA) = 4/11
6 × 11 = 4(6 + BA)
66 = 24 + 4BA
24 + 4BA = 66
4BA = 66 - 24
4BA = 42
BA = 42/4
BA = 10.5 units
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Mike is buying dinner for his family. He buys 5 lemonades that each cost $1.50, and 5 hamburgers that each cost $8.25. If
the prices include tax, and he also leaves a $6 tip, how much does he spend in all? Write equations to show your work.
Write an equation for the cost of the lemonades. Select the correct choice below, and fill in the answer box to complete
your choice.
(Do not include the $ symbol in your answer.)
OA. 5x1.50 +6=
ETTE
OB. 1.50+5=
OC. 5x1.50 =
OD. 1.50+5+6=
The linear equation for the cost of lemonades is 1.50*x+6 where x=5 i.e. A and he spends $54.75 in total.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Cost of lemonade=$1.5, number of lemonades=5
Cost of hamburger=$8.25, number of hamburgers=5
Tip=$6
Hence,
Total cost=5*1.5+5*8.25+6
Total cost =$54.75
Cost of lemonades only = 5*1.5+6
In type of linear equation 1.50*x+6 where x=5
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∠FGK and ∠KGH form a linear pair. Find m∠KGH.
Applying the linear pair definition, m<KGH = 60°.
What is a Linear Pair?In geometry, a linear pair is a pair of adjacent angles that are supplementary, meaning that their measures add up to 180 degrees. The two angles must be adjacent, meaning that they share a common side or vertex, and they must be linear, meaning that they are formed by two intersecting lines.
Therefore:
m<FGK + m<KGH = 180
Substitute
120 + m<KGH = 180
m<KGH = 180 - 120
m<KGH = 60°
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Find the image of A(4, 2) after the following transformations
a. (1,4) ∘ (−) (4, 2)
b. (−) ∘ (1,4) (4, 2)
HELP PLEASE
use the definition of continuity and limits to find values of the constants a and b so that the piece-wise cubic function
The constants a and b can be found by ensuring the function is continuous and that the limits at each point match. This can be done by setting the values of a and b so that the function and its derivative are equal at each point.
To find the constants a and b for the given piece-wise cubic function, we must consider the definition of continuity and limits. Firstly, for the function to be continuous, the function and its derivative must be equal at each point. Thus, we need to set the values of a and b so that the function and its derivative are equal at the points x=1, x=2 and x=3. We can use this to create a system of equations to solve for a and b. Once we have determined the values of a and b, we can then check that the limits at each point match. This can be done by computing the left and right hand limits at each point, and ensuring they are equal. If the limits are equal, then the function is continuous and the constants a and b are correct.
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G(-3,-2). What would be the reflection point G
The reflection of point G across the x-axis would be at (-3, 2).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The coordinates of point G in the question are (-3,-2)
When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate is changed.
Therefore, the reflection of point G, which is located at (-3, -2), across the x-axis would be at (-3, 2).
The x-coordinate is the same, but the y-coordinate has changed from negative to positive.
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The question seems incomplete, the completed question would be as:
The coordinates of point G are (-3,-2)
What would be the reflection point G across the x-axis?
when ur answering please just give the answer! thank uuu! :)
The equation of the exponential function is y = 0.2⋅2^x
Find the equation of the exponential functionThe steps for this process are as follows:
Step 1: Set up the equation.
The equation of an exponential function has the form y = a⋅b^x
where a and b are constants and b is greater than 0 and not equal to 1.
Step 2: Find the constants.
We can use the given points to find the constants in the equation. For example, when x = 0, y = 0.2.
So we can set 0.2 = a⋅b^0.
This means that a = 0.2 and b^0 = 1,
so b = 1.
Step 3: Write the equation.
Substituting a = 0.2 and b = 1 into the equation gives us y = 0.2⋅2^x.
This is the equation of the exponential function represented by the table.
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Several college students conduct a survey at their local community college. They find that 67% of the students live with their parents in the house they grew up in. Of the students who live with their parents 23% live within walking distance to campus. Of the students who do not live with their parents only
6% live within walking distance to campus. a) What is the probability of a student living within walking distance to campus? ( 1 point) b) What is the probability given a student lives within walking distance to campus they live with their parents? (1 point) c) Are living with parents and living within walking distance independent events? (2 points)
a) The probability of a student living within walking distance of campus is 0.1521.
