Graph the system of constraints and find the value of x and y that maximize the objective function.
Answers
We want to maximize C, which is C= 7x - 3y. Let's explore our intuition regarding how this will look. We know that both y and x are greater than or equal to zero, which means -3y will be a negative number (or 0) and x is a positive number (or 0). We want to get x as big as possible, given the constraints, we want y to be zero, if possible
We see that, based on the constraints, y is greater than or equal to zero,
but it has no other minimum value established. We only know that y and x add up
to 5, and that y is less than or equal to (1/5)x + 2. That means y could be
0 and still satisfy the constraints.
In order to maximize C, we want to be 5 as possible
and y to be zero:
C = 7 (5) - 3(0)
C=35
Answer: Solving Systems Using Matrices Quiz Part 1
1. c) (5,0)
2. a) 20 of type A; 20 of type B
3. d) no solution
4. a) -5
5. d) 11 -12 7 5 12 -7
6. a) (-6,8)
Related Questions
Byron earns $11.00 per hour. How many hours will Byron have to work to earn $143.00?
1. 7.7 hours
2. 13.0 hours
3. 14.3 hours
4. 15.7 hours
Answers
divide 143.00 by 11.00
143/11 = 13
Answer is 2. 13.0 hours
Answer:
Step-by-step explanation:
Byron earns $11.00 per hour.
Lets say he works for x hours
for x hour Byron earn =11x
It is given that
Byron have to work to earn= $143.00
so
11x= 143
x=143/11
x=13
so He must work for 13.0 hours .
Lines that never intersect are perpendicular True or False
Answers
The answer is false. Two lines that intersect and form right angles are called perpendicular lines.
Hope this helps!
Which best describes the relationship between the 125° angle and angle A? They are same side interior angles. Angle A measures 55°. They are alternate interior angles. Angle A measures 125°. They are vertical angles. Angle A measures 125°. They are corresponding angles. Angle A measures 55°.
Answers
Answer:
a. They are same side interior angles. Angle A measures 55°.
They are same side interior angles. Angle A measures 55° which is correct option(A).
What are Interior angles?Interior angles is defined as those that lie inside a shape, or those that are located in the region enclosed by two parallel lines that cross each other at a horizontal angle.
What are Alternate Interior Angles?Alternate Interior Angles is defined as these angles are created when a transversal intersects two parallel lines. The opposing sides of the transversal produce this non-adjacent pair of angles.
What are Vertical angles?Vertical angles is defined as when two lines meet each other at a point. They are always equal to each other, In other words, four angles are created anytime two lines cross or intersect.
What are corresponding angles?Corresponding angles is defined as any pair of angles that are both on the same side of the transversal and of one of the two lines that it intersects.
Given angle measure as 125°
Therefore, they are same side interior angles. Angle A measures 55°.
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Naomi has 50 red and white beads.the number of red beads is 1 more than 6 times the number of white beads. how many red beads does naomi have
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How would I solve
-1+2i / -1-3i
Answers
(-1+2i)(-1+3i) / (-1-3i)(-1+3i)
1-5i+6i² / 1-9i²
-5-5i / 10
-5/10 - 5i/10
-1/2 - 1i/2
Tanisha bought 4 bundled packs of comic books. The price of each pack was the same. After she bought the packs, her account balance showed a change of −$86.64. What would have been the change to Tanisha's account balance had she bought only 1 bundled pack of comic books?
A) 21.60
B) -21.60
C) 21.66
D) 21.66
Answers
Find the length of the hypotenuse of a right triangle with legs of lengths 12 ft and 16 ft answer
Answers
Answer:
Step-by-step explanation:
but what ab this one: Find the length of the hypotenuse of a right triangle with legs of 5 ft and 12 ft.
A right triangle in which one angle is the right angle and the two sides are perpendicular to each other. Hence, the length of the hypotenuse is [tex]20ft[/tex].
What s the right triangle?
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.
Here, the lengths of the triangle are [tex]12ft[/tex] and [tex]16ft[/tex] .
