The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot
Answers
The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot. The base of the rectangular prism is not a square and the width is greater than 2 feet. What is the length and width of the rectangular prism?
let
x-------> the length of the base of the rectangular prism
y-------> the width of the base of the rectangular prism
we know that
volume of the prism=area of the base*height
volume=48 ft³
height of the prism=3/4 ft
area of the base=volume/height--------> 48/(3/4)---> 48*4/3----> 64 ft²
area of the base=64 ft²
area of the base=x*y
64=x*y--------> equation 1
y=x+2--------> equation 2
substitute equation 2 in equation 1
64=x*[x+2]-----> 64=x²+2x------> x²+2x-64=0
using a graph tool----> to resolve the second order equation
see the attached figure
the solution is
x=7.062 ft
y=x+2-----> y=7.062+2-----> y=9.062 ft
the answer is
the length of the base of the rectangular prism is 7.062 ft
the width of the base of the rectangular prism is 9.062 ft
Related Questions
Centennial park is evaluating the capacity of the park and have determined that 15 people can comfortably stand in a section that is 5ft by 8ft , the park has dimensions that are 400yds by 200 yds estimate the number of people who can fit in the park
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We have been given that 15 people can comfortably stand in a section that is 5ft by 8ft .
Hence, the area of this section is given by
[tex]A=5\times 8\\ A=40 ft^2[/tex]
Hence, we can say that 15 people can comfortably stand in an area 40 square feet.
Now, we know that 1 yard is equal to 3 feet.
Hence, the area of the section 400yds by 200 yds is equal to
[tex]400\times 3 \times 200 \times 3\\ =720000 ft^2[/tex]
Now, in 40ft^2, 15 people can stand comfortably.
Hence, in 720000 ft^2, number of people can stand comfortably is
[tex]\frac{15}{40} \times 720000\\ \\ =270000[/tex]
Therefore, 270000 people can stand in the park of dimension 400 yds by 200 yds
A car tire has a radius of 15 inches. Suppose the car is traveling at 60 miles per hour (1 mile = 5,280 feet). What is the approximate rate of spin, in revolutions per minute, of the tire? Round the answer to the nearest whole number.
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Speed of the car = v = 60 miles per hour
= 60 x 5280 feet per hour
= 316800 feet per hour
= 316800 x 12 inches per hour
= 3801600 inches per hour
= 3801600/60 inches per minute
= 63360 inches per minute
Angular velocity = w = ?
v = r w
w = v/r
So,
w = 63360/15
= 4224 radians per minute
= 4224/2π revolutions per minute
= 672 revolutions per minute
So, the angular velocity of the tire is 672 revolutions per minute
Circumference = 2π×15/12 = 7.85398 feet. (1 foot=12 inches)
7.85398 feet = 7.85398/5280 = 0.001487496522 miles
In 1 hour, it travels 60 miles. This means it travels (60/60) miles in 1 minute.
So, it travels 1 mile in 1 minute.
The rate of rotation = 1/0.001487496522
= 672.27rpm
To the nearest whole number = 672 rpm
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
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The dog will win the race.
the answer would be 90% because when you multiply 30% x 30% =90% its the same as 3 x 3 = 9
hey can you please help me posted picture of question
Answers
1. The figure shows a parabola whose vertex is (0,0).
2. The x² indicates that the red parabola shown in the figure is vertical
3. and the sign - indicates that the red parabola opens down.
Therefore, you can conclude that the red parabola has the equation f(x)=-x²
So, the answer is B.
Shifting 4 units down means subtracting 4 from the function value.
So, G(x) = 4 - x²
Thus,
F(x) = G(x) - 4
F(x) = 4 - x² - 4 = - x²
Therefore, the correct answer is option B
Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and C(9, 5)?
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[tex]AB= \sqrt{ (2+3)^{2} + (1-6)^{2} } =5 \sqrt{2} \\ \\ BC= \sqrt{ (9-2)^{2} + (5-1)^{2} } =\sqrt{65} \\ \\ CA = \sqrt{ (-3-9)^{2} + (6-5)^{2} } = \sqrt{145} \\ \\ [/tex]
None of the side lengths are equal, so the triangle formed by the given vertices is a Scalene Triangle. Moreover, the Pythagorean theorem is also not satisfied with given side lengths, so the triangle is NOT a Right Angled Triangle.
A suit regularly costs $389.90., Bob buys it on sale for $ 265.00 . How much does he save?
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Hey can you please help me posted picture of question
Answers
So, shifting to right by 9 units means, subtracting 9 from x.
