A car traveling on the highway for 4 hours used 2 gallons of gasoline each hour.
How many gallons did it use during those 4 hours?
Which choice shows the correct product and answer?
4×(−2)=−8; The car used 8 gallons of gasoline.
4×(−2)=2; The car gained 2 gallons of gasoline.
.
4×(−2)=−2; The car used 2 gallons of gasoline.
Answers
Answer: The first one is correct
Step-by-step explanation: 4x(-2)=-8; The car used 8 gallons of gasoline.
Related Questions
You plan to retire in 30 years. After that, you need $75,000 per year for 20 years (first withdraw at t=31 ). At the end of these 20 years, you will enter a retirement home where you will stay for the rest of your life. As soon as you enter the retirement home, you will need to make a single payment of 2 million. You want to start saving in an account that pays you 8% interest p.a. Therefore, beginning from the end of the first year (t=1), you will make equal yearly deposits into this account for 30 years. You expect to receive $350,000 inheritance at t=30 from your late uncle and you will deposit this money to your retirement account. What should be the yearly deposits?
6587.25
7198.40
8066.36
8744.81
Answers
The yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.
To calculate the yearly deposits needed, we can use the concept of future value of an annuity. The future value formula for an annuity is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity
P = Yearly deposit amount
r = Interest rate per period
n = Number of periods
In this case, the future value needed is $2 million, the interest rate is 8% (0.08), and the number of periods is 30 years. We need to solve for the yearly deposit amount (P).
Using the given formula:
2,000,000 = P * [(1 + 0.08)^30 - 1] / 0.08
Simplifying the equation:
2,000,000 = P * [1\(.08^3^0 -\) 1] / 0.08
2,000,000 = P * [10.063899 - 1] / 0.08
2,000,000 = P * 9.063899 / 0.08
Dividing both sides by 9.063899 / 0.08:
P = 2,000,000 / (9.063899 / 0.08)
P ≈ 2,000,000 / 113.298737
P ≈ 17,650.23
Therefore, the yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.
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I am confused. what is 5r– 7 = 2r+ 14
Answers
Answer:
r=7
Step-by-step explanation:
5r-7=2r+14
add sevento both sides
5r=2r+21
Subtract 2r from both sides.
3r=21
divide both sides by 3
r=7
show that the feit-thompson theorem is equivalent to the state- ment that every finite nonabelian simple group has even order
Answers
The Feit-Thompson theorem is equivalent to the statement that every finite nonabelian simple group has even order.
The Feit-Thompson theorem states that every finite group of odd order is solvable. On the other hand, the statement that every finite nonabelian simple group has even order is equivalent to saying that the only finite groups of odd order are cyclic groups of prime order.
To show that these two statements are equivalent, we need to prove that if every finite nonabelian simple group has even order, then every group of odd order is solvable, and vice versa.
First, suppose that every finite nonabelian simple group has even order. Let G be a group of odd order, and let P be a Sylow 2-subgroup of G. Since the order of P is a power of 2, it is nontrivial and hence contains an element of order 2. This element generates a subgroup H of P that is isomorphic to Z_2. By the normalizer centralizer theorem, the normalizer of H in G is itself, so H is a normal subgroup of G. Since H is abelian, G/H is a nontrivial group of even order, and hence solvable. It follows that G is also solvable.
Conversely, suppose that every group of odd order is solvable. Let G be a finite nonabelian simple group, and let P be a Sylow p-subgroup of G for some odd prime p dividing the order of G. Since G is simple, P is a nontrivial proper subgroup of G, and hence its order is strictly less than the order of G. But since the order of G is odd, p cannot be 2, so P is a Sylow p-subgroup for some odd prime p. By the Frattini argument, G is generated by the normalizer of P and some subset of P. Since the order of P is odd, the normalizer of P has index divisible by 2 in G. It follows that G has even order, as claimed.
Therefore, the Feit-Thompson theorem is equivalent to the statement that every finite nonabelian simple group has even order.
