The dimensions which will give Margo the largest area is 6 m by 6 m
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, Margo has 24 meters of wood to build a fence around her garden. She wants to create the largest area possible
Let the length be L and the width be W
So the perimeter equation is
2L + 2W = 24
2(L+W) = 24
L+ W= 12
L= 12-W
To find the largest area
area = L×W
area = (12-W) ×W
area= 12W- W²
A= -W²+ 12W
The vertex of the parabola is the point (h, k) where h=
= 6
to find the k part
k= (-6)² + 12(6)= 108 m²
The largest possible area is 108 m²
putting the value of W in
L= 12-W
L= 12-6 = 6 m
Hence, the length and width is same, 6 m by 6 m
For more references on area, click;
https://brainly.com/question/27683633
#SPJ1
Ms. Williams counted students by eye color. The table shows how many students had each eye color.
Brown 21
Blue 6
Green 3
Write a ratio to compare blue eyes to green eyes.
The simplest ratio of blue eyes to green eyes expresses as 2:1.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The table shows how many students had each eye color.
Brown: 21
Blue: 6
Green: 3
In order to calculate the ratio of two quantities, we can use the following steps
First, we have to find the quantities of both scenarios for which we are determining the ratio. In this case, it is 6 blue eyes and 3 green eyes.
Write it in the fraction form a/b. So, we write it as 6/3.
Simplify the fraction further, if possible. The simplified fraction will give the final ratio.
Here, 6/3 can be simplified to 2/1.
Therefore, the simplest ratio of blue eyes to green eyes expresses as 2:1.
Learn more about the Ratios here:
brainly.com/question/1504221
#SPJ2
A man has $460,000 invested in three rental properties. One property earns 6.5% per year on the investment, the second earns 7%, and the third earns 9%. The total annual earnings from the three properties is $36,350, and the amount invested at 9% equals the sum of the first two investments. Let x equal the investment at 6.5%, y equal the investment at 7%, and z represent the investment at 9%. Complete parts (a) through (d) below.
The system of equations representing the amount invested are;
(a) x + y + z = 460,000
(b) 0.065·x + 0.07·y + 0.09·z = 36,350
(c) z = x + y
(d) There is one solution. The man invested $90,000 at 6.5%, $140,000 at 7% and $230,000 at 9%
What is a system of equations?A system of equations are two or more equations that have variables that are common to the equations in the system.
The questions in the parts (a) to (d) obtained from a similar question are;
(a) An equation stating the sum of the three investments
(b) The equation that states that of the sum of the return is 36,350
(c) The equation that states that the amount invested at 9% equals the sum of the other two investments
(d) Solve the derived system of equations
(a) The amount the man invests in the three rental properties = $460,000
Amount invested in the property that earns 6.5% = x
Amount invested in the property that earns 7% = y
The amount invested in the property that earns 9% = z
The equation that represents the sum of the three investments is therefore;
x + y + z = 460,000...(1)
(b) The equation that represents the sum of the returns from the three investment is found as follows;
6.5% = 0.065, 7% = 0.07, 9% = 0.09
0.65·x + 0.07·y + 0.09·z = 36,350...(2)(c) The equation stating the amount invested at 9% equals the sum of the other two investment is; z = x + y...(3)
(d) The system of equations is solved as follows;
From equation (1) and (2), we get;
x + y + z = 460,000
z + z = 460,000
2·z = 460000
· = 460,000 ÷ 2 = 230,000
The amount invested in the property that earns 9% per year is $230,000
Equation (3) indicates;
0.65·x + 0.07·y + 0.09 × 230,000 = 36,350
0.65·x + 0.07·y = 36,350 - 0.09 × 230,000 = 15650
The interest earned in the properties that earn 6.5% and 7% = $15650
0.65·x + 0.07·y = 15650...(4)
x + y = 230000...(5)
Equation (4) and (5) indicates;
y = 230,000 - x
0.065·x + 0.07×(230,000 - x) = 15650
16100 - 0.005·x = 15650
0.005·x = 16,100 - 15,650 = 450
x = 450 ÷ 0.005 = 90,000
The amount invested in the property that yields 6.5% per year = $90,000
Therefore;
The amount invested in the property that earns 7% per year = $230,000 - $90,000 = $140,000
There is one solution, the man invested $90,000 at 6.5%, $230,000 at 7%, and $230,000 at 9%
Learn more about systems of linear equations here:
https://brainly.com/question/14323743
#SPJ1
Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 3x²
Also, we have
Vertex = (5, 9)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (5, 9)
Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 5)² + 9
This also means that
f(x) = -3(x - 5)² + 9
The -3 is gotten from f(x) = -3x²
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
Read more about parabola at
brainly.com/question/1480401
#SPJ1
f(x)=3x-6 draw the graph
Check for extraneous solutions when plugging -7 into x-5=2(x+1).
