The quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
As it is given that the length and the width of the centre area are 72 inches and 36 inches, respectively. When the dimensions of the centre area are converted into the feets, it will be,
[tex]\rm Length = \dfrac{72\ inches}{12} = 6\ feet[/tex]
[tex]\rm Width= \dfrac{36\ inches}{12} = 3\ feet[/tex]
If we take the borders of the table into account, the length and the breadth of the table will become,
Length = (6+x+x) = (6+2x)
Width = (3+x+x) = (3+2x)
We know that the area of a rectangle is given as the product of the length and width, and also it is mentioned that the area of the entire table is 3,276 square feet. Therefore, the area of the table can be written as,
[tex]{\rm Area=Length \times Width}\\\\3276 = (6+2x)(3+2x)\\\\3276= 18+ 12x+ 6x + 4x^2\\\\4x^2+18x+18-3276=0\\\\4x^2+18x-3258=0\\[/tex]
Thus, the quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.
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The rule for the number of fish in a home aquarium is 1 gallon of water for each inch of fish length. Marta's aquarium holds 39 gallons of water and Hank's aquarium hold 51 gallons of water. The aquarium holds two types of fish, fish A and fish B. If Marta bought 3 of fish A and 2 of fish B, and Hank bought 3 of fish A and 4 of fish B, how long is fish A and how long is fish B?
Answer: Fish A: 9 inches ; Fish B: 6 inches
Step-by-step explanation:
This can be turned into a systems of equation, where x equals the length of fish A and y equals the length of fish B:
3x + 2y = 39 → -3x - 2y = -39
3x + 4y = 51 → 3x +4y = 51
Combine: 0 + 2y = 12 → y = 6 inches.
Plug back in: 3x + 2(6) = 39 → 3x = 27 → x = 9 inches.
What is the value of y in the solution to the system of equations?
1 x + 2 y = 1
2x – 3y = -30
0-8
0-3
03
O 8
Answer: y = 32/7
Step-by-step explanation:
Solve the first equation for x by subtracting the 2y from the left side and getting: x = 1 - 2y.
Plug this in to the second equation: 2(1 - 2y) - 3y = -30 → 2 - 4y - 3y = -30 →
-7y = -32 → y = 32/7. Hope this helps!
To turn a decimal into a percent you move the decimal 2 spaces to which direction.
Answer:
Right
Step-by-step explanation:
You move the decimal to the right to make the decimal a whole number :)
Example below:
0.25
Move 2 places to the right
25%
Have a great day!!
Please rate and mark brainiest!!
Answer: You move the decimal point two spaces to the right.
Step-by-step explanation:
Multiply by 100.
You are going to the mall with your
friends, and you have $200 to spend.
you find a store that has all jeans for
$25 and all shirts for $10. you buy a
total of 14 items. how many of each
item did you buy?
Answer:3 jeans and 11 shirts with 15 dollars leftover
Step-by-step explanation:
3x25=75
11x10=110
110+75=185
200-185=15
25x4 will make the leftover money higher, so 3 and 11
coach wilson hopes to have no more than 15 turnovers during today's basketball game which inequality best represents this situation
Answers are A t is greater than or equal to 15. B is t is greater than 15. C is t less than 15. D is t less than or equal to 15
Answer:
it is D
Step-by-step explanation:
since he wants no more than 15
Answer:
D
Step-by-step explanation:
Since it says "no more than 15" coach Wilson wants either 15 turnovers or less in his game. Therefore, t is equal to less than or equal to 15.
Write down the irrational numbers from the following.
1/3, 0.65, square root 6, 2/5, cube root 8, pie
As we can see the value of root 6 does not terminate after 3 decimal places. It can still be extended further. Hence, this makes √6 an irrational number.
hope it will help you..
Consider nick draws 3 cards from a pack of 52 cards. What is the probability of getting no kings?
The probability of getting no kings is 0.7826
What is the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The random experiment follows a hypergeometric distribution with,
N = 52 since there are 52 cards in a deck.
k = 4 since there are 4 kings in a deck.
n = 3 since we randomly select 3 cards from the deck.
x = 0 since we want no kings.
The probability of getting no kings is;
[tex]\rm = \dfrac{^4C_0 \times ^{48}C_3}{^{52}C_3}\\\\=\dfrac{1 \times 17296}{22100}\\\\= 0.78[/tex]
Hence, the probability of getting no kings is0.7826.
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The measure of an angle is 27. 5°. What is the measure of its complementary angle?
