Answer:
[tex]Max\ Area = \frac{x^2}{16}[/tex]
Step-by-step explanation:
Given
[tex]P = x[/tex] ---- the perimeter of fencing
Required
The maximum area
Let
[tex]L \to Length[/tex]
[tex]W \to Width[/tex]
So, we have:
[tex]P = 2(L + W)[/tex]
This gives:
[tex]2(L + W) = x[/tex]
Divide by 2
[tex]L + W = \frac{x}{2}[/tex]
Make L the subject
[tex]L = \frac{x}{2} - W[/tex]
The area (A) of the fence is:
[tex]A = L * W[/tex]
Substitute [tex]L = \frac{x}{2} - W[/tex]
[tex]A = (\frac{x}{2} - W) * W[/tex]
Open bracket
[tex]A = \frac{x}{2}W - W^2[/tex]
Differentiate with respect to W
[tex]A' = \frac{x}{2} - 2W[/tex]
Set to 0
[tex]\frac{x}{2} - 2W = 0[/tex]
Solve for 2W
[tex]2W = \frac{x}{2}[/tex]
Solve for W
[tex]W = \frac{x}{4}[/tex]
Recall that:
[tex]L = \frac{x}{2} - W[/tex]
[tex]L = \frac{x}{2} - \frac{x}{4}[/tex]
[tex]L = \frac{2x- x}{4}[/tex]
[tex]L = \frac{x}{4}[/tex]
So, the maximum area is:
[tex]A = L * W[/tex]
[tex]A = \frac{x}{4}*\frac{x}{4}[/tex]
[tex]Max\ Area = \frac{x^2}{16}[/tex]
Help me please
The question is in the picture above..
Please helpp I will mark brainliest!!<3
Step-by-step explanation:
x+4=12
In this equation, x is a unknown value,
x plus four is twelve.
So, it also represents four more than x is twelve.
Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east. Find the distance and bearing of runner B from runner A after 30 minutes
Answer: [tex]7.81\ km[/tex]
Step-by-step explanation:
Given
Runner A runs towards North at speed of 10 km/h
Runner B runs towards East at speed of 12 km/h
After half hour, they covered a distance of
[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]
[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]
They are running in perpendicular direction to each other
So, the distance between them is given by
[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]
Please help thank you!
Answer:
24.
(-24 ÷
[tex] {6}^{2} [/tex]
16+8= 24
A line that includes the point (2, 9) has a slope of 8. What is its equation in slope-intercept
form?
Answer:
y-8x+7=0
Step-by-step explanation:
slope(m)=8
using slope intercept form of equation of staright line we get
y=mx+b
y=8*x+b
y-8x=b ................ eq(i)
since the line include the point (2,9) it satisfies the euation,
here x=2 and y=9
equation: y-8x=b
9-8*2=b
9-16=-b
-7=b
substituting the value of b in eq(i) we get
y-8x=-7
y-8x+7=0 is a required equation of the line.
A full waterbed mattress is 6 ft by 2 ft by 1 ft. The mattress is to be filled with water that weighs 62.4 lb /ft3. Find the weight of the water in the mattress to the nearest pound.
Answer:
749 lbs
Step-by-step explanation:
weight of the water in the mattress = volume of the mattress x weight of water
volume of the mattress = volume of a cuboid = length x width x height
6 x 2 x 1 = 12 ft³
weight of the water in the mattress = 12 x 62.4 = 748.8 lbs
749 lbs to the nearest pound
Help! What is the answer?
Answer:
c ......................
HELP PLEASE! for 20 points
PLEASE HELP ME, THANK YOU!!
EXPLAIN YOUR ANSWER FOR BRAINLIEST
A prism with an volume of 148 cubic cm is dilated by a factor of 5.5.
The volume of the dilated prism is ___ cubic cm.
(this is just a word question)
Answer:
24623.5 cubic cm
Step-by-step explanation:
A prism with an volume of 148 cubic cm is dilated by a factor of 5.5.
