The foci of the hyperbola is (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].
What is foci of the hyperbola?The two fixed points that are located inside each curve of a hyperbola are known as its foci, and they are important for the formal description of the curve.
Here the given equation of the hyperbola is [tex]4y^2-x^2=16[/tex] .
Now writing the given equation into standard form then,
=> [tex]4y^2-x^2=16[/tex]
=> [tex]-x^2+4y^2=16\\[/tex]
=> [tex]\frac{-x^2}{4}+\frac{4y^2}{4}=\frac{16}{4}[/tex]
=> [tex]\frac{-x^2}{4}+y^2=4[/tex]
=> [tex]\frac{-x^2}{4\times4}+\frac{y^2}{4}=1[/tex]
=> [tex]\frac{-x^2}{16}+\frac{y^2}{4}=1[/tex]
Here we know that [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex] then a=2 and b=4 , (h , k)=(0,0)
Then c=[tex]\sqrt{a^2+b^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}[/tex].
Then foci is (0,0+c) and (0,0-c) then,
=> (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex]
Hence the foci of the hyperbola is (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].
To learn more about foci refer the below link
https://brainly.com/question/26250569
#SPJ9
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
(1 point) help me pls D;
please D:
b equal for the top of the bookcase to have the correct area= 5 cm2
What is surface area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
L × b = 300
b = 300 / L
b = 300 / 60 = 5
Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.
learn more about surface area click here:
brainly.com/question/16519513
#SPJ1
which of the following values are needed to determine the area of the trapezoid? choose all that apply
A. 5 mm
B. 6 mm
C. 8 mm
D. 10 mm
PLEASE PLEASE HELP ME!!!!!!!!
The trapezoid A’B’C’D is a dilation of the trapezoid ABCD. What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
PLEASE LOOK AT PICTURE!!!!!!
All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]
How to find factor of dilation?We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.
Let's start with the original quadrilateral ABCD. The length of AB is:
[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]
Similarly, the lengths of BC, CD, and DA are:
[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]
[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]
[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]
Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:
[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]
Similarly, the lengths of B'C', C'D', and D'A' are:
[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]
[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]
[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]
Now we can find the ratio of corresponding side lengths:
[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]
[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]
[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]
[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]
Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.
To know more about Dilation visit:
brainly.com/question/10855880
#SPJ1
(x³ + kx² - 34x +56) ÷ (x + 7)
Answer:
Step-by-step explanation:
Because this problem is not easily solvable through factoring, we must use long division to find the answer.
_______________ x+7 | x3 + kx2 - 34x + 56
When performing long division on polynomials, we should try to cancel out the term with the greatest power first. So, we must figure out how many x's go into x3, because x is the first term of the first polynomial and x3 is the first term of the second polynomial. x*x2 = x3, so:
x2
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
Then, we see how many x's go into (k-14)x2. x*(k-14)x = (k-14)x2, so:
x2 + (k-14)x
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
(-) (k-14)x2 - 7kx - 98x
-7kx - 132x + 56= (-7k-132)x + 56
x*(-7k-132) = (-7k-132)x, so:
x2 + (k-14)x + (-7k-132)
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
(-) (k-14)x2 - 7kx - 98x
(-7k-132)x + 56
(-) (-7k-132)x - 7k - 924
-7k - 868
The answer is x2 + (k-14)x + (-7k-132) - [(7k-868)/(x+7)]
What is the measure of ∠m
Answer:
26° 180 -81 - 73 = 26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
triangle= 180
81 + 73 = 154
180 - 154= 26
if y varies jointly with the square of x and inversely as z, what is the change in y when both x and z are tripled
Step-by-step explanation:
y = x^2 / z now triple x and z
y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z <==== this is 3 times the original
y is tripled
14. (Find LCM of) : ax² - (a² + ab)x+ a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x+ c²a
Answer:
Step-by-step explanation:
To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.
ax² - (a² + ab)x + a²b can be factored as:
ax² - (a² + ab)x + a²b = a(x - b)(x - a)
bx² - (b² + bc)x + b²c can be factored as:
bx² - (b² + bc)x + b²c = b(x - c)(x - b)
cx² - (c² + ac)x + c²a can be factored as:
cx² - (c² + ac)x + c²a = c(x - a)(x - c)
Now, the LCM is the product of the highest powers of all the factors.
