The equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.
What are linear equations?Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
The definition of linear equations, the standard form for linear equations involving one variable, two variables, or three variables, and examples of each will all be covered in detail in this article.
Find the value of the variable that causes the equation to be true in order to solve linear equations.
Utilize the inverse of the variable's multiplier and divide or multiply both sides by it.
To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.
So, we have the pair of linear equations:
x – y = 8 and 3x – 3y = 16
(a1/a2) = 1/3
(b1/b2) = -1/-3 = 1/3
(c1/c2) = 8/16 = 1/2
Since, we know that (a1/a2) = (b1/b2) ≠ (c1/c2).
The equations have no solutions and run parallel to one another. The pair of linear equations is hence incoherent.
Therefore, the equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.
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Complete question:
Find out whether the following pairs of linear equations x – y = 8 and 3x – 3y = 16 are consistent/inconsistent.
Overview
Question Progress
Here is a list of numbers.
-45 -21
-16
12 33 40
11
a) Write down two numbers from the list that add up to -9.
c) Work out the sum of all the numbers in the list.
12 13 14
b) Write down two numbers from the list that have a difference of 29.
-21 + 12
Answer:
Step-by-step explanation:
fly
HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
find formula for growth of city
y intercept of 300,000 because the function starts here
the slope is 1.08 because it grows by 8 percent each year
population at x year = 300,000(1.08)^x
you can better understand why the x is in the exponent by this example
in one year, it grows 8 percent
300,000 * 1.08 = 324,000
the next year, that previous year grows 8 percent
324,000 * 1.08 = 349,920
300,000 * 1.08 * 1.08 =349,920
300,000 * 1.08^2 = 349,920
in 2 years it grows to that
just do it to the 14th power now
300,000 * 1.08^14 = 881,158
hope this helps :)
if you got any questions just comment
How do you solve 2/x = 7/9?
Answer:
2x=9+7
2x=16
x= 2/16
x=8
Step-by-step explanation:
Alan and Jorge are selling popcorn to earn money for a school trip.
Alan's popcorn sales can be represented by the equation y=2x, where x is the number of bags of popcorn sold and y is the amount of money raised.
Jorge's popcorn sales can be represented by this graph.If both boys sell the same amount of popcorn, who will raise the most money? Why?
Select the answer that is entirely correct.
Responses
Jorge will raise more money because he is selling the popcorn for $3 per bag, and Alan is selling the popcorn for $2 per bag.
Jorge will raise more money because he is selling the popcorn for 3 dollars per bag, and Alan is selling the popcorn for 2 dollars per bag.
Alan will raise more money because he is selling the popcorn for $3 per bag, and Jorge is selling the popcorn for $2 per bag.
Alan will raise more money because he is selling the popcorn for 3 dollars per bag, and Jorge is selling the popcorn for 2 dollars per bag.
Jorge will raise more money because he is selling the popcorn at 2 bags for a $1, and Alan is selling the popcorn at 3 bags for $1.Jorge will raise more money because he is selling the popcorn at 2 bags for a 1 dollars and Alan is selling the popcorn at 3 bags for
Alan will raise more money because he is selling the popcorn at 2 bags for a $1, and Jorge is selling the popcorn at 3 bags for $1.Alan will raise more money because he is selling the popcorn at 2 bags for a 1 dollars and Jorge is selling the popcorn at 3 bags for
The answer that is entirely correct based on the sales of popcorn is;
A: Jorge will raise more money because he is selling the popcorn for $3 per bag, and Alan is selling the popcorn for $2 per bag.
How to interpret Linear Equations?
The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, For Alan, we are told that her popcorn sales can be represented by the equation; y = 2x
where;
x is the number of bags of popcorn sold.
y is the amount of money raised.
Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $2
Now, for Jorge, looking at the graph, we can see that;
y -intercept = 0
Slope = (15 - 6)/(5 - 2)
Slope = 3
Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $3.
Looking at the options, the correct one are Options A,
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let s 5 {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s. must there be two integers whose sum is 15? why?
The given set have two integers whose sum is 15 because if we selcet the element from the given set then there sum is equal to 15.
In the given question, let s = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s.
We have to check there be two integers whose sum is 15.
As we know that,
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The letter Z or the chalkboard Z is frequently used to represent the set of integers in mathematical terminology.
There are total 10 elements.
We have to choose two element from the given set which sum is equal to 15.
If we choose 3 and 12 then there sum is 15.
Similarly, if select (5,10), (6,9), (7,8) the sum of all these selection is 15.
So the given set have two integers whose sum is 15.
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the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal. what is the square of the ratio of the short side to the long side of this rectangle?
As per the Pythagoras theorem, the ratio of the short side to the long side of this rectangle is (√5 - 1)/ 2
In math Pythagoras theorem is defined as the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
Here we have given that the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal.
