Answer: Maximum area = 200m
Dimensions:
Length = 10m
Width = 20m
Such that there is only one side of 20m fenced because the other side of 20m is against the rock wall.
Step-by-step explanation:
We have the next problem.
Suppose that the vegetable area is a rectangle of length L and width W.
Such that the width side coincides with the rock wall, then we have that:
The perimeter is:
P = 2*L + 2*W
But because one of the width sides coincides with the wall, the amount of fence needed will be:
P = 2*L + W = 40m
And the area can be written as:
A = W*L
We want to find the maximum area that we can have.
First, write our two equations:
40m = 2*L + W
A = W*L
First we must isolate one of the variables in the first equation, and replace it into the second equation:
40m - 2*L = W.
then:
A = (40m - 2*L)*L = 40m*L - 2*L^2
We can write this as a quadratic equation:
A(L) = -2*L^2 + 40m*L
Now, notice that it has a leading coefficient negative, then the maximum of the area function will be at the vertex of the quadratic equation.
For a quadratic equation:
f(x) = a*x^2 + b*x + c
The vertex is at:
x = -b/2a
and the point is (-b/2a, f(-b/2a))
In this case we have:
b = 40m
a = -2
Then:
we must evaluate the area function in:
L = -40m/(-2*2) = 10m
A(L) = -2*L^2 + 40m*L
A(10m) = -2*100m^2 + 400m = 200m
Now we can find the width using one of the above equations:
W = 40m - 2*L = 40m - 2*10m = 20m
Then the dimensions that the farmer should use are:
Two sides of length 10m, and one side of length 20m
(7 x 18 + 45) divide 3 x 2
Answer:
28.5
Step-by-step explanation:
7 x 18 =126
126 +45=171
171/6=28.5
i hope this helps!
Please help urgent
Answer:
x < 50
Step-by-step explanation:
No more means that it cannot equal 50. Therefore we can remove the 1st two options.
We now have the 3rd option and 4th option to choose from.
The 4th option is incorrect because the inequality is saying that a number is greater than 50.
∴ x < 50 is our answer.
The current Powerball jackpot is estimated to be $193 million. The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2. A ticket is defined as a set of five white and 1 red number.
Answer:
"2.660503478" would be the right answers to the key statement.
Step-by-step explanation:
Drawing 5 balls out of 69 can be done in ([tex]\frac{69}{5}[/tex])
= [tex]\frac{69\times 68\times 67\times 66\times 65}{5!}[/tex]
Drawing 1 ball out of 26 red balls can be done in ([tex]\frac{26}{1}[/tex])
= [tex]26[/tex]
Then the chance of drawing 5 out of 69 balls including 1 out of 26 red balls and then both matching the jackpot
= [tex]\frac{1}{11238513\times 26}[/tex]
= [tex]\frac{1}{292201338}[/tex]
Since the sum of the jackpot is $193-106 and then one ticket costs $2, the estimated value of buying one ticket again for jackpot is $2.
= [tex]\frac{1}{292201338}\times 193\times 10^6+\frac{292201338-1}{292201338}\times 2[/tex]
= [tex]2.660503478[/tex]
a cars tire pressure decreased by 0.098 of its original pressure write 0.098 as a percent
Translate: half a number decreased by 12
Answer:
1/2n - 12Step-by-step explanation:
Let the number be n
Then
1/2n - 12 is the translationAnswer:
1/2n - 12
Step-by-step explanation:
Half a number: 1/2n
Decreased by 12: - 12
Put together: 1/2n - 12
Best of Luck!
John sent 45 text messages in 9 minutes. What is the unit rate? Explain your answer.
Answer: 5 texts per minute
Step-by-step explanation: 45 / 9 = 5
What is the middle term and first term of (2x-4)2
Answer:
First term: 4x
"Middle" term: -8
Step-by-step explanation:
2(2x-4) is the same thing as 4x-8.
Please help me! I will mark brainliest.