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80% of 35
PLZ ANSWER
Answers
Answer:
28
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
80% × 35 =
(80 ÷ 100) × 35 =
(80 × 35) ÷ 100 =
2,800 ÷ 100 =
28
hope this helps
first answer = brainliest thanksss
Answers
Answer:
volume of this sphere is 500 cm³
Step-by-step explanation:
\(V=\frac{4}{3} \pi r^{3}\)
here 3 for π
\(V=\frac{4}{3}* 3* 5^{3}\)
\(V = 500 cm^{3}\)
Determine the domain of the following graph:
Answers
Answer:
Our domain is -5 < x < 5 or (-5,5) in interval notation form.
Step-by-step explanation:
Domain is a set of all x-values. If we want to find the domain through the graph, we will just look whenever if the graph has an open-dot/closed-dot or not. The following that you'll commonly see in finding domain through graph:
1. Closed Dots
They are dots that have solid color (generally black) to indicate that the interval there do include that x-value. An example is if there's a closed dot or solid dot at x = 4 then the value x = 4 is included in.
2. Opened Dots
They are white dots - they only have outlines but no color of the dot. They work quite similar to the closed dots, except that the value at that point will not be included in. An example is if there's an opened dot at x = 4 then the value x = 4 will not be included in.
However, x = 4.0001 or values that are very close to x = 4 will be included in, just not x = 4.
----------------------------------------------------------------------------------------------------------
Now since we are finding the domain through interval, we will ignore all y-values and y-axis. We will only be looking at x-axis and x-values.
The initial opened dot starts at x = -5 and the final opened dot ends at x = 5 as shown in the graph. Keep in mind that graphing visualization is a mandatory skill in mathematics!
The domain's interval has structure of initial x-value < x < final x-value (Only for opened dots, for closed dots, use ≥ or ≤) so from the structure, we can conclude that:
Our domain is -5 < x < 5 or (-5,5) in interval notation form.
Find the bank discount and proceeds using ordinary interest for a loan to michelle anders for 7,200 at 8.25% annual simple interest from august 8 to november 8
Answers
Answer:
$145.5
Step-by-step explanation:
Period, t = August 8.to November 8 = 3 months
Simple interest formula :
A = P(1 + rt)
A = final amount =. 7200
7200 = P(1 + (0.0825 * 3/12))
7200 = P(1 + 0.020625)
7200 = P(1.020625)
7200 = 1.020625P
P = 7200 / 1.020625
P = 7054.5009
Bank discount :
A - P
7200 - 7054.5009
= $145.4991
= $145.5
Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months. Month 2 3 4 5 Sales 924 91
Answers
Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.
One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.
In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.
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Р P 4) Prove that (a+b) = a +b (med P) pls aprime number! 3 prime numbers
Answers
We can factor out a common factor of b:
(a^(p-1) * b + (p^2 - p) / 2 * a^(p-2) * b^2 + ... + a * b^(p-1)) = b * (a^(p-1) + (p^2 - p) /
To prove that (a + b)^p = a^p + b^p for any prime number p, let's use the binomial theorem. The binomial theorem states that for any positive integer n and any real numbers a and b,
(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n,
where C(n, k) represents the binomial coefficient, given by C(n, k) = n! / (k! * (n - k)!).
In our case, we want to prove that (a + b)^p = a^p + b^p, where p is a prime number.
Using the binomial theorem, we have:
(a + b)^p = C(p, 0) * a^p * b^0 + C(p, 1) * a^(p-1) * b^1 + C(p, 2) * a^(p-2) * b^2 + ... + C(p, p-1) * a^1 * b^(p-1) + C(p, p) * a^0 * b^p.
Now, let's evaluate each term:
C(p, 0) * a^p * b^0 = 1 * a^p * 1 = a^p,
C(p, 1) * a^(p-1) * b^1 = p * a^(p-1) * b,
C(p, 2) * a^(p-2) * b^2 = (p * (p-1) / (2 * 1)) * a^(p-2) * b^2 = (p^2 - p) / 2 * a^(p-2) * b^2,
...