Check for extraneous solutions when plugging 1 into x-5=-2(x+1)
Please hurry
There are no extraneous solutions when plugging -7 into x-5=2(x+1).
So extraneous solutions means the solutions that you get by solving an equation, but after you try plugging it back into your original equation, the solution does not work.
Now we have our solutions of x=7, and we just need to check whether it is extraneous or not. We can do this by taking x=1 and plugging it back into your original equation x - 5 = 2(x + 1)
x - 5 = 2(x + 1)
-7 - 5 = 2(-7 + 1)
-12 = -14 + 2
-14 + 14
0 = 0
We end up getting that 0 = 0 which is correct,
Thus, there are no extraneous solutions.when plugging -7 into x-5=2(x+1).
To learn more about extraneous solutions refer here
https://brainly.com/question/12361474
#SPJ9
Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x^4+3x^3−2x^2+48x−288
The factoring of the polynomial f(x) = x^4 + 3x³ - 2x² + 48x - 288 is given as follows:
f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).
How to factor the polynomial?The polynomial is factored by it's linear factors, given as follows:
f(x) = (x - x')(x - x'')(x - x''')(x - x'''').
In which x', x'', x''' and x'''' are the roots of the polynomial f(x).
In this problem, we have that -4i is a root, hence, by the Conjugate Roots Theorem, 4i is also a root and hence:
f(x) = (x - 4i)(x + 4i)(x - x''')(x - x'''').
f(x) = (x² + 16)(x - x''')(x - x'''').
As a fourth order polynomial can be the product of two second order polynomials, hence:
x^4 + 3x³ - 2x² + 48x - 288 = (x² + 16)(ax² + bx + c)
x^4 + 3x³ - 2x² + 48x - 288 = ax^4 + bx³ + (c + 16)x² + 16bx + 16c.
Hence the coefficients are given as follows:
a = 1.b = 3.16c = -288 -> c = -18.Then the equation for the final two factors is:
x² + 3x - 18 = 0.
Which is simplified as follows:
x² + 3x - 18 = (x + 6)(x - 3).
Hence the simplified polynomial is:
f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).
More can be learned about the factoring of a polynomial at brainly.com/question/19030198
#SPJ1
Evaluate -69(3)-(3--6)/6÷3-1
Answer:
-188
Step-by-step explanation:
The Ruffins are negotiating with two banks for a mortgage to buy a house selling for $190,000. The terms at bank A are a $25% down payment, an interest rate of 11%, a 25 -year conventional mortgage, and 2 points to be paid at the time of closing. The terms at bank B are a 15% down payment, an interest rate of 10.0%, a 30 -year conventional mortgage, and no points. Which loan should the Ruffins select in order for the total cost of the house to be less?
Click the icon to view the table of monthly payments.
From which bank should the Ruffins take the loan?
Bank B
Bank A
Bank A grants a shorter payment period and is the least costly, so the Ruffins should take the loan from Bank A.
How the payment period influences the cost of a loan?In finance literature and practice, the loan interest (cost) increases with a more extended payment period.
In other words, a shorter payment period reduces the interest cost of a loan. The loan cost is also influenced by the amount of the principal and the interest rate.
Bank A Terms:Down payment = 25%
Interest rate = 11%
Mortgage period = 25 years
2 points at closing
N (# of periods) = 300 months (25 years x 12)
I/Y (Interest per year) = 11%
PV (Present Value) = $142,500 ($190,000 - $47,500)
FV (Future Value) = $0
Results:
Period Payments (PMT) = $1,396.66
Sum of all periodic payments = $418,998
Total Interest = $276,498
Total Costs:Down payment = $47,500 ($190,000 x 25%)
2 points = $2,850 ($142,500 x 2%)
Sum of periodic payments = $418,998
Total costs = $469,348 ($47,500 + $2,850 + $418,998)
Bank B Terms:Down payment = 15%
Interest rate = 10%
Mortgage period = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 10%
PV (Present Value) = $161,500
FV (Future Value) = $0
Results:
Period Payments (PMT) = $1,417.28
Sum of all periodic payments = $510,220.08
Total Interest = $348,720.08
Total Costs:Down payment = $28,500 ($190,000 x 15%)
Sum of periodic payments = $510,220.80
Total costs = $538,720.80 ($28,500 + $510,220.80)
Thus, we can recommend the Ruffins should go for a Bank A loan that costs less than Bank B's.