As we know,
[tex]H^{2}=P^{2}+B^{2}[/tex] ..........[tex](1)[/tex]
Now, substituting the values in the equation [tex](1)[/tex], we get
[tex]H^{2}=(12)^{2}+(16)^{2}\\H^{2}=144+256\\H^{2}=400\\H=\sqrt(400)\\H=20ft[/tex]
Hence, the length of the hypotenuse is [tex]20ft[/tex].
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Use a quadratic equation to find two real numbers that satisfies the situation. The sum of the two numbers is 2, and their product is –48.
Answers
To find two real numbers whose sum is 2 and product is -48, we form a quadratic equation x^2 - 2x - 48 = 0. Using the quadratic formula, we get two pairs of numbers (8, -6) and (-6, 8) that satisfy the given conditions.
Explanation:To find two real numbers that satisfy the given conditions, namely their sum being 2 and their product being –48, we can set up a system of equations or use a . Let's denote the two numbers as x and y. We know:
x + y = 2xy = -48We can express y in terms of x from the first equation: y = 2 - x. Substituting this into the second equation gives us:
x(2 - x) = -48
This simplifies to a quadratic equation:
x^2 - 2x - 48 = 0
Using the, x = (-b ± √(b^2 - 4ac)) / (2a), with a = 1, b = -2, and c = -48, we find the two possible values for x, which in turn gives us the corresponding values for y:
x = (2 ± √(4 + 192)) / 2
x = (2 ± √196) / 2
x = (2 ± 14) / 2
Therefore, the two solutions are x = 8 or x = -6. Since we were looking for two numbers, using x + y = 2, the corresponding y values are y = -6 and y = 8, respectively. Hence, the two pairs of numbers that satisfy the conditions are (8, -6) and (-6, 8).
What is the measurement of angle R?
Answers
make sure your calculator is in Degree mode.
A gas station sells regular gas for $2.30 per gallon and premium gas for $3.00 a gallon. at the end of a business day 250 gallons of gas had been sold, and receipts totaled $631. how many gallons of each type of gas had been sold?
Answers
Newton uses a credit card with a 18.6% APR, compounded monthly, to pay for a cruise totaling $1,920.96. He can pay $720 per month on the card. What will the total cost of this purchase be?
Answers
Somebody help me on this real quic plz
Answers
x y
0 = 0
1 = 2
2 = 4
3 = 6
5 = 10
I hope this helps love! :)
Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function : A = 24x-x^2 , where x = width , gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area ?
PLEASE HELP ASAP!! *if you can give explanation/work it would be great* if not that is okay ..
Answers
and this one is not exception, so where's the vertex? what's A or the y-coordinate when the vertex is reached?, well, let's check.
[tex]\bf A=24x-x^2\implies A=-1x^2+24x+0\\\\ \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} A = &{{ -1}}x^2&{{ +24}}x&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{24}{2(-1)}~~,~~0-\cfrac{24^2}{4(-1)} \right)\implies \left(12~~,~~ 0+\cfrac{576}{4} \right) \\\\\\ \left(\stackrel{width}{12}~~,~~\stackrel{Area}{144} \right)[/tex]
so, that's the vertex, and when the width is that much, the Area reaches a maximum of that much.
The width that gives the maximum area of the rectangular pen is 12 feet, and the maximum area is 144 square feet.
Explanation:To maximize the area of a rectangle with a fixed perimeter, you want to make the rectangle as close to a square as possible. This maximizes the area because it distributes the available fencing evenly among the sides, optimizing the area enclosed. The given function, A = 24x - x^2, represents the area of a rectangle with width 'x' and length 'L' where L = (48-2x) / 2.
Maximization or minimization of a function occurs at its turning point. For a quadratic function like ours, the maximum or minimum happens at the vertex. The x-coordinate of the vertex is given by -b/2a. So, in our function A = -x^2 + 24x (which is the same as 24x - x^2), a = -1, b = 24.
