A farmer has 300 feet of fence available to
enclose a 4500 square foot region in the
shape of adjoining squares, with sides of
length x and y. The big square has sides of
length x and the small square has sides of
length y. Find x and y.
UUUULTTUUL
x= ? feet
y = ? feet
Answers
Given :
A farmer has 300 feet of fence available to enclose a 4500 square foot region in the shape of adjoining squares, with sides of length x and y.
The big square has sides of length x and the small square has sides of length y.
To Find :
The value of x and y.
Solution :
From attached figure perimeter is given by :
x + x + x + y + y + y + ( x-y ) = 300 ft
4x + 2y = 300
2x + y = 150 ...1)
Now, area is given by :
A = x² + y²
x² + y² = 4500 ...2)
Putting value of y in equation 2), we get :
[tex]x^2 + ( 150 - 2x)^2 =4500\\\\x^2 + 4x^2 + 22500-600x =4500\\\\5x^2 -600x + 18000=0\\\\x^2 - 120x +3600=0\\\\x^2-2\times x\times 60 + 60^2 =0\\\\(x-60)^2 =0\\\\x = 60\ ft[/tex]
y = 150 - ( 2× 60 )
y = 30 ft
Therefore, the value of x and y is 60 ft and 30 ft respectively.
Related Questions
1. Graham is hiking at an altitude of 14,040 feet
and is descending 50 feet each minute. Max is
hiking at an altitude of 12,500 feet and is
ascending 20 feet each minute. How many
minutes will it take Graham and Max to meet at
the same altitude ?
a. Equation:
1
2
. Solution:
2. At what altitude will Graham and Max meet?
3
Answers
Answer: Equation 1 to find the time: A₁ - r₁t = A₂ + r₂t Solve for t
14040 - 50t = 12500 + 20t t is the number of minutes
Equation 2 to find the altitude: A₁ - r₁t = A₂ + r₂t A₁ and r₁ are Grahams initial altitude and rate. Use given rates, calculated time and solve for A.
A₂ and r₂ are Max's initial altitude and rate.
They will meet in 22 minutes
They will meet at 12940 ft altitude
Step-by-step explanation: Their original heights plus/minus the altitude change per minute (rate) and the time will be equal when they meet.
14040 - 50t = 12500 + 20t subtract 12500 from both sides; add 50t to both sides.
14040-12500 = 20t + 50t
1540 = 70x
22 = t They will meet in 22 minutes.
To get the altitude where they meet, Multiply the time by the rate for each climber. Add or subtract per equation: A₁ - r₁t = A₂ + r₂t
14040 - 22(50) = 12500 + 22(20)
Graham: 22 min × 50ft/min = 1100 ft
Subtract from his starting altitude:
14040 - 1100 = 12940 ft
Max: 22 min ×20 ft/min = 440 ft
Add to his starting altitude
12500 + 440 = 12940 ft
Answer:
Answer:
M=22, hope this helps
Step-by-step explanation:
Set up Graham's altitude function A(m):
A(m) = 14040 - 50m <-- we subtract for descending
Set up Max's altitude function A(m):
A(m) = 12500 + 20m <-- we add for ascending
Set the altitudes equal to each other to solve for m:
14040 - 50m = 12500 + 20m
We type this equation into our search engine to solve for m and we get:
m = 22
Dominic invested $19,000 in an account paying an
interest rate of 6.1% compounded monthly. Assuming
no deposits or withdrawals are made, how much
money, to the nearest dollar, would be in the account
after 16 years?
Answers
Answer:
A≈50298
Step-by-step explanation:
45% of _____________is 165
Answers
Answer:
366.666666Step-by-step explanation:
Let the number be x
45% of x = 165x*45/100 = 165x = 165*100/45x = 366.666666please help its timed
Answers
Answer:
no solutions
Step-by-step explanation:
What is it? I don't understand it or know it.
Answers
Answer:
3+6n=
Step-by-step explanation:
8% as a fraction in its simplest form
Answers
Answer:
8/100 Simplified is 2/25 in it's simplest form!
Step-by-step explanation:
Hope this helps! :)
Have a great day!
The number 8 % as a fraction in the simplest from is 2/25
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as A
Now , the value of A is = 8 %
So , the equation will be
The value of A = 8 %
Now , the value 8 percentage can be written as a fraction of 100
So , the value of A will be
The value of A = 8/100
Now , on dividing the numerator and denominator by 4 , we get
The value of A = 2 / 25
So , the value of A in the simplest form of the number A is 2/25
Hence , The number 8 % as a fraction in the simplest from is 2/25
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
Evaluate (-7)2.
p l e a s e
a n s w e r
q u i c k\
Answers
Answer:
(-7)2 = -14
Step-by-step explanation:
The parenthesis basically mean "multiply". So, this is a simple equation meaning -7 x 2. And remember, anytime we multiply a positive by a negative, you get a negative. So, simply multiply 7 x 2 = 14 and add a negative sign to make the solution true. So, -7 x 2 or (-7)2 = -14
Hope this helps! If you have any additional questions, please don't hesitate to ask me or your teacher to be sure you master the subject. Also thank you for the generous points!! Stay safe and please mark brainliest!!
Answer:
-14
Step-by-step explanation:
just act as if -7 were positive then you know 7x2 = 14 cause' "()" means multiplication.
last, since 7 was negative in the first place then you turn your product back to a negative and you get -14
mark brainliest :)
A car traveled 180 miles at a constant rate. Write an equation that would make it easy to find the rate at which the car was traveling in miles per hour r, if it traveled for t hours
Answers
Answer:
A. Distance travelled at constant rate = 180 miles
Rate of travel (r) = distance travelled (d) /time (t)
Travel time (hrs) ==> rate of travel (miles/hr)
5 ==> 180/5 = 36
4.5 ==> 180/4.5 = 40
3 ==> 180/3 = 60
2.25 ==> 180/2.25 = 80
B. t = time travelled in hrs,
r = rate (miles/hr)
d = distance travelled = 180
Answer:
180/t
Step-by-step explanation:
Speed=distance/time
13
Complete the table of equivalent ratios.
9
5
10
20
25
Answers
Answer:
Step-by-step explanation:
3 6 9 12 15
5 10 15 20 25
Jeremiah sees a maple tree and a pine tree in the forest. He knows that the pine tree is
21.65 feet tall. On a sunny day, the shadow of the pine is 4.1 feet long while the maple's shadow is 15.01 feet long. Estimate the height of the maple tree.
Answers
Answer:
The height of the tree is
18.67
feet
step explanation: i probably got it wronggggg
The area of the parallelogram below is _____ square meters.
Numerical answers expected!
Answers
Answer:
48
Step-by-step explanation:
Answer:
Yes, the correct answer is 48, the person above me is right :)
Step-by-step explanation:
6 x 8 = 48
There are 12 circles and 15 triangles. What is the simplest ratio of circles to triangles
Answers
Answer:
4:5
Step-by-step explanation:
solve the right angle trig problem.
Answers
Answer:
x = 9.23919
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tan∅ = opposite over adjacentStep-by-step explanation:
Step 1: Define
We are given a right triangle. We can use trig to find the missing length.
Step 2: Identify Variables
POV from the angle measure
Angle = 57°
Opposite = x
Adjacent = 6
Step 3: Solve for x
Substitute: tan57° = x/6Isolate x: 6tan57° = xEvaluate: 9.23919 = xRewrite: x = 9.239199514 1404 393
Answer:
x ≈ 9.24H ≈ 11.02Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships.
Tan = Opposite/Adjacent
tan(57°) = x/6
x = 6·tan(57°) ≈ 9.24
__
The complete solution of the triangle will also find a value for H.
Cos = Adjacent/Hypotenuse
cos(57°) = 6/H
H = 6/cos(57°) ≈ 11.02
_____
Comment on the figure
We note that, in relation to the given angle, the markings O and A are reversed. The side labeled 6 is adjacent (A) to the marked angle, and the side labeled x is opposite (O) to the marked angle.