The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:
LCM = a²b²c²(x - a)(x - b)(x - c)
Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).
Find the average rate of change of g(x) = 3x² + 3 on the interval [ - 9, 4].
Answer:
-15
Step-by-step explanation:
You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].
Average rate of changeThe average rate of change is defined as ...
AROC(g) = (g(b) -g(a))/(b -a)
We can evaluate this directly, or we can simplify it a bit first.
AROC = ((3b² +3) -(3a² +3))/(b -a)
= (3b² -3a²)/(b -a)
= 3(b -a)(b +a)/(b -a)
= 3(b +a)
Interval [-9, 4]The AROC on the interval [a, b] = [-9, 4] is then ...
AROC = 3(4 +(-9)) = 3(-5)
AROC = -15
__
Additional comment
In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.
Regines father is given a yearly increase in salary of 15%. How much is he receiving now if he's salary 2 years ago was 25250
Regine's father is currently receiving a salary of 29037.50.
What is percentage increase?A percentage increase in mathematics is the proportion by which a quantity or value has grown in comparison to its initial value. It is computed by subtracting the original value from the new value, multiplying the result by 100, and then subtracting the difference between the two values. The percentage increase formula is:
(new value - original value) / 100% of the original value is the percentage increase.
The yearly increase is 15%, thus:
salary increase = 25250 x 0.15 = 3787.50
The current salary is:
current salary = salary from two years ago + salary increase
current salary = 25250 + 3787.50
current salary = 29037.50
Hence, Regine's father is currently receiving a salary of 29037.50.
Learn more about percentage increase here:
https://brainly.com/question/20818421
#SPJ1
I please need help matching the angles. I cannot seem to get it right.
The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description are;
Alternate Interior Angles; 2. ∠4 and ∠8
Consecutive Exterior Angles; 5. ∠1 and ∠6
Alternate Exterior Angles; 3. ∠1 and ∠5
Transversal; line l
Consecutive Interior Angles; 4. ∠3 and ∠4
Corresponding Angles; 1. ∠1 and ∠7
What is a transversal line?A transversal is a line that intersects two or more other lines.
The description of the relationship between the angles in the question are;
Alternate Interior Angles
Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.
Consecutive Exterior Angles
Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal
Alternate Exterior Angles
Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.
Consecutive Interior Angles
Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.
Corresponding Angles
Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.
Learn more on transversal lines here: https://brainly.com/question/24607467
#SPJ1
2. Suppose a consumer has $30 available to be divided between commodities A and B and the unit price of B is fixed at $3. What will be his demand equation for A if his utility function is U = 4XgXb?
The demand equation for commodity A is Xa = (4/10)Xb.
What is demand equation?A demand equation is a mathematical representation of the relationship between the quantity of a good or service that consumers are willing to buy and the various factors that influence that demand, such as price, income, and preferences.
In the given question,
To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.
Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:
3Xb + pXa = 30
where p is the price of commodity A. We also know the utility function:
U = 4XgXb
To maximize U subject to the budget constraint, we can use the Lagrangian method:
L = 4XgXb + λ(30 - 3Xb - pXa)
where λ is the Lagrange multiplier.
To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:
∂L/∂Xa = -λp = 0
This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:
L = 4XgXb + 0(30 - 3Xb - pXa)
L = 4XgXb
To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:
∂L/∂p = -4XgXb/Xa = -30/3
Xa = (4/10)Xb
So the demand equation for commodity A is Xa = (4/10)Xb.
To know more about demand equation, visit:
https://brainly.com/question/13245362
#SPJ1
The demand equation for commodity A is Xa = (4/10)Xb.
What is demand equation?
A demand equation is a mathematical formula that expresses the relationship between the quantity of a good or service that consumers are willing and able to purchase and various factors that affect that quantity, such as price, income, and the prices of other goods.
According to given information:To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.
Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:
3Xb + pXa = 30
where p is the price of commodity A. We also know the utility function:
U = 4XgXb
To maximize U subject to the budget constraint, we can use the Lagrangian method:
L = 4XgXb + λ(30 - 3Xb - pXa)
where λ is the Lagrange multiplier.
