URGENT!! HELP PLEASE!!
Linear programming problems can also be solved using a graphing calculator. The following instructions will work for most commonly used graphing calculators, but note that they might vary slightly based on calculator model. Now that you’ve learned how to use a graphing calculator to solve linear programming problems, solve the following problems.
Part A
Consider the given system
{2x+y ≤20
{3x+2y ≤30
{x,y ≥0
Graph the inequalities on your graphing calculator, and find the vertex points of this system
Part B
In part A, you obtained the vertex points of the given system. Test these vertex points in the objective function, f(z)=4x+6y using a graphing calculator. Find the maximum point.
Answers
Answer:
A. see below for a graph
B. f(x, y) = f(0, 15) = 90 is the maximum point
Step-by-step explanation:
A. See below for a graph. The vertices are those defined by the second inequality, since it is completely enclosed by the first inequality: (0, 0), (0, 15), (10, 0)
__
B. For f(x, y) = 4x +6y, we have ...
f(0, 0) = 0
f(0, 15) = 6·15 = 90 . . . . . the maximum point
f(10, 0) = 4·10 = 40
_____
Comment on evaluating the objective function
I find it convenient to draw the line f(x, y) = 0 on the graph and then visually choose the vertex point that will put that line as far as possible from the origin. Here, the objective function is less steep than the feasible region boundary, so vertices toward the top of the graph will maximize the objective function.
The vertex points of this system are (0, 0), (0, 15) and (10, 0). And the maximum point of the system is 90.
What are systems of inequalities?At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.
The given system:
2x+y ≤20
3x+2y ≤30
x, y ≥0
To find the vertex points,
first, we take inequalities in slope-intercept form.
y = 20 - 2x
And y = -3x/2 + 15
x, y ≥0
From that we interpreted the graph.
And the graph is given in the attached image.
A:
Check out the graph below. Given that the first inequality entirely encloses it, the vertices are those defined by the second inequality: (0, 0), (0, 15), (10, 0).
B:
We have objective function f(z) = 4x + 6y
To find the maximum point:
Substituting (0,0) to the function,
4x + 6y
= 4(0) + 6(0)
= 0
Substituting (0,15) to the function,
4x + 6y
= 4(0) + 6(15)
= 0 + 90
= 90
Substituting (10,0) to the function,
4x + 6y
= 4(10) + 6(0)
= 40 + 0
The maximum point is 90.
Therefore, (0, 0), (0, 15) and (10, 0) are the vertex of the system. And the maximum point is 90.
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Related Questions
Find the turning point of y=x^2+10x+12
Answers
Answer:
vertex = (- 5, - 13 )
Step-by-step explanation:
given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the turning point ( vertex) is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 10x + 12 ← is in standard form
with a = 1, b = 10 , then
x = - [tex]\frac{10}{2}[/tex] = - 5
substitute x = - 5 into the equation and evaluate for y
y = (- 5)² + 10(- 5) + 12 = 25 - 50 + 12 = - 13
turning point = (- 5, - 13 )
Kenji and Isabel are standing exactly opposite one another on the banks at the edge of either side of a 40 m wide river. Isabel turns and walks 13 m along the bank of the river. About how far apart is Isabel from Kenji after Isabel walks along the bank of the river? Enter your answer, rounded to the nearest meter, in the box.
Answers
Answer:
42
Step-by-step explanation:
40^2+13^2=x^2
1600+169=x^2
1769=x^2
1769−−−−√=x2−−√
±42≈x
sin(α)=725 sin ( α ) = 7 25 and α is in quadrant II and cos(β)=8/7
Answers
Answer:
sin (α )= 72 5sin (α) = 725
Step-by-step explanation:
I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
To find the missing angle's measure
⇒ important to understand the sum of the angles of a triangle
⇒ the sum of every angle of any triangle in all cases equal to 180
degrees
What is the information given:
⇒ one angle is of 94 degrees and the other of 46 degrees
Using the information in the first section and the information given in the diagram, let's set up an equation:
[tex]94+46+x = 180\\140+x = 180\\x = 40[/tex]
The measure of the missing angle is 40 degrees
Hope that helps!
