Answer:
Maximum area = 10000 square units.
Step-by-step explanation:
We are given the following information:
Rectangular perimeter of coral = 400 units.
Let length of the coral be x. Then,
Perimeter = 400 = 2(Length +Breadth)
[tex]400 = 2(x + Breadth)\\Breadth = 200 - x[/tex]
Thus, the area of rectangle is given by,
[tex]Area = Length\times Breadth = x\times (200-x) = 200x - x^2[/tex]
Thus, we have to maximize the function:
[tex]f(x) = 200x - x^2[/tex]
We will use double derivative test.
First we differentiate with respect to x.
[tex]\displaystyle\frac{d(f(x))}{dx} = \displaystyle\frac{d(200x - x^2)}{dx} = 200 - 2x[/tex]
Equating this to zero to obtain critical points,
[tex]200 - 2x = 0\\200 = 2x\\x = 100[/tex]
Now, again differentiating with respect to x.
[tex]\displaystyle\frac{d^2(f(x))}{dx^2} = -2 < 0[/tex]
Thus, by double derivative test, local maxima occurs for this function at x = 100
So, Length = x = 100 units
Breadth = 200 - x = 100 units
Maximum area = 10000 square units.
Suppose that the length of a certain rectangle is 5 meters less than four times its width. the perimeter of the rectangle is 40 meters. find the length and width of the rectangle.
What is the sum of 4 times a number and 3 is bigger than 15, but also -21 at most?
What is the solution of the linear quadratic system or equations?
Y=x^2+5x-3
Y-x=2
The solution to the system of equations are (1, 3) and (-5, -3)
Given the following functions
Y=x^2+5x-3
Y-x=2; y = x + 2
Equating both outputs will give
x^2+5x-3 = x + 2
x^2+5x-3 - x - 2 = 0
x^2 + 4x - 5 = 0
Factorize the equation
x^2 + 5x - x - 5=0
x(x+5) - 1(x+5) = 0
(x-1)(x+5) = 0
x = 1 and -5
Recall that y = x + 2
y = 3 and -3
Hence the solution to the system of equations are (1, 3) and (-5, -3)
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The solution to a linear quadratic system of equations can be found by substitifying one equation into the other and solving. In this case, the solutions are (1,3) and (-5,-3).
Explanation:To find the solution of a linear quadratic system of equations, you need to substitute one equation into the other. In this case, for the equations [tex]Y = x^2 + 5x - 3[/tex] and [tex]Y - x = 2[/tex], you would first isolate Y in the linear equation, resulting in [tex]Y = x+2.[/tex]
Then, you substitute (x + 2) for Y in the quadratic equation, leading to [tex]x + 2 = x^2 + 5x - 3.[/tex]
Next, rearrange the equation to get it in the standard quadratic form: 0 = [tex]x^2 + 5x - x - 3 - 2.[/tex] Simplifying this results in the equation [tex]0 = x^2 + 4x - 5.[/tex]
Finally, solve this equation by factoring or using quadratic formula, which gives the solutions as x = 1, -5. Substituting both 1 and -5 into the equation Y = x + 2 gives the corresponding y-values, Y = 3 and -3. Therefore, the solutions to the system of equations are (1,3) and (-5,-3).
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The probability of choosing either a girl or a boy is
what is the answer to y-3.5=-2.1
The value of variable y in y - 3.5 = -2.1 is 1.4 .
Given , equation : y-3.5=-2.1
To get the value of y isolate the variable y.
y - 3.5 = -2.1
Combine like terms,
Take -3.5 from LHS to RHS . The sign will be changed from negative to positive.
y = 3.5 - 2.1
y = 1.4
Therefore the value of y that will satisfy the equation is 1.4 .
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Amy, who is 17 years old, is 5 years older than twice Moe's age.Write an equation that you could solve to find Moe's age. Solve the equation and describe your steps.
Luigi is an urban planner. as an independent contractor, he charges $140 fee plus $ 25 per hour for each contract with the city.
Write a function to represent this scenario where Y represents the total amount her changes for a project and x represents the number of hours worked on a project
x = hours 25 per hour = 25x
y = total
so y = 25x +140
Answer: y = 140+25x
Step-by-step explanation:
Since According to the question, Luigi initally charged $140.
And, per hour he charged an additional amount $25 for each contract with the city.
Here, x represents the number of hours worked on a project.
Thus the additional amount after x hours = 25x
So, the total amount he charged in x hours= 140+ 25x
And, according to the question y represents the above change.
Thus, we get a function for the given situtaion
which is , y= 140+ 25x , where x is number of hours and y is total amount charged.