And we need to find is the square of the ratio of the short side to the long side of this rectangle
While we looking into the given question we have identified that the short side of the rectangle be a and let the long side of the rectangle be b.
Therefore, the diagonal, according to the Pythagorean Theorem, is
√(a²+b²)
Now we can write the equation:
a / b = b /√ a² + b²
Then we have to find the square of the ratio of a to b.
Let us consider the answer, be k.
When we squaring the above equation,
a²/ b² = b² / a² + b² = k
When we solve this one then we get the value of k = 1.
Now we have to Multiply each side of the equation by k,
=> k² = 1 - k.
And then adding each side by k,
k² + k − 1 = 0.
Now, we have to Solving for k using the Quadratic Formula,
= > k = -1 ± √[1² − 4(1)(−1)] / 2
=> k = -1±√5/2
As we know that the ratio of lengths and diagonals of a rectangle cannot be negative.
Therefore, the resulting value is √5 - 1/2
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A= (a, b} B = {1,2,3} Select the expression that is an element of AxBxB. O (1,2,3) (a, a,1) (,22 (2.1.1)
The expression that has the element of A*B*B is Option A - (b,2,3)
Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
The "elements" of a set are the objects that make up the collection. Sets are equal if and only if they have the same elements, therefore a = A denotes that 'a' is one of A's elements. For sets, repetition and order are irrelevant.
Given, A={a.b} and B=[1,2,3]
Since the required expression was supposed to have the element of A*B*B the correct option would be A since it has elements b from A, 2 from B, and 3 from B, fulfilling all the required elements.
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a general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as
A general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as Probability sampling.
A probability sampling method is an any method of sampling that utilizes some from of random selection. Probability sampling refers to the selection of a sample from a population, when the selection is based on the principle of randomization, that is random selection or chance.
In simple random sampling each sampling unit of a population has an equal chance of being included in the sample. Consequently, each possible sample also has an equal chance of being selected.
The advantage of simple random sampling is that it does not require any information on the survey frame other than the complete list of units of the survey population along with contact information. In a simple random sample, every number of the population has an equal chance of being selected.
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Can someone please help me to convert 2,8hours to hours, minutes and seconds ?
convert 2.8hours to hours, minutes and seconds is 2.8 hours = 2 hours 48 minutes 0 seconds
The conversion of 2.8 hours into hours, minutes and seconds is relatively simple. To begin, we must first convert 2.8 hours into minutes. To do this, we multiply 2.8 by 60, which equals 168 minutes. Now, we need to convert those minutes into hours and seconds. To do this, we divide the 168 minutes by 60, which gives us 2 hours. We then take the remainder, which is 48 minutes, and divide it by 60, which gives us 0 seconds. Therefore, 2.8 hours is equivalent to 2 hours 48 minutes 0 seconds.
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Which of the following are the roots of the quadratic equation 3x^2 + 7x + 2 = 0?
Step-by-step explanation:
In 200920092009, Usain Bolt set the world record for sprinting 100 \text{ m}100 m100, start text, space, m, end text in approximately 9\dfrac359
5
3
9, start fraction, 3, divided by, 5, end fraction seconds.
Find his average speed in meters per second.
Average speed of Usain Bolt is 10.41 m/s.
What is Speed?The distance travelled by an object in relation to the amount of time it takes to travel that distance can be used to define speed. In plainer terms, it is a gauge of how quickly an object moves.
Average speed = (Total distance travelled)/(Total time required)
SI unit of speed is m/s.
Distance Travelled by Usain Bolt = 100m
Time required to travel this distance = [tex]9\frac{3}{5}[/tex] = 48 ⁄ (5 sec)
Average speed = (Total distance travelled)/ (Total time required)
Average speed = 100/ (48/5)
= 500/48
= 10.41 m/s
Therefore, average speed of Usain Bolt is 10.41 m/s.
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$32.75. Find the total cost if the tax is 9.25% and you want to leave an 18% tip.
Answer:About 155 results (0.47 seconds)
Tax and Tip - Illustrative Math Taskshttps://tasks.illustrativemathematics.org
Step-by-step explanation:
this may help
A particular fungal cell weighs 0.0009 gram. If this weight, in grams, is written in scientific notation as 9 x 10^q , what is the value of q?
Answer:
q = -4
Step-by-step explanation:
0.0009 = 9 × 10^(-4)
q = -4
Bryan estimate the cost of a vacation to be $730. The actual cost of the vacation is $850. Find the percent error. Round to the nearest whole percent if necessary. Is the percent positive or negative? Explain.
Answer: 14%
The percentage is positive because the actual cost is a result of the estimated cost increased by 14%
Step-by-step explanation:
Formula
Subtract the actual value from the estimated value
850-730=120
Divide the results from step 1 by the real value
120/850= 0.14117647058*100
Multiply the results by 100 to find the total percentage
0.14117647058*100=14.1176
Round
14%
elise buys only soft drinks at the higher price. her demand curve is linear. what is the appropriate compensation?