Answer:
Its -5
Step-by-step explanation:
-100 divided by 10= -10 divided by -5= 2
How do you write 0.1 as a fraction? Please help
Answer:
1 over 9
Step-by-step explanation:
Answer:
The correct answer is A.) 1/9
Step-by-step explanation:
50 POINTS !!!
A restaurant needs to purchase custom tablecloths. Company O charges a flat fee of $175 plus $35 per tablecloth. Company P does not have a flat fee but charges $45 per tablecloth.
What is the minimum number of tablecloths that must be ordered for company O to be a better deal than company P?
Enter your answer in the box.
"_____tablecloths"
Answer:
The answer is 20
Step-by-step explanation:
Company O:
Equation: 175 + 35t
175 + (35)20 = 875
Company P:
Equation: 45t
45 x 20 = 900
20 tablecloths Is the minimum amount of tableclothes they can order.
Hopefully this helps you
pls mark brainlest
find all missing variables and measures of each angle
Answer:
y = 21
x = 48
Step-by-step explanation:
for y:
5y - 17 + 2y + 50 = 180
add like terms
7y + 33 = 180
subtract 33 from 180
7y = 147
divide 7 from 147
y = 21
for x:
x + 44 + 7x -248
add like terms
8x - 204 = 180
add 204 to 180
8x = 384
divide 8 from 384
x = 48
now plug it in to find angle measurements:
for y:
5 (21) - 17 = 88°
7 (48) - 248 = 88°
for x:
2 (21) + 50 = 92°
48 + 44 = 92°
I hope this helps!❤
"The solution to the system is (#,#)." I'm really tired and for my life don't know the solution. Help please!
Answer: (4,-5)
Step-by-step explanation:
8y = -40
(divide by 8)
y = -5
(plug it in to one of the equations)
3x + 6*-5 = -18
3x + -30 = -18
3x = 12
x = 4
Kirk bought 811.8 ounces of chocolate. 134.3 ounces of it was milk chocolate and the rest was dark chocolate. How much dark chocolate did Kirk buy? pls hurry
Answer:
677.5
Step-by-step explanation:
811.8-134.3 is 677.5
Answer:
567.5 ounces
Step-by-step explanation:
811.8
-134.3
--------------
567.5
What is the equation written in vertex form of a parabola
with a vertex of (9, -1) that passes through (7, 7)?
Answer:
y = 2(x - 9)² - 1
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (9, - 1 ) , thus
y = a(x - 9)² - 1
To find a substitute (7, 7 ) into the equation
7 = a(7 - 9)² - 1 ( add 1 to both sides )
8 = 4a ( divide both sides by 4 )
2 = a , then
y = 2(x - 9)² - 1
Solve for x.
5(x−3)= 3(x−2)
Answer:
x = 9/2 or x= 4.5
Step-by-step explanation:
you factor out the equation:
5x-15=3x-6
+15 +15
5x=3x+9
-3x -3x
2x=9
x=9/2 or 4.5
Write 3/9 in the lowest terms
Answer:
3/9 is 1/3 because if you simply by 3, it will be 1/3 of 9
The list below shows all the possible outcomes for tossing a coin and rolling a 1 to 6 number
cube. What is the probability that Max tosses heads and rolls a number greater than 2?
{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
Answer:
1/3
Step-by-step explanation:
There is a total of 12 possible different outcomes.
The outcomes that are heads and a number greater than 2 are: H3, H4, H5, H6.
There are 4 outcomes that are heads and a number greater than 2.
p(heads & number greater than 2) = 4/12 = 1/3
Answer: 1/3
is f(x)=x^2-2x+3 a quadratic function
Answer:
yes
Step-by-step explanation:
A quadratic function has the general form
fx) = ax² + bx + c ( a ≠ 0 )
f(x) = x² - 2x + 3 ← is in this form and is a quadratic function
True or False: subtracting a negative integer is the same as adding a positive integer
Answer:
False
Step-by-step explanation:
For example, if I have -12- (-10) it equals-2, but if you have -12 + 13= 1
Answer:
False
Step-by-step explanation:
I Think
What is the value of n in the proportion below?
n/28 = 4/7
A-1
B- 12
C- 14
D- 16
Answer:
d
Step-by-step explanation:
Add.
