A pool measuring 8 meters by 24 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 720 square meters, what is the width of the path? 8 + 2x 8 24 - 2x
The Width of the path is ____ meters
Answers
The real answer is 6
Step-by-step explanation:
the width of the path is 6 meters.
Let's assume the width of the path is represented by 'x' meters.
The overall dimensions of the combined pool and path would be:
Width = 8 + 2x
Length = 24 + 2x
To calculate the area of the combined pool and path, we multiply the width and length:
Area = (8 + 2x) * (24 + 2x)
Given that the area is 720 square meters, we can set up the equation:
(8 + 2x) * (24 + 2x) = 720
Expanding the equation:
192 + 16x + 48x + 4x² = 720
4x² + 64x + 192 = 720
Rearranging the equation:
4x² + 64x - 528 = 0
Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. After solving the equation, we find that x = 6.
Therefore, the width of the path is 6 meters.
Learn more about Area here
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Related Questions
I’m taking my dog to get groomed in the morning
Answers
The monthly utility bills in a city are normally distributed, with a mean of $ and a standard deviation of $. Find the probability that a randomly selected utility bill is (a) less than $, (b) between $ and $, and (c) more than $. (a) The probability that a randomly selected utility bill is less than $ is 0.0076. (Round to four decimal places as needed.) (b) The probability that a randomly selected utility bill is between $ and $ is 0.6859. (Round to four decimal places as needed.) (c) The probability that a randomly selected utility bill is more than $ is 0.0764. (Round to four decimal places as needed.)
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(X < 65) = 0.003467[/tex]
b
[tex]P(86 < X < 110 )= 0.63928 [/tex]
c
[tex]P(X > 120 ) =0.062024[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$ 100[/tex]
The standard deviation is [tex]\sigma = \$ 13[/tex]
Generally the probability that the monthly utility bills is less than $65 is mathematically represented as
[tex]P(X < 65) = P(\frac{X - \mu }{\sigma } < \frac{65 - 100 }{13 } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The\ standardized \ value \ of\ X )[/tex]
So
[tex]P(X < 65) = P(Z < -2.70 )[/tex]
From the z-table
[tex]P(Z < -2.70 ) = 0.003467[/tex]
So
[tex]P(X < 65) = 0.003467[/tex]
Generally the probability that a randomly selected utility bill is between $86 and $110 is mathematically represented as
[tex]P(86 < X< 110 )= P( \frac{86 -100}{ 13} < \frac{X - \mu}{\sigma } < \frac{86 -100}{ 13} )[/tex]
=> [tex]P(86 < X < 110 )= P( \frac{86 -100}{ 13} < Z < \frac{110 -100}{ 13} )[/tex]
=> [tex]P(86 < X < 110 )= P(-1.08 < Z < 0.77 )[/tex]
=> [tex]P(86 < X < 110 )= P(Z < 0.77 ) - P(Z < -1.08 ) [/tex]
From the z-table
[tex]P(Z < 0.77 ) = 0.77935[/tex]
and
[tex]P(Z < -1.08 ) = 0.14007[/tex]
So
[tex]P(86 < X < 110 )= 0.77935 - 0.14007 [/tex]
=> [tex]P(86 < X < 110 )= 0.63928 [/tex]
Generally the probability that the monthly utility bills is more than $120 is mathematically represented as
[tex]P(X >120 ) = P(\frac{X - \mu }{\sigma } > \frac{120 - 100 }{13 })[/tex]
=> [tex]P(X > 120 ) = P(Z > 1.538 )[/tex]
From the z-table
[tex]P(Z > 1.54 ) = 0.062024[/tex]
So
[tex]P(X > 120 ) =0.062024[/tex]
please help asap.. 15 points!
Answers
Answer:
the answer is b
Step-by-step explanation:
C
B
120
...
...
900
.
.60
140-
350
450400
180
Ray OB divides 2 COA into two angles of equal measure.
True
False
Answers
Consider a number line with 40, 60 and 80 marked.
The value 60 is the midpoint of 40 and 80 since (40+80)/2 = 120/2 = 60
If we curved the number line to fit along the round edge of the protractor, then we'll get the diagram you see here.
Ray OB cuts angle COA in two equal pieces (angle COB, angle BOA). This is another way of saying "ray OB bisects angle COA".
what is the reflection of (5, -3.5) across x-axis
Answers
Answer:
(-5,-3.5)
Step-by-step explanation:
Answer:
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located.
Step-by-step explanation:
If (44)x = 432, what is the value of x?
Answers
Answer:
about 9.82
Step-by-step explanation:
i just divided 432 by 44 in order to isolate x
i hope that correct ans helps
Answer:
x = 9 ⁹/₁₁Step-by-step explanation:
(44)x = 432
divide both side by 44
x = 432 / 44
x = 9 ⁹/₁₁
Kimberly has a credit card with a 19% APR and a balance of $4,350. With her current monthly payment, Kimberly will be
able to pay off the credit card in a mere 16 months. But when Kimberly's car breaks down, she is forced to charge an
additional $1,600 to her credit card. How much will Kimberly's minimum monthly payment increase if she still wants to
pay off her credit card in 16 months?
a.
