There is a maximum value of 7/6 located at (x, y) = (5/6, 7).
The function given to us is f(x, y) = xy.
The constraint given to us is 6x + y = 10.
Rearranging the constraint, we get:
6x + y = 10,
or, y = 10 - 6x.
Substituting this in the function, we get:
f(x, y) = xy,
or, f(x) = x(10 - 6x) = 10x - 6x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = 10 - 12x ... (i)
Equating to 0, we get:
10 - 12x = 0,
or, 12x = 10,
or, x = 5/6.
Differentiating (i), with respect to x again, we get:
f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.
The value of y, when x = 5/6 is,
y = 12 - 6x,
or, y = 12 - 6*(5/6) = 7.
The value of f(x, y) when (x, y) = (5/6, 7) is,
f(x, y) = xy,
or, f(x, y) = (5/6)*7 = 7/6.
Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).
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In the right triangular prism below, BG Perpendicular FC
A right triangular prism is shown. Triangles A E D and B F G are the base triangles. A perpendicular bisector is drawn from point B to point G on side F C.
The volume of the prism is 900 cubic centimeters. The height of the prism is 15 centimeters and the height of the triangular base is 10 centimeters. What is the length of edge FC?
cm
The length of edge FC in the triangular prism is: 12 cm.
What is the Volume of a Right Triangular Prism?Volume of a right triangular prism = 1/2(Length of triangular base × height of triangular base × height of the prism).
Considering the image given showing a right triangular prism, we have the following:
Volume of triangular prism = 900 cubic centimeters
Length of triangular base = FC = ?
Height of triangular base = 10 centimeters
Height of the prism = 15 centimeters
Plugin the values
900 = 1/2(FC × 10 × 15)
900 = 1/2(FC × 150)
Multiply both sides by 2
2(900) = 2(1/2(FC × 150))
1,800 = FC × 150
Divide both sides by 150
1,800/150 = FC × 150/150
12 = FC
FC = 12 cm
The length of edge FC is: 12 cm.
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Answer: 12
Step-by-step explanation:
Consider the sets below.
A {xlx is a polygon}
B {x|x is a triangle}
Which is true?
A = B
B =A
Ac= B
Bc = A
A sequence is defined by the recursive function f(n 1) = one-halff(n). if f(3) = 9 , what is f(1) ?
[tex]f(1)[/tex] is [tex]81.[/tex]
What is a recursive function?A recursive function generates a series of phrases by repeating or using its own prior term as input.Problems that can be split down into smaller, repeating problems are ideal for recursion to solve. It is particularly useful when working on issues with numerous potential solutions that are too complex to handle iteratively. Searching a file system is an effective illustration of this.A recursive formula is one that defines each term in a sequence by reference to the one before it.To find f(1):
f(n 1) = one-half(n).
f(3) = 9.
[tex]f(3) = 9If n = 1,f(2) = 9×3f(2) = 27If n = 0,f(1) = 27 ×3f(1) = 81[/tex]
A sequence is defined by the recursive function [tex]f(1)[/tex] is [tex]81.[/tex]
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Answer:
36
Step-by-step explanation:
Assuming I understand the question correctly
[tex]\text{one-halff(n)} = \frac{1}{2} f(n)[/tex]
We have the recursive relationship
[tex]f(n+1) = \frac{1}{2} f(n)[/tex]
[tex]f(3) = 9[/tex]
[tex]f(3) = \frac{1}{2} f(2)[/tex]
[tex]f(2) = \frac{1}{2} f(1)[/tex]
So
[tex]f(3) = \frac{1}{2} (\frac{1}{2} f(1) = \frac{1}{4} f(1) \\[/tex]
So [tex]f(1) = 4f(3) = 4(9) = 36[/tex]
Verifying
If f(1) = 36 then f(2) = (1/2)f(1) = (1/2)36 = 18
f(3) = (1/2) f(2) = (1/2)(18) = 9
Which digit is in the hundredths place?
18.36
8
3
1
6
Answer:
6.becuase after the decimal or "." it goes 00.tenth, hundredth, thousandth, and so on
Step-by-step explanation:
PLEASE GIVE BRAINLIEST OR 5 ⭐
In the year 2018, it was estimated that approximately 28,000 Floridians were homeless. A social worker estimates that 78% of these people were age 18 and up. In the distribution of ages of homeless Floridians, an 18 year old would be considered what percentile
At 22nd percentile in the distribution of ages of homeless Floridians, an 18 year old would be considered.