Question is in picture
Answers
Answer: Heat pollution.
If you are to search up
heat pollution occurs because?
the answer that will pop up is:
The main reasons of thermal pollution are industries and power plants, withdrawing water (a powerful sink for heat waste) from streams for cooling their generators and machines, and then releasing back into the water bodies, which elevates the temperature of freshwater habitats (Miara et al., 2018).
What is 56 ÷ (-8) = ___ need fast will give brainliest
Answers
Answer:
-7
Step-by-step explanation:
^
Answer:
-7
Step-by-step explanation:
What does the notation P(B|A) mean?
Answers
Answer:
the answer for this one it should be the probability or chances that the event b occurs when the event a has occured.
Step-by-step explanation: I hope this help you pal or folk and have a great day.
In centimeters, what is the unknown length in this right triangle?
A right triangle with side length 60 centimeters, x, and hypotenuse of 61 centimeters.
Answers
Answer:
Given:-Side length ( perpendicular = 60 cm)
Hypotenuse = 61 cm
To find :-Base length
Solution:By Pythagoras theorem ,
Hypotenuse² = Perpendicular² + Base²
61² = 60² + base²
3721-3600 = Base²
√121 = base
11cm = base
Answer:
Base = x = 11 cmStep-by-step explanation:
In the question we are given ,
Side length ( Perpendicular ) = 60 cm Hypotenuse = 61 cmAnd we have asked to find the length of base that is denoted by x .
Solution : -
According to Pythagoras Theorem ,
[tex] \longrightarrow \purple{\boxed{H {}^{2} = P {}^{2} + B {}^{2} }} \longleftarrow[/tex]
Where ,
H = HypotenuseP = PerpendicularB = BaseNow , substituting value of hypotenuse, perpendicular and base :
[tex] \hookrightarrow \: 61 {}^{2} = 60 {}^{2} + x {}^{2} [/tex]
Now by squaring 61 and 60 , we get :
[tex] \hookrightarrow \:3721 = 3600 + x {}^{2} [/tex]
Now transposing 3600 to left hand side :
[tex] \hookrightarrow \:3721 - 3600 = x {}^{2} [/tex]
Now subtracting 3600 from 3721 :
[tex] \hookrightarrow \:121 = x {}^{2} [/tex]
[tex] \hookrightarrow \: \sqrt{121} = x[/tex]
We know that 11 × 11 is equal to 121 that means square root of 121 is 11 . So :
[tex] \hookrightarrow \: \red{ \boxed{11 \: cm = x}}[/tex]
x = baseHenceforth, length of base of right triangle is 11 cm .#Keep LearningFind the area of the regular 18-gon with Radius is 7 mm
Answers
Jajaj Josh’s but link.bio hope that helps
Please help meeee!!!!!
Answers
Answer:
Now plot those points in graph and find intersection hope it helps you.......
Convert the decimal to a percent. 0.725
Answers
Answer:
72.5% out of 100%
Step-by-step explanation:
0.725 is 72.5% of 1. 100% technically counts as 1. so 72.5%
.725 is out of 1, and you multiply that number by 100 to get the percentage
Edna, Fatimah and Toby had a sum of money. The amount of money Edna had was 4 times the amount of money Fatimah had. The ratio of the amount of money Fatimah had to the total amount of money Toby and Fatimah had was 5:8. After Fatimah gave $30 to Toby, Toby had as much money as Fatimah. How much more money did Edna have than Toby in the end?
HELP ME PLEASE ! HOMEWORK DUE IN LESS THAN 2 HOURS! NO CLUE ON HOW TO DO THIS ! OFFERING 15 POINTS
Answers
Answer:
Edna had $510 more amount of money than Toby in the end.