Learn more about the loan costs at brainly.com/question/29369088
#SPJ1
For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the effective rate, and (c) the time to reach $10 comma 000.
$5200 at 3.7%
(a) the future value after 9 years is $7254.76 .
(b) the effective rate of interest is 3.769% .
(c) the time required to reach $10000 is 1.77 years .
The Continuous Compounding formula for the principal P , rate of interest r , and time t is
A = P×[tex]e^{rt}[/tex]
In the question ,
it is given that
Part(a)
the amount deposited (P) = $5200
rate percent (r) = 3.7% = 3.7/100 = 0.037
time = 9 years
Amount = 5200×[tex]e^{0.037\times9}[/tex]
= 7254.76
the future value after 9 years is $7254.76 .
Part(b)
the effective rate is calculated using the formula
effective rate = [tex]e^{r}[/tex] - 1
effective rate = [tex]e^{0.037}[/tex] - 1
= 1.03769 - 1
= 0.03769
= 3.769%
Part(c)
the time to reach $10000 is calculated using the formula
10000 = 5200[tex]e^{0.037\times t}[/tex]
[tex]e^{0.037\times t}[/tex] = 10000/5200
[tex]e^{0.037\times t}[/tex] = 100/52
taking ㏑both the sides , we get
0.037×t×㏑(e) = ㏑(100/52)
0.037t = 0.65392
t = 0.65392/0.037
t = 1.76735
t ≈ 1.77 years
Therefore , (a) the future value after 9 years is $7254.76 .
(b) the effective rate of interest is 3.769% .
(c) the time required to reach $10000 is 1.77 years .
Learn more about Continuous Compounding here
https://brainly.com/question/14468790
#SPJ1
How do I graph this?
Answer:
first solve for y and simplify
y+5=[tex]\frac{2}{3} x[/tex]+4/3
y=[tex]\frac{2}{3} x[/tex]+4/3-5
y=[tex]\frac{2}{3} x[/tex]-11/3
Now graph this
y intercept=(0,-11/3)
use the slope to find another point
(3,-1.667)
draw a line using both points
Frodo ran 2 1/5 miles in 7/12 of any hour. How many miles can Frodo run in one hour?
Frodo ran 132/35 miles in one hour.
Given, that Frodo ran 2(1/5) miles in 7/12 of an hour.
Now, 2(1/5) miles = 7/12 hour
11/5 miles = 7/12 hour
7/12 hour = 11/5 miles
1 hour = (11/5)×(12/7)
1 hour = 132/35 miles
So, Frodo ran 132/35 miles in one hour.
Hence, Frodo ran 132/35 miles in one hour.
Learn more about Unitary Method here https://brainly.com/question/28627316
#SPJ1
From a research paper, it is known that the number of soldiers who died annually
by being kicked by a horse followed a Poisson distribution with an average of 0.61
death in an army corps each year.
(a) Find the standard deviation of death in an army corps each year.
The standard deviation of death in an army corps each year is 0.78
How to determine the standard deviation?From the question, we have the following parameters that can be used in our computation:
Distribution type = Poisson distribution
Average of the distribution = 0.61
The standard deviation of the distribution is calculated as:
Standard deviation = √Average of the distribution
Substitute the known values in the above equation, so, we have the following representation
Standard deviation = √0.61
Evaluate the square root expression
So, we have
Standard deviation = 0.78
Hence, the standard deviation is 0.78
Read more about Poisson distribution at
https://brainly.com/question/7879375
#SPJ1
Which statements are true about exponential decay functions? Check all that apply.
O The domain is all real numbers.
O As the input increases, the output increases.
O The graph is the same as that of an exponential growth function.
The base must be less than 1 and greater than 0.
O The function has a constant multiplicative rate of change.
The correct options are:
The domain is all real numbers.The base must be less than 1 and greater than 0.The function has a constant multiplicative rate of change.Given,
In the question:
Which statements are true about exponential decay functions?
Now, According to the question;
We know that the exponential function is given by:
[tex]f(x) = ab^x[/tex]
where a>0 and b are constants.
Also, it represents a growth function if b>1
and a decay function if 0<b<1
where b is the base.
x belongs to whole of the real numbers( since the exponential function is well defined for all the real values of x.Hence, the domain of the function is all the real numbers )
Also, the graph of a decay function decreases continuously i.e. with the increasing input value the output value decreases.The exponential decay function always have a constant multiplicative rate of change i.e. b.Learn more about Exponential Function at:
https://brainly.com/question/14355665
#SPJ9
Question 7
Complete the equation so that it has no solution.