Given that 78% of the ages are greater than or equal to 18 years. Hence.
18 years will be (100 - 78)th percentile
i.e. 22nd percentile.
Historically, policymakers and practitioners at every level of government have focused special attention on specific subpopulations.
Decision-makers are often concerned about children and young people due to their vulnerability. People in families with children make up 30 percent of the homeless population. Unaccompanied youth (under age 25) account for six percent of the larger group.
Finally, due to their service to our country, veterans are often analyzed separately from the larger group. They represent only six percent of people experiencing homelessness.
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Consider a function that goes through the two points (0, 5) and (1, 20). Find the formula for the function if(a) the function is linear (of the formf(x) =mx b)
The formula for the linear function which is passing the points (0, 5) and (1, 20) is f(x) = 15x + 5.
According to the given question.
The linear form of the function is
f(x) = mx + b
Also, the function is passing through the points (0, 5) and (1, 20).
So, the given points (0, 5) and (1, 20) must satisfy f(x) = mx + b.
Now,
At (0, 5)
f(0) = m(0) + b
⇒ 5 = 0 + b
⇒ b = 5 ..(i)
Also,
at (1, 20)
f(1) = m(1) + b
⇒ 20 = m + 5 (from i)
⇒ m = 20 - 5
⇒ m = 15
Therefore, the formula for the linear function which is passing the points (0, 5) and (1, 20) is given by
f(x) = 15(x) + 5 (on substituting the vale of m and b in f(x) = mx + b).
⇒ f(x) = 15x + 5
Hemce, the formula of the function is f(x) = 15x + 5.
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PLS HELP pq has endpoints at p(-5,4) and q(7,-5).what is the midpoint of pq? what are the cordinates of the point 2/3 of the way from p to q?
The midpoint of PQ is (1, -0.5)
The coordinates of the point 2/3 of the way from p to q are (-0.2, 0.4)
What is the midpoint of a line segment?
the midpoint is the middle point of a line segment. It is equidistant from both endpoints.
The midpoint of PQ
To calculate this, we use the midpoint formula;
(x,y) = {(x1 + x2)/2 , (y1 + y2)/2}
From the question; (x1,y1) = (-5,4) and (x2,y2) = (7,-5)
So (x,y) = (-5+7)/2 , (4-5)/2 = 2/2, -1/2 = (1,-0.5)
The coordinates of the midpoint of PQ are (1,-0.5)
What is the internal division of the line segment?
we will use here the internal division formula of the section formula;
Mathematically the coordinates can be calculated using the formula;
(x,y) = (mx2 + nx1)/m+ n , (my2 + ny1)/m + n
in this case, m = 2 and n = 3
(x1,y1) = (-5,4)
(x2,y2) = (7,-5)
So substituting these values, we have;
(x,y) = (2(7)+ 3(-5))/(2+3) , 2(-5) + 3(4)/(2+3)
(x,y) = (14 -15)/5 , (-10 + 12)/5
= (-1/5, 2/5) = (-0.2, 0.4)
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A complex point of the form a 3i has a distance of 29 units from –9 24i. what is the value of a? –1 5 11 19.8
The value of a = 11
What is complex numbers ?
Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).Let a + i b = (a,b)
c + i d = (c , d)
the distance between two points = [tex]\sqrt{( a - c)^{2} + (b -d )^{2} }[/tex]
put values in the formula -
[tex]\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }[/tex] = 29
square both sides
[tex]{(a + 9)^{2} + (21)^{2} } = 29^{2}[/tex]
(a + 9)² = 841 - 441 ⇒ 400
(a + 9) = √400 = + 20
a = +20 -9
So, a = -29 or 11
Therefore, the value of a = 11
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My brain stopped. I need help
Answer:
x = 99°
y = 91°
Step-by-step explanation:
For Cyclic quadrilateral, the sum of the opposite angles = 180°
Let's find x :-
x + 81° = 180°
x = 180 - 81
x = 99°
Let's find y :-
y + 89° = 180°
y = 180 - 89
y = 91°
Hope this helps you !
For a given rabbit population, the relationship between the number of adult female rabbits, F, and the number of offspring, R, that survive to maturity, is given by this equation: R=3+(350F/F+625)
Considering the given function in the problem, it is found that:
a. 9.6 offspring survive to maturity when there are 12 female rabbits in the population.
b. At least 18 female rabbits are required for there to be 13 offspring.
