Answer:
Step-by-step explanation:
Perimeter of a garden = 2(L+W)
Area of the gerden = LW
L is the length
W is the width
Given
Perimeter = 155ft
Area = 1400ft²
Substitute
1400 = LW
155 = 2L+2W
from 1;
W = 1400/L
Substitute into 2;
155 = 2L + 2(1400/L)
155 = 2L + 2800/L
155L = 2L² + 2800
2L²-155L + 2800 = 0
Factorize
L = 155±√155²-4(2)(2800)/4
L = 155±√24025-22400/4
L = 155±√1625/4
L = L = 155±40.31/4
L = 194.31/4
L = 48.82 feet and;
L = 155-40.31/4
L = 28.67ft
Hence the approximate length of the garden is at least 28.67 feet and at most 48.82 feet.
The possible lengths of the garden are:
The least approximate length = 29 feet
The most approximate length = 49 feet
The area of the rectangle is at least 1400 square feet
That is:
Area ≤ 1400
Let the length be represented by L
Let the width be represented by W
Let the area be represented by A
The area of a rectangle is:
Area = Length x Width
A = LW
LW ≥ 1400....................(1)
The perimeter of the rectangle is 155 feet
P = 2(L + W)
2(L + W) = 155............(2)
Make W the subject of the formula
L + W = 155/2
L + W = 77.5
W = 77.5 - L.............(3)
Substitute W = 77.5 - L into equation (1)
L(77.5 - L) ≥ 1400
77.5L - L² ≥ 1400
-L² ≥ 1400 - 77.5L
0 ≥ L² - 77.5L + 1400
L² - 77.5L + 1400 ≤ 0
Solving the quadratic inequality above
29 ≤ L ≤ 49
The least approximate length of the garden = 29 feet
The most approximate length of the garden = 49 feet
Learn more here: https://brainly.com/question/19308936
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 8 liters of synthetic oil. In order to make 884liters of Petrolyn oil, how many liters of natural oil are needed?
9514 1404 393
Answer:
340
Step-by-step explanation:
The ratio of natural to synthetic is give as ...
5 : 8
Then the ratio of natural to total would be ...
5 : (5+8) = 5 : 13
The amount of natural oil in 884 total liters of oil will be ...
(5/13)(884 L) = 340 L
884 liters of Petrolyn oil will contain 340 liters of natural oil.
Answer:
340
Step-by-step explanation:
Hope I helped
Simplify 2•5^2 . Please
Help
Answer:50
Step-by-step explanation:
Answer: 50
Step-by-step explanation: according to pemdas you do exponets first so 5 over 2=5*5=25 then multiply by 2=25*2=50
neil runs every day after school. the table shows the distance run in minutes.
No. one variable is always a constant value times the other. That constant is know as the "constant of proportionality". This does not have that. Hope this helped
=3
<3
What is (1 +i)5?
-4-4i
-4+4i
4-4i
4+4i
Answer:
It's -4 -4i
Step-by-step explanation:
Because it is
A
-4-4i
For the person that commented. the 5 is an exponent.
What is the value of the expression All of 3.6 multiplied by 10 to the power 8 over all of 1.2 multiplied by 10 to the power 3?
Write the equation for a line that passes through (5,-4) and is perpendicular to the
linear function 2x - 10y = 0
Answer:
y = -5x -24
Step-by-step explanation:
Given parameters:
Coordinates of the line = (5, - 4)
Linear function ;
2x - 10y = 0
Solution:
The equation of the line perpendicular to this line will have a slope that is the a negative inverse of the given line;
2x - 10y = 0
Equation of a line is given as;
y = mx + c
y and x are the coordinates
m is the slope
c is the y-intercept
We find the slope and y-intercept of the new line;
From: 2x - 10y = 0
Rewrite;
-10y = -2x
y = [tex]\frac{-2}{-10}[/tex]x
y = [tex]\frac{1}{5}[/tex]x
The slope of this line is [tex]\frac{1}{5}[/tex] , the line perpendicular will have slope of -5
For the new line;
y = mx + c
let us find c;
-4 = -5( -4) + c
-4 = 20 + c
c = -20 - 4
c = -24
The equation of the perpendicular line is;
y = -5x -24
can please eplain solution
Answer:
a 37
b 90
c 39
d r0
Step-by-step explanation:
The Farmers Market sells apples by the bushel, and each bushel of apples weighs 42 lbs. A bushel of large apples contains 84 apples. If a bushel of small apples contains twice as many apples as a bushel of large apples, how many small apples are in 1 lb of apples?
Megan purchased a bushel of apples from the Farmers Market that contained only large and small apples. There were exactly 129 apples in the bushel Megan purchased. Based on this and information from the previous problem, what is the positive difference between the number of large apples and the number of small apples in the bushel of apples Megan purchased?
Suppose 56V% of politicians are lawyers. If a random sample of size 787787 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4%4%
Answer: 0.0238
Step-by-step explanation:
Given : Proportion of politicians are lawyers: p= 0.56
Sample size : n= 787
Let [tex]\hat{p}[/tex] be th sample proportion.