Substitution gives: x = -(24) / 2*(-1) = 12 feet. Therefore, the width that gives you the maximum area is 12 feet.
Substitute x = 12 into the function to find the maximum area: A = 24*12 - 12^2 = 288 - 144 = 144 square feet.
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Find the tangent of the angle in standard position in which the terminal side passes through the point (3,4)
Answers
angle = 36.87 degrees
Mrs. hensen cataloged a group of incoming library books in 8 hours. mr. taylor can catalog the same number of books in 4 hours. mrs. phillips can catalog them in 6 hours. how long would it take if they all worked together?
Answers
Mrs. Hensen's working rate is
x = n/8 books/h
Mr. Taylor's working rate is
y = n/4 books/h
Mrs. Phillip's working rate is
z = n/6 books/h
When they work together, they can catalog n books in
(n books)/(x+y+z books/h)
= n/(n/8 +n/4 + n/6)
= 1/(1/8 + 1/4 + 1/6)
= 1/(13/24)
= 24/13 hours
The time required is 24/13 h = 1.8462 h = 1 hour, 51 min
Answer: 1.8462 hours (or 1 hour, 51 minutes)
PLEASE ANSWER QUICK
Isaac and his sister plan to surprise their parents by buying them each a pair of shoes. They agree that Isaac will pay 68% of the price since he receives a greater allowance. Use an estimation strategy to determine how much Isaac will pay if the total bill is $97.65. Show the step-by-step process you used to solve the problem.
Answers
Issac will pay $66.40.
This finds 1% of 97.65
0.9765 x 68 = 66.402
This finds 68% of 97.65
Isaac will pay $66.40
if 161 is 35% of students at school who play sports how many students are at school?
Answers
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 161&35 \end{array}\implies \cfrac{x}{161}=\cfrac{100}{35}\implies x=\cfrac{161\cdot 100}{35}[/tex]
Plz see picture and question attached
Answers
because it is square, meaning the width and height are the same, so therefore the width is also 4. to get the area of a square of rectangle, you times the width by the height. 4 × 4 = 16. so the answer is 16m² because the unit is metre so we write m²
A bag contains 80 marbles: 40 are red, 20 are blue, and 20 are black. what is the probability of selecting a red or blue marble at random
Answers
20% out of 80 for blue
An angle measures 150° less than the measure of a supplementary angle. what is the measure of each angle?
Answers
The measure of the angle is 30 degrees
What is a supplementary angle?A supplementary angle can be defined as an angle that sum up t0 180 degrees.
The two angles must add up to 180 degrees, that is, angles on a straight line.
The properties of supplementary angles are;
The two angles are supplementary angles when they add up to 180°The two angles together make a straight line, but the angles need not in a place“S” of supplementary angles represents a “Straight” line. This means they form 180°From the information given, we have that;
The angle measures 150 degrees less of supplementary angles
Then,
180 - 150
30 degrees
Hence, the value is 30 degrees
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The two supplementary angles in question measure 15° and 165° respectively, with one angle being 150° less than the other.
We are given that one angle measures 150° less than its supplementary angle. By definition, supplementary angles add up to 180°. Let's call the angle in question 'A', and its supplementary angle 'B'.
We thus have the following relationship:
A = B - 150°
and
A + B = 180°
Substituting the first equation into the second, we get:
(B - 150°) + B = 180°
This simplifies to:
2B - 150° = 180°
2B = 330°
B = 165°
Now that we know the measurement of B, we can find A:
A = 165° - 150°
A = 15°
So, the two angles are 15° and 165° respectively.
Holes drilled several kilometers into Earth’s crust provide direct evidence about Earth’s interior in the form of a. seismic waves. b. rock samples. c. liquid iron. d. volcanic eruption. Please select the best answer from the choices provided A B C D
Answers
Answer:
b. Rock Samples
Explanation:
Rock samples are obtained by drilling with special drills into the substance.
So, holes drilled several kilometers into Earth's crust provide direct evidence about Earth's interior in the form of a rock samples.