What is the given function in this problem?The function gives the relationship between the number of adult female rabbits F and the number of offspring R as follows:
[tex]R = 3 + \frac{350F}{F + 625}[/tex]
When there are 12 female rabbits, we have that F = 12, hence:
[tex]R = 3 + \frac{350 \times 12}{12 + 625} = 9.6[/tex]
9.6 offspring survive to maturity when there are 12 female rabbits in the population.
For at least 13 offspring, we have that the number of rabbits needed is given as follows:
[tex]R \geq 13[/tex]
[tex]3 + \frac{350F}{F + 625} \geq 13[/tex]
[tex]\frac{350F}{F + 625} \geq 10[/tex]
[tex]350F \geq 10F + 6250[/tex]
[tex]F \geq \frac{6250}{340}[/tex]
[tex]F \geq 18[/tex]
At least 18 female rabbits are required for there to be 13 offspring.
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G(x)=2x-8, f(x)=5-g(x) what is the value of f(10)
Answer:
-7
Step-by-step explanation:
[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]
The length of a spring with no applied force acting on it is 10.00 centimeters. Juanita applied different forces to the spring and recorded the new lengths of the spring in a table. She also graphed a scatterplot from the results in the table. Based on the scatterplot, which equation BEST represents these data?
Answer:
the second option L = 0.05F + 10
Step-by-step explanation:
the first one
F = 0.05L + 10
does not make any sense, as for length = 10 the force has to be 0. but this function here gives us
0.05×10 + 10 = 0.5 + 10 = 10.5
which is clearly not 0. so, this is wrong.
the second one is correct.
L = 0.05F + 10
it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.
the third
L = 0.05F
fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.
the fourth
F = 0.05L
fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.
RSM wants to send 4 of its 18 teachers into a conference. How many ways can they do this?
There are 18c4 ways that RSM wants to send 4 of its 18 teachers into a conference. that means there are 3060 ways to send
there are 18 teachers and RSM wants to send 4 mem out of 18
so, we use combinatorics for this
Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. It includes the enumeration or counting of objects having certain properties. Counting helps us solve several types of problems such as counting the number of available IPv4 or IPv6 addresses.
It is used to find solutions easily for possible ways of a problem
For that we are using the formula for combinatorics
NCr = n!/ (r! (n – r)!)
similarly 18c4 = 18!/ (4! (18 – 4)!)
= 3060
Therefore , there are 3060 ways that RSM wants to send 4 of its 18 teachers into a conference.
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Five pounds is equal to 2.268 kilograms. How many kilograms is 2 pounds?
Mass is the amount of matter that a body possesses and its unit in the international system of units is the kilogram.
How many kilograms is 2 pounds?Knowing that 1 pound is 2.205 kilograms.Therefore ⇒ 2 lb * 1 kg / 2.205 lb = 0.907 kgAnswer: In 2 pounds there are 0.907 kilograms.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
What are the characteristics of quadratic equations?
Herein we have a quadratic equation of the form f(x) = a · x² + b · x + c. To determine the direction of the parabola, we must transform this expression into its vertex form and looking for the sign of the vertex constant:
f(x) = a · x² + b · x + c
f(x) = a · [x² + (b / a) · x + (c / a)]
f(x) + b² / (4 · a) - c = a · [x² + (b / a) · x + b² / (4 · a²)]
f(x) + b² / (4 · a) - c = a · [x + b / (2 · a)]²
If a > 0, then the direction of the parabola is upwards, but if a < 0, then the direction of the parabola is downwards.
The y-intercept is found by evaluating the quadratic equation at x = 0:
f(0) = a · 0² + b · 0 + c
f(0) = c
And the zeros are determined by the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
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A bucket contains exactly 3 marbles, one red, one blue and one green. a person arbitrarily pulls out each marble one at a time. What is the probability that the last marble removed is non-red?
The probability that the last marble removed is non-red is 2/3.
According to the given question.
Total number of marbles in a bucket = 3
And, a person arbitary pulls out each marble one at a time.
So, there are 6 possible sequences of removing 3 marbles.
Let R be the red marble, B be the blue marble and G be the green marble.
The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.
Let A denotes the event of removing the non-red marbles at the last.