To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:
∂L/∂Xa = -λp = 0
This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:
L = 4XgXb + 0(30 - 3Xb - pXa)
L = 4XgXb
To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:
∂L/∂p = -4XgXb/Xa = -30/3
Xa = (4/10)Xb
So the demand equation for commodity A is Xa = (4/10)Xb.
To know more about demand equation, visit:
brainly.com/question/13245362
#SPJ1
help finding the area of compound shapes
Answer: what shape?
Step-by-step explanation:
More info please
What is the solution set of √
x + 7 − 1 = x?
Answer:
x = 9
Step-by-step explanation:
Solving radical equations:√x + 7 - 1 = x
√x + 6 = x
Isolate √x,
√x = x - 6
Square both sides,
(√x)² = (x - 6)²
Use identity (a -b)² = a² - 2ab + b²
x = x² - 2*x*6 + 6²
x = x² - 12x + 36
x² - 12x + 36 - x = 0
x² - 13x + 36 = 0
We look for two integers which when added give (-13) and when multiplied gives 36.
So, the factors are (-9) and (-4).
-9 + (-4) = -13 & (-9)*(-4) = 36.
Rewrite the middle term using the factors.
x² - 13x + 36 = x² - 9x - 4x + 36
Take out the common factor 'x' from first and second term & take out the common factor (-4) from third and fourth term.
=x(x -9) -4(x - 9)
= (x -9)(x- 4)
x - 9 = 0 ; x - 4 = 0
x = 9 ; x = 4
But 4 doest not satisfy the equation. So, only 9 is the solution.
Pleaseeeeeee helps meeeeeeee I'd really appreciate it
Answer:
5683200
Step-by-step explanation:
Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.
10. Point A is located at (4, 3). Point A is reflected
across the line y = -2, then rotated 90 degrees
clockwise about the origin. What is the final
location of A after both transformations?
If Point A is located at (4, 3). Point A is reflected. the final location of A after both transformations is (-4, -7).
What is the final location of A after both transformations?To reflect point A across the line y = -2, we need to find the point that is the same distance from the line but on the other side. The line y = -2 is a horizontal line that is 5 units above the point A (since the y-coordinate of A is 3). Therefore, the reflected point will be 5 units below the line, which gives us:
A' = (4, -7)
To rotate point A' 90 degrees clockwise about the origin, we can use the following rotation matrix:
| 0 1 |
| -1 0 |
Multiplying this matrix by the coordinates of A', we get:
| 0 1 | | 4 | | -7 |
| -1 0 | * | -7 | = | -4 |
So the final location of A after both transformations is (-4, -7).
Learn more about matrix here:https://brainly.com/question/1279486
#SPJ1
WILL GIVE BRAINLYEST AND 60 POINTS EACH HELP ASAP
Answer:
The cone takes up one-third of the volume of the cylinder. (the cylinder is 3x bigger than the cone)
Step-by-step explanation:
Answer:
B. is right.
Step-by-step explanation:
Volume of cone = volume of cylinder/3
Therefore the volume of the cylinder is 3 x that of cone
Y=3x^2-4x-1 what is the sign of leading coefficient
Answer:The leading term in a polynomial is the term with the highest degree.
Step-by-step explanation:
Step-by-step explanation:
y = 3 x^2 - 4 x - 1
leading coefficient is 3 and its sign is ' + ' or positive
Can someone help me, please
Step by step please
The number of bacteria in a culture is given by the function
n(t)=90e^0.15t
(a) What is the relative rate of growth of this bacterium population?
Your answer is ---------percent
(b) What is the initial population of the culture (at t=0)?
Your answer is---------
(c) How many bacteria will the culture contain at time t=5?
Your answer is----------
(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.
(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:
relative rate of growth = (dn/dt) / n(t)
= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])
= 0.15
Therefore, the relative rate of growth is 15%.
(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):
n(0) = 90[tex]e^0.15[/tex]*0
= 90
Therefore, the initial population of the culture is 90.
(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):
n(5) = 90[tex]e^0.15[/tex]*5
= 385.97 (rounded to two decimal places)
Therefore, the culture will contain approximately 385.97 bacteria at time t=5.
