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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Related Questions
how do you divide fractions
Answers
Dividing fractions is basically the same thing as multiplying fractions but by the reciprocal.
For example, [tex]\frac{3}{8}[/tex] ÷ [tex]\frac{1}{4}[/tex] you would change this so in the second fraction that is being divided, the numerator and the denominator would switch places. Instead, it would be...
[tex]\frac{3}{8}[/tex] x [tex]\frac{4}{1}[/tex]
Please help, I'm stuck on this answer.
True or false? Explain your answer.
The inequality −2(x + 10) ≥ 75 says the same thing as −2x − 20 ≥ 75. I can multiply by -2 on the left side without reversing the inequality symbol.
Answers
Multiply the outer -2 with the inner x to get -2 times x = -2x
Multiply the outer -2 with the inner term 10 to get -2 times 10 = -20
So overall, -2(x+10) = -2x-20
--------------------------------------------
So that's how we're able to go from this [tex]-2(x+10) \ge 75[/tex] to this [tex]-2x-20 \ge 75[/tex]
The only thing that changes is the left side. The inequality sign will not flip. It only flips if we multiply both sides by a negative number.
Answer:True
Step-by-step explanation:
Yes, you don't have to reverse the inequality symbol since the variables are not from the other side (right).
Which expression is equivalent to (3−22)+5 ?
A. 22−5
B. 5−32
C. 32−5
D. 5−22
Answers
The expression (3-22)+5 simplifies to -14. None of the provided options: A. 22-5, B. 5-32, C. 32-5, or D. 5-22 are equivalent to the original expression.
Explanation:Let's break this question down for you. The initial expression given is (3−22)+5. In math, operations inside the parentheses are performed first according to the order of operations (PEMDAS/BODMAS), which is followed by addition or subtraction. However, the expression inside the parentheses here results in a negative number, since 3−22 equals -19. Then add 5 to -19 gives you -14.
So, the none of the options A, B, C or D are equivalent to the original expression (3−22)+5.
It's important to understand order of operations in math because it helps to ensure that calculations are done correctly and consistently.
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none of the provided options (A, B, C, or D) match this value.
We start with the given expression (3−22)+5. It can be simplified step-by-step as follows,
Calculate inside the parentheses first: 3 - 22.
Since subtracting 22 from 3 is performed, we get: 3 - 22 = -19.
Next, add 5 to the result: -19 + 5 = -14.
Let's evaluate each of the provided options:
A. 22−5: This evaluates to 17, which does not match -14.
B. 5−32: This simplifies to 5 - 9 = -4, which does not match -14.
C. 32−5: This evaluates to 9 - 5 = 27, which does not match -14.
D. 5−22: This simplifies to 5 - 22 = -17, which does not match -14.
None of the provided expressions are equivalent to (3−22)+5. Therefore, the correct answer is: None of the above.
How to find the x and y intercepts when given two points and no slope?
Answers
1) Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.
2) Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.
If two angles are complementary to the same angle, then they are
Answers
A point on a coordinate plane is located 3 units to the right of the origin and 7 units above the origin. What are the coordinates of this point? Use the drop-down menus to enter the coordinates below.
The coordinates of the point are
(
( ,
)
)
Answers
This question is based on the coordinates of a plane. Therefore, ( 3, 0) and ( 0, 7) are coordinates of this points.
Given:
A point on a coordinate plane is located 3 units to the right of the origin and 7 units above the origin.
We need to determined the coordinates of the points.
According to the question,
It is given that, 3 units to the right of the origin means that, 3 units on positive x - axis.
As we know that,
On x -axis, y is equal to zero.
Therefore, the co-ordinate of this point is located on ( 3, 0).
Now, 7 units to the above the origin means that, 7 units on positive y - axis.
As we know that,
On y -axis, x is equal to zero.
Therefore, the co-ordinate of this point is located on ( 0, 7).
Hence, ( 3, 0) and ( 0, 7) are coordinates of this points.
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if angle m acd = 100 and angle m b =60, find angle m a
Answers
m<B = 60
so
m<ACB = 180 - m<ACD
m<ACB = 180 - 100
m<ACB = 80
m<A = 180 - (60 + 80)
m<A = 180 - 140
m<A = 40
Answer:
The measure of ∠BAC is 40° .
Step-by-step explanation:
As given the figure in the question be as follow .