What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y? 5xy 15x3y 45x3y5 75x5y7
Answer: 15x3y
Step-by-step explanation:
We rewrite the expressions by using factorisation method of their primes. This will give:
60x4y7= 2×2×3×5×x×x3×y×y6
45x5y5= 3×3×5×x×x4×y×y4
75x3y= 3×5×5×x×x2×y
Common factors= 3 × 5 × x3 × y
= 15x3y
Answer:
its B
Step-by-step explanation:
Rose leaves her apartment to take her dog for a walk. She goes 3 blocks due south, 8 blocks due east, 5 blocks due north, and 8 blocks due west. At this point, where is Rose in relation to her apartment?
Answer:
3 blocks due west
Step-by-step explanation:
parallelogram ESTA has vertices E (10,0), S(14,3),T(6,9) and A (2,6). to calculate its area, Jamal will first determine the equation of the line through point E and perpendicular to ST. What is the equation of this line?
The law of detachment can be used to draw a conclusion from the following statements: "It will be sunny on Tuesday." "I will always go outside if the weather is nice."
Final answer:
Using the law of detachment, if it is sunny on Tuesday and there is a habit of going outside in nice weather, one can conclude that they will go outside on Tuesday.
Explanation:
The law of detachment is a concept in logic used to form conclusions given a conditional statement and its hypothesis being true. For instance, in the scenario provided:
If it is sunny on Tuesday (hypothesis).
I will always go outside if the weather is nice (conditional statement).
By applying the law of detachment, we can conclude that:
I will go outside on Tuesday (conclusion).
This logical reasoning assumes that a 'nice' weather includes a sunny day. Hence, if it is indeed sunny on Tuesday, the condition for going outside is met.
You and your family attend your brother’s championship baseball game. Between innings you decide to go to the snack stand. You go to the snack stand with $15 and find that sodas are $2.50 and that popcorn is $3.75. Write an inequality that models the number of sodas you can buy if you get a bag of popcorn too. What is the maximum number of sodas you can buy in this situation?
If CDEF ≅ MNPQ, then EF≅ _____
.
PQ.
QM.
MN.
NQ
Final answer:
In the context of congruent polygons, side EF of polygon CDEF is congruent to side PQ of polygon MNPQ due to the corresponding order of sides in congruent figures.
Explanation:
The question refers to congruent figures in geometry, specifically congruent polygons. If polygons are congruent, all corresponding sides and angles are congruent as well. Therefore, if CDEF ≅ MNPQ, then side EF must be congruent to the side of polygon MNPQ that corresponds to EF in the order of letters given. Following the order, side EF corresponds to side PQ.
Twice a number, increased by one, is between negative three and seven. find all the numbers.
To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.
Explanation:The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.
To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.
First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.
-4 < 2x < 6
Now, divide all parts of the inequality by 2, which yields:
-2 < x < 3
All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.
There are 300 coins of the same type in two stacks. One stack is 380 millimeters tall. The other is 220 millimeters tall. Find the thickness of one coin
In 2010, the national debt of the United States was about 14 trillion dollars. In 2003 it was about 7 x 10 to the 12 dollars. About how many times larger was the national debt in 2010 than 2003? THIS IS SCIENTIFIC NOTATION
Answer: About 2 times.
Step-by-step explanation:
Given : In 2010, the national debt of the United States was about 14 trillion dollars.
We know that 1 trillion [tex]=1,000,000,000,000= 10^{12}[/tex]
then, In 2010, the national debt of the United States was about [tex]14\times10^{12}[/tex]
dollars.
In 2003 it was about [tex]7\times10^{12}[/tex] dollars.
Now, the number of times the national debt was larger in 2010 than 2003 :-
[tex]\dfrac{ 14\times10^{12}}{7\times10^{12}}\\\\=\dfrac{14}{7}\times10^{12-12}\\\\=2\times10^0=2[/tex]
Hence, national debt was about 2 times larger in 2010 than 2003 .
two workers paint lines for angled parking spaces. One worker paints a line so that m<1= 65. The other worker paints a line so that m<2= 65. Are their lines parallel? Explain
given f(x)=x^3 and g(x)=1-5x^2, find (fog) (x) and its domain
Answer:
answer is b
Step-by-step explanation:
which conjunction or disjunction is equivalent to the given absolute value inequality?
|x + 2| > 16
a. x + 2 > 16 and x + 2 < - 16
b. x + 2 < 16 and x + 2 > - 16
Answer:
a.
Step-by-step explanation:
|x+2|>16
x+2>16 or x+2<-16
So, tecnically a and b are incorrect, but if you change the "and" to "or" the correct would be a.
There are 18 boys and 60 girls working on a community service project. they work in groups where each group has the same number of boys and the same number of girls. what is the first step to finding the greatest number of groups possible? what is the greatest number of groups possible? what is the first step in finding the solution?