To find the probability of a student living within walking distance of the campus, we can use the formula for conditional probability:
P(A and B) = P(A) * P(B|A).
For this situation, An is "living within walking distance to campus" and B is "living with parents."
Thus, P(A and B) = (0.23)(0.67) + (0.06)(0.33) = 0.1521.
Hence, the probability of a student living within walking distance of campus is 0.1521.
b) The probability given a student living within walking distance of campus they experience with their parents is 0.67.
To find the probability given a student day to day routines within walking distance to campus they experience with their parents, we can use the formula for conditional probability:
P(A|B) = P(A and B)/P(B).
In this situation, A is "living with parents" and B is "living within walking distance to campus."
Thus, P(A|B) = P(A and B)/P(B) = (0.23)(0.67)/0.1521 = 0.67.
Subsequently, the probability gave a student living within walking distance of campus experience with their parents is 0.67.
c) Living with parents and living within walking distance are independent events.
To decide whether living with parents and living within walking distance are independent events, we can analyze P(A|B) with P(A).
On the off chance that P(A|B) = P(A), the events are independent. For this situation, P(A|B) = 0.67 and P(A) = 0.67, so living with parents and living within walking distance are independent events.
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there exists an intewger that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers
there exists an integer that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers ∃x∈ℤ: x > 5 ∧ x² < 40
1. Start by writing down the equation: x² < 40
2. Take the square root of both sides of the equation to isolate the variable x: √x² < √40
3. Simplify both sides of the equation: x < √40
4. Check that the result makes sense: x < 6.3
5. Take the integer part of the result: x < 6
6. Since the requirement is that x is greater than 5, the answer is x = 6.
We start by writing the equation x² < 40 and then take the square root of both sides to get x < √40. We check that the result is reasonable and then take the integer part of the result to get x < 6. Since the requirement is that x is greater than 5, the answer is x = 6. To confirm, we can calculate that x² = 36 which is smaller than 40, and indeed, 6 is greater than 5. Therefore, the integer that is greater than 5 and whose square is smaller than 40 is 6. This can be expressed mathematically as ∃x∈ℤ: x > 5 ∧ x² < 40 which translates to: There exists an integer x such that x is greater than 5 and the square of x is smaller than 40.
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a bicycle has wheels 32 inches in diameter. a tachometer determines the weheels are rotating at 150 rpm(revolutions per minute). Find the speed the bicycle is traveling down the road.
The speed of the bicycle is 381 meters per minutes
we know that,
revolutions per minute = speed in meters per minute / circumference in meters.
Diameter = 32 inches
Circumference of the wheel = 2πr
r = Diameter/2 = 32/2 = 16
Circumference = 2 × π × 16
= 100.5714 inches
Approximately = 100 inches
we know that,
1 inch = 0.0254 meter
100 inches = x
x = 100 × 0.0254 meters
x = 2.54 meters
Hence:
Revolutions per minute = Speed in meters per minute / circumference in meters.
Speed = Revolutions per minute × circumference in meters.
Speed = 150 RPM × 2.54 meters
Speed = 381 meters per minutes
so, the speed of the bicycle is 381 meters per minutes.
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49, 34, and 48 students are selected from the sophomore, junior, and senior classes with 496, 348, and 481 students respectively.
The sampling used in this situation is Stratified sampling
In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.
We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.
This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.
Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes.
This is, therefore, a stratified sampling.
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Q: 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?
At the start of a trip, you fill up your car's fuel tank with gas. After you drive for x hours, the amount y (in gallons) of gas remaining is given by the equation y = 18 - 2x.
a. Find the x-intercept and the y-intercept of the given equation's
graph. Use the intercepts to graph the equation.
b. Interpret What real-life quantities do the x- and y-intercepts
represent in this situation?
c. After how many hours of driving do you have only tank of gas left?
Use the intercepts to graph the equation y = 18-2x
What is meant by graph ?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.A graph that has any two vertices connected by a path is said to be connected. Any two vertices or nodes in a disconnected graph are those that are separated by a path.Graph that completes a cycle is called a cycle graph. Complete Graph: A graph is said to be complete when every pair of vertices is connected by an edge.A graph is a type of non-linear data structure composed of nodes, also known as vertices and edges. The edges in the graph connect any two nodes, and the nodes themselves are also known as vertices.Interpret What real-life quantities do the x- and y-intercepts
represent in this situation:
when x = 0, y = 18, when y = 0 x = 9
The x intercept is 9, y intercept is 18.
