Answer:
400 ft^2
Step-by-step explanation:
It can be shown that a square area is the most efficient way in which to use fencing. If the area is not square, the area will inevitably be smaller.
Calculus is the tool most often used in higher math to solve optimization problems.
But the same goal can be achieved in this problem by working with constraints:
If x and y are the length and width respectively, then
2x + 2y = 80 ft, or x + y = 40, or x = 40 - y. This is one constraint.
The other constraint involves the area: A = x*y, or A = (40 - y)*y. To maximize this, we need to rewrite (40 - y)*y in standard form:
A = 40y - y^2, or, finally, A = -y^2 + 40 y. The coefficients of this quadratic are -1, 40 and 0; the axis of symmetry is thus
x = -b/ [2a], or, in this case, x = -40/[2*(-1)], or x = 20.
Thus, If x = 20, y = 20 also, proving that the shape of the enclosed yard is that of a square.
Then Mrs. L' 80 feet of fencing is sufficient to construct a 20 ft by 20 ft space, which comes out to a maximum area of 400 ft^2.
40 -
What is the slope of the line represented by the equation y = -1/2x + 1/4
Answer:
The slope is -1/2 and the y intercept is 1/4
Step-by-step explanation:
y = -1/2x + 1/4
This equation is in slope intercept form
y = mx+b where m is the slope and the y intercept is b
The slope is -1/2 and the y intercept is 1/4
what is the hcf of 12 45 and 75
Answer:
3
HCF of 12, 45 and 75 by Prime Factorization
As visible, 12, 45 and 75 have only one common prime factor i.e. 3. Hence, the HCF of 12, 45 and 75 is 3.
Step-by-step explanation:
In the triangle below, what is the sine of 60°?
site
60°
2
1
30°
13
ОА.
NI
O B. 2
O c. 1
D. VE
Answer:
[tex]{ \boxed{ \bf{formular : } \: { \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }}}} \\ \sin(60 \degree) = \frac{ \sqrt{3} }{2} \\ { \underline{ \blue{ \tt{ {beckerjnr}}}}}[/tex]
The value of expression sine of 60° is,
⇒ √3 / 2
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Triangle is shown in image.
Now, We know that;
Sin x = Opposite / Hypotenuse
Hence, We get;
⇒ sin 60° = √3 / 2
Thus, The value of expression sine of 60° is,
⇒ √3 / 2
Learn more about the triangle visit;
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SURFACE AREA PLEASE HELP
Answer:
486 yd^2
Step-by-step explanation:
Surface area is just finding the area of each face in a figure and adding it all up.
For the surface area of a cube, use this formula:
(a^2) 6
(a is the side length) a^2 is the area of one face of a cube, then multiply it by 6 since there are 6 faces on a cube.
Use formula with given dimensions:
(9^2) 6 = 486
Surface area is measured in square yards
(yards in this case)
Therefore, the surface area of the cube is 486 yd^2
Hope this helps!
factorise using suitable identities
x^2 (y+z)^2
Answer:
Step-by-step explanation:
[tex]x^2 ( y +z)^2 = x^2 (y+z)(y+z)[/tex] [tex][ \ (a+b)^2 = (a+b)(a+b) \ ][/tex]
[tex]x^2 - ( y +z)^2 = (x - ( y +z)) (x + (y+z))[/tex] [tex][ \ a^2 - b^2 = (a-b)(a+b) \ ][/tex]
[tex]=(x-y-z)(x+y+z)[/tex]
what is the solution to the equation below?
please help!!
Answer:
Have you tried photo math.? It can help you find the answer
Step-by-step explanation:
here is the answer bae. Feel free to ask for more
Lola's salary is $40,000 plus a 2% commission on all sales. The rate of change for her salary is a constant rate.
True
False
Answer:
False
Step-by-step explanation:
Helllpppp my teacher is being a chihuahua and won’t help meeeee
Answer:
the constant of proportionality is 9 here as the division of all the numbers leads to the answer 9
Step-by-step explanation:
Answer:
Your constant proportionality is 9 because 2x9=18, 3x9=27, 4x9=36, and 5x9=45.
Step-by-step explanation:
Which one could NOT be the probability of an event occuring?
A. 23
B. 3/4
C. 2.3
D. 0
Please help !!!
