We will see that the path should be 4 feet wide.
How wide should the path be?
For a rectangle of length L and width W, the area is:
A = L*W
In this case, we know that the dimensions of the garden are:
L = 50 ftW = 70 ftNow if we add a path of width x that surrounds it, the new length and width will be:
L' = 50 ft + 2xW' = 70 ft + 2xAnd the area of this rectangle must be 4524 ft^2, then we have:
(50 ft + 2x)*(70 ft + 2x) = 4524 ft^2
Now we can solve this for x.
Ignoring the units, so the math is easier to read, we have:
(50 + 2x)*(70 + 2x) = 4524
50*70 + 50*2x + 2x*70 + 2x*2x = 4524
3500 + 240x + 4x^2 = 4524
4x^2 + 240x + 3500 - 4524 = 0
4x^2 + 240x - 1024 = 0
Now to simplify the quadratic equation, we can divide both sides by 4 to get:
x^2 + 60x + 256 = 0
The solutions of the quadratic equation are given by Bhaskara's formula:
[tex]x = \frac{-60 \pm \sqrt{60^2 - 4*1*(-256)} }{2*1} \\\\x = \frac{-60 \pm 68 }{2}[/tex]
We only care for the positive solution (the negative one does not make physical sense).
x = (-60 + 68)/2 = 4
So the width of the path must be 4 ft.
If you want to learn more about quadratic equations, you can read:
https://brainly.com/question/1214333
The perimeter of a rectangle is 56 centimeters. If the length of the rectangle is four centimeters less
than three times its width, what are the dimensions of the rectangle?
Answer:
Let the length be x and the width be y, then
2x + 2y = 56
x + y = 28 . . . (1)
x = 4 + 3y . . . (2)
Putting (2) into (1) gives
4 + 3y + y = 28
4y = 28 - 4 = 24
y = 24/4 = 6
x = 4 + 3(6) = 4 + 18 = 22
Therefore, length is 22 inches and width is 6 inches.
HELP! whats bigger -3/2 or -5!?
Answer:
-3/2
Step-by-step explanation:
-5 = -10/2
-10/2 < -3/2
Answer:
-5 is bigger
It is bigger because if you would convert it to a whole number it would be -1.5
Olivia works at a travel agency. She earns 7% commission her sales of airline tickets. How much does she earn when she sells 4 airline tickets, each costing $359.50
Answer:
395.5*.07=27.685* 4 = 110.74
5 Given the diagram, prove x=23.
(4x) (5x – 27)°
What is the missing numerator and denominator?
Start Fraction 4 over 14 EndFraction plus blank equals StartFraction 8 over 14 EndFraction
The missing numerator is
.
The missing denominator is
.
Which fraction represents Eight-fourteenths in lowest terms?
Answer:
the missing numerator is 4 and denominator is 4
8/14 In simpliest form is 4/7
Step-by-step explanation:
4/14+4/14=8/14
8 divded by 2=4 14 divded 2=7
help with this question
Answer:
b
Step-by-step explanation:
some1 help plz lol
The relationship between the Celsius (C) and Fahrenheit (F) scales for measuring temperature can be represented by a linear function. A temperature of 50 °F corresponds to 10 °C, and a temperature of 212 °F corresponds to 100 °C.
Which statement is the best interpretation of the slope of the graph of this function?
Question 1 options:
For each change of one degree in the Fahrenheit scale, there is a change of 59
5
9
degree in the Celsius scale.
A temperature of 0 °F corresponds to -17.78 °C.
A temperature of 0 °C corresponds to 32 °F.
For each change of one degree in the Fahrenheit scale, there is a change of 95
9
5
degree in the Celsius scale.
The slope is 9/5, this means that for each change in degree in the Celsius scale there is a change of 9/5 degree in the Fahrenheit scale.
The y intercept is 32, this means that a temperature of 0 °C corresponds to 32 °F
A linear equation is given by:
y = mx + b
where y, x are variables, m is the slope of the graph and b is the y intercept.
Let F represent the temperature in Fahrenheit and C represent the temperature in Celsius.
50 °F corresponds to 10 °C it is given as (10, 50), while 212 °F corresponds to 100 °C, it is given as (100, 212). Hence:
[tex]F-F_1=\frac{F_2-F_1}{C_2-C_1} (C-C_1)\\\\\\F-50=\frac{212-50}{100-10}(C-10) \\\\\\F-50=\frac{9}{5}(C-10) \\\\\\F=\frac{9}{5}C+32[/tex]
The slope is 9/5, this means that for each change in degree in the Celsius scale there is a change of 9/5 degree in the Fahrenheit scale.