To learn more about derivative please click on below link
https://brainly.com/question/29090070
#SPJ1
20 points! please help please give the right answer
Answer:
260
Step-by-step explanation:
First you find the area of the triangle
1/2×base×height
1/2×20×10
=100
Then you find the area of the rectangle
A=l×b
=20×8
=160
Then you add the area of the triangle with the area of the rectangle
160+100=260
During the candy sale, nick sold 100 bars,Olivia sold 94,Brandon sold 53, and Grace sold 75. (Rank from greatest to least
The ranking from greatest to least goes on Nick, Olivia, Grace, and Brandon.
So in this, we have to rank the person who got most of the candy bars first and that is Nick.
After Nick Olivia has 94 candy bars so she is second in order.
Then on the third Grace had 75 candy bars.
And at the least Brandon is there with 53 candy bars.
Nick sold 100 candy bars
Olivia sold 94 candy bars
Grace sold 75 candy bars
Brandon sold 53 candy bars
Therefore, the ranking from greatest to least is Nick, Olivia, Grace, and Brandon.
To know more about greatest to least visit:
https://brainly.com/question/30061833?
#SPJ1
there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream. What is the constant of proportionality in terms of vanilla to chocolate.
The constant of proportionality for vanilla to chocolate ice cream is 2/3.
Constant of Proportionality for Vanilla to Chocolate Ice CreamThe constant of proportionality represents the fixed relationship between two quantities in a proportional relationship.
In this case, we are given that there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream.
To find the constant of proportionality in terms of vanilla to chocolate, we need to express this relationship as a fraction with the same units.
We can start by setting up the ratio of vanilla to chocolate ice cream, which would be 2:3.
This can then be expressed as
2/3
Therefore, the constant of proportionality for vanilla to chocolate ice cream is 2/3.
Read more about proportional relationship at
https://brainly.com/question/14425347
#SPJ1
Pls help meee!!
Anybody!!!
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
can y’all show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11х - 4.
Answer:
To show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4, we need to show that f(a x - 4) = 0 for all values of x.
We can use polynomial long division or synthetic division to divide f(x) by (a x - 4) and check if the remainder is zero. Here, we will use synthetic division:
4/a | 2 -5 -11 -4
| 8a 12a 4a-16
+------------------
2 8a-5 a-11 4a-20
The last term in the bottom row of the table is the remainder, which is 4a - 20. We can see that this remainder is equal to zero if a = 5.
Therefore, if we substitute x = (5/ax - 4) into the function f(x), we get:
f(a x - 4) = 2(5/ax - 4)^3 - 5(5/ax - 4)^2 - 11(5/ax - 4) - 4
Simplifying this expression, we get:
f(a x - 4) = 0
This means that a x - 4 is indeed a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4 when a = 5.
Each side of a regular hexagon measures 20 inches. What is the exact area of the hexagon?
Answer:
1039.23 square inches
Step-by-step explanation:
a = 20 inches
[tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]
[tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]
Please help asap, will give brainliest if correct. What is the constant of proportionality of this table?
Show your work.
The constant of proportionality of this table is: k = 1/7.
Explain about the constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional.Proportional relationships appear as straight lines that go through the origin on a graph. The slope of a graph is equal to the constant of proportionality in the equation, and it refers to how steep a line is relative to other lines.When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.
Thus, using the x and its respective y values.
As the values are in direct proportion.
The constant of proportionality is:
k = 1/7
know more about the constant of proportionality
https://brainly.com/question/28413384
#SPJ1
Makesha lost 58.5 pounds in 18 weeks. Find her rate of loss in pounds per week.
Use graphical methods to solve this linear programming problem.
Maximize z = 3x + 4y
subject to 2x - 3y ≤ 12
x + y ≥ 3
3x + 4y ≥ 24
x ≥ 0
y ≥ 0
What is the maximum value of z? Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A. The maximum value is ___ (Simplify answer)
B. There is no maximum.
At what point(s) does the maximum value of z occur? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The maximum value of z occurs only at the point(s) ___
(Type an ordered pair. Use a comma to separate answers as needed.)
B. The maximum value of z occurs at the points ___ and at all points on the line segment connecting them. (Type an ordered pair. Use a comma to separate answers as needed.)