Answer:
D
Step-by-step explanation:
there is zero chance of it happening
The best description of a dilation of a figure is:
A. an enlargement or a reduction of the figure
B. a slide of the figure
C. a turning of the figure about some fixed point
D. a mirror image of the figure
Answer:
A. an enlargement or a reduction of the figure
Step-by-step explanation:
The answer is choice A.
dilation A. an enlargement or a reduction of the figure
translation B. a slide of the figure
rotation C. a turning of the figure about some fixed point
reflection D. a mirror image of the figure
Which of the following steps were applied to ABCD to obtain A'B'C'D
Answer:
B. 3 units right and 4 units up
The correct steps were applied to ABCD to obtain A'B'C'D is,
⇒ 3 units right and 4 units up
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
Translation applied to ABCD to obtain A'B'C'D.
Now, We get;
Coordinate of A = (2, 3)
Coordinate of A' = (5, 7) = (2 + 3, 3 + 4)
Hence, The correct steps were applied to ABCD to obtain A'B'C'D is,
⇒ 3 units right and 4 units up
Learn more about the transformation visit:
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The sum of the interior angle measures of a convex polygon with n sides is given by the expression 180n–360 . Factor the expression.
Answer: 180(n-2)
You use the distribution rule to factor
The distribution rule is a(b+c) = a*b+a*c
I need help please and thank you!!!
Answer:
Area: 288 m^2
Step-by-step explanation:
First find the area of the big rectangle:
A= L•W
A= 24 • 12
Area = 288 meters squared
So this is the area of the shaded one heh heh…
Hope this helps, have a great summer!
out of 75 student 3 were a scent what percentage was present
Answer:
To find a percentage, divide the number present by the total number of students, then multiply that number by 100.
Answer:
96% were present.
Step-by-step explanation:
75/100 , 72/? Find percent (?)
(72*100 / )75
96%
Encuentra la solución a los triángulos que cuentan con las siguientes características y represéntalos gráficamente
Answer:
unce de Grenada! Nani de suburban don't listen to me in trying to get points here
What are the x-intercepts of the graphed function?
(–3, 0) and (0, 1.5)
(–3, 0) and (1,0)
(–1, 2) and (1, 0)
(0, 1.5) and (1, 0)
Answer:
Step-by-step explanation:
d
Answer:
D
Step-by-step explanation:
Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x2 + 1 into the quadratic formula?
Answer:
a = 3, b = - 2 , c = 0
Step-by-step explanation:
The equation is
[tex]1 = - 2 x + 3 x^2 + 1 \\\\3 x^2 -2x +0 = 0[/tex]
By comparing with the standard equation
[tex]ax^2 + bx + c = 0[/tex]
So,
a = 3, b = - 2 , c = 0
m∠MNO =____because they are_____ (Fill in the blanks)
Answer:
No answer is possible from the information provided
Step-by-step explanation:
The is no∠MNO in the image.
Answer:
But then there is no < MNO on the diagram
A regular hexagon abcdef is shown. Work out the size of angle x
Please help
Answer:
30
Step-by-step explanation:
cause the angles in a hexagon should add up to 720degrees(area) which means each angle in a hexagon is 120.
Angles in a triangle add up to 180
we know that A is 120 and the angles of F and B are equal (this is an assumption) so 180-120=60 then 60/2 (because we have 2 angles) 30
So X=30
(sorry if the answer is incorrect)
Answer:
30
(6-2)(180)/6
=120
∆FAB=180°
180-120=60
x=60/2
=30
somebody help pls im stuck on this one
Answer:
x=77 degrees
Step-by-step explanation:
The angles of a triangle always add to 180 degrees.
26 is already taken up 180-26=154
There are 2 angles left 154/2=77
x=77
Write an algebraic equation to represent the following problem:
Five friends went out to dinner. Each one of them left an $18 dollar tip and they also split the $148 bill evenly. How much did each person pay for dinner?
PLS I NEED THIS!! I'll give brainiest if correct!!!!!!
Answer:
$47.60
Step-by-step explanation:
[tex]18+\frac{148}{5} =47.60[/tex] ($)
Which of the following is an irrational number? OA. 67 OB. 564 OC. 19 9 OD. 1.9
Answer:
D. 1.9
Step-by-step explanation:
An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.
