Answer:
Length = 22.98 feet
Width = 9.66 feet
Step-by-step explanation:
Let the length of the rectangle be L.
Let the width of the rectangle be W.
Given the following data;
Area of rectangle = 222 feet²
Translating the word problem into an algebraic expression, we have;
L = 3W - 6 ...... equation 1
We know that the area of a rectangle is given by the formula;
A = L * W
Substituting
222 = L * W ....equation 2
Substituting eqn 1 into eqn 2, we have;
222 = (3W - 6) * W
222 = 3W² - 6W
Rearranging the equation, we have;
3W² - 6W - 222 = 0
Next, we would use the quadratic formula to solve for the roots.
Note: the standard form of a quadratic equation is ax² + bx + c = 0
a = 3, b = -6 and c = -222
Solving the quadratic equation using the quadratic formula;
The quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the equation, we have;
[tex] x = \frac {-(-6) \; \pm \sqrt {6^{2} - 4*3*(-222)}}{2*3} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 - (-2664)}}{6} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 + 2664}}{6} [/tex]
[tex] x = \frac {6 \pm \sqrt {2700}}{6} [/tex]
[tex] x = \frac {6 \pm 51.96}{6} [/tex]
[tex] x_{1} = \frac {6 + 51.96}{6} [/tex]
[tex] x_{1} = \frac {57.96}{6} [/tex]
x1 = 9.66
We do not need the negative value of x, so we proceed.
Therefore, Width, W = x1 = 9.66 feet
For the length;
L = 3W - 6
L = 3(9.66) - 6
L = 28.98 - 6
L = 22.98 feet
HELP ME PLEASEEEEEEEEEEEE
Answer:
A) 3.5 m
Step-by-step explanation:
3.5 x 2 = 7/2 = 3.5
Simplify: -4r + s - 2r - 3s
Answer:
-6r - 2s
Step-by-step explanation:
Combining Like Terms like this
-4r + s-2r - 3 s <<<
-6r + s - 3 s
= -6r - 2s <<<
Answer:
-6r - 2s
Step-by-step explanation:
The sum of a number and 45 plz need the answe
Answer:
n + 45
Step-by-step explanation:
The question is asking to write an algebraic expression for the sum of a number and 45. We know we are adding a number to 45. So we use addition. But, we don't which number we are adding to 45. So we just use a variable. I used "n", but use whatever letter you want ( x, y, z, etc). I recomend using the same variable that your intrcuctor uses.
Hope this helps.
why is coal a non-renewable energy source
10 (-2 + 3y) + 8y = -20
PLEASE HELP!!!!1!1!1! suppose one particular pyramid in egypt has a square base of side length 280 meters and a perpendicular height of 144 meters what is the surgace area of the pyramid?
Answer:
Pyramid Surface Area = .5 * Perim of Base * Slant Height
Slant Height^2 = 144^2 + 140^2
Slant Height^2 = 20,736 + 19,600
Slant Height^2 = 40,336
Slant Height = 200.8382433701
Surface Area = .5 * perim of base * slant height
Surface Area = .5 * 1,200 * 200.8382433701
Surface Area = 120,503 square meters
Source = www.1728.org/volpyrmd.com
Step-by-step explanation:
Please help quickly as possible thank you! :)
Answer:
329.5ft
Step-by-step explanation:
First one: ((4+18+26)x10)/2
Second: +(18x4)
Third: (7x5)/2
=240+72+17.5
=329.5
It took lan three years to collect 25,413 aluminum cans to recycle. In the first year he collected 8,917 cans, and in the second year he collected 7.639 cans Which equation can be used to find x, the number of cans tan collected in the third year? A X = 25,413-8,917 - 7,639 B X = 25,413 +8,917 + 7,639 CX-8,917 +7,639 D 8,917-7,639
Answers:
1. 24 cans/lb x 15,000 lb/trailer = 360,000 cans/trailer
2. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 15,000 lb = $9,000
3. 15,000 lbs/trailer / 30 lbs/collector = 500 can collectors/trailer
4. 15,000 lbs/trailer / 800 lbs/bale = 18 complete bales (and 3/4 of another bale)/trailer
5. 24 cans/lb x 800 lb/bale = 19,200 cans / bale
6. 100 bales/boxcar x 800 lbs/bale = 80,000 lb. cans / boxcar
7. 100 bales/boxcar x 19,200 cans/bale = 1,920,000 cans / boxcar
8. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 80,000 lb/boxcar = $48,000/boxcar
Pick the right one.