C. There is no maximum value of z.
Answer:
B. There is no maximum value.
C. There is no maximum value of z.
Step-by-step explanation:
To solve this linear programming problem using graphical methods, start by graphing the feasible region determined by the given constraints:
2x - 3y ≤ 12x + y ≥ 33x + 4y ≥ 24x ≥ 0y ≥ 0We can graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.
Rearrange the first three inequalities to isolate y:
[tex]\boxed{\begin{aligned}2x - 3y & \leq 12\\2x - 12 & \leq 3y \\3y &\geq 2x - 12\\y& \geq \dfrac{2}{3}x-4\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}x + y & \geq 3\\y & \geq -x+3\\ \phantom{w}\\\phantom{\dfrac12}\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}3x + 4y & \geq 24\\4y & \geq -3x + 24\\y & \geq -\dfrac{3}{4}x + 6\\\phantom{w}\end{aligned}}[/tex]
Graph the inequalities.
If the inequality sign is ≥, draw a solid line and shade above the line.If the inequality sign is ≤, draw a solid line and shade below the line.The feasible region is the region that is shaded by all of the inequalities.
Please see the attached graph.
A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.
If a feasible region is unbounded, and the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum, since there is no limit on how big it can get.
Therefore, as the feasible region for the given constraints is unbounded, and the coefficients of the objective function z = 3x + 4y are all positive, there is no maximum value.
The perimeter of a rectangle is 343434 units. Its width is 6.56.56, point, 5 units.
Write an equation to determine the length (l)(l)left parenthesis, l, right parenthesis of the rectangle.
The length of the rectangle is 10.5 units.
What is perimeter?
Perimeter is the distance of a two-dimensional shape. It is equal to the sum of the lengths of all the sides of the shape. The perimeter is measured in units, such as centimeters, meters, feet, or inches, depending on the unit of measurement used for the dimensions of the shape.
The perimeter of a rectangle is given by the formula:
P = 2l + 2w
where P is the perimeter, l is the length, and w is the width.
In this case, we know that the perimeter is 34 units, and the width is 6.5 units. So we can substitute these values into the formula and solve for the length:
34 = 2l + 2(6.5)
Simplifying, we get:
34 = 2l + 13
Subtracting 13 from both sides, we get:
21 = 2l
Dividing both sides by 2, we get:
l = 10.5
So the equation to determine the length of the rectangle is:
2l + 2w = P
Substituting the known values, we get:
2l + 2(6.5) = 34
Simplifying and solving for l, we get:
2l + 13 = 34
2l = 21
l = 10.5
Therefore, the length of the rectangle is 10.5 units.
To learn more about perimeter visit the link:
https://brainly.com/question/397857
#SPJ9
Complete question: The perimeter of a rectangle is 34 units, its width is 6.5 units. Write an equation to determine the length (l) of the rectangle.
Look At Screen Shot
Look At Screen ShotLook At Screen ShotLook At Screen ShotLook At Screen ShotLook At Screen Shot
Answer:
There is 5% of the juice left.
Step-by-step explanation:
We know that originally, the container had 80 oz of orange juice, this is 100% in our case.
Then we can write a relation:
80 oz = 100%
Now there are 4 ounces left, in the same way as before, we can write this as:
4 oz = X%
We want to find X%
First, let's write our equations:
4 oz = X%
80 oz = 100%
We can take the quotient between these two equations to get:
(4oz/80oz) = (X%/100%)
We need to solve this for X%, then we get:
(4oz/80oz)*100% = X% = 5%
This means that 4 oz is 5% of the initial volume of the juice container.
Then we can conclude that there is 5% of the juice left.
A farmer is studying the amount of solid particles in a small pond. He determines that the average density of particles in the water is 100 milligrams per liter. The pond contains 200,000 liters of water. What is the total mass in KILOGRAMS of the particles in the pond?
(1000 milligrams = 1 gram and 1000 grams = 1 kilograms)
A.
0.2 kg
B.
20 kg
C.
200 kg
D.
20,000 kg
Answer:
Step-by-step explation: Revised 8/15. F001. Surface area of a pond, acres = Length, ft x Width, ft. 43560. F002. Volume