This is calculated as:
Let the volume of the dilated prism = x
Hence:
x/148 = (5.5)³
Cross Multiply
x = 148 cm³ × 5.5³
x = 24623.5 cm³
The volume of the dilated prism is 24623.5 cubic cm.
Match them BRAINLIEST IF CORRECT
Answer:
1/2 for the red card
1/52 for queen of hearts
1/4 for clubs
3/13
Step-by-step explanation:
the red card is 1/2 because the only other color is black
there is only one queen of hearts
it is one of four possible symbols
because that is the only one left
37 + (-37) im looking for the answer
Answer:
0
Step-by-step explanation:
37 + (-37)
open the bracket
remember when u multiply the bracket - sign and + sign also gets multiplied and (-) * (+) is( -) . So
37 - 37
0
Pls I need this before midnight (USA)
Answer:
I can’t post an image, but I’ll explain below
Step-by-step explanation:
Start at a point where the line crosses through a coordinate exactly, like (0,1), and find a second one. Draw a line from the first to the right until it’s over the second point, then go down to the second point. It should look like half of a rectangle. Just follow the lines of the graph :)
Tell whether the triangle with the given side lengths is a right triangle. Y/N question
Answer: need a picture of the traingle but if it's at a 90 degree angle on any sides then yes
Step-by-step explanation:
Math help please urgent
Answer:
16 m^2
Step-by-step explanation:
Area of triangle = (Base * Height) / 2
Area of triangle = ( 8 * 4 ) / 2
Area of triangle = 16
What are the coordinates of the point 1/6 of the way from a to b?
Answer:
B. (2, 6)
Step-by-step explanation:
Xp = 1 + (1/6 × (7-1)) = 1 + (1/6×6) = 1+1 = 2
Yp = 8 + (1/6 × (-4-8)) = 8+(1/6×(-12))
= 8+(-2) = 6
the coordinate => (2, 6)
The ratios a: B and B :c are equivalent to one another
Select all the statements that must be true
Answer:
Options (2) and (5)
Step-by-step explanation:
Given ratio is a : b and b : c
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
[tex]\frac{b}{a}= \frac{c}{b}[/tex] [Option 2]
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
b × b = a × c
b² = ac
If a = b,
b² = bc
b = c [Option 5]
Therefore, Options (2) and (5) are the correct options.
Dana enters a race where she has to cycle and run. She cycles a distance of 25km and then runs for 20km. Her average running speed is half of her average cycling speed. If dana completes the race in 5 hours, what is her average cycling speed !
Step-by-step explanation:
Let running speed = x.
So, cycling speed = 2x.
Total distance traveled = 20 + 25 = 45km
Time taken running = 20/x
Time taken cycling = 25/2c
Total time taken = 5 hours
So, 5 = 20/x + 25/2x
Solving this equation for x gives:
10x = 65. Thus x = 6.5
Since cycling speed = 2x, cycling speed = (6.5)(2)
So cycling speed is 13 km/h.
Hope it helps.
Please help thanks this is due today!
D. [tex] ({ - 8})^{2} - 9 + ( - 7)[/tex] ✅
Step-by-step explanation:
[tex] {( - 32 \div4 })^{2} - 9 + ( - 7) \\ \\ = ({ - 8})^{2} - 9 +(- 7 )\\ \\=64-9-7\\\\ = 64 - 16 \\ \\ = 48[/tex]
Note:-
[tex]\sf\red{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\sf\red{(+\:x\:-)\:=\:-}[/tex]
[tex]\sf\red{(-\:x\:-)\:=\:+}[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Will
Give BRIANLIST
Write the sentence as an equation use x to represent a number
“Six times the difference of 11 and a number is -72”
Answer:
6 × (11 - x) = -72 => x = 23
or
6 × (x - 11) = -72 => x = -1
Step-by-step explanation:
there are at least two possibilities, as the "difference between two numbers a and b can be excised as either a-b or b-a.
in any case, just following the sentence
Six times = 6 ×
difference of 11 and a number = 11 - x
is -72 = -72
so,
6 × (11 - x) = -72
and that is true for x = 23
but
the other direction is possible too
6 × (x - 11) = -72
and that is true for x = -1
Consider the systems of equations:
y=4/5 x−3
y=4/5 x+1
Without graphing, determine and explain how many solutions you would expect this system of equations to have.