If two angles of a traingle measure 54° and 77° what is the measure of the third angle
Answers
Answer:
49°
Step-by-step explanation:
The total sum of angles in a triangle is 180°. You already know two of the angles, so you can find the last one.
Third angle = 180° - 54° - 77°
= 49°
Describe the transformation of the graph y = (x)^3 + 6
Answers
The graph of y = x^3 + 6 is the result of shifting y = x^3 up 6 units
If f(x) = x^3, then g(x) = f(x) + 6 leads to g(x) = x^3+6.
The reason we shift up 6 is because we're adding 6 to the y coordinate.
Think of y = f(x), so f(x)+6 is the same as y+6.
What is the slope for this (-1,5) (2,-4)
Answers
Answer:
Slope = -[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
To find the slope, you have to calculate the rise over run between two points.
[tex]\frac{rise}{run}[/tex] = [tex]\frac{2-(-1)}{(-4)-5}[/tex]
= [tex]\frac{3}{-9}[/tex]
= -[tex]\frac{1}{3}[/tex]
what 25 time 358 divided by 1.6
Answers
Answer:
5593.75
Step-by-step explanation:
A number x with an exponent of -n means
blank. a) Find the nth root of x
b) Find the xth root of n
c) Take the reciprocal of x
d) Take the reciprocal of x to the nth power
Answers
Answer:
C) Take the reciprocal of x
Step-by-step explanation:
That's my answer
This month, a marching band has 60 musicians. If the number of musicians in the band last month was 51 members, what percent of increase was this? (Round to the nearest percent)
Answers
Answer: Happy holidays!
We need to solve for x
Answers
The height h of a square pyramid can be determined from the equation h = l2−(s2)2−−−−−−−−√ , where l is the slant height of the pyramid and s is the side length of the square base. What is the slant height l of the square pyramid shown?
Answers
Answer:
I believe the answer is 34 cm (I may be wrong but I'm 98% that my answer is correct)
Step-by-step explanation:
(excuse my handwriting on the ss its hard to write on a computer lol)
hope this helps :)
Is y=4x+6 a proportional relationship?
Answers
The answer is proportional
what is 3231.07607315 rounded two decimal places
Answers
Answer:
3231.08
Step-by-step explanation:
6 rounds up
Answer:
3231.08
Step-by-step explanation:
Help pls
Solve one step equation
-6x - 13 =23
Answers
Answer:
x=-6
Step-by-step explanation:
Answer:
x = -6
Step-by-step explanation:
move the 13 to the right side of the equation
-6x = 36 and the divide by -6
x= -6
Solve for w. 57 =4w + 13 Simplify your answer as much as possible.
Answers
Step-by-step explanation:
57=4w+13
57-13=4w
44=4w
w=11
Which pair of angles must be supplementary?
O 1 and 6
O 2 and 5
O 5 and 4
O Z6 and2
Answers
Where’s the image? There has to be an image showing the angles to see which pairs of angles are supplementary.
What is value of 1/3 ÷ 1/12 *
4
1/4
1/36
1/6
Answers
Answer:
its the first one 4
ldentify the type of function represented by f(x)= 3(1.5)x.
A. Linear
B. Quadratic
C. Exponential decay
D. Exponential growth
Answers
Answer:
the function is represented by linear because the units are the same
I will give lotta points and brainly, find the area and plz make it correct
Answers
Answer:
The area of what?? Is there a picture or something to go with this...
Step-by-step explanation:
Also the area of a rectangle, square, or parallelogram is Base x Height
The area of a triangle is (base x height) ÷ 2
The area of a circle is πr²
The area of a hexagon is ([tex]\frac{3\sqrt{3} }{2}[/tex]) x length of 1 side
The area of a trapezoid is [(base 1 + base 2) ÷ 2] x height
If there is a shape inside of another shape, find the area of the smaller shape and subtract it from the area of the larger shape.
That's all I can do to help because I don't know what you want me to find the area of :/
Solve the following word problems using a system of equations. The sum of two numbers is 36. One number is two more than the other. Find the numbers.
Answers
Answer:
24,12
Step-by-step explanation:
suppose,
x+y=36
x=2y
2y+y=36
y=12
x=24