The y intercept is 32, this means that a temperature of 0 °C corresponds to 32 °F
Find out more at: https://brainly.com/question/13911928
need help with 1,2,3
13 points
Answer:
1
function yes
domain 1,2,3,4,5,6,7,8
range 2,3,4,5,6,7,8,9
2
function no
domain 0,1,1,2,3
range 9,9,7,5
Write the equation of the line in slope intercept form
Answer:
y = 2x + 1
Step-by-step explanation:
Find the solution to the above system (answer is an ordered pair):
Answer:
x
=
9
,
y
=
1
Explanation:
Adding both equations we get
2
x
=
18
so
x
=
9
and we get for
y
9
+
y
=
10
y
=
1Step-by-step explanation:
(1,4) and (6,-1) in slope intercept form
Answer:
[tex]Y = -X+5[/tex]
Step-by-step explanation:
To find the slope you need to do [tex]m = \frac{y2-y1}{x2-x1}[/tex]
Using that formula you will get [tex]m = -1[/tex]
Now you need to use the slope -1 and a given point (1,4) to substitute for x1 and y1 in point slope form
[tex]y-4 = -1*(x-1)[/tex]
now you need to solve for y
and you get....
[tex]y= -x + 5[/tex]
What is the estimate product of 210×733.
Answer:
153930
Step-by-step explanation:
Solve each system of linear equations by substitution
Answer:
x=-6-3y/2
Step-by-step explanation:
Name the scale of the number line shown. 9 13 17 21 25 29
(please hurry)
Answer:
The answer is 4 because the difference of two numbers is 4.
Write an equation of slope intercept form for the line that passes through (-4,2) with a slope of 3
what's 9 + 10?
Choose the item that applies to the sentence.
order in which actions occur
Answer:
19
Step-by-step explanation:
A hand-held digital music player was marked down by 1/4 of the original price. If the sales price is $200. What is the original price?
Group of answer choices
$266.67
$270.00
$225.00
$250.00
Someone plz help me :(
Answer:
option (A) is correct 360minutes
Please answer this as soon as possible!! Please and thank you!
Answer:
D
Step-by-step explanation:
If the condition like the symbol which on the graph
Solve
14(x-2) +3(x+5) _3(x+8) +5
Answer:
14x - 32Step-by-step explanation:
Solve
14*(x-2) +3*(x+5) -3*(x+8) +5 =
14x - 28 + 3x + 15 - 3x - 24 + 5 =
14x - 32
urgent sil vous plaît
Answer:
27 and 64
Step-by-step explanation:
(URGENT BIG REWARD!) SOLVE FOR X
x2 - 3|x - 2| - 4x = - 6
x=4,3,0,1
Hope this helped :)
HELP QUICK
The interest rate at a bank is 5.5%. Which decimal is equivalent to 5.5%
5.5
0.55
0.055
0.0055
Answer:
0.055
Step-by-step explanation:
You want to move the decimal from the % left two places.
Answer:
005
Step-by-step explanation:
which graph has a a Y intercept of negative one over two
Answer:
B.
Step-by-step explanation:
8 foot long piece of wood each piece is 5/6 foot long.What is the greatest number of wood
Answer:
The greates amount of pieces he would be able to use would be 9 because 8 divided by 5/6= 9 and 3/5.the 3/5 piece is too short.
Step-by-step explanation:
Solve the problem. At a lumber company, shelves are sold in 3 types of wood, 3 different widths and 6 different lengths. How many different types of shelves could be ordered
Answer:
54
Step-by-step explanation:
3*3*6=54
Rewrite 3.768 – 1.2 to make the divisor a whole number. Select the answer choice that shows the correct setup for long division and answer. O A. A. 12) 3.768 = 3.14 O B. 12) 3.768 = 0.314 O c. 12) 37.68 = 3.14 O D. 12) 37.68 = 3.41 SUBMIT
Answer:
Step-by-step explanation:
That answer is: 12 divided by 37.68 = 3.14
What is the value of 6(2b-4) when b=5?
Answer:
36
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
6((2)(5)−4)
=(6)((2)(5)+−4)
=(6)((2)(5))+(6)(−4)
=60−24
=36
The sum of three numbers is 164. The second number is 3 more than twice the first number, and the third number is four times the first number. What are the three numbers
Answer:
23, 49, and 92
Step-by-step explanation:
three numbers x, y, z
x+y+z=164
y=2x+3
z=4x
we have three equations and two of them are in terms of x so we can solve for x first by plugging in the two equations to our first equation
x+2x+3+4x=164
7x+3=164
7x=161
x=23
then find y
y=2(23)+3=46+3=49
then find z
z=4(23)=92
Mr. Walker is looking at the fundraiser totals for the last five years. A 2-column table with 5 rows. The first column is labeled year with entries 1, 2, 3, 4, 5. The second column is labeled total (in dollars) with entries 896, 925, 880, 963, 914. How does the mean of the totals compare to the median? The median is $1. 60 greater than the mean.
Answer: B
Step-by-step explanation: edge