Tessellations
Determine whether the given figure tessellates the plane.
a. yes
b. no
Please select the best answer from the choices provided
Answer:
B. No
Step-by-step explanation:
I calculated it logically
WILL
GIVE
BRAINLIST ANSWER
Answer:
22 is the range for the data set.
stay safe healthy and happy.Q3) There are 200 passengers on a plane. 84 of them are women and 12 are children.
What percentage of them are:
a) women
b) children
c) neither women nor children?
PLEASE I NEED HELP
SSS
AAS
NOT CONGRUENT
SAS
ASA
SAS IS YOUR ANSWER!
HOPE THISE HELPS
Find the area of the figure shown below and choose the appropriate result.
Answer:
B 14 cm
Step-by-step explanation:
First, rectangle equation formula is w x l which means 4 x 2 = 8 then triangle formula is b x h which base is 4 and height is 3 which gets 6. So 8 + 6 = 14.
What is 3/4-5/8?
? Give your answer in its simplest form.
Answer:
1 over 8
1
8
=0.125
Step-by-step explanation:
Mrs. Simpson is frosting circular sugar cookies. Each cookie is 6 cm in diameter. About how many square centimeters will she need to frost each cookie?
Answer:
9 pi
Step-by-step explanation:
Answer:
28.274 cm^2 (remember units are important)
Step-by-step explanation:
The answer is the area of the cookie. The area of the cookie (neglecting its thickness) is:
A = pi(r^2)
here the radius is 1/2 the diameter of 6 cm:
A = 3.14159 * 3^2 or A = 3.14159* 9 = 28.274 cm^2
In the image, two circles are centered at A. The circle containing was dilated to produce the circle containing B!
What is the scale factor of the
dilation?
O A. 1
OB. 2
OC. 0.5
OD.
-0.5
Find the area of the parallelogram shown below 5 3
Answer:
15 square units
Step-by-step explanation:
If you were to cut off the bottom triangle (separated by the dotted line), and put it on top of the other triangle, you would get a rectangle.
All you have to do is length x height
5 x 3 = 15
State if the triangles in the pair are similar. If so, complete the similarity statement
Answer:
they similar
triangle SRQ - SBC
Answer:
similarity statement =RS/BS=QS/CS=RQ/BC OR,
triangle RSQ≅triangle BSC
Step-by-step explanation:
James wants to 3D-print 8 model car pieces per hour for 10 hours. He can produce 5 model car
pieces using 50 grams of plastic.
How many grams of plastic will he need?
Answer:
80 grams of plastic
Step-by-step explanation:
5 model cars -- 50 grams
1 model car -- (50/5) = 10 grams
8 model cars -- (10 * 8) = 80 grams
Thenks and mark me brainliest :)))
Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 3.5%. Non money is added or withdrawn from the account. How much will be in the account after 5 years? How much will be in the account after 20 years?
Answer:
5 years : 1781.52
20 years: 2984.68
Which expression is equivalent to 128?
Answer: 2^3 x 2^4
Step-by-step explanation:
The value of the exponential expression is A = 2³.2⁴ = 128
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the value of the exponential equation be A
Now , the first expression is p = 2³
The value of p = 8
Now , the second expression is q = 2⁴
The value of q = 16
From the laws of exponents , we get
p.q = 2³.2⁴ = 2³⁺⁴
The value of A = 2⁷ = 128
Hence , the exponential equation is 2⁷ = 128
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ5
Suppose a call center receives 4000 calls on average during their Friday evening shift. Next Friday several people have put in for time off, so the center will be staffed by 178 call center employees. When working continuously, the average call center employee can handle 22 calls per evening shift (with a standard deviation of 5 calls). Assuming the center receives its expected 4000 calls next Friday, what is the probability that the center will have enough employees to handle this call volume
Answer:
The probability that the center will have enough employees to handle this call volume is 0.2764
Step-by-step explanation:
Probability is defined as the ratio of favorable outcomes to the total number of outcomes.
Here the total mean expected number of outcomes=u = 4000
The favorable expected outcomes are = x= 22* 178= 3916
The standard deviation= σ= 5
The random variable X =178 has normal distribution with mean 4000/22 and standard deviation 5
So z= x-u/σ
Z= (3916-4000)/22/5
z= -0.764
From the table of areas under normal curve
P ( x= 3916)= P( -0.764 ≤ Z≤ 0)
P ( x= 3916)= 0.2764
The probability that the center will have enough employees to handle this call volume is 0.2764
Work out the perimeter of this shape. Please help!
Answer: 138
Step-by-step explanation:
(65*2)=130
(4*2)=8
130+8=138
Answer:
2 (l+b )=2 (65+4)=2×69=128
Select the correct answer from each drop down menu. The square root of 15 look at image
Answer:
a=15
b=7
c=4
Step-by-step explanation:
[tex]\sqrt[4]{15^{7} } = 15^{\frac{7}{4} }[/tex]
In the first region are located 6 Rattatta Pokemon hidden in the grass at any given time and 8 Pidgey Pokemon. What would be the probability of running a Rattatta Pokemon?