The favorable cases for event A are: RBG, RGB, BRG and GRB.
As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.
Thereofre,
The probability that the last marble removed is non-red
= 4/6
= 2/3
The probability that the last marble removed is non-red is 2/3.
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I NEED HELP WITH MY MATH PLEASE
I NEED HELP ASAP! The two cylinders below are similar. What is the volume of the larger cylinder?
Answer:
E
Step-by-step explanation:
We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.
I chose the second way to work out.
Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:
[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]
The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]
The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.
Thus, we have
[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]
help on this math problem!! if there is any work that can be shown it would be great thanks!!!
Answer:
4230.44
Step-by-step explanation:
in how many ways can 20 identical balls be distributed among 5 distinct bins?
Answer:
put four balls in each been
Step-by-step explanation:
The sum of two numbers is 84. The square of the first number is 6 more than the second number.
Write a system of equations to find the value of x, the first number, and y, the second number.
y = -x +
y = x² +
The system of equations to find the value of x, the first number, and y, the second number are;
y = -x + 84
y = x² + 6
System of equationThe system of equation are equations that contains more than two equation and unknown.
Let the two unknown numbers x and y
If the sum of two numbers is 84, hence;
x +y = 84
y = -x + 84
If the square of the first number is 6 more than the second number, hence;
x² = y + 6
Substitute equation 2 into 2 to have:
x² = y + 6
x² = (-x+84) + 6
x² = -x+84 + 6
x² +x+84 + 6 = 0
x² +x + 90 = 0
Hence the system of equations to find the value of x, the first number, and y, the second number are;
y = -x + 84
y = x² + 6
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what is the component form of the vector that translates the top triangle to the bottom triangle
The component form of the vector that translates the top triangle to the bottom triangle is (3, -5). This is further explained below.
What is a vector?Generally, a number with both direction and magnitude, especially when used to map out where one point in space is in relation to another.
In conclusion, The vector that converts the top triangle to the bottom triangle has the following component form: (3, -5).
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x-13=x+1
Please help mee
x = 2, y = 7
x = 5, y = 2
x = 3, y = 5
x = 7, y = 3
Find the measure of the angle indicated.
Step-by-step explanation:
I think the above picture should help
A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm.which expression represents the volume of the pyramid?(5.2)h cm3(5.2)h cm3(5.2)h cm3(5.2)h cm3
volume of pyramid = 1/3(5.2)h cm3
What is a Prism?Prism is a three dimensional figure. A prism is a 3-dimensional shape with two identical shapes (bases) facing each other.
we know that,
The volume of the pyramid is equal to
volume = (1/3) × base area × height
we have height = h cm
area of base = 5.2 cm^2
substitute in the formula
v = 1/3 × 5.2 × h
volume = 1.73h cm^3
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f(x) = 4x² - 7x - 15
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Look at the attached image above ☝️for explanation
Hope it helps! and if it's not pls tell me on the comment.
M angle JKL=
Help me please thank u so much
Answer:
22°
Step-by-step explanation:
Since IJ is a diameter, arc LJ measures 68 degrees.
Therefore, the measure of angle JKL is (112-68)/2=22°
Number
8.6134
5.5218
...to the nearest tenth ...to the nearest hundredth
..to the nearest thousandth
Concepts and Applicati
The following numbers are rounded up as follows:
8.6134
nearest tenth = 8.6nearest hundredth = 8.61nearest thousandth = 8.6135.5218
nearest tenth = 5.5nearest hundredth = 5.52nearest thousandth = 5.522How to round up?Rounding up a number means to round a number to the smallest integer that is not less than it, or to some other greater value.
Thousandth, hundredth and tenth are used after the decimal point.
nearest tenth means one number after the decimal pointnearest hundredth means two numbers after the decimal pointnearest thousandth means three numbers after the decimal point8.6134
nearest tenth = 8.6nearest hundredth = 8.61nearest thousandth = 8.6135.5218
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i cant get this wrong or i fail
Answer: x < -2
Step-by-step explanation:
[tex]\frac{1}{2} x-7 < -8[/tex]
First add 7 to both sides
[tex]\frac{1}{2} x-7 +7 < -8+7[/tex]
[tex]\frac{1}{2} x < -1[/tex]
Now multiply by 2 to cancel out 1/2 and leave you with x
[tex]2*\frac{1}{2} x < -1(2)[/tex]
[tex]x < -2[/tex]