-15x + 4x + 2 - x =
x+3
Answer:
x=-1/13
Step-by-step explanation:
To find the area of △KNM, the length of the base, segment MK, is 2b, and the height is a. So an expression for the area of △KNM is
An expression for the area of △KNM is = 1/2 x 2b x a
Given,
In the question:
In triangle KNM ;
The length of the base (MK) = 2b
and, height of the triangle is= a
To write an expression for the area of △KNM .
Now, According to the question:
We know that :
Area of triangle is = 1/2 x base x height
The length of the base (MK) = 2b
and, height of the triangle is= a
Plug all the values in the area of triangle :
Here, Area of triangle is = 1/2 x 2b x a
Hence, An expression for the area of △KNM is = 1/2 x 2b x a.
Learn more about Triangle at:
https://brainly.com/question/16886469
#SPJ9
road trip
What is the Pennington's rate of change (slope)?
What is the Williams' rate of change (slope)?
Which family is traveling faster?
Pennington's rate of change is; 80 miles per hour.
William's rate of change is; 60 miles per hour.
The family which is travelling faster is; Pennington's family.
What is the rate of change in each case?It follows from the task content that the rate of change, otherwise termed slope is to be determined for each of Pennington and Williams.
For Pennington;
As evident in the given graphs; the distance travelled and time of travel are proportional.
Hence, by observation; Pennington's family travelled 40 miles in 0.5 hours and hence;
the rate of change = Distance / time is;
= 40/0.5
= 80 miles per hour.
For Williams;
As evident in the given graphs; the distance travelled and time of travel are proportional.
Hence, by observation; William's family travelled 180 miles in 3 hours and hence;
the rate of change = Distance / time is;
= 180/3
= 60 miles per hour.
On this note, the Pennington's family are traveling faster as their rate of change is greater.
Read more on rate of change;
https://brainly.com/question/25184007
#SPJ1
Which of the following statements is equivalent to 18 + 6?
3(15+3)
3(6+2)
3(5+3)
3+ (15+3)
Answer: 3(6+2), 3(5+3)
Step-by-step explanation:
Since 18+6 equals 24, you need to find the answers that are equivalent to 24.
3(6+2)
If you do order of operations, it would look like this
3(6+2)
3(8) or 3x8
24
3(5+3)
5+3 equals 8, so this is the same as the first answer.
A plant grows six inches per season. How many centimeters did it grow in 2 years?
Answer: 48in
Step-by-step explanation: 4 seasons per year, 4 x 2 is 8, so you would do 6 x 8 = 48.
Please help due tomorrow!!
Answer: 63
Step-by-step explanation:
When there are two lines intercepting the two angles opposite each other are the same
and GHK and IHF are opposite of each other so there for are equal
IXL Please Help Fast I Still Have A Few More... :(
Answer:
x=3
Step-by-step explanation:
I’m pretty sure these 2 angles are equivalent
64-4x=58-2x
6-4x=-2x
6=2x
3=x
Hopes this helps please mark brainliest
Elizabeth buys a microscope priced at $83. Shipping and handling are an additional 20% of
the price. How much shipping and handling will Elizabeth pay?
According to the given percentage, the shipping and handling fee that Elizabeth will pay is $16.6
Percentage:
Percentage refers one-hundredth (1/100) of something. And it refers to the rate or proportion of that one hundred.
Given,
Elizabeth buys a microscope priced at $83. Shipping and handling are an additional 20% of the price.
Here we need to find the shipping and handling will Elizabeth paid.
We know that, the price of the product is $83.
And the charges for the shipping and handling is 20%.
So, it can be written as the following form,
=> Additional charges = 20% of 83
=> Additional charges = 20/100 x 83
=> Additional charges = 20 x 0.83
=> Additional charges = 16.6
Therefore, the shipping and handling charges is $16.6
To know more about Percentage here.
https://brainly.com/question/24159063
#SPJ9
i need help with math agian lol
-3/4 ÷ 1/9 divide.
Answer:
-6 3/4
Step-by-step explanation:
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
−34×91=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
−3×94×1 = −274
This fraction cannot be reduced.
The fraction
−274
is the same as
−27÷4
Convert to a mixed number using
long division for -27 ÷ 4 = -6R3, so
−274 = −6 3/4
Therefore:
−34÷19 = −6 3/4
can you make it to italy in 6 hours from chicago to milan italy? or no Answer asap for brainlist
Write the INTERCEPT FORM equation of a parabola with x-intercepts at (-5,0) and (
9,0) that passes through the point (10, 30).