Answer:
62.5 degrees.
Step-by-step explanation:
Complementary angles add up to 90 degrees.
So the answer is 90 - 27.5.
Find the total amount
$20,700 at 9% compounded
semiannually for 4 years
Answer:
41,246.046 which could be rounded to .05 cents at the end.
Step-by-step explanation:
[tex]20700(1.09)^8[/tex]
we use this equation since we are working with interest, and we are compounding interest twice per year, for 4 years or 8 times.
hope this helps, please rate and mark as brainelst.
Jonah's lunch cost $27.50, he paid $1.65 sales tax. What is the percent of sales tax?
Answer:
6%
Step-by-step explanation:
To get sales tax, you multiply the percentage of sell tax to the total price. In this case, we were looking for the percent of sell tax so we needed to divide the total amount into the amount he payed in sells tax. You will get the decimal value so you will have to multiply it by 100 to get the percent.
When you have coordinates of two points A(1, 2) and B(2,6) slope is:
Answer: 4
Step-by-step explanation:
Find the derivative of 76x + 1 at x = 1.
Answer:
76
Step-by-step explanation:
We know the rule when finding the derivative :
dy/dx = nxⁿ⁻¹Deriving
dy/dx = 76x + 1dy/dx = 1 * 76 * (x)¹⁻¹ + 0 * 1¹⁻¹dy/dx = 76The x = 1 becomes irrelevant because there is no 'x' present in the derivative[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{d}{dx}(76x + 1) [/tex]
[tex]\qquad \sf \dashrightarrow \:76 {x}^{1 - 1} + 0[/tex]
[tex]\qquad \sf \dashrightarrow \:76 {x}^{0} + 0[/tex]
[tex]\qquad \sf \dashrightarrow \:76[/tex]
Here, we have got a constant number, therefore for any value of x it will be 76
Therefore, derivative of 76x + 1 at x = 1 is 76
What is the volume of the cylinder in terms of pi 2 m 6m
Answer:
6πm³
Step-by-step explanation:
To work out the volume of a cylinder, use the formula πr²h
Next, substitute the known values into the equation (remember that the radius is half of the diameter):
volume = π × 1² × 6
The volume of the cylinder is 6πm³
Hope this helps!
Please help I will give brainliest.
Answer:
See below
Step-by-step explanation:
1. Two numbers that multiply to 17 and add to 18.
17 x 1 = 1717 + 1 = 181 and 172. Two numbers that multiply to 36 and add to -20.
-18 x -2 = 36-18 + -2 = -20-18 and -2please help QUICK I WILL GIVE YOU BRAINLIST
Answer:
P = 59°Step-by-step explanation:
HELP!
An animal shelter has a total of 20 cats, dogs, and
parrots. There are at least twice as many cats as dogs
and at least 3 times as many parrots as dogs. What is the
maximum number of dogs they could have?
Answer:
The answer is 4 dogs
Step-by-step explanation:
Let the number of dogs be x
=>The number of cats = 2x
=> The number of parrots = 3x
2x + 3x = 20
=>5x = 20
=>5x ÷ 5 = 20 ÷ 5
=>x = 4
They could have the maximum number of dogs is 4 dogs.
The given is,
An animal shelter has a total of 20 cats, dogs, and parrots.
There are at least twice as many cats as dogs and at least 3 times as many parrots as dogs.
What is a maximum number?
A maximum is a unique number for a given set of data. This number can be repeated, but there is only one maximum for a data set.
Let the number of dogs be x
The number of cats = 2x
The number of parrots = 3x
2x + 3x = 20
5x = 20
5x / 5 = 20 / 5
x = 4
Therefore the are 4 dogs.
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PLS PLS PLS HELP ME!!!
Answer:
[tex]x = 180 - (37 + 53)[/tex]
is the answer
What is the slope for a line that is perpendicular to the line x = -6?
Answer:
There is not a slope perpendicular to the lie x = -6
Step-by-step explanation:
In this equation, you are given a line, x = -6.
This is in fact a line with an undefined slope. The slope for a perpendicular intersection is the opposite reciprocal of the slope.
Eg. If you have the line y = 2x
The reciprocal is y = 1/2x, the opposite means negative
So the slope that would intersect this line perpendicularly is y = -1/2x.
There is an undefined slope in this, therefore, you cannot find the slope for a line perpendicular to x = -6.
If it were an option, I would choose "no slope"
m
A.
Which of the following equations is equivalent to p = + at?
a=t(p-on)
t=a(p)
B.
=
m
גנן
C.
1 =
p-at
D.
r
m =
p-at
Answer:
M Because the evolution of algebraic combinations is disordered and Fibonacci is wrong
Eliminate the parameter to complete the statements describing the equations
x = 3cos(t) - 2 and y = 2sin(t) + 1.
The rectangular form of this equation is
A. 4(x + 2)2 + 9(y – 1)2 = 36
B. 9(x + 2)2 + 4(y - 1)2 = 36
C. 4(x - 2)2 + 9(y + 1)2 = 36
D. 9(x - 2)2 + 4(y + 1)2 = 36
The equations represent a/an
Answer:
A
ellipse
Step-by-step explanation:
Answer:
1.) The rectangular form of this equation is (A)
.2.) The equations represent a/an (ellipse)
.
Step-by-step explanation:
Edge 2022
this question is to hard
Answer:
A
Step-by-step explanation:
it aligns with the other dots, and you can do exactly 1-1
Answer:
C. (9,4.5)
Step-by-step explanation:
with each ordered pair, the y axis is half of the x axis.HELPP PLSSS!!!
Find the volume of the following objects.
Answer:
1. 314.159
2. 3,801.327
3. 1,407.433
A deposit earns $102 after 36 months at a simple interest rate of 5%
What is the time and total value
Answer:
285.6
Step-by-step explanation:
formula= I=PRT
i=?
p=102
r=5
t=36 months
5=0.05
102(1+(0.05x36)=285.6
Answer:
Step-by-step explanation: 276.9
Name the postulate that proves these two triangles congruent.
Answer:
the postulate that proves these two triangles congruent is AAA or angle angle angle.
the graph of the money jake earns while babysitting is shown below. put a scale on each axis that makes sense for this situation. explain why chose the scales you did.
Answer:
Hi uddin
Step-by-step explanation:
Do u remember me
I am the ghost of the uchiha i searched ur this question and found ur brainly thing
In 2005, 12.2 out of every 50 employees at a company were women. If there are 48,744 total company employees, estimate the number of women.
Answer:
12000
Step-by-step explanation:
Using this information, you can make a ratio: 12.2/50 = x/48744
By simplifying this ratio you get that 50x = 594676. Dividing both sides by 50 you get about 11900, which you can round up to 12000
Answer:
11,894 women
Step-by-step explanation:
ratio of women to employees = 12.2 : 50
Let x = number of women employees to 48744 employees
12.2 : 50 = x : 48744
⇒ 12.2 / 50 = x / 48744
⇒ 0.244 = x / 48744
⇒ x = 0.244 · 48744
⇒ x = 11893.536
⇒ x = 11894 (nearest whole number)
Therefore, there are approximately 11,894 women in a company with a total of 48,744 employees
what is the answer for this?
Answer:
0.729 cubic millimeters
Step-by-step explanation:
Here,
Length ( l ) = 0.9 mm
Base ( b ) = 0.9 mm
Height ( h ) = 0.9 mm
l = b = h = 0.9 mm = a
To find : Volume
This shape is a cube.
Formula : -
Volume of cube = a³
Volume of cube
= 0.9³
= 0.9 x 0.9 x 0.9
= 0.729 cubic milimeters
Answer:
Formula for volume of cube;
V = [tex]s^{3}[/tex]
Where 's' represents one side of a cube which is being cubed.
or
V = w · l · h
Where 'w' stands for the width, 'l' is the length, and 'h' represents the height.
For this, I'll be using the formula [tex]s^{3}[/tex].
What we know:
Width = 0.9 mmLength = 0.9 mmHeight = 0.9 mmUse one of these sides to substitute for 's';
V = [tex]s^{3}[/tex]
V = 0.9^3 ← (The " ^ " symbol is another way of showing to the power of.)
V = (0.9 · 0.9 · 0.9)
V = 0.729 mm, the volume of this cube is 0.729 cubic millimetres.
Can some please explain and solve how to do these unit rate equations?
4 ft
4 ft
3.5 ft
7 ft
4 ft
Answer:
The answer is 1,568 in a multiplication problem.
4 x 4 x 4 = 64
3.5 x 7 = 24.5
64 x 24.5 = 1,568
Let me know if this was not what you were looking for, I may or may not be able to change it.
Help with any questions
1.) right triangle, as it has a right angle
2.) scalene triangle no equal sides
hope this helps