Elise only purchases the more expensive soft drinks. There is a linear demand curve. The relation is directly proportional is then the suitable compensation.
Explain the relation of directly proportional?The relationship between two values where their ratio equals a constant number is known as a direct proportion and direct variation.It is symbolized by the proportional sign (∝).When the ratio x:y is constant, two values, x and y, are seen to be directly proportional to one another.Linear demand curve
A line reflecting the relationship between both the demand for a good or service and its price is called a linear demand curve. Everyone is aware that sales are inversely correlated with price: the higher the price you ask for an item, and fewer you may anticipate selling.Elise only purchases the more expensive soft drinks. Her supply curve is straight.
Thus, the relation is directly proportional is then the suitable compensation.
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determine if the following functions are increasing or decreasing 
Answer:
D both are decreasing
Step-by-step explanation:
In both, as x is increasing, y is decreasing.
suppose you have calculated a two-way anova where the interaction was not significant. how should you next proceed?
The connection test is performed prior to making any ends in view of the tests for the primary impacts. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.
Before drawing any conclusions based on the tests for the main effects, the interaction test is carried out. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.
There may be an interaction if the plot's lines don't line up in the same direction. A collaboration demonstrates that the method for the Y information at the levels of the main X variable are different at each level of the second X variable. The interaction's strength increases with the number of nonparallel lines.
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From the sum of 3x +4y -3xy and 5x +3y -2xy subtract the sum of 2x +y – 3xy and 10x -9y -8xy.pls sent fast dont spam
Answer:
The answer is (-4x + 15y - 6xy)
Step-by-step explanation:
(3x + 4y - 3xy + 5x + 3y - 2xy)
= 8x + 7y - 5xy
(2x + y - 3xy + 10x - 9y - 8xy)
= 12x - 8y - 11xy
Now,
(8x + 7y - 5xy) - (12x - 8y - 11xy)
8x + 7y - 5xy - 12x + 8y + 11xy
= -4x + 15y - 6xy
Thus, The answer is (-4x + 15y - 6xy)
Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=98.13, y=100.6, r=0.904, P-value=0.000, ŷ=14.68+0.88x, where x represents the IQ score of the twin born first. Find the best predicted value of ModifyingAbove y with caret given that the twin born first has an IQ of 104? Use a significance level of 0.05.
The predicted value of the twin born first has an IQ of 104 is 106.2..
We have given that,
sample size n = 10
x = 98.13
y = 100.6
r = 0.904
p-value = 0.000
y'= 14.68 + 0.88x
significance level = 0.05
and we have to find predicted value of the twin born first has an IQ of 104.
We know that x represents the IQ score of the twin born first.
Therefore value of x is 104.
Hence the predicted value P will be,
P = 14.68 + 0.88(104)
= 14.68 + 91.52
P = 106.2
Therefore the best predicted value of the twin born first has an IQ of 104 is 106.2.
The positive predicted value is the probability that a test gives result for a true statistic. The negative predictive value is the probability that a test gives a false result for a false statistic.
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Find the general solution of the given differential equation.
(x + 1) dy/dx + (x + 2)y = 2xe?x
y=
Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points.)
(??, ?)
(0, 1)
(?1, ?)
(0, ?)
(??, 1)
The general solution of the given differential equation is y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2) and the largest interval is (-infinity, -2) U (-1, infinity).
The general solution of the mentioned differential equation will be calculated as follows -
Firstly rewriting the differential equation in standard form:
(x+1) dy/dx + (x+2)y = 2x[tex] {e}^{(xy)} [/tex]
Calculating the integrating factor to make the LHS as a total derivative:
As known, formula for integrating factor is:
mu = [tex] {e}^{(integral of (x+2)/(x+1) dx)} [/tex]
= [tex] {e}^{(ln(x+1) + ln(x+2))} [/tex]
= (x+1)(x+2)
Now multiplying both sides of the equation by the integrating factor:
(x+1)(x+2) × (x+1) dy/dx + (x+1)(x+2) × (x+2)y = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)
LHS will be a total derivative. Rearrange the equation for the same -
d/dx((x+1)(x+2)y) = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)
Integrating both sides of the equation:
(x+1)(x+2)y = integral of 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2) dx
= 2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C
Now find the equation for y:
y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2)
Equation for y is the general solution of the differential equation where constant C is the arbitrary constant of integration.
The general solution is not defined at the position x=-1 and x=-2. Hence, the largest interval over which the general solution is defined is (-infinity, -2) U (-1, infinity).
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the+population+of+a+town+is+2500+and+is+decreasing+at+a+rate+of+3%+per+year+5+years
2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.