The equation of the parabola is y = -x² + 12x - 27
Parabola is the locus of a point such that the same distance from a fixed line, called the directrix, and a fixed point (the focus) is the same.
The equation of a parabola is in quadratic form. Hence it is given as:
y = ax² + bx + c
At point (-5, 0):
0 = a(-5²) + b(-5) + c
25a - 5b + c = 0 (1)
At point (9, 0):
0 = a(9²) + b(9) + c
81a + 9b + c = 0 (2)
At point (10, 30):
30 = a(10²) + b(10) + c
100a + 10b + c = 30 (3)
Solving equations 1, 2, 3 gives: a = -1, b = 12, c = -27
The equation of the parabola is hence y = -x² + 12x - 27
Learn more about Intercept form here:
brainly.com/question/21685473
#SPJ9
Find the derivative of [tex](\sqrt{3x+x^2}+3sin(3x))^2[/tex] and evaluate the derivative at x=1. Round to 1 decimal place. Make sure that the calculator is in radians mode.
The first derivative of the function f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x], whose value at x = 1 is - 35.909.
How to find the derivative of a given function
Herein we find a function whose first derivative has to be found. This can be done by using the following derivative rules:
Derivative of a power
f(x) = c · xⁿ → f'(x) = n · c · xⁿ ⁻ ¹
Chain rule
f[g(x)] = (df / dg) · (dg / dx)
Derivative of a sum of functions
d / dx [f(x) + g(x)] = df / dx + dg /dx
Derivative of the sine
d / dx [sin x] = cos x
Now we proceed to find the derivative of the function:
f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x]
And we evaluate the derivative at x = 1:
f'(1) = 2 · [√(1 + 1²) + 3 · sin 3]² · [(1 + 2) / [2 · √(1 + 1²)] + 9 · cos 3]
f'(1) = 2 · (√2 + 0.423)² · (3 / 2 - 8.910)
f'(1) = - 35.909
To learn more on derivatives: https://brainly.com/question/25324584
#SPJ1
I am having trouble with this one really badly and I need help!
Answer: 7 hours
Step-by-step explanation:
525 x 4.5= 2362.5
2362.5 / 6= 393.75
393.75 / 60= 6.5625
Solve 2/3c - 1 = 1+2/3c
No solution
Infinite Solution
c = 6/4
c = 2/3
The variable 'c' in the given expression has No Solution.
Given, that
2/3c - 1 = 1 + 2/3c
Now, as we have same coefficient of the variable c i.e. 2/3
So, On subtracting 2/3c from both the sides, we get
2/3c - 2/3c - 1 = 1 +2/3c - 2/3c
-1 ≠ 1
Hence, we got no solutions that can satisfy the given expression.
So, the variable 'c' in the given expression has No Solution.
Learn more about Linear Equations here https://brainly.com/question/25858757
#SPJ1
The line 2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5. True or False?
Answer:
this is Ture
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
By changing both equations to slope-intercept, it is easier to determine whether two lines are perpendicular.
Since [tex]y = \frac{5}{2} x+ 5[/tex] is already in slope-intercept form, we just need to change the first given equation.
2x + 5y + 3 = 0
2x + 5y = -3
5y = -2x -3
[tex]y=\frac{-2}{5}x-\frac{3}{5}[/tex]
Two lines are perpendicular when the slope of the lines (coefficient of x) are negative reciprocals (opposite sign of the inverse of a number).
Comparing the two slopes [tex]\frac{5}{2}[/tex] and [tex]\frac{-2}{5}[/tex], we can see they they both fit the criteria of being opposite signs and inverses of each other.
So 2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5.
When the same constant is added to the numbers 60, 100 and 180 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
The common ratio of the resulting sequence is 1.4.
Given that, the three terms are 60, 100 and 180.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
Let the same constant is added to the given number is x.
60+x, 100+x and 180+x
Now, the common ratio is
(100+x)/(60+x) = (180+x)/(100+x)
⇒ (100+x)(100+x)=(180+x)(60+x)
⇒ (100+x)²=10800+180x+60x+x²
⇒ 10000+200x+x²=10800+180x+60x+x²
⇒ 10000+200x=10800+180x
⇒ 20x=800
⇒ x=40
The three number are 100, 140 and 220
The common ratio is 140/100 =1.4
Therefore, the common ratio of the resulting sequence is 1.4.
To learn more about the geometric sequence visit:
https://brainly.com/question/11266123.
#SPJ1
PPEASE HELPPPPPPPPP!!!!