What is the common difference of the arithmetic sequence 1/5, 6/5 , 11/5 ,16/5 , ...?
Answers
hope this helps
Mario baked cookies for the class party. the students ate 3/4 of what mario bought. the students on his bus ate 1/3 of what was left. mario had 6 left when he got home. how many cookies did mario bake?
Answers
What two numbers can you multiply to get 84?
Answers
Check it to make sure.
2 × 42 = 84
42 and 2 can be multiplied to get 84.
What is the benefit of using statistical sampling versus nonstatistical sampling?
Answers
Carly is making 3 and 1/2 batches of biscuits. If one batch calls for 2and 1/3 cups of flour, how much flour will she need?
Answers
how many times must 24 be added until the sum is 1500
Answers
60 times must 24 be added until the sum is 1500
What is the equation in point-slope form for the line parallel to y = -2x + 10 that contains J(6, 8)?
a. y - 8 = -2(x - 6)
b. x - 8 = 2(y - 6)
c. y - 8 = 2(x - 6)
d. y + 8 = -2(x - 6)
Answers
m = slope
b = y-intercept
x = variable
y = what you get
Answer: Hello mate!
A linear equation has the form y = ax + b
where x is the variable, a is the slope and b is the x-intercept.
We want to find the pararel line to y = -2x + 10
A paralel line of this, will be another line with the same slope ( -2 in this case) and a different x-intercept; then our line has the shape of:
y = -2x + b
and we know that this line pases through the point (6,8), and with this info we could find the value of b:
8 = -2*6 + b
b = 8 + 12 = 20
then y = -2x + 20 is the pararel line that passes through the point (6.8)
Then the correct answer is the option a:
a) y - 8 = -2(x - 6) = -2x + 12
y = -2x + 12 + 8 = -2x + 20
Which linear system of equations does the matrix represent?
-3 5 | 15
2 3 | -10
Answers
-3x + 5y = 15
2x + 3y = -10
The matrix represents the system of linear equations: -3x + 5y = 15 and 2x + 3y = -10.
Explanation:The matrix represents the system of linear equations. Each row corresponds to an equation and each column to a coefficient of the unknowns. So, the given matrix:
-3 5 | 15
2 3 | -10
Represents the system of linear equations:
-3x + 5y = 15
2x + 3y = -10
Where x and y are the unknown variables that we are trying to solve for.
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Sofia cuts a piece of felt in the shape of a kite for an art project. The top two sides measure 20 cm each and the bottom two sides measure 13 cm each. One diagonal, EG, measures 24 cm. What is the length of the other diagonal, DF? 5 cm 16 cm 21 cm 32 cm
Answers
x + y = 24 where x and y are the 2 parts of diagonal Other diagonal wil be smaller that 24.
x^2 + z^2 = 13^2
y^2 + z^2 = 20^2 where z = 0.5 * length of smaller diagonal)
form last 2 equations
y^2 - x^2 = 20^2 - 13^2 = 231
now y = 24-x so we have
(24 - x)^2 - x^2 = 231
576 - 48x = 231
48x = 345
x = 7.1875
z^2 = 13^2 - 7.1875^2 = 117.34
z = 1.83
so smaller diagonal = 21.66 cm
looks like its the third choice.
The length of the other diagonal, DF is 44 cm.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Since the kite has two pairs of congruent adjacent sides, we know that the diagonals of the kite are perpendicular bisectors of each other.
Therefore, we can use the Pythagorean theorem to find the length of the other diagonal DF.
Let x be the length of the other diagonal, DF.
We know that one diagonal EG has a length of 24 cm, so we can use the Pythagorean theorem to find the length of the perpendicular bisector of EG, which is half of DF.
By the Pythagorean theorem, we have:
[tex](20/2)^2 + (x/2)^2 = 24^2\\100 + (x/2)^2 = 576\\(x/2)^2 = 476\\x/2 = \sqrt(476)\\x = 2 \times 21.86\\x = 43.72\\x = 44[/tex]
Therefore,
The length of the other diagonal DF is 44 cm
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