Step-by-step explanation:
LET :-
Edna's amount of money - x
Fatimah's amount of money - y
Toby's amount of money - z
Now,
By the question,
x = 4y
y : (y + z) = 5 : 8
y - 30 = z + 30
Now,
y : (y + z) = 5 :8
or, y/(y + z) = 5/8
or, 8y = 5y + 5z
or, 3y = 5z
so, y = 5z/3
Now,
y - 30 = z + 30
or, 5z/3 - 30 = z + 30
or, (5z - 90)/3 = z + 30
or, 5z - 90 = 3z + 90
or, 5z - 3z = 90 + 90
or, 2z = 180
so, z = 90
Toby's amount of money - $90
Now,
y = 5z/3
or, y = 5 * 90/3
or, y = 5 * 30
so, y = 150
Fatimah's amount of money - $150
Again,
x = 4y
or, x = 4*150
or, x = 600
Edna's amount of money - $600
Now,
$600 - $90
= $510
Therefore,Edna had $510 more amount of money than Toby in the end.
Find the measures of the angles in each triangle.
Answers
Answer:
55°
Step-by-step explanation:
so,area of a triangle is equal to 180°which means:(x-2)° + x° + 72° =180°take 72° to the other side and it will be negative(x-2)°+x°=180°-72°=108x-2+x=108x+x=1102x=110x=55I hope that helps
Variability ? I'm confused
Answers
5x+2y=-3
-3x-y=2
Use determinant method and Gauss Jordan Elimination method to solve the systems of linear equation.
please with working out
Answers
X' + 2y' + x = 0 , x' - y' + y = 0 x(0) = 0 and y(0) = 1
Answers
This looks like a system of differential equations.
[tex]\begin{cases}x' + 2y' + x = 0 \\ x' - y' + y = 0 \\x(0)=0, y(0)=1\end{cases}[/tex]
Eliminating x' gives
[tex](x'+2y'+x)-(x'-y'+y) = 0 - 0 \implies 3y' - y + x = 0[/tex]
and eliminating y' gives
[tex](x'+2y'+x) + 2(x'-y'+y)=0+2\times0 \implies 3x' + x + 2y = 0[/tex]
so that we can rewrite the system as
[tex]\begin{cases}3x' = -x - 2y \\ 3y' = -x + y\end{cases}[/tex]
or equivalently in matrix form as
[tex]\begin{bmatrix}x\\y\end{bmatrix}' = \dfrac13 \begin{bmatrix}-1&-2\\-1&1\end{bmatrix} \begin{bmatrix}x\\y\end{bmatrix}[/tex]
Compute the eigenvalues for the coefficient matrix:
[tex]\det\begin{bmatrix}-1-\lambda&-2\\-1&1-\lambda\end{bmatrix} = (-1-\lambda)(1-\lambda) - 2 = \lambda^2 -3 = 0 \implies \lambda=\pm\sqrt3[/tex]
Compute the corresponding eigenvectors:
[tex]\lambda=\sqrt3 \implies \begin{bmatrix}-1-\sqrt3&-2\\-1&1-\sqrt3\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix} \\\\ \implies v_1=(1-\sqrt3)v_2 \implies \vec v = \begin{bmatrix}1-\sqrt3\\1\end{bmatrix}[/tex]
[tex]\lambda=-\sqrt3 \implies \begin{bmatrix}-1+\sqrt3&-2\\-1&1+\sqrt3\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix} \\\\ \implies v_1 = (1+\sqrt3)v_2 \implies \vec v = \begin{bmatrix}1+\sqrt3\\1\end{bmatrix}[/tex]
We end up multiplying the matrix by 1/3, so the eigenvalues also get scaled by 1/3 and λ = ±1/√3. The eigenvectors stay the same.