Answer:
no solutions; the lines are parallel
Step-by-step explanation:
The eqautions are in slope intercept form.
The slope of both lines is 4/5; therefor the lines are parallel
The y-intercept of one line is -3 and the other is 1
That means the parallelines never meet.
There are no solutions
There are no solutions for the system of equations y=4/5 x−3
and y=4/5 x+1
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The system of equations,
y=4/5 x−3
y=4/5 x+1
The equations are in slope intercept form.
As we observe the equations, the slopes of two equations is 4/5.
The slope of both lines is 4/5
Therefor the lines are parallel
The y-intercept of one line is -3 and the other is 1
That means the parallel lines never meet. There are no solutions
Hence there are no solutions for the system of equations y=4/5 x−3
and y=4/5 x+1
To learn more on slope intercept form click:
https://brainly.com/question/9682526
#SPJ2
Fifty-five petcent of people in a survey said that they do exercise on a fairly regular basis. If 12,000 people were sureveyed, how many of them exercised on a fairly regular basis? A. 5,000 B. 5,500 C. 6000 D. 6,600
please help with number 53!!!!
pretty please
Answer:
The sequence would be arithmetic. This is because an arithmetic sequence has a common number multiplying, adding, subtracting etc. The common rule for this set of numbers was x5. 9x5=45, 45x5=225 etc. We simply used this method with negative numbers, but the rule was still multiplying.
Happy learning!
--Applepi101 :)
Answer:
Arithmetic
Step-by-step explanation:
It has a constant difference between each number whilst Geometric usually has the same difference between each number
Which data set could be represented by the box plot shown below?
Answer:
The answer is C
Step-by-step explanation:
the lowest point of the box plot is at 1 and the highest is at 19, so by that it can't be A.
The box plot shows 12 being the median so that automatically leaves C but just to make sure the first half would be 6 and half of the last part would be 16 if that makes sense.
What is the probability of an event that is certain?
Answer:
Nvm my answer is wrong
An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.
I NEED HELP WITH C , help i dont understand
Answer:
SAS
Step-by-step explanation:
SAS (Side-Angle-Side) is a proof of congruence for two triangles. Since C stipulates that [tex]\angle ENM=\angle ZNM[/tex], the two triangles would share two sides and the angle between them, thus being congruent from SAS.
G
A right rectangular prism has a height of 15 meters, a length of 4 meters, and a width of 3 meters. Which expressions
show how to calculate the volume? Check all that apply.
Answer:
180m^3
Step-by-step explanation:
Given data
Height = 15m
Lenght= 4m
Width=3m
We know that the volume of a rectangular prism is expressed as
Volume= L*W*H
Substitute
Volume= 4*3*15
Volume= 180m^3
у=-3x+3
y = -9x + 15
Answer:
(2, - 3 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 3 → (2)
y = - 9x + 15 → (2)
Substitute y = - 3x + 3 into (2)
- 3x + 3 = - 9x + 15 ( add 9x to both sides )
6x + 3 = 15 ( subtract 3 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Substitute x = 2 into either of the 2 equations and solve for y
Substituting into (1)
y = - 3(2) + 3 = - 6 + 3 = - 3
solution is (2, - 3 )
se cumple que: A^2 + B = 486 y el M.C.D. de A y B es 9. ¿Cuál es el valor de B
Answer:
i dont know spanish
Step-by-step explanation:
What is the product?
(x − 3)(2x2 − 5x + 1)
Answer:
5x2+20x−15
Step-by-step explanation:
(5x-3)=(3x+27) I dont understand
Answer:
x = 15
Step-by-step explanation:
(5x-3)=(3x+27)
Subtract 3x from each side
(5x-3x-3)=(3x-3x+27)
2x-3 = 27
Add 3 to each side
2x-3+3 = 27+3
2x= 30
Divide by 2
2x/2 = 30/2
x = 15