After 9 hours the gas is run not .
The amount of gas in a car when it is not running
18 × 1/4 = 4.5
4.5 = 18-2x
x= 6.75 hours
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The circle graph shows the results of a national survey on the most popular afternoon activities of seventh graders. What percent of those students surveyed said that their favorite afternoon activity is playing video games?
Answer:
it is easy to add all the numbers up then you will get 77 then tell me how many number should you add to get to 100 it is easy trust me
Step-by-step explanation:
Find the value of x PLEASE I NEED HELPP :(
Answer: [tex]2\sqrt{13}-\sqrt{697}[/tex]
Step-by-step explanation:
Since ABD is a right triangle, 14^2 = 12^2 + BD^2
196 = 144 + BD^2
52 = BD^2
BD = [tex]\sqrt{52} = 2\sqrt{13}[/tex]
ADC is also a right triangle, so 29^2 = 12^2 + DC^2
841 = 144 + DC^2
DC^2 = 697
DC = [tex]\sqrt{697}[/tex]
Since x = BD + DC,
x = [tex]2\sqrt{13} +\sqrt{697}[/tex] :>
1.) Leila wants to sell her homemade candles at the Linwood Street Craft Fair. She decides to
sell her candles for $12 apiece. The materials for one candle cost Leila $2. If she also pays
$40 to rent the booth for the day, how many candles must Leila sell to cover all of her
expenses? How much will her sales and expenses be at that point?
The total cost of materials for one candle is $2 and she pays $40 for the booth for the day.
Therefore, the total cost for making and selling one candle is $2 + $12 + $40 = $54
To cover all her expenses, Leila must sell enough candles to make $54 from each candle.
She must sell 54/$12 = 4.5 candles
Therefore, Leila needs to sell at least 5 candles to cover all her expenses.
At that point, her sales and expenses will be 5 candles x $12/candle = $60
Therefore, Leila's sales and expenses will be $60 at that point.
Zac and Malcolm each wrote short stories. Zac’s story is 273 lines long. Malcolm’s story is 145 lines longer than Zac’s. How long is Malcolm’s story? Explain what operation you used to solve this problem.
Length of malcom's story is 418lines, the operation used to solve this problem is; lines of zac story+ extra lines of malcom story.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
Given;
Number of lines in zac story=273
Number of lines in malcom story= 273+145
Now.
Total number of lines in malcom story
=273+145
=418
Therefore, the answer after simplification will be 418
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5. THOUGHT PROVOKING
To find the arithmetic mean of n numbers, divide
the sum of the numbers by n. To find the geometric
mean of n numbers a₁, a₂, a3,..., an, take the nth
root of the product of the numbers.
geometric mean =
a₁a₂ a3 •...• An
Compare the arithmetic mean to the geometric
mean of n numbers.
Arithmetic mean deals will middle number while geometric mean deals with typical value
How to compare the different types of meansFrom the question, we have
Arithmetic mean and Geometric mean
The arithmetic mean is the sum of a set of numbers divided by the number of items in the set, and is often used to find the "middle" value of a dataset.
On the other hand, the geometric mean is the nth root of the product of a set of numbers and is often used to find the "typical" value of a dataset when dealing with quantities that can increase or decrease exponentially.
The above definitions imply that the difference between the arithmetic mean and geometric mean can be significant when dealing with sets of numbers that have large variations in values.
In general, the geometric mean will be less than or equal to the arithmetic mean.
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inspect a sketch of typical solution curves to determine the points for which the initial value problem has a unique solution.
We have to find solutions for the given differential equation when
y = 0, y = 1/(k-x) and y(a) = b using ordinary differential equations.