∠ACD = 100° , ∠B = 60°
Noe by using the the exterior angle is equal to the sum of the interior angle .
Thus
∠ACD = ∠CBA + ∠BAC
Put all the values in the above
100° = 60° + ∠BAC
∠BAC = 100° - 60°
= 40°
Therefore the measure of ∠BAC is 40° .
How would the distance formula be used in real life?
Answers
Assume RST MNO. If MN = 6, NO = 7, and MO = 11, what is the length of RS?
Answers
Answer with explanation:
It is given that,
R ST ≅ M NO.
Also, MN=6 unit
NO=7 Unit
MO=11 unit.
When two triangles are congruent , their corresponding Sides and Angles are Congruent, that is equal.
So,Corresponding Side to MN is RS .
So, MN=RS
MN=6 unit
RS=6 unit
The set of complex numbers is the set of all numbers of the form a + bi, where a and b are real numbers and i=
Answers
Answer:
i = [tex]\sqrt{-1}[/tex]
Step-by-step explanation:
A complex number is that one having two parts:
One called real part, represented by a.And another called imaginary part, represented by bi, where b is also a real number plus i, as it was describe in the answer [tex]i = \sqrt{-1}[/tex].Although [tex]i =\sqrt{-1}[/tex], it is also [tex]i^{2} = -1[/tex], which has some interesting properties like [tex]i^{3}[/tex] = [tex]i * i^{2}= i * -1 = -i [/tex] , and so on.
These numbers came along when it was necessary to take the squared root of negative numbers:
[tex]\sqrt{-4} = \sqrt{-1} * \sqrt{4} = 2i ; -2i[/tex] .
One positive integer is 3 less than twice another. the sum of their squares is 233. find the integers.
Answers
x-3= 2y
x=2y+3______(1)
x²+y²= 233_____(2)
sub eqn (1) into (2)
{2y+3}²+y²=233
4y² + 12y +9 +y²=233
5y²+12y+9-233=0
5y²+12y-224=0
y= -8 or 5.6
recall they are positive integers so y=5.6
now sub y=5.6 into eqn (1)
x=2(5.6)+3 = 11.2+3=14.2
the two integers are 14.2 and 5.6
Can you determine the number of digits in the quotient of 637 divided by 7 without dividing?explain.
Answers
write two equations for a horizontal line and a vertical line.
Answers
Two equations for a vertical line could be x = 2 & x = 6
Horizontal lines are created when y is always equal to one number, while vertical lines are created when x is always equal to one number.
Hope this helps!
Which set of ordered pairs represents a function?
{(0, 0), (2, 3), (1, -4), (2, -2)}
{(5, 6), (2, 6), (-3, 4), (-1, 4)}
{(3, -2), (-4, -1), (0, 3), (0, 5)}
{(-5, 1), (-4, 2), (-5, 3), (-4, 4)}
Answers
which inequality best represents the situation of you must be at least 52 inches tall to ride the water ride
Answers
Answer:
Option C is the correct choice.
Step-by-step explanation:
We have been given a graph and we are asked to find the correct option which represents the inequality for the situation of one must be at least 52 inches tall to ride the water ride.
At least 52 inches means one should not be less than 52 inches. This means the length of one should be 52 inches or any number greater than 52 inches.
Let us see our given inequalities one by one.
A) Our first inequality represents height less than or equal to 52, which means that one should be at-most 52 inches, therefore, 1st inequality is not true for our given situation.
B) Our 2nd inequality represents height less than 52, therefore, 2nd inequality is not true for our given situation.
C) We can see from our inequality represented in option C that height is greater than or equal to 52 inches. It is including 52 (at least) and greater heights than 52, therefore, option C is the correct choice.
D) Option D shows an inequality that represents heights greater than 52 as it is not including 52, therefore, option D in not a correct choice.
What is the domain of the function f(x)=x+3
Answers
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 108.7-cm and a standard deviation of 0.6-cm. For shipment, 22 steel rods are bundled together.
Find the probability that the average length of rods in a randomly selected bundle of steel rods is less than 109.1-cm.
Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.
Answers
Let x be the lengths of the steel rods and X ~ N (108.7, 0.6)
To get the probability of less than 109.1 cm, the solution is computed by:
z (109.1) = (X-mean)/standard dev
= 109.1 – 108/ 0.6
= 1.1/0.6
=1.83333, look this up in the z table.