G(x) = F(x - 9)
G(x) = |x - 9|
So, option D is the correct answer
Josh is hiking Glacier National Park. He has now hiked a total of 1 7 km 17 km17, space, k, m and is 2 km 2 km2, space, k, m short of being 1 2 2 1 start fraction, 1, divided by, 2, end fraction of the way done with his hike. Write an equation to determine the total length in kilometers ( h ) (h)left parenthesis, h, right parenthesis of Josh's hike.
Answers
17 + 2 = 19 km is 1/2 of the total length, that is,
19 = (1/2)h
(1/2)h = 19 multiply both sides by 2
h = 2*19
h = 38 km
The total length in kilometers is 38 km.
Now evaluate f(x) = 2x4 - 4x3-11x2+3x-6 for x=-2 f (-2) =
Answers
The answer to the given solution is 8.
Given that,
The equation is [tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6[/tex].The x = -2.Based on the above information, the calculation is as follows:
[tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6\\\\= 2(-2)^4 - 4(-2)^3-11(-2)^2+3(-2)-6\\\\= 2\times 16 - 4\times -8 - 11\times 4+ 3 \times -2 - 6\\\\[/tex]
= 32 + 32 - 44 - 6 - 6
= 8
Therefore we can conclude that the answer is 8
Learn more: brainly.com/question/17429689
What is the gcf of 108 and 132
Answers
Answer:
12
Explanation:
The greatest common factor (GCF) is the largest factor two numbers share within their respective factor trees. In order to find the GCF, list factors of each number and then select the biggest one they have in common.
Factors of 108 are:
1, 108; 2, 54; 4, 27; 6, 18; 9, 12
Factors of 132 are:
1, 132; 2, 66; 3, 44; 4, 33; 6, 22; 11, 12
As can be observed, the largest number they have in common is 12. Therefore the GCF of 108 and 132 is 12.
Alexander is riding his bicycle to school. After one mile he is a third of the way there. How much more does he have to ride
Answers
1 mile = (1/3)*(distance to school)
Multiply this equation by 3 and you have
3 mile = (distance to school)
You also know that
(distance ridden so far) +(remaining distance) = (distance to school)
Subsituting given information, this is
1 mile + (remaining distance) = 3 mile
Subtracting 1 mile from this equation gives
(remaining distance) = 2 miles
Alexander has 2 miles more to ride.
Use multiplying by 1 to find an expression equivalent to 3/14 with a denominator of 14 y.
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now, "same" could be anything whatsoever, you name it, a whole polynomial, a whole anything whatsoever.
[tex]\bf \cfrac{\sqrt{2}}{\sqrt{2}}=\cfrac{\sqrt{3}}{\sqrt{3}}=\cfrac{100000000}{100000000}=\cfrac{eggs}{eggs}=\cfrac{miles}{miles}=\cfrac{\frac{\quad \sqrt{3}}{\sqrt[5]{17}}\quad }{\frac{\sqrt{3}}{\sqrt[5]{17}}}=\cfrac{whatever}{whatever}=1[/tex]
now, that said, let us use 1 in this case then ... hmmmm we simply need a "y" in the denominator, so we simply multiply the denominator AND numerator by "y", y/y = 1 btw.
[tex]\bf \cfrac{3}{14}\cdot \cfrac{y}{y}\implies \cfrac{3y}{14y}[/tex]
plz help me
it sounds confusing
Answers
[tex]2700 \times 3^m = 2700 \times 3^{-3}= \dfrac{2700}{3^3} = \dfrac{2700}{27} = 100[/tex]
m = -3
3^-3 = 1/27
1/27 × 2,700 = 2,700/27
2,700/27 simplified = 100
Answer = 100
Hope this helped☺☺
What is the midpoint between the points (1, 3) and (5, 7)?
A. (4, 4)
B. (7, 9)
C. (3, 5)
D. (2, 2)
Answers
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have [tex]A(1;\ 3);\ B(5;\ 7)[/tex]
Therefore
[tex]M_{AB}\left(\dfrac{1+5}{2};\ \dfrac{3+7}{2}\right)\to M_{AB}\left(\dfrac{6}{2};\ \dfrac{10}{2}\right)\to M_{AB}(3;\ 5)[/tex]
Answer: C. (3; 5)
A jar contains two red marbles, three green marbles, ten white marbles and no other marbles. two marbles are randomly drawn from the jar without replacement. what is the probability that these two marbles drawn will both be red? express your answer as a common fraction.
the denominator HAS to be 15C2
but what's the numerator?
Answers
Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
method. Which method is most efficient? Explain.
Answers
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8
Distributive property:
(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8
Both methods are efficient, it all depends with the users preference
Final answer:
To simplify (3x+8)(x+1), we can use the FOIL method, the Distributive Property, or a multiplication table, all leading to the same simplified expression: 3x² + 11x + 8. The FOIL method is typically the most efficient for binomials.