The the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4% will be :-
[tex]P(|\hat{p}-0.56|>0.04)=P(-0.04>\hat{p}-0.56>0.04)=\\\\ P(-0.04+0.56>\hat{p}>0.04+0.56)\\\\=P(0.52>\hat{p}>0.60)\\\\=P(\dfrac{0.52-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{787}}}>\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.60-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{787}}})\\\\=P(-2.26>z>2.26)\ \ \ [Z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=1-P(-2.26<z<2.26)\\\\=1-(2P(Z > 2.26)-1)\ \ \ [P(-z<Z<z)=2P(Z > |z|)-1]\\\ =2-2P(Z > 2.26)\\\\=2-2(0.9881)=0.0238[/tex]
Hence, the required probability = 0.0238
Given a quadratic function that is reflected across the
1
X-axis, vertically compressed by a factor of shifted
3
3 units to the right, and 2 units down, write the equation
of this quadratic function in vertex form.
Answer:
y=1/3 x2
Step-by-step explanation:
What is the estimated sum of 69,129,139,97
Answer:
440
Step-by-step explanation:
70 + 130 + 140 + 100 = 440
Enter the equation of the line in slope-intercept form.
Slope is 3, and (1, 3) is on the line.
The equation of the line is y =
Answer:
y=3x
Step-by-step explanation:
For f (x) = x2 - 5, find f (x) when x = 0 and when x = 3
f (0) =
f (3) =
Answer:
1 minus 1 is 0
Step-by-step explanation:
1-1 equals 0
5 1/5 - 5/12 ÷ (1/6 × 2/3)=
Answer:
47.8
Step-by-step explanation:
What you want to do first is 5 1/5 - 5/12 which is 4.78,
then 1/6 x 2/3, which is 0.1,
then you do 4.78 divided by 0.1, which is 47.8
Can someone check This answer for me and tell me if it’s 7 or 6 PLEASE ASAP THX
Answer:
im pretty sure its 6
Step-by-step explanation:
What’s the value of the missing angle
Once again I’ll give brainliest
120,110,149, or 108
Answer:
The answer is 120
Number of 16ths when 12 13/16 is changed to an improper
fraction.
Plzzzzz help
Answer:
105/16
Step-by-step explanation:
12 * 16 = 192
192 + 13 = 205
I hope this helped, please mark Brainliest, thank you!
Write 5/15 in simplest form.
Answer:
its 1/3
Step-by-step explanation:
take the fraction divided by 5
Find the value of x.
Answer:
The answer is 109 degrees.
Step-by-step explanation:
Any triangle's angles add up to 180 in total, so we can create the equation 64+45+__=180. Using some simple algebra we can change this equation into the equation 180-109=71. This solves the inner triangle, and the outside angle, x is supplementary (meaning it adds up to 180) to 71. 180-71 = 109.
Glad I could help!
16 x 0.2 please answer correct
Answer:
3.2
Step-by-step explanation:
Answer:
I believe it's 3.2!
A friend wants to borrow money from you. He states that he will pay you 3300 every 6 months for 8 years with the first payment exactly 6 years and 6 months from today. The interest rate is an apr of 5.6 percent with semiannual compounding. What is the value of the payments today
What is so important about points?
Answer:
What do you mean ?? Say it clearly I really want to help you.
Solve for the missing variables.
x= ?
y= ?
Add or subtract as indicated.
(3 + 3i) - (3 + 2i) + (1 + 41)
Answer:
i+42
Step-by-step explanation:
(3+3i) - (3+2i) + (1+41)
= 3+3i-3-2i+1+41
= 3i-2i+1+41
= i+42
The difference of 2 numbers is 2 and their product is 224. Find the numbers
Answer:
Step-by-step explanation:
12
Answer:
Step-by-step explanation:
The two numbers are 14 and 16 their product is 224 and their difference is 2
Scotty bought a used truck for $3,000. If it had been new, he
-would have paid $15,000.-What is the percent decrease?
Answer:
20%
Step-by-step explanation:
Percentage Calculator: 3000 is what percent of 15000? = 20%
1. Solve the equation. (1 point)
5x-1= 14
Answer:
the answer is 3
Step-by-step explanation:
you multiply 5 by 3 and subtract it by 1 to get 14
Which car will travel the greatest distance (in miles) per gallon?
A. The total distance that a Toyota Prius can travel in miles (M) given any gallons of gas (g) is given by M
= 35g.
B. A Toyota Sienna used 2.5 gallons to travel 55 miles.
C AND D ATTACHED
BEST ANSWER GETS BRAINLIEST
Complete the slope-intercept form equation of the line with slope 9 that passes through the point (0,2)
Answer:
2=2
Step-by-step
Y=mx+b
2=9(0)+2
9 x 0=0
2=2
I hope I got it correct and helped you.
Which equation represents the statement: Three times the sum of a number and 5 is -30
Answer:
Not 100 percent but im pretty sure it is 3(n+5)=-30 i found other sites saying its that its up to you if you wanna believe me
Step-by-step explanation: