The dimensions that would guarantee that the garden has the greatest possible area is 190 feet on the shorter side and 380 feet on the longer side to produce an area of 72,200 square feet.
A dimensions of a rectangle is the length of each side.
Let x = length of the shorter side
y = length of the longer side
If one side of the garden is bordered by a river and so it does not need any fencing, and assume that the longer side is this side, then the perimeter that only needs to be fenced by 760 feet of fencing materials is
2x + y = 760
y = 760 - 2x
The area of the rectangular garden is the product of the shorter side and the longer side of the garden. Hence,
A = xy
A = x(760 - 2x)
A = 760x - 2x²
To obtain the largest area possible, the first derivative of the area should be equal to zero.
A(x) = 760x - 2x²
A'(x) = 0
760 - 4x = 0
Solve for x.
760 - 4x = 0
4x = 760
x = 190
length of the shorter side = 190 feet
y = 760 - 2x
y = 760 - 2(190)
y = 380
length of the longer side = 380 feet
Solve for the greatest possible area.
A = xy
A = 190 feet(380 feet)
A = 72,200 square feet
" A gardener has 760 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. What dimensions would guarantee that the garden has the greatest possible area? "
Learn more about area of rectangle here: https://brainly.com/question/28383419
#SPJ4
The directions on a seed packet say to plant the seeds 1 7/8 inches apart. What is the decimal equivalent of this mixed number?
Enter your answer in the box.
Answer:
1 7/8 inches is 1.875 in decimal form.
Which postulate could we use to prove that the angles
The postulate that could be used is the: linear pair postulate.
What is the Linear pair Postulate?If two angles share a common side and also a common vertex lie on a straight line, they both form a special angle relationship that is called the linear pair.
Based on the linear pair postulate, it is proven that angles that form a linear pair add up to 180 degrees and are therefore regarded as supplementary.
Angle CAD and angle CAB have a common side, side CA, and a common vertex, angle A. They are also on the straight line, line AB.
Thus, it can be proved that the angles CAB and CAD are supplementary based on the linear pair postulate.
Learn more about linear pair postulate on:
https://brainly.com/question/13890989
#SPJ1
What is the probability of
spinning an A?
B B
A
B
A
[?]%
Answer:
I believe you have a 25% of spinning an A
Step-by-step explanation:
If there are two possible A's to land on and there are 8 different choices,
2/8 = 1/4 and 1/4 is equal to 25%
So the probability would be "not likely"
Hope this helps! Please have an amazing day! :)
Solve {2c+8}={10c} . Answer in simplest fraction form.
Answer: c=1
Step-by-step explanation:
Move the variable to the left side
2c+8−10c=0
Subtract the terms
−8c+8=0
Move the constant to the right side
−8c=0−8
Subtract the terms
−8c=−8
Divide both sides
−8c = −8
−8 -8
Simplify
For each ordered pair, determine whether it is a solution to 5x + 2y = -1. (x, y) (1, − 3) (2,8) (-4, -6) (-3,7) what is the soulsion
The following ordered pairs are the solutions to 5x+2y=-1 :
(1,-3) and (-3,7)
Given we have the ordered pairs and the equation.
To find out whether the ordered pair is a solution or not, we just need to replace the x and y values from the ordered pair (x,y) and check if both the sides equate.
a. (1,-3)
5x+2y=-1
5(1)+2(-3) = -1
consider L.H.S
5-6
= -1
Therefore, L.H.S = R.H.S
hence the ordered pair (1,-3) is a solution to 5x+2y=-1.
b. (2,8)
5x+2y=-1
5(2)+2(8) = -1
consider L.H.S
10+16
= 16
Therefore, L.H.S ≠ R.H.S
hence the ordered pair (2,8) is not a solution to 5x+2y=-1.
c. (-4,-6)
5x+2y=-1
5(-4)+2(-6) = -1
consider L.H.S
-20-12
= -32
Therefore, L.H.S ≠ R.H.S
hence the ordered pair (-4,-6) is not a solution to 5x+2y=-1.
d. (-3,7)
5x+2y=-1
5(-3)+2(7) = -1
consider L.H.S
-15+14
= -1
Therefore, L.H.S = R.H.S
hence the ordered pair (2,8) is a solution to 5x+2y=-1.