Explanation:
The question asks to simplify the expression (3x+8)(x+1) using a table, the Distributive Property, and the FOIL method and to determine which method is most efficient.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last and represents a quick way to multiply two binomials:
First: Multiply the first terms in each binomial (3x×x = 3x²).
Outer: Multiply the outer terms (3x×1 = 3x).
Inner: Multiply the inner terms (8×x = 8x).
Last: Multiply the last terms in each binomial (8×1 = 8).
Adding these products together, we get 3x² + 3x + 8x + 8, which simplifies to 3x² + 11x + 8.
Using the Distributive Property
This involves expanding the expression by multiplying each term in the first polynomial by each term in the second: (3x+8)(x) + (3x+8)(1), which also simplifies to 3x² + 11x + 8.
Using a Table
Create a table where you list each term of the first polynomial in the first row and the terms of the second polynomial in the first column, and then fill in the table with the products of the intersecting terms. The sum of these products will also yield 3x² + 11x + 8.
While all three methods will give the correct answer, the FOIL method is generally seen as the most efficient for this particular problem, as it provides a straightforward, step-by-step process that is easy to follow and remember for multiplying two binomials.
The rate of the number of bags mishandled by the airlines fell to 4.77 bags per 1000 passengers in 2011. At this rate,
estimate how many bags would be mishandled for 1650 passengers.
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-5n+22>=-73
[tex] - 5n + 22 \geqslant - 73 = [/tex]
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(note: I know it's greater than or equal to, but I'm just going to use > for the sake of time)
-9n > -95
Divide both sides by -9 (This will flip the sign):
n < -95/9
n [tex] \leq [/tex] -10 5/9
(I'm not sure if you wanted a mixed fraction or not, so...)
describe a situation where it is easier to use decimals than fractions and explain why
Answers
When you must multiply non whole numbers, decimals are easier to manipulate in the sense that setting up a multiplication problem with decimals rather than fractions is much simpler and easier to calculate.
Lupe has 14 stickers that she wants to give to 2 friends. She wants each friend to have the same number of stickers. Select the three statements that describe how Lupe should give the stickers to her friends. Each friend gets 14÷2 stickers. Each friend gets 2 of the 14 stickers. Each friend gets 142 stickers. Each friend gets 7 of the 14 stickers.
Answers
Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
It is given that Lupe has 14 stickers that she wants to give to 2 friends.
Total number of stickers Lupe has is 14.
The number of friends is 2.
She wants each friend to have the same number of stickers. It means each friend will get half of 14.
The number stickers Lupe should give to her friends is 14 divided by 2.
[tex]\text{Number of stickers}=14\div 2[/tex]
Write this value in fraction form.
[tex]\text{Number of stickers}=\frac{14}{2}[/tex]
[tex]\text{Number of stickers}=7[/tex]
It means the correct statements are
1. Each friend gets 14÷2 stickers.
3. Each friend gets (14)/2 stickers.
4. Each friend gets 7 of the 14 stickers.
Hence correct options are 1, 3 and 4.
a golf course charges $10 to golf or $150 for a summer pass. Write an inequality to represent the number of times you would need to golf in order for the summer pass to be a better deal
Answers
We have then:
x: the number of times you would need to golf
We write now the inequality:
10x> 150
Answer:
An inequality to represent the number of times you would need to golf in order for the summer pass to be a better deal is:
10x> 150
Answer:I
Step-by-step explanation:
how many ounces of 30% hydrochloric acid solution and 80% hydrochloric acid solution must be mixed to get 10 oz of 50% hydrochloric acid solution
Answers
This diagram tells you the constituents 80% and 30% solution are in the proportion 20:30 or 2:3 or 4:6 to make the mix having 50% hydrochloric acid. Note that the numbers 4 and 6 add to 10, the number of ounces of solution we want.
4 ounces of 80% solution must be mixed with 6 ounces of 30% solution to make 10 ounces of 50% solution.
Tree a lived for 6 decades and 5 years. Tree b lived for 58 years. Which tree lived longer
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Final answer:
Tree A, which lived for 65 years (6 decades and 5 years), lived longer than Tree B, which lived for 58 years.
Explanation:
To answer which tree lived longer, we can calculate the age of both trees. Tree A lived for 6 decades and 5 years. Since one decade is equal to 10 years, 6 decades would be 6 x 10 years, which is 60 years. Adding the additional 5 years, Tree A lived for a total of 60 + 5 = 65 years.
Tree B lived for 58 years. Comparing both ages, Tree A lived for 65 years while Tree B lived for 58 years. Therefore, Tree A lived longer than Tree B.
Solve the given differential equation. y' = 5x^2