We have dy / dx = y^2
a. let's define the given y = 1/(k-x)
derive the above equation with respect to x :
dy / dx = y' = 1/(k-x)^2
So this is the general solution.
b) We would want a singular solution that is not included in the general form. Here we could use y = 0
dy / dx = 0 = 0^2
so,this is a trivial singular solution.
c) If we have y(a) = b,
then, y = 1(k-a) = b
To find the value of k we use the other condition: y'(^2) = 4 x y(2)
1/(k-a)^2 = 4 x 1/(k-a)
k - 2 = 1/4
therefore, k = 9/4
hence we got, y = 1/(9/4 - a) = b
So the points (a, b) are of the form: (a, 1/(9/4 - a))
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The complete question is :
Find a general solution of the differential equation dy/dx=y2
b. Find a singular solution that is not included in the general solution.
c. Inspect a sketch of typical solution curves to determine the points (a,b) for which the initial value problem (y′)2=4y,y(a)=b
25. There were 13 gummies in a packet. Mrs. Sooklal bought a few packets of gummies. After giving 3 sweets to each of her 27 students, she has 10 gummies remaining, how many packets of gummies did she purchase?
Which graph represents an exponential decay function?
The graph that represents an exponential decay function is the second graph.
For you to determine which of the graphs represents an exponential decay, we will need to check the curve that passes through or lies on the x-axis.
we can draw a graph by putting the value of x and we are getting the value of y in this way we get the coordinates of a point
From both figures, we can see that the curve of the second graph almost lies on the x-axis as it curves downwards. This makes it an exponential decay function.
Hence the graph that represents an exponential decay function is the second graph.
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complete question is
Which description matches the function represented by this graph?
A. exponential growth
B. linear growth
C. linear decay
D. exponential decay
Answer:
B or 2
Step-by-step explanation:
The answer above is correct.
1 The equation, A = P(1 + 0.037t), represents the amount of money earned on a savings account with 3.7% annual simple interest. If the amount after 5 years is equal to $1,422, what is the amount of the principal investment? $1,200 $1,422 $274.25 $294.86
The amount of the principal investment is, $1200. So option A is correct
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
A = P(1 + RT)
Given that,
A = $1422
R = 3.7%
T = 5 year
P = ?
After 5 year total amount
1422 = P ( 1 + 0.037 × 5)
P = 1422/( 1 + 0.037 × 5)
= 1422/1.185
P = 1200
Hence, the principal amount is $1200
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Can someone help me please
Answer: 3 + y = 24
Step-by-step explanation: Hello!
If she rode 3 miles one day and y miles the other 6 days of the week, and in total that adds up to 24 miles, that means the equation should be addition.
3 miles + y miles = 24 miles
Monday, other 6 days, total seven days
The equation should be:
3 + y = 24
shatter cones are key features that uniquely characterize impact structures (i.e., their presence provides evidence that an impact occurred). shatter cone surfaces exhibit a texture with a series of intersecting ridges that produce its conical geometry. based on the labeled version below, what is the general direction in which the shatter cone ridges converge (or point)? choose one: a. s b. e c. w d. n
As per the cone surface, the general direction in which the shatter cone ridges converge is south.
The term cone in math is defined as a three-dimensional shape in geometry that narrows smoothly from a flat base to a point called the apex or vertex.
Here we have given that Shatter cones are key features that uniquely characterize impact structures
In this one their presence provides evidence that an impact occurred. Here we also know that the Shatter cone surfaces exhibit a texture with a series of intersecting ridges that produce its conical geometry.
Based on the definition of cone surface we have identified that the the correct option is (a) that is the south.
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If a shipment has at least 5% defective light bulbs, it will be replaced. If a sample of 60 light bulbs has 2 that are which statement is true? defective,
A The shipment will be replaced.
B The shipment will not be replaced.
C The shipment has 12 defective light bulbs.
D The shipment has 30 defective light bulbs.
The sample has 3.33% of defective bulbs so, B. The shipment will not be replaced.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, If a shipment has at least 5% defective light bulbs, it will be replaced.
Now, A sample of 60 light bulbs has 2 that are defective.
Therefore, The percentage of defective bulbs is,
= (2/60)×100%.
= (1/30)×100%.
= 3.33%, So, the shipment will not be replaced.
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5x - y = -5
3x - 6y = 24
Solve using substitution
Answer:
x = -2
y = -5
Step-by-step explanation:
5x - y = -5
3x - 6y = 24
First, multiply the first equation by -6
-30x + 6y = 30
3x - 6y = 24
-27x = 54
x = -2
Now, put in -2 for x and solve for y
5(-2) - y = -5
-10 - y = -5
-y = 5
y = -5
Let's Check
5(-2) -(-5) = -5
-10 + 5 = -5
-5 = -5
So, x = -2 y = -5 is the correct answer.