Therefore the ordered pairs which are solutions to 5x+2y=-1 are:
(1,-3) and (-3,7)
Learn more about Ordered pairs here:
brainly.com/question/1528681
#SPJ1
What is the equation of the line?
Answer:
Thr equation is y=x-1
Step-by-step explanation:
The y intercept is negative 1 so that eliminates options 1 and 3 and the slope goes up which leaves only option 2 left
line has an x-intercept of -5 and a y-intercept of 3. Use this information for questions
8 through 10.
8.
Find the slope of the line.
9. Write the equation of the line in slope-intercept form.
10. Write the equation of the line in standard form.
Answer:
[tex](1)\;\;\;\text{Slope }= \dfrac{3}{5}\\[/tex]
(2) Equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]
(3) Equation of line in standard form is:
[tex]5y - 3x = 15[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept
Slope = [tex]\dfrac{y2 - y1}{x2-x1}[/tex]
where (x1, y1) and (x2, y2) are two points on the line.
y2 - y1 is known as the rise
x2 - x1 is known as the run
Slope is also defined as rise/run
We are given x-intercept = -5.
The ex-intercept is the point at which the line crosses the x-axis. At this point the y-value = 0.
So we get one of the points (-5, 0)
We are given y-intercept = 3
The y-intercept is the point at which the line crosses the y-axis. At this point the x-value is 0
So another point on the line is (0, 3)
Knowing this we can compute rise and run
rise = y2 - y1 = 3 - 0 = 3
run = x2 - x1 = 0 - (-5) = 0+5 = 5
[tex](1)\;\;\;\text{Slope = $\dfrac{3}{5}$}[/tex]
(2) Equation is
y = mx + b where m = slope and b = y-intercept
Slope = 3/5 from (1) and y-intercept = 3
So equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]
(3) Equation in standard form
In (2) subtract (3/5)x from both sides.
[tex]y - \dfrac{3}{5}x = 3[/tex]
We can multiply both sides by 5 to get
[tex]5(y - \dfrac{3}{5}x )= 5 \times 3\\\\= 5y - 3x = 15[/tex]
we know that on average the time it takes to complete a homework assignment is 2.3 hours with a standard deviation of .5 hours. with 13 students in the class, the average to complete the homework was 1.5 hours. what is the percentile of this class
In standard deviation, 120 is the percentile of this class.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.Test statistic (z) = (weekly study time - average study time)/standard deviation
weekly study time = 2.3 hours
average study time = .5 hours
standard deviation = 1.5 hours
z = (2.3 - 0.5)/1.5
= 1.8/1.5 = 1.2 (to 2 decimal places)
Cumulative area of the test statistic is 1.2
Percentile = 1.2×100 = 120
Learn more about standard deviation
brainly.com/question/15199375
#SPJ4
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer in simplest form. ( wouldn't allow me to insert full picture. will message it to you.)
To find the scale factor, we just have to divide
[tex]\frac{8}{20}=\frac{2}{5}[/tex]Hence, the scale factor is 2/5.soyala went to the college traveling 25 mph and returned home traveling 15 mph. if the total trip took 8 hours, how long did soyala travel at each speed?
Soyala travelled for 3 hours with a speed of 25 mph and 5 hours with a speed of 15 mph
We know that Distance = Rate x Time. The distance traveled to the library is assumed to be same as the distance traveled on the way to home from the library. Let t be the time it took to travel to the library after which (8 - t) = the time it took to travel back home. We can write following two equations using the formula for distance:
d = 25t ---------> (1)
d = 15(8 - t) = 120 - 15t -----------> (2)
Since the distance d is equal for both trips, let's set the two expressions of time t equal to each other.
25t = 120 - 15t
40t = 120
t = 3 hours
Therefore, Soyala travelled for 3 hours at 25 mph and for 8 - 3 = 5 hours at 15 mph. Each rate will yield a distance traveled of 125 miles.
To learn more about Distance click here:
brainly.com/question/19773192
#SPJ4
Question content area top Part 1 The temperature in a town is 31.6 during the day and -17.2 at night. Find the difference in the temperatures.
Answer: The difference in temperature is 45.9F.
Sandra Keegan worked 38 hours at $12.95 per hour and 6 hours of overtime at time and a half what was her pay for the week?
Answer:
$569.80
Step-by-step explanation:
She worked $12.95 per hour for 6 hours of overtime, meaning we would multiply $12.95 by 6 which is equal to $77.70, since she worked for 38 hours that week, we would multiply $12.95 by 38 which is $492.10, so now we add how much she earned for the total. Her overtime pay was $77.70 + her regular pay was $492.10 which adds up to $569.80
How to draw two equilateral triangles that are not congruent
No, it is not feasible to produce any two structuring elements that is not always congruent with one another. This is because equilateral triangles have no internal angles.
This is further explained below.
What is an equilateral triangle?Generally, In the field of geometry, a triangle is said to be equilateral if all three of its sides have the same length.
In the well-known geometry of Euclidean, an equilateral triangle is also an equiangular triangle. This means that all three of the triangle's interior angles are equivalent to each other and are each 60 degrees.
No, it is not possible to create any two equilateral triangles that are not always congruent with one another.
In conclusion, The logic for this is that while each angle in an equilateral triangle is 60 degrees, the sides of the triangle cannot always be identical.
Read more about equilateral triangles
https://brainly.com/question/3461022
#SPJ1
What is the slope of the line that passes through the points (10, 8) and
(7, 14)? Write your answer in simplest form.
Answer:
Formula for slope is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).
Slope of line = (14-8)÷(7-10)
= 6÷(-3)
= -2
The slope of MN¯¯¯¯¯¯¯ is −6. what segments are parallel to MN¯¯¯¯¯¯¯?
The slope of the parallel line to line MN -6
How to determine the slope of the line?From the question, the line is given as
Line MN
Also, we have the slope of line MN to be
Slope of MN = -6
As a general rule in linear functions and parallel lines
The slopes of parallel lines are equal
This means that any line that is parallel to the line MN and the line MN would have the same slope of -6
Hence, the slope of the line segments that are parallel to line MN is -6
Read more about slopes at
https://brainly.com/question/3493733
#SPJ1
-3x+14-11+11x I tried getting help with this question and it didn’t give me enough information to fully understand.
Answer:
0.375
Step-by-step explanation:
-3x+14-11+11x
-3x+11x = 8x
14-11 = 3
8x=3
÷8 on both sides
if 2 x 2 whats the divided by -3 to 4
Answer:its 2
Step-by-step explanation:
what set of numbers dose -17 belong to?
A. integers, rational numbers, real numbers
B. rational numbers, real numbers
C. whole numbers, integers, real numbers
D. whole numbers, integers, rational numbers, real numbers
A
-------------------------------------------------------
bc it is an integer but not whole numbers
The relationship between the number of $4 lunches you buy with a $105 school lunch card and the money remaining on the card
The relationship will be a solid line.
How many $4 meals you may purchase with a $100 school lunch card and how much money is still on the card.
Given that the slope is common and linear, the connection will be a solid line. The balance on the card will drop by $5 each time you purchase lunch.
Let x be the amount of lunches you purchase.
Let the balance on the card be = y.
Equation then becomes:
y= 105-4x
when x=1
y = 105 - 4(1) = 101
when x= 2
y= 105 - 4(2) = 97
when x=3
y= 105 - 4(3) = 93
We can see that the decline is gradual and same.
On the graph that is provided, you can also observe that a straight line is created.
To know more about graph refer to https://brainly.com/question/4917542
#SPJ1
In a class of 25 students, 13 are female and 15 have an A in the class. There are 10 students who are female and have an A in the class. What is the probability that a student has an A given that the student is female?
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
25 students in total.
13 are female. therefore, 25-13 = 12 students are male.