P(x < 109.1) = P(z < 1.8333) = 0.97 or 97%
Which statement is true about this argument?
Premises:
If two lines are parallel, then the lines do not intersect.
Lines m and n do not intersect.
Conclusion:
Lines m and n are parallel.
Which statement is true about the argument?
The argument is not valid because the premises are not true.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of detachment.
The argument is valid by the law of syllogism.
Answers
Although parallel lines cannot intersect, that does not mean that two lines are parallel just because they do not intersect. Two lines can be not parallel and still not intersect.
In the year 2016, the estimated population of Canadian geese in a city was 750. The Canadian geese population is expected to grow at a rate of 12% each year. What is the Canadian geese population in 2022? Round the answer to the nearest whole number.
Answers
Keywords:
population, Canadian geese, growth rate
For this case, we must find the population of Canadian geese for the year 2022, taking into account that in 2016 the estimated population of geese was 750 and as additional data, the population of geese has a growth rate of 12% each year.
Then, we started finding the Canadian geese population for 2017, for this we make a rule of three:
750 -----------> 100%
x --------------> 12%
DOnde "x" represents the number of geese that is added to the base population of 2016.
[tex]x = \frac {12 * 750} {100}\\x = 90[/tex]
Thus, the geese population for 2017 is: [tex]750 + 90 = 840[/tex]
We find the population of Canadian geese for the year 2018, following the previous steps since the annual growth rate is constant:
840 -----------> 100%
x --------------> 12%
where "x" represents the number of geese that is added to the base population of the year 2017.
[tex]x = \frac {12 * 840} {100}\\x = 100.8[/tex]
Thus, the geese population for 2018 is: [tex]840 + 100.8 = 940.8[/tex]
We found the population of Canadian geese for the year 2019, following the previous steps since the annual growth rate is constant:
940.8 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that is added to the base population of the year 2018.
[tex]x = \frac {12 * 940.8} {100}\\x = 112.896[/tex]
Thus, the geese population for 2019 is: [tex]940.8 + 112.896 = 1053.696[/tex]
We find the population of Canadian geese for the year 2020, following the previous steps since the annual growth rate is constant:
1053.696 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that adds to the base population of the year 2019.
[tex]x = \frac {12 * 1053.696} {100}\\x = 126.44[/tex]
Thus, the geese population for 2020 is: [tex]1053.696 + 126.44 = 1180.12[/tex]
We found the population of Canadian geese for the year 2021, following the previous steps since the annual growth rate is constant:
1180.12 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that is added to the base population of the year 2020.
[tex]x = \frac {12 * 1180.12} {100}\\x = 141.6[/tex]
Thus, the population of geese for 2021 is:[tex]1180.12 + 141.6 = 1321.7[/tex]
We found the population of Canadian geese for the year 2022, following the previous steps since the annual growth rate is constant:
1321.7 -----------> 100%
x --------------> 12%
[tex]x = \frac {12 * 1321.7} {100}\\x = 158.6[/tex]
Where "x" represents the number of geese that adds to the base population of the year 2021.
Thus, the population of geese for 2022 is: [tex]1321.7 + 158.6= 1480.3[/tex]
ANswer:
The population of Canadian geese by 2022 will be approximately 1480 geese
Logan's only debt obligations are a car loan payment of $512 and a credit card payment of $70 every month. What is the minimum amount of money he must take home every month in order to avoid being in danger of credit overload?
Answers
20% for paying up debts, 10 % for savings, and 70% for everything else.
So, assuming that x is the minimum amount of money, we know that
$ 512 + $70 = 20% . X
$ 582 = 0.2 . x
$ 582 / 0.2 = x
x = $ 2910
Answer:
$ 2910
Step-by-step explanation:
Order the numbers 0.2, 1/5, 0.02, 0.022 from least to greatest.
Answers
$10,000 is compounded semiannually at 12% interest for t years. what expression represents the amount of money after t years?
Answers
0.12t=10,000(2)
The expression that represents the amount of money after t years when $10,000 is compounded semiannually at 12% interest is [tex]10000(1.06)^{(2t)}[/tex].