What is the exponential decay function?In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.
It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.
So, we got:
r = 3.5%/100% = 0.035
We have our exponential function:
P(t) = 2500*(1 - 0.035)^t
The number after 5 years is provided by substituting t = 5, we will get:
P(5) = 2500*(1 - 0.035)^5 = 2,092.1
Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.
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Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years
In a hurry, will give 40 points.
Answer:
A: 74.9
B: 51.4
C: 53.7
Sorry I don't have enough time for the rest
Step-by-step explanation:
all angles should add up to 180
If you wanted to shingle the roof and each package of shingles covered an area of 5.6 m² , what would be the minimum number of packages of shingles needed to do the job?
HINT:you only need to cover the top of the roof. You need to find the side length of each roof side first.
The minimum number of packages of shingles that would be needed to do the job would be = 0.285 package.
What is an area of an object?An area of an object is defined as the total area that is being covered by the shape of that object.
This given object has the total of five sides with two triangles, and three rectangles.
The top part of the object is what is needed to be roofed therefore the area of the 2 rectangles should be determined as follows.
Area of rectangle =2( l ×w)
l = 14cm
w = X cm ( this is calculated using the Pythagorean theorem)
w² = 4.1² + 4²
w² = 16.81 + 16
w² = 32.81
w = √ 32.81
w = 5.7cm
Area of rectangle = 2× (14 × 5.7)
= 2× 79.8 = 159.6 cm²= 1.596m²
If 1 package of shingles = 5.6 m²
X package = 1.596m²
make X package the subject of formula = 1.596× 1/5.6
= 0.285 package.
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how much do national football league players weigh on aerage in a random sample of 50 nfl players the average weight is 244.4 pounds
This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.
This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.
In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.
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Estimate 64.5 divided by 12.3 using rounding 60 divided by 10
64.5 divided by 12.3 using rounding 60 divided by 10 gives 5.33.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given numbers are,
64.5 and 12.3.
When 64.5 is divided by 12.3.
The 64.5 can be rounded as 64
And 12.3 can be written after rounded as 12
Now divide 64 by 12.
64 / 12 = 5.333
The value of 64.5 divided by 12.3 is 5.33.
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Find the gradient vector field of f. f(x, y) =xe9xy
The gradient vector field of function f(x,y) is given as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
The gradient vector field of a function
Suppose that a function defined as follows:
f(x,y).
The gradient function is defined considering the partial derivatives of function f(x,y), as follows:
grad(f(x,y)) = fx(x,y) i + fy(x,y) j.
The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.
In which:
fx(x,y) is the partial derivative of f relative to variable x.
fy(x,y) is the partial derivative of f relative to variable y.
The function in this problem is defined as follows:
f(x,y) = xe^(9xy).
The partial derivative relative to x as follows:
fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).
The partial derivative relative to y as follows:
fy(x,y) = 9x²e^(9xy).
Hence the gradient vector field of the function is defined as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
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Type the correct answer in each box. Use numerals instead of words.
Multiply the expressions.
Answer:
[tex]$\frac{x^{2}+12x-27}{x^{2}-x-6}$[/tex]
Step-by-step explanation:
See picture below :)
the ratio 1:4 os equivalent to
Answer:
2/8, 3/12, 4/16 and etc
Step-by-step explanation:
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number
according to the united states census bureau, the average single-family home constructed in 2016 was 2,412 square feet. carmen wondered if families in her area still want a smaller home in comparison to the average. she randomly selected 53 people and asked what the ideal square footage of a home is for them. from the responses, she calculated the sample mean equals 1,230 square feet with a sample standard deviation of 56 square feet. calculate the value of the test statistic.
The correct hypothesis relation is is H₀ : μ ≥ 2,412. and Ha : μ < 2,412
According to the United States Census Bureau, the average area = 2, 412 square feet
Then the null hypothesis is
H₀ :μ ( mean ) area is greater than or equal to 2,412
H₀ : μ ≥ 2,412.
But, according to Jane, in her area, still families want a small home comparison to average.
Alternative hypothesis is that, mean area is less than 2,412 .
Ha : μ < 2,412.
Therefore, H₀ : μ ≥ 2,412. and Ha : μ < 2,412
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Taylor Swift is having 2 concerts at the same venue on Friday and
Saturday nights. On Friday, the ratio of the number of tickets sold to the
number of tickets still available is 5 to 3. On Saturday night, the ratio of the
number of tickets that were sold to the number of tickets available was
7:1. If 1,300 tickets were still available for the Saturday night concert, How
many tickets were sold for the Friday night concert?
Answer:
When using raitos you want to do P=2 +2+2+2
P=8
when L equals Ochoa
what will the answer be?
B2 + 62 + 25 gives us 169 - 25 and that gives us C Ronaldo
Step-by-step explanation:
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