C(p, p-1) * a^1 * b^(p-1) = p * a * b^(p-1),
C(p, p) * a^0 * b^p = 1 * 1 * b^p = b^p.
Adding up all these terms, we get:
(a + b)^p = a^p + p * a^(p-1) * b + (p^2 - p) / 2 * a^(p-2) * b^2 + ... + p * a * b^(p-1) + b^p.
Notice that p is a prime number, so all the coefficients p, p^2 - p, etc., are divisible by p. Therefore, we can rewrite the expression as:
(a + b)^p = a^p + b^p + p * (a^(p-1) * b + (p^2 - p) / 2 * a^(p-2) * b^2 + ... + a * b^(p-1)).
Now, let's focus on the terms inside the parentheses. Each term is a product of a and b raised to a power, and each power is less than p. Thus, we can factor out a common factor of b:
(a^(p-1) * b + (p^2 - p) / 2 * a^(p-2) * b^2 + ... + a * b^(p-1)) = b * (a^(p-1) + (p^2 - p) /
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Fungsi f(x) = x³ - 12x² + 45x -18 merupakan fungsi naik pada interfal
Answers
Step-by-step explanation:
f(x) = x³ - 12x² + 45x -18
to find the interval of the function :
f'(x) > 0
3x²-24x+45 > 0
x²-8x +15 >0
(x-5) (x-3) >0
x<3 or x >5
the solutions :
{x < 3 or x > 5}
Show that vectors (
1
−1
),(
1
2
) and (
2
1
) are linearly dependent. Hint: use a complete set of bases
Answers
The vectors (1, -1), (1, 2), and (2, 1) are linearly dependent because they can be expressed as linear combinations of each other.
To show that the vectors are linearly dependent, we need to demonstrate that at least one of them can be expressed as a linear combination of the others. In this case, let's express the vector (2, 1) as a linear combination of the other two vectors.
We can write the vector (2, 1) as follows:
(2, 1) = a(1, -1) + b(1, 2)
Expanding the right side, we have:
(2, 1) = (a + b, -a + 2b)
By comparing the corresponding components, we get the following system of equations:
2 = a + b
1 = -a + 2b
Solving this system of equations, we find that a = 1 and b = 1. Therefore, the vector (2, 1) can be expressed as a linear combination of the vectors (1, -1) and (1, 2), indicating that the three vectors are linearly dependent.
Since we have found a nontrivial solution to the equation, it confirms that the vectors (1, -1), (1, 2), and (2, 1) are linearly dependent.
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f(x)=-x^2+7x-13 {Find }f(-3) it's not -25....so if that's ur answer..it's wrong
VERY IMPORTANT THAT U CAN ANSWER AS FAST AS POSSIBLE!!!!!!! IM ON A TIME CRUNCH!!!!!!
Answers
Answer:
-43
Step-b-y-step explanation:
f(x)= -x^2+7x-13 so
f(-3)= - (-3)^2 + 7(-3) - 13
= -9 - 21 - 13
= -43.
you would like to study whether the demographics of the gmu student body match that of the us population. from the latest us census you find that 76% of the population is white, 14% black, 1% american indian or alaskan native, 6% asian, 1% native hawaiian, and 2% two or more races. let's say you are able to poll 2100 gmu students about their race. given your answers above, what is your statistical decision?
Answers
By performing a chi-squared test of independence on the sample of 2100 GMU students, we can determine whether their demographics match those of the US population, and either reject or fail to reject the null hypothesis.
Based on the information provided, the expected proportions of different races in the US population are: 76% white, 14% black, 1% American Indian or Alaskan Native, 6% Asian, 1% Native Hawaiian, and 2% two or more races.
To determine whether the demographics of GMU students match those of the US population, we can use a hypothesis test. We will use a chi-squared test of independence to compare the observed frequencies of each race in the sample to the expected frequencies based on the US population demographics.