The amount of money after t years can be represented by the following expression:
[tex]A = P(1 + \frac{r}{n})^{(n*t)}[/tex]
Where:
A is the amount of money after t years
P is the principal amount (initial investment), which is $10,000 in this case
r is the interest rate, which is 12% expressed as a decimal (0.12)
n is the number of times interest is compounded per year, which is semiannually (2 times per year)
Substituting the values into the expression, we have:
[tex]A = 10,000(1 + \frac{0.12}{2})^{(2*t)}[/tex]
Simplifying further, we get:
[tex]A = 10000(1.06)^{(2t)}[/tex]
Therefore, the expression that represents the amount of money after t years when $10,000 is compounded semiannually at 12% interest is [tex]10000(1.06)^{(2t)}[/tex].
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50 points! Write a compound inequality to represent all of the numbers between -4 and 6.
Answers
you want x >-4 and x<6
s0 the equation would be: -4<x<6
Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a^2?
A.22.63
B.54.63
C.9.37
D.3.10
Answers
180 - 45 = 135
135/2 = =67.5
A = 45
B = 67.5
C = 67.5
a = ?
b = 4
c = 4
Since we know two sides and all three angles, we can use the law of sines to find a.
b/sin B = a/sin A
4/(sin 67.5) = a/(sin 45)
a = 4(sin 45)/(sin 67.5)
a^2 = (4(sin 45)/(sin 67.5))^2
a^2 = 9.37
Multiply 436.2 × 0.74 = ____
Answers
Changes made to your input should not affect the solution:
(1): "0.74" was replaced by "(74/100)". 2 more similar replacement(s)
Step 1: Simplify 37/50
Equation at the end of step 1:
4362 / 10 * 37 / 50
Step 2:
Equation at the end of step 2:
2181 / 5 * 37 / 50
Step 3:
80697 / 250 = 322.78800
Final Answer: 322.78800
How can 52 over 9 be expressed as a decimal?
1. 4.3 with bar over 3
2. 4.7 with bar over 7
3. 5.3 with bar over 3
4. 5.7 with bar over 7
Answers
Answer:
so divide 52 divided by 9 and your awnser would be 5.7 with bar over 7 and the awnser would be the fourth one hope it helped.
Step-by-step explanation:
Answer:
D. 4. 5.7 with bar over 7
you sasy bacass
Step-by-step explanation:
you sasy bacass you sasy bacass you sasy bacass you sasy bacass
Miko’s restaurant bill was $16. She used the expression 1.18(16) to find the total cost, including an 18% tip.
Which expression is equivalent to the amount Miko paid?
A. (1+0.18)16
B. 16+0.18(16)
C. 16 + 1.18
D. 1+0.18(16)
Please explain your answer
Answers
Ms. Weasley
Answer:
D) 16 + 0.18(16)
Step-by-step explanation:
Name the property of real numbers illustrated by the equation.
-3(x+4)=-3x-12
A: Distributive property
B: Associative property of addition
C: Associative property of multiplication
D: Commutative property of addition
Answers
We're multiplying the outer -3 with the inner x to get -3x
Also, multiply the outer -3 with the inner +4 to get -12
So that's why -3(x+4) = -3x-12
Please help! 3 questions, 1. Determine if the ordered pair is a solution of the equation. Is (-1,-30) a solution of y =10x?: a) True b) False
2.The point (5, -1) is a solution of the equation: y = 2x − 11 options: a) True b) False 3.Which ordered pairs are a solution to the equation? y = 8x options: a) (-1,-7) b) (2,16) c) (1,8) d) (-2,-6)
Answers
(-1,-30)...x = -1 and y = -30
y = 10x...so we sub
-30 = 10(-1)
-30 = -10 (incorrect)...so this is not a solution
================
(5,-1)...x = 5 and y = -1
y = 2x - 11
sub
-1 = 2(5) - 11
-1 = 10 - 11
-1 = -1 (correct)....so this is a solution
==============
y = 8x
sub in (2,16)...x = 2 and y = 16
16 = 8(2)
16 = 16 (correct)...so (2,16) is a solution
y = 8x
subbing in (1,8)...x = 1 and y = 8
8 = 8(1)
8 = 8 (correct)...so (1,8) is also a solution
thats all...just those 2 are the solutions
shana wants to make a birthday cake for her mother. her old fashioned recipe calls for 3/12 Of a teaspoon of salt but she only has measuring spoons that use fourths. How many fourths of a teaspoon should she use ?
I get 2/4 because I did 1/4 of 3/12
Answers
The answer is 1/4ths because if you do the equation correctly you get 1/4.
Your welcome