Then the characteristic solution to the system is
[tex]\begin{bmatrix}x\\y\end{bmatrix} = C_1 e^{t/\sqrt3} \begin{bmatrix}\frac{1-\sqrt3}3\\\frac13\end{bmatrix} + C_2 e^{-t/\sqrt3} \begin{bmatrix}\frac{1+\sqrt3}3\\\frac13\end{bmatrix}[/tex]
Use the initial conditions to solve for the constants.
[tex]\begin{bmatrix}0\\1\end{bmatrix} = C_1 \begin{bmatrix}\frac{1-\sqrt3}3\\\frac13\end{bmatrix} + C_2 \begin{bmatrix}\frac{1+\sqrt3}3\\\frac13\end{bmatrix}[/tex]
[tex]\implies \begin{cases}(1-\sqrt3) C_1 + (1+\sqrt3) C_2 = 0 \\ C_1 + C_2 = 3\end{cases}[/tex]
[tex]\implies C_1=\dfrac{3+\sqrt3}2, C_2=\dfrac{3-\sqrt3}2[/tex]
Then the particular solution is
[tex]\begin{bmatrix}x\\y\end{bmatrix} = \dfrac{3+\sqrt3}6 e^{t/\sqrt3} \begin{bmatrix}1-\sqrt3\\1\end{bmatrix} + \dfrac{3-\sqrt3}6 e^{-t/\sqrt3} \begin{bmatrix}1+\sqrt3\\1\end{bmatrix}[/tex]
or
[tex]\begin{cases}x(t) = -\dfrac1{\sqrt3} e^{\sqrt3 \, t} + \dfrac1{\sqrt3} e^{-\sqrt3\,t} \\\\ y(t) = \dfrac{3+\sqrt3}6 e^{\sqrt3\,t} + \dfrac{3-\sqrt3}6 e^{-\sqrt3\,t}\end{cases}[/tex]
Please help me solve this question
Answers
Answer:D
Step-by-step explanation: Multiply the expression
Nancy Regan purchased a new diamond bracelet for $12,600. The state sales tax is 6% and the federal excise tax on the jewelry is 11%. What is the total purchase price of the bracelet? Round your answer to the nearest cent.
Answers
Using proportions, it is found that the total purchase price of the bracelet is of $10,769.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, we consider the two taxes, of 6% and 11%, hence the price suffers an increase of 17%, that is, the price is multiplied by 117% = 1.17 to reach $12,600, hence:
1.17p = 12600
p = 12600/1.17
p = 10769.
The total purchase price of the bracelet is of $10,769.
More can be learned about proportions at https://brainly.com/question/24372153
68 is 17% of what number?
68 = 0.17 • X
x = [?]
Answers
Answer:
400
Step-by-step explanation:
Division cancels multiplication. Divide by 0.17 to isolate "x" on the right side of the equation.
68 = 0.17 * x
divide both sides by 0.17
400 = x
68 is 17 percentage of the number 400.
To find the number that 68 is 17% of, we can set up the equation:
17% of x = 68
To solve for x, we need to divide both sides of the equation by 17% (or 0.17 as a decimal):
x = 68 / 0.17
Evaluating the division:
x=400
Therefore, 68 is 17% of 400.
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Question 8 of 10
If a student answered 69 exam questions correctly out of 100, what fraction
and what percentage of questions did the student answer incorrectly?
Choose two answers. Need help ASAP
A.
30/100
B. 0.69%
C. 31%
D. 69%
E. 31/100
F. 69/100
Answers
Answer: I believe B and F
Step-by-step explanation:
Hope this help?!
Please please help!!! will give brainliest
Answers
Answer: i think the answer is 116. if it is not i am terribly sorry.
Step-by-step explanation:
Fifty is a composite number. Use
a factor tree to find the prime
factorization of 50.
Answers
Answer:
2*5*5
Step-by-step explanation:
50 ---> 25 * 2
25 = 5*5
50 = 2*5*5
Hope this helps :)
Have a nice day!
PLEASE ANSWER! WILL GIVE BRAINLIEST!
The horizontal lines (l and m) are parallel. They are crossed by two transversals (lines a and b).