$100.00
b. $113.99
C. $309.90
d. $423.89
Mom
Answers
Answer:
B. $113.99
Step-by-step explanation:
when seventeen is reduced by two-thirds of a number, the result is 11
Answers
Answer:
9Step-by-step explanation:
Let the number be x, then:
17 - 2/3x = 112/3x = 17 - 112/3x = 62x = 6*32x = 18x = 18/2x = 9I have to do step by step why the answer of (5x - 1) (5x - 1) is 25x^2 - 10x + 1.
How do i do it?
(5x - 1) (5x - 1)
Ans: 25x^2 - 10x + 1
Answers
Answer:
(5x - 1)(5x - 1) = 25x² - 10x + 1
Step-by-step explanation:
Let us solve the question step by step
We need to find the product of (5x - 1) and (5x - 1)
The first step multiply 1st term in 1st bracket by 1st term in 2nd bracket (5x by 5x)∵ 5 × 5 = 25
∵ x × x = [tex]x^{1+1}[/tex] ⇒ multiply same base means add their powers
∴ x × x = x²
∴ 5x × 5x = 25x²
The second step multiply 1st term in 1st bracket by 2nd term in 2nd bracket (5x by -1)∵ 5x × -1 = (5 × -1)x
∴ 5x × -1 = -5x
The third step multiply 2nd term in 1st bracket by 1st term in 2nd bracket (-1 by 5x)∵ -1 × 5x = (-1 × 5)x
∴ -1 × 5x = -5x
The fourth step multiply 2nd term in 2nd bracket by 2nd term in 2nd bracket (-1 by -1)∵ -1 × -1 ⇒ (-)(-) = (+)
∴ -1 × -1 = 1
The fifth step add them up∵ (5x - 1)(5x - 1) = 25x² + -5x + -5x + 1
∵ -5x and -5x are like term, then add their coefficients
∵ -5x + -5x = (-5 + -5)x
∴ -5x + -5x = -10x
∴ (5x - 1)(5x - 1) = 25x² + -10x + 1
∵ (+)(-) = (-)
∴ (5x - 1)(5x - 1) = 25x² - 10x + 1
PLEASE PLEASE PLEASE HELP. This is a geometry worksheet.
Answers
Answer:
where's the question?
A boat is 2000m from a cliff. If the angle of depression from the top of the cliff to the boat is 10 degrees, how tall is the cliff.
Answers
Answer:
Let AB is the height of the cliff = H and p is the posit ion of the boat.Angle of depression= angle of elevation= 15 degrees therefore angle APB= 15 degrees tan 15=AB=h/1,000 h=(1,000)*tan 15=(1,000)(0.26794919243112)=268.94919243112 meters or
Simply: 268meters..........Ans
-4(3x + 2) =
what is it I need it as fast as you guys can please help
Answers
Answer:
-12x-8
Step-by-step explanation:
Use Math Way
Answer:
-12x-8
Step-by-step explanation:
-4(3x+2)
-4*3x= -12
-4*2=-8
I will give you branilest!
What equation could you use to find the total entrance cost for a vehicle with any number of people?
Answers
Answer:
You are correct, and you could also write an expression where m = money, p = people, and v = vehicle
m · p · v = ___
I hope this helps you ^‿^
What is the Reciprocal of 10/3
Answers
Answer:
3/10
Step-by-step explanation:
If you flip 10/3 you get 3/10
8/9 + 4/9 simplify answer and write as a mixed number
Answers
Answer: 1 1/3
Step-by-step explanation: Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
Hope this Helps :3
Step-by-step explanation:
Hey there!
Given;
[tex] = \frac{8}{9} + \frac{4}{9} [/tex]
Adding them.
[tex] = \frac{8 + 4}{9} [/tex]
[tex] = \frac{4}{3} [/tex]
Change into mixed number.
[tex] = 1 \frac{1}{3} [/tex]
Hope it helps....
Write the product as a power:
(a–b) (a–b)
Answers
Answer:
(a - b)²
Step-by-step explanation:
We are given 2 (a - b) terms.
We can rewrite this as (a - b)².