A mathematical scale in which the concentration of hydrogen ions in a solution is expressed as a number from 0 to 14
Amelia knits 1/10 of a scarf in 48 minutes. What fraction of a scarf can she knit in an hour? A. 5/24 B. 1/480 C. 1/8 D. 2/25
if TRAP is an isosceles trapezoid what is the value of x ?
the answer to this question is 19!
Complete the expression so it forms a perfect-square trinomial. x² +___ x + 49 A. 14 B. 7 C. 7/2
The expression so it forms a perfect square trinomial is 14x.
We have given that,
The expression so it forms a perfect-square trinomial.
We have to determine the x² +___ x + 49.
What is the factor?
A divisor of an integer n also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
In this case, one also says that n is a multiple of m.
(x + 7)(x + 7)
x^2 + 14x + 49
The expression so it forms a perfect square trinomial is 14x.
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Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation. The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware. The total bill for the catering services is $1,512. Which equation can be used to determine the total number of guests, g, who attend the dinner party? 13.50g + 540 = 1,512 13.50g - 1,512 = 540 5400g + 13.50 = 1,512 540g - 1,512 = 13.50
Answer:
The equation can be used to determine the total number of guests is 13.50g + 540 = 1512 and the total number of guest are 72 .
Step-by-step explanation:
As given
Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation.
The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware.
The total bill for the catering services is $1,512.
Total number of guests, g .
Than the equation becomes
1512 = 540 + 13.50 g
1512 - 540 = 13.50 g
972 = 13.50 g
[tex]g = \frac{972}{13.50}[/tex]
g = 72
Therefore the equation can be used to determine the total number of guests is 13.50g + 540 = 1512 and the total number of guest are 72 .
In a school election, 3/4 of the students vote. There are 1464 ballots. Write and solve and equation to find the number of students.
x = total number of students
equation is:
(3/4)x = 1464
to solve for x divide both sides by 3/4
x = 1464 / 3/4 = 1952
x = 1952
there are 1952 total students
anonymous 4 years ago A technical writer makes $45,000 per year and has just begun contributing 8% of her salary to her 401(k) plan. If her employer matches 6% of her contributions, how much will have been contributed to the 401(k) plan after 2 years?
Answer:
$7,632 would have been contributed to the 401(k) plan after 2 years.
Step-by-step explanation:
A technical writer makes salary per year = $45,000
She contributing 8% of her salary to her 401(k) plan = 8% of 45,000
0.08 × 45,000 = $3,600
Her employer matches 6% of her contributions = 6% of 3,600
= 0.06 × 3,600 = $216.00
Total contribution for one year = 3,600 + 216.00 = $3,816
After 2 years = 3,816 × 2 = $7,632.00
$7,632 would have been contributed to the 401(k) plan after 2 years.
the expression 12x+15x-11x can be combined because of which property
A. commutative property of addition
B. distributive property
C. additive inverse property
D. multiplicative property
The expression 12x+15x-11x can be combined using the associative property of addition.
Explanation:The expression 12x+15x-11x can be combined by using the associative property of addition.
First, combine the like terms which have the same variable, in this case 'x'. Add the coefficients of the like terms, which are 12, 15, and -11. 12x + 15x - 11x = (12 + 15 - 11)x = 16x.Therefore, the simplified expression is 16x. The associative property of addition allows us to group the terms in any order and still get the same result.
Final answer:
The expression 12x + 15x - 11x can be simplified due to the associative property of addition, enabling terms to be grouped and combined to yield a simplified form of 16x. The correct option is not provided in the choices, but would be the associative property, not listed in the student's options.
Explanation:
The expression 12x + 15x - 11x can be simplified by combining like terms, which is possible because of the associative property of addition. This property allows us to group numbers in an addition expression in any way we choose without changing the result.
Therefore, using the associative property, we can group and combine the terms with 'x' to get (12x + 15x) - 11x, which simplifies to 27x - 11x, and then further to 16x.
The correct answer to the question is Option A: associative property of addition, though it is important to note that this option was not listed in the initial question provided. The commutative property allows us to change the order of the terms without changing the result, but does not directly apply to the combination of like terms.
Nevertheless, both the associative and commutative properties are used when combining like terms in algebra.
Heather's fish tank has 18 liters of water in it. she plans to add 4 liters per minute until the tank has more than 58 liters. what are the possible numbers of minutes heather could add water?
Hidemi is a waiter. He waits on a table of 4 whose bill comes to $69.98. If Hidemi receives a 20% tip, approximately how much will he receive?
$3.50
$14.00
$84.00
$7.00