Transversals a and b intersect to make a triangle. The m∠1 = 75°, and the m∠4 = 50°.
1. What is the m∠5? Explain how you know. (2 points)
2. What is the measure of the sum of the angles in a triangle? (2 points)
3. ∠3 is in a triangle with ∠4 and ∠5. Write and solve an equation to find the m∠3. (2 points)
4. What is the measure of a straight angle? (2 points)
5. ∠2 is in a straight line with ∠1 and ∠3. Write and solve an equation to find the m∠2. (2 points)
Answers
1. m∠5 = 75° (corresponding angles theorem)
2. Sum of angles in a triangle = 180°
3. m∠3 = 55°
4. Straight line angle = 180°
5. m∠2 = 50°
What is the Corresponding Angles Theorem?If two corresponding angles are formed when a transversal intersect parallel lines, they are both congruent based on the corresponding angles theorem.
1. m∠5 = m∠1 (corresponding angles theorem)
m∠5 = 75°
2. Sum of angles in a triangle = 180°
3. m∠3 + m∠4 + m∠5 = 180° (sum of triangle)
Substitute
m∠3 = 180 - 50 - 75 = 55°
4. Straight line angle = 180°
5. m∠2 = 180 - m∠3 + m∠1 (straight line angle)
m∠2 = 180 - 55 - 75
m∠2 = 50°
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A raffle ticket is sold for $3.50 each and the prize for winning the raffle is $250. If 100
people entered the raffle, what is:
the expected value? =
are you expected to win or lose the raffle? =
a fair price for the raffle ticket? =
Answers
Write the multiplication equation that represents the model
Answers
Answer:
2/3 × 2/5 = 4/15
Step-by-step explanation:
see image. If you just look at the horizontal lines the rectangle is divided into thirds. Two of the sections are highlighted indicating 2 out of 3, or 2/3.
If you then consider the vertical lines. There are 5 sections and 2 out of the 5 are highlighted indicating 2/5.
When you overlap both images (which is what the original image you posted was) you get a small section that is doubly highlighted. In your original image it is kind of purple (I marked them in yellow) In the double-layered image, there are 15 small sections. 4 are highlighted (double-highlighted) This is 4/15.
2/3 × 2/5 = 4/15
I supposed it could also be
2/5 × 2/3 = 4/15
Numerically, these are the same. They have the same result. I hope this helps!
Simplifly the expression: x-3x-(-5x)
Answers
Answer:
The answer is 3x.
Step-by-step explanation:
I used a calculator
solve 3/8[-8+16-(-2 1/2)]
Answers
3.375
hope it helps...!!
Which of the following sets of numbers is a Pythagorean triple?
14, 40, 50
7, 24, 31
7, 20, 27
14, 48, 50
Answers
Answer:
the answer your looking for would be 14, 48, 50.
Step-by-step explanation:
Hope this helps!
Answer:
14, 48, 50 have a good day
Step-by-step explanation:
the final price of a book is $27 dollars. An 8% sales tax was added to the original price, then you used a coupon for 50% off. What was the original price of the book?
Answers
Answer:
14.58
Step-by-step explanation:
x\27 = 54/100 cross multiply then divide by 100% x=Original price
so then you'll get 14.58
Please help!!!!!!!! Determine the function which corresponds to the given graph.
Answers
The rational function shown in the graph is:
[tex]y = \frac{x - 6}{x - 5}[/tex]
How to determine the function?
First, we can see that we have an asymptote at x = 5, so the denominator becomes equal to zero when x = 5.
Then the rational function is something like:
[tex]y = \frac{g(x)}{x - 5}[/tex]
We also can see that when x = 6, the function intercepts the x-axis, then we must have that:
g(6) = 0
So we can define:
g(x) = x - 6
So the rational function is:
[tex]y = \frac{x - 6}{x - 5}[/tex]
If you want to learn more about rational functions, you can read:
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