Assuming a significance level of 0.05, if our calculated chi-squared value is greater than the critical value from the chi-squared distribution with (6-1=5) degrees of freedom, we will reject the null hypothesis that the demographics of GMU students match those of the US population.
If we obtain a p-value less than 0.05, we reject the null hypothesis and conclude that the demographics of GMU students are significantly different from those of the US population. If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference between the demographics of GMU students and those of the US population.
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If 4x² = 16, then x =
A20
B12
C4
D2
Answers
because 2 to the power of 2 is 4
and then you multiply 4 by 4 and you get 16
- Mariana debe tomar dos pastillas; una cada 6 horas y otra cada 9 horas. Si a cierta hora toma las dos pastillas juntas, ¿después de cuantas horas volverá a tomarlas simultáneamente?
Answers
Answer:
Mariana takes the two pills together after 18 hours.
Step-by-step explanation:
Mariana must take two pills; one every 6 hours and another every 9 hours.
She take two pills together. Let she takes the two pills together after t hours at the time when she take initially.
To find the time to take the two pills together, take the least common multiple of 6 and 9.
6 = 2 x 3
9 = 3 x 3
So, the least common multiple is 2 x 3 x 3 = 18
So, she takes the two pills together after 18 hours.
. A doughnut mix requires 3 cups of sugar for every 15 doughnuts. How much sugar is used per doughnut?
Answers
Answer:
45
Step-by-step explanation:
15x3=45
Find the perimeter of the rectangle
Answers
Answer:
6x^2 + 8x + 28
Step-by-step explanation:
2 times the length plus 2 times the width gives the perimeter
2(3x^2 + 3x + 6) + 2(x + 8)
6x^2 + 6x + 12 + 2x + 16
6x^2 + 8x + 28
Answer:
12x²+ 28
Step-by-step explanation:
Since to find the perimeter we need to add all the side lengths together. That would give us, 12x²+ 28.
PLEASE ANWSER ASAP
Below, a two-way table is given
for student activities.
Sports Drama Work Total
7
3
13
2
5
5
Sophomore 20
Junior
20
Senior
25
Total
Find the probability the student is a sophomore,
given that they are in work.
P(sophomore | work) = P(sophomore and work) = [? ]%
P(work)
Round to the nearest whole percent.
Answers
The probability of P(sophomore | work) is 0.30.
Given that:
Sports Drama Work Total
Sophomore 20 7 3 30
Junior 20 13 2 35
Senior 25 5 5 35
Total 65 25 10 100
The probability is given as,
P = (Favorable event) / (Total event)
The probability of P(sophomore | work) is calculated as,
P = (3/100) / (10/100)
P = 3 / 10
P = 0.30
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In a control chart application, we have found that the grand average over all the past samples of 6 units is X-Double Bar = 25 and R-Bar = 5.
a) Set up X-bar and R Control charts.
A2= 483 D3=0 D4=2.004
.483*5=2.415+25=27.415=UCL
.485*5=25-2.415=22.585=LCL
LCL(R bar)=0
UCL=10.020
b) The following measurements are taken from a new sample: 33, 37, 25, 35, 34 and 32. Is the process still in control?
Answers
Based on the given data, the process is out of control.
To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.
For the X-bar chart:
The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:
UCL = 25 + (0.483 * 5) = 27.415
The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:
LCL = 25 - (0.483 * 5) = 22.585
For the R chart:
The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:
UCL = 2.004 * 5 = 10.020
The LCL (Lower Control Limit) for the R chart is 0.
Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.
Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.