7/11
+
9/12
All you have to do is add. Somehow I got it wrong
Answer:
1 51/132
Step-by-step explanation:
7/11+ 9/12 =
84/132 + 99/132 = 183/132 = 1 51/132
make the denominator of the fraction the same by using LCM.
See my other articles for quiz and assignment in my site.
Just copy and paste "learningandassignments diy4pro" to google search engine.
Hope it helps.
I need this math answer now and explain it to me please
Answer:
C
Step-by-step explanation:
i dont have an explanation its just C
Answer:
the answer is 35.
Step-by-step explanation:
So first you look for 75 on the x-axis because this represents the number of people in attendance. 75 would be the line between 50 and 100. Then you need to follow the 75 line up until you see the point that the graphed line intersects the "75 line". When you drag you finger from that point over to the y-axis, you see the number of recyclables is about 35.
Solar-powered cars use energy from the Sun to work. A panel on the car absorbs light energy from the Sun, which then generates an electric current. This electric current, in turn, allows the car to move. Which shows the correct order of energy transformations that take place in a solar-powered car? electrical, chemical, kinetic electrical, kinetic, radiant radiant, chemical, electrical radiant, electrical, mechanical
Answer:
It is D
Step-by-step explanation:
The correct order of energy transformations that are seen in the electrical cars are:
radiant, electrical, mechanicalWhat is energy transformation?This is what is also known as energy conversion. It is the way that energy is converted from one form to another form.
In the case of electrical cars. energy is transformed from radiant energy to electrical energy and then to mechanical energy.
Read more on energy transformation here: https://brainly.com/question/961052
ina problem what is Six less than seven times a number is equal to -20.
Answer:
-2
Step-by-step explanation:
write the problem using numbers
-6 + 7x = -20
rearrange
7x - 6 = -20
solve using inverse operations
7x - 6 = -20
+6 + 6
7x = -14
/7 /7
x = -2
Madison Finance has a total of $22 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars. On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 13% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category to maximize its returns P in millions of dollars.Maxmize P=total loansdistributtion of loans
Answer:
Maximum returns = $1,980,000
x = Homeowner loans = $17,600,000
y = Auto loans = $4,400,000
Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000
Step-by-step explanation:
From the question we are told that:
Madison Finance has a total of $22 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars.
On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 13% annual rate of return.
We have the equation:
Maximum Return = 8% × x + 13% × y
= 0.08x + 0.13y
We are told in the question that
Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans.
Hence,
x ≥ 4y
So:
x + y = $22,000,000
4y + y = $22,000,000
5y = $22,000,000
y = $22,000,000/5
y = 4,400,000
x = 4y
x = 4(4,400,000)
x = 17,600,000
Maximum Return = 0.08x + 0.13y
= 0.08 × 17,600,000 + 0.13 × 4,400,000
= $1,980,000
Therefore, Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000
represent 5 rational number between -1 and 0
Answer:
It could be any fraction such as -1/2, -4/5,-20/50, -1/3, -5/11 ...
As long as the fraction is larger than -1 but smaller than 0 it will work
Step-by-step explanation:
solve the following equation: x÷3-5=-7
Answer:
- 6
Step-by-step explanation:
Step 1:
x ÷ 3 - 5 = - 7 Equation
Step 2:
x ÷ 3 = - 2 Add 5 on both sides
Answer:
x = - 6 Multiply 3 on both sides
Hope This Helps :)
pleaseeeee
factor 16x2 + 9
Answer:16x2+9
Step-by-step explanation:
What is the solution of the equation: 6x = - 48
Answer choices
-8
-7
7
8
Answer: I think its -8
Step-by-step explanation: all you do I'd divide
convert into a mixed fraction 3/5+ 3/5
Answer:
1 1/5
Step-by-step explanation:
3/5 + 3/5 = 6/5 = 5/5 + 1/5 = 1 1/5