HELP PLS helppppppppppppppppppppppppp
Answers
Answer:
The number of text messages is 85 ⇒ B
Step-by-step explanation:
To solve this question
Assume that the number of the text message is x and the total cost is yMake a linear equation represented each plan, then equate their total cost (y) to find the number of the text message (x)The form of the linear equation is y = m x + b, where
m is the rateb is the initial valuePlan A:
∵ The fee per message is $0.10
∴ m = 0.10
∵ The monthly fee is $35
∴ b = 35
∴ The total cost y = 0.10 x + 35
Plan B:
∵ The fee per message is $0.30
∴ m = 0.30
∵ The monthly fee is $18
∴ b = 18
∴ The total cost y = 0.30 x + 18
∵ Both plans cost is the same for one month
→ Equate the right sides of the two equations
∴ 0.30 x + 18 = 0.10 x + 35
→ Subtract 0.10 x from both sides
∴ 0.30 x - 0.10 x + 18 = 0.10 x - 0.10 x + 35
∴ 0.20 x + 18 = 35
→ Subtract 18 from both sides
∴ 0.20 x + 18 - 18 = 35 - 18
∴ 0.20 x = 17
→ Divide both sides by 0.20
∴ [tex]\frac{0.20x}{0.20}=\frac{17}{0.20}[/tex]
∴ x = 85
∴ The number of text messages is 85
Which Function is represented in the graph?
Answers
Answer:
B
Step-by-step explanation:
The part of the function where x <=2 is a line, so we can rule out C and D. Lastly, the part of the function where x<=2 has a slope of -2, so we can rule out A. That leaves us with the only possible answer B
HELP PLZ I DONT HAVE MUCH TIME!!! 38PTS IS ALL I HAVE PLS ANSWER CORRECTLY!!!
In Ms. Miller's English class, students are given five tests in a semester. At the end of the semester, the scores that a student has earned on the five tests are averaged to obtain that student's class average. So far, DeShawn has taken the first four tests, and his scores are 71%, 90%, 82%, and 77%. Which of the following is the range of all the class averages that DeShawn could possibly receive at the end of the semester?
Answers
Answer:
The range is 81
Step-by-step explanation:
Please put the following numbers in order from smallest to largest: 12% 4/28 0.15
Answers
12%, 4/28, 0.15
Pretty simple.
Answer:
12%<4/28<0.15
Step-by-step explanation:
12%=0.12
4/28=1/7=0.143
0.15
the number of 8 x 10 to the 11th power is what
Answers
Answer:
800000000000
Step-by-step explanation:
simplify
start with 10 to the 11th power=
100000000000
then *8 =
800000000000
Translate the sentence into an equation.
Eight times the sum of a number and 9 equals 5.
Use the variable x for the unknown number.
Answers
Answer:
8(x +9) = 5
Step-by-step explanation:
The words "the sum of a number and 9" mean "x+9" when x is used to represent the number. The "8 times the sum" is 8(x+9). When that "equals 5", then we have the equation ...
8(x +9) = 5
A proportion often shows the relationship between:
Answers
Answer:
It compares two numbers that can represent many of things. For example, people, food & items.
Step-by-step explanation:
the slant asymptote of f(x)=(x^2-4x+1)/(2x-3)
Answers
Answer:
y=1/2x-5/4
I hope this helps you and I hope you do well on whatever you are working on.
Answer:
True
Step-by-step explanation:
what is the slope of f(x)=12x-19
Answers
Answer: y=1/4+3
Step-by-step explanation:
1. The slope is 12
2. (6 - 2)/(12+4)= 4/16= 1/4
y - 2 = 1/4(x + 4)
y - 2 = 1/4x + 1
y = 1/4x + 3
Calculate the circumference of a rug having a diameter of 8ft
Answers
Answer:
C= 25.13ft
Step-by-step explanation:
To find the circumference use the formula C=2 * PI * R
we know that the diameter is 8 which means that the radius is half that amount therefore R=4
Now plug those numbers into the formula
C=2(pi)(4)
= 8(pi)
=25.13
Write the converse of the following conditional: If it is raining, then the ground is wet.
If it is not raining, then the ground is not wet.
If it is not raining, then the ground is not wet.
It is raining if and only if the ground is wet.
It is raining if and only if the ground is wet.
If the ground is not wet, then it is not raining.
If the ground is not wet, then it is not raining.
If the ground is wet, then it is raining.
Answers
Answer:
it is raining if and only if the ground is wet
Step-by-step explanation:
Answer:
you are correct
Step-by-step explanation:
A carton contains 5 1/2 cups of juice one servings is 3/4 of cup how many servings of juice are in carton
Answers
Answer:
7 1/3 servings
Step-by-step explanation:
0.75x=5.5
x=5.5÷0.75
x=7.33333
-or-
7 1/3 servings
What is the definition of supplementary angles.
Answers
Answer: either of two angles whose sum is 180°.
Step-by-step explanation:
Answer:
either of two angles whose sum is 180°
Step-by-step explanation:
Nina's garden is 4 1/5 meters long and 3/qo meters wide. What is the area of Nina's garden?
Answers
Answer: 63/50 meters^2 or in mixed number 1 13/50 meters^2
Step-by-step explanation:
area= length x width
length = 4 1/5= 21/5 . multiply the whole number with the denominator 4x5= 20 add 20 with the numerator 20+1=22
width = 3/10
21/5 x 3/10 ( multiply the denominators together)
21x3 / 5x10
= 63/50 meters^2 or in a mixed number 1 13/50 meters^2
(by the way I'm guessing you meant 3/10 and not 3/q0)