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The expanded form of 128,005
Answers
Answer:
(100,000 x 1) + (10,000 x 2) + (1,000 x 8) + ( 1 x 5)
Step-by-step explanation:
Please help me quick
Answers
\( \:\:\:\:\:\:\longrightarrow \sf \underline{V_{(cylinder) } = \pi\:r^2\:h \: cubic \:units }\\\)
Where -
V= Volume of cylinder π = \(\sf\dfrac{22}{7} \)= 3.1416..........r = Radius of cylinder. h = Height of cylinder.As per question, we are given that-
V= 1800 in³ r = 7 inchπ =3.14Now that, we are given all the required values, so we can put all the values into the formula and solve for the height -
\( \:\:\:\:\:\:\longrightarrow \sf \underline{Volume _{(cylinder) } = \pi\:r^2\:h }\\\)
\( \:\:\:\:\:\:\longrightarrow \sf 1800= 3.14 \times \bigg(7\bigg)^2 \times h\\\)
\( \:\:\:\:\:\:\longrightarrow \sf 1800 = 3.14 \times 7\times 7\times h\\\)
\( \:\:\:\:\:\:\longrightarrow \sf 1800 =3.14 \times 49 \times h\\\)
\( \:\:\:\:\:\:\longrightarrow \sf 1800 =153.86\times h\\\)
\( \:\:\:\:\:\:\longrightarrow \sf 153.86\times h=1800\\\)
\( \:\:\:\:\:\:\longrightarrow \sf h = \dfrac{1800}{153.86}\\\)
\( \:\:\:\:\:\:\longrightarrow \sf h = 11.69894...........\\\)
\( \:\:\:\:\:\:\longrightarrow \sf \underline{ h =11.69\: inch }\\\)
Therefore, the length of height \( \sf \underline{ \pink{11.69\: inch }}\\\)
Jeremy is $124.60 in debt to his grandparents. He determines that he can pay them back in five months. What effect will his repayment have on his monthly bank account? Will give brainliest!
Answers
Answer:
https://brainly.com/question/11536615
Step-by-step explanation:
based on the data shownin the graph how many boxes can the shipping company to pack in a 18 hour period
Answers
The equation of line is y = 12x and the number of boxes the shipping company can pack in 18 hour period is 216 boxes
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the number of hours be x
Let the number of boxes be y
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 5 , 60 )
Now , the slope of the line m = y/x
Substituting the values in the equation , we get
Slope m = 60 / 5 = 12
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 60 = 12 ( x - 5 )
y - 60 = 12x - 60
y = 12x
Now , when x = 18 hours
y = 12 ( 18 ) boxes
y = 216 boxes
Hence , the number of boxes is 216 boxes
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What is 24/240 as a decimal
Answers
Answer:
0.1
Step-by-step explanation:
Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator
your gross income is $4,000 per month. your federal state tax is 10%, state tax is 7%, city tax is 3%, and you pay 7% to social security. what is your monthly disposable income?
Answers
If the gross income per month is $4000 , then the monthly disposable income will be $2920 .
To find the monthly disposable income, we subtract the various taxes from the gross income.
The Federal tax is = 10% of $4000 = $400 ;
The State tax is = 7% of $4000 = $280 ;
The City tax is = 3% of $4000 = $120 ;
and the Social security tax is = 7% of $4000 = $280 ;
So , the Total monthly tax is = $400 + $280 + $120 + $280 = $1080 ;
We know that the Monthly disposable income = Gross income - Total tax ;
⇒ Monthly disposable income = $4000 - $1080 ;
⇒ Monthly disposable income = $2920 .
Therefore, the monthly disposable income after taxes is $2920.
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A. Find the indicated number of geometric mean/s between the given two numbers.
1. 5 and 20 [ 1 term ]
2. 8 and 512 [2 terms]
3. 2 and 50 [ 1 term ]
4. 6 and 486 [3 terms]
5. 4 and 108 [2 terms]
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The ratio of the given terms is the common ratio raised to a power equal to the number of means plus 1.
1)For example, the common ratio in the sequence 5, __, 20 will be r, where ...
r^2 = 20/5 = 4 ⇒ r = 4^(1/2) = 2
Then the mean is found by multiplying 5 by this ratio: 5×2 = 10.
__
2-5)The same method is used for finding the common ratio and then the intermediate means. Each mean is the previous term multiplied by the common ratio. Results are summarized in the attached table.
_____
Additional comment
When there are a number of similar calculations to be done, it is convenient to let a spreadsheet do them.