15 students have an A.
10 students are female and have an A.
therefore, 15-10 = 5 male students have an A.
"given that a student is female".
this reduces our totally possible cases to 13.
so, the probability that a female student has an A is
10/13 = 0.769230769...
What is equivalent to 0.325 in as a fraction
Answer:
0.325 as a fraction is expressed as 13/40
Step-by-step explanation:
What is a fraction ?
A fraction is a portion of any quantity out of a whole. It consists of a numerator and a denominator.
To convert a decimal number into a fraction, we write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly. Then, this fraction can be simplified.
In this case, 0.325 has three numbers after the decimal, so, we place 1000 in the denominator and remove the decimal point.
⇒ 325/1000
After reducing this fraction we get,
⇒ (325 ÷ 25) / (1000 ÷ 25) = 13/40
So, 0.325 as a fraction is 13/40.
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
Please help me with this question, if it’s wrong I will report you, thank you for your help!
IN THE ATTACHED PICTURE YOU CAN SEE THE YELLOW VERTICAL LINE TOUCHED THE GRAPH ONCE IT MEANS THE GRAPH ABOVE IS A FUNCTION.
THEREFORE THE LAST OPTION IS THE SOLUTION. THE GRAPH IS A FUNCTION BECAUSE IT PASSES THE VERTICAL LINE TEST .
HOPE THIS HELPS
Determine whether the given function is even, odd or neither. *(1 Point)f(x) = x3 - 2x
Given:
The function is,
[tex]f(x)=x^3-2x[/tex]Replace x by -x in the given function,
[tex]\begin{gathered} f(x)=x^3-2x \\ f(-x)=(-x)^3-2(-x) \\ =-x^3+2x \\ =-(x^3-2x) \\ =-f(x) \end{gathered}[/tex]It is observed that, when the x is replace by -x the function end up with exactly opposite of the given function.
Thus, the given function is odd.
3/4 + 1/3 as a fraction
Answer:
Step-by-step explanation:
Answer:1 1/12
Step-by-step explanation: 3/4+1/3=13/12=1 1/12
how does x equal y in three dimesional math
Step-by-step explanation:
in 3-dimensional math we have 3 dimensions, and not just 2.
we have
forwards - backwards
left- right
up- down
so, we have there x, y and z.
and the equations typically are
z = ax + by
or even more general
cz = ax + by
or more complex functions of x and y.
z = f(x, y).
I am not sure what else you could mean with that question.
For Items 12–14, use the figure shown.
Two vertical parallel lines are intersected by two diagonal transversals, one slanting up and one slanting down. They intersect the left line at the same point, creating 6 angles, starting at the bottom left of the right line and moving clockwise, they are: 3, 2, 1, left parenthesis 4 y times 3 right parenthesis, left parenthesis 3 x times 9 right parenthesis, and left parenthesis 5 x right parenthesis. The line slanting up intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 6, 4, 5, and left parenthesis 9 x times 3 right parenthesis. The line slanting down intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 8, 7, left parenthesis 7 y times 6 right parenthesis, and 9.
What is m∠2?
A. 12
B. 18
C. 45
D. 120
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
To know more about lines refer to https://brainly.com/question/18831322
#SPJ1
What is the slope of the line that passes through the points (7,-6) and (6, -6)
Write your answer in simplest form
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, - 6 ) and (x₂, y₂ ) = (6, - 6 )
m = [tex]\frac{-6-(-6)}{6-7}[/tex] = [tex]\frac{-6+6}{-1}[/tex] = [tex]\frac{0}{-1}[/tex] = 0
Andrew would like to put six different Rubik's cubes onto 3 shelves. The order of the cubes does not matter.
In how many ways can Andrew do this if a shelf can have zero cubes?
What if each shelf must have at least one cube?
Answer:
540
Step-by-step explanation:
help please
What is the correct way to break 12 into parts and multiply each part by 6?
Answer:
2nd one
Step-by-step explanation:
Hope I helped!
HELPHELPHELPHELP plssssssssssssssssssssssss