PLEASE HELP LAST QUESTION MATH
9514 1404 393
Answer:
A = 48°B = 115°C = 115°D = 67°E = 48°Step-by-step explanation:
A and the angle marked 48° are vertical angles, hence congruent.
A = 48°
B is part of a linear pair with the angle marked 65°, so it is supplementary to that angle.
B = 115°
C is an alternate interior angle with angle B, so is congruent.
C = 115°
D is a vertical angle with the one marked 67°, so is congruent.
D = 67°
E is an alternate exterior angle with the one marked 48°, so is congruent. It is also a corresponding angle with A, so congruent to that as well.
E = 48°
2.8-5.3n - 4n + 5 =
plss help again
Thank you!
Answer:
7.8-9.3n
Step-by-step explanation:
2.8-5.3n - 4n + 5
Combine like terms
2.8 +5 -5.3n -4n
7.8-9.3n
Answer:
In simplest form: 7.8 - 9.3n
Step-by-step explanation:
Equation: 2.8 - 5.3n - 4n + 5
Combine like terms: 2.8 + 5 = 7.8
-5.3n + -4n = -9.3n
Put it all together: 7.8 - 9.3n
Hope this helps! :)
12 Rose and Haydn share £250 in the ratio 2:3
Rose gives all her share of the money to charity.
Haydn gives 42% of his share of the money to charity.
Rose gives more money to charity than Haydn gives to charity.
Work out how much more.
Answer:
Amount = £37
Step-by-step explanation:
Let Rose be represented by R.
Let Haydn be represented by H.
Given the following data;
Total amount = £250
Ratio of R:H = 2:3 = 2 + 3 = 5
To find how much Rose earned;
R = 2/5 * 250
R = 500/5
R = £100.
For Haydn;
H = 3/5 * 250
H = 750/5
H = £150
Next, we calculate the amount Haydn gave to charity;
Percent = 42% = 42/100 = 0.42
H = 0.42 * 150
H = £63
To find how much more Rose gave to charity than Haydn;
Amount = R - H
Amount = 100 - 63
Amount = £37
Describe fully the single transformation that mata tange onto anges
3
2
1
4
5320
4
2
-4
Answer:
mee.com/pbj-kbyh-bzm
join it fast
A car company sells a scale model to of the size of one of its cars.
Complete the following table.
Scale Model
Real Car
2
Area of windscreen (cm)
135
V25
[3]
3
Volume of storage space (cm)
408000
Answer:
[tex]w = 13500[/tex] --- real windscreen
[tex]v = 408[/tex] --- scale volume
Step-by-step explanation:
Given
[tex]k = \frac{1}{10}[/tex] --- scale factor
See attachment
Required
Complete the table
To get the windscreen (w) of the real car, we do the following computation
[tex]w = \frac{w_{scale}}{k^2}[/tex]
This gives:
[tex]w = \frac{135}{(1/10)^2}[/tex]
[tex]w = \frac{135}{1/100}[/tex]
[tex]w = 13500[/tex]
Next, the volume (v) of the scale mode
We make use of the following computation
[tex]v = v_{real} * k^3[/tex]
So, we have:
[tex]v = 408000 * (1/10)^3[/tex]
[tex]v = 408000 * 1/1000[/tex]
[tex]v = 408[/tex]
Complete the solution of the equation. Find the
value of y when x equals 1.
927y=-12
Enter the correct answer
OOD
DONE
?
x^(2)-2x+7 I need to find Find the vertex and the axis of symmetry.
Answer:
Vertex: (1, 6)
Axis of symmetry: x = 1
Step-by-step explanation:
find AD and AB
hhjhh
Answer:
y = 13
x = 20.6155281281
Step-by-step explanation:
5^2 + 12^2 = y^2
25 + 144 = y^2
169 = y^2
[tex]\sqrt{169}[/tex] = y
y = 13
y^2 + 16^2 = x^2
13^2 + 16^2 = x^2
425 = x^2
20.6155281281 = x
Hope this helps!
simple Answer:
y = √(119)
x = √(375)
Step-by-step explanation:
harder answer:
12^2 - 5^2 = y^2
y = √(119)
16^2+ √(119) = 375
x = √(375)