![A. Find the indicated number of geometric mean/s between the given two numbers.1. 5 and 20 [ 1 term ]2.](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/YeJCbPqFtVuUKkjzfYWwrhYlPRMDf3JT.png)
explain why in any group of 1500 people there must be at least 3 people who share first and last name initials from the english alphabet (like zexie manatsa and zivanai masango share zm
Answers
In a group of 1500 people, there must be at least 3 individuals who share first and last name initials from the English alphabet due to the pigeonhole principle.
This principle states that if you have more objects than there are places to put them, at least two objects must go into the same place.
In this case, each person's initials consist of two letters from the English alphabet. Since there are only 26 letters in the English alphabet, there are only 26*26 = 676 possible combinations of initials (AA, AB, AC, ..., ZZ).
If we have more than 676 people in the group (which we do, with 1500 people), it means there are more people than there are possible combinations of initials. Thus, by the pigeonhole principle, at least three people must share the same initials.
Therefore, in any group of 1500 people, it is guaranteed that there will be at least 3 individuals who share first and last name initials from the English alphabet.
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Create the equation of the line that goes
through the point and slope. (you can use
slope-intercept form or point-slope form) (4 pts)
Through = (1, 19) slope = 0
Equation:
SOMEONE PLEASE HELP!!
Answers
Answer:
The answer is
\(y = 19\)
Step-by-step explanation:
Since
\(y = mx + c \\ m = 0 \\ c = 19 \\ y = 0 \times x + 19 \\ y = 19\)
Consider the LP below. The BFS ("corners") are (0,0) (0,4) (1,4) (3,2) (3,0). The optimal solution is at x_{1} = 3 and x_{2} = 2
max z = 2x_{1} + x_{2}
s.t.
matrix x 1 +x 2 &<= 0 \\ x 1 &<=3\\ x 2 &<4 matrix
x_{1}, x_{2} >= 0
(a). What is the range of c_{1} the objective coefficient of x_{1} (currently 2) for which this BFS remains optimal:
(b). What is the range of b_{2} the right hand side of the second constraint (currently 3) for which this BFS remains optimal:
(c). What is the dual price of the second constraint?
Answers
(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.
(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.
(c) The dual price of the second constraint is 0.
(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.
(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.
(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.
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Factorise xsquared+ 5x + 6
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Answer:
\((x+2)(x+3)\)
Step-by-step explanation:
⭐What does factorisation mean?
factorisation is the process of writing a number or a polynomial in terms of its factors⭐What are factors?
factors are the terms that multiply together to create a number or a polynomialThus, we have to write \(x^2+5x+6\) in terms of its factors.
I have a picture attached to this response to show you how factorisation works, but I will also explain it here.
How to factorise:
Look at the constant in your polynomial (the term without a variable). In this problem, the constant is 6. Look at the coefficient middle term in your polynomial (the number next to the variable). In this problem, the middle coefficient is 5. Find what numbers multiply together to have a product of 6, and add together to have a sum of 5.The numbers +2 and +3 multiply together to have a product of 6, and add together to have a sum of 5. In the next line, write the polynomial again, but write 5x in terms of the numbers we found.You'll get: \(x^2 + 2x +3x + 6\)Now, we can factorise the binomials we see here.⭐What are binomials?just as "bi" means 2, binomials are equations with 2 termsThe binomials are \(x^2 + 2x\) and \(3x + 6\)To factorise the binomials, find the GCF for both terms of each binomial.The GCF for \(x^2 + 2x\) is x.The GCF for \(3x+6\) is 3.Now, write the GCFs outside of the parentheses for each binomial and rewrite what's in the parentheses.You'll get: \(x(x+2) +3(x+2)\)You should have the same expression in both parentheses.Now, we have to rewrite this expression by keeping what's inside of the parentheses, and putting the terms outside of the parentheses inside parentheses.You'll get: \((x+2)(x+3)\)That's it!The picture of factorisation is attached to this response.
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