Identify the terminal point for a 30° angle in a unit circle.
O A (1,
O R. (4,4)
O c. (9.12)
OD. (1,7)
SUBMIT
Answer:
The coordinates for the point on a circle of radius at an angle of are At the radius of the unit circle, 1, serves as the hypotenuse of a 30-60-90 degree right triangle, as shown in (Figure).
Step-by-step explanation:
Please help!! Math
What is the missing value of the missing angle?
A. 43*
B. 133*
C. 90*
D. 47*
A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at time t according to the relationship,
cos theta 2x/2y + gt2
where theta = the angle of elevation of the launcher and g = the acceleration due to gravity An artilleryman is firing at an enemy bunker located 2450 feet up the side of a hill that is 6175 feet away. He fires a round, and exactly 2.27 seconds later he scores a direct hit.
(a) What angle of elevation did he use?
(b) If the angle of elevation is also given by sec θ = υ0t/x. where υ0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
Answer:
a. 22.3°
b. 2940.16 ft/s
Step-by-step explanation:
Here is the complete question
A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at the relationship cot theta = 2x/2y + gt^2 where theta is the angle of elevation of the launcher and g is the acceleration due to gravity (32.2 feet/second^2). An artillery man is firing at an enemy barker located 2275 feet up the side of a hill that is 6325 feet away. He fires a round, and exactly 2.84 seconds later he scores a direct hit.
a. What angle of elevation did he use? theta = degree (Do not round until the final answer. Then round to one decimal place as needed.)
b. f the angle of elevation is also given by sec theta = v_0 t/x, where v_0 is the velocity of the weapon, find the muzzle velocity of the artillery piece he used. v_0 = feet/second (Round to two decimal places as needed.)
Solution
(a) What angle of elevation did he use?
Given that cosθ = 2x/(2y + gt²) where x = horizontal distance of projectile = 6175 feet away,y = vertical distance of projectile = 2450 feet up, g = acceleration due to gravity = 32 ft/s² and t = time of hit = 2.27 s
So, cosθ = 2x/(2y + gt²)
cotθ = 2 × 6175 ft/(2 × 2450 ft + 32 ft/s² × (2.27 s)²)
cotθ = 12350 ft/(4900 ft + 32 ft/s² × 5.1529 s²)
cotθ = 12350 ft/(4900 ft + 164.8928 ft)
cotθ = 12350 ft/(5064.8928 ft)
1/tanθ = 2.4384
tanθ = 1/2.4384
tanθ = 0.4101
θ = tan⁻¹(0.4101)
θ = 22.3°
(b) If the angle of elevation is also given by sec θ = υ0t/x. where υ0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
Making u0 subject of the formula, we have
u0 = xsecθ/t
u0 = x/tcosθ
since x = 6175ft, t = 2.27 s and θ = 22.3°, then
u0 = x/tcosθ
u0 = 6175 ft/(2.27 s × cos22.3°)
u0 = 6175 ft/(2.27 s × 0.9252)
u0 = 6175 ft/(2.1 s)
u0 = 2940.16 ft/s
I need answer tho this please help me
Answer:
there is two diagram 2,3, 4 and 5 this is the answer give
What is an equation of the line that passes through the point(-1,-3) and is perpendicularly to the line x-2y=14
Answer:
the equation will be
Step-by-step explanation:
2x+y+5=0
Answer:
2x + y + 5 = 0
Step-by-step explanation:
The equation of line is x-2y = 14 and we need to find the equⁿ of line which passes through (-1,-3) and is perpendicular to given line.
Find the slope of given line by converting it into slope intercept form.=> x - 2y = 14
=> 2y = x - 14
=> y = x-14/2
=> y = x/2 - 7
Comparing to y = mx + c ,=> Slope (m) = 1/2 .
Now the slope of line perpendicular to it , will have a slope ,
=>[tex] m_{perp}[/tex] = -1/m
=>[tex] m_{perp}[/tex] = -1/½
=> [tex] m_{perp}[/tex] = -2
Using point slope form ,=> m = (y - y₁) / ( x - x₁)
=> -2 = { y - (-3) } / { x - (-1) }
=> -2 = y + 3/x + 1
=> -2(x + 1) = y + 3
=> -2x -2 = y + 3
=> y + 2x +3+2 = 0
=> 2x + y + 5 = 0
Hence the equation of line perpendicular to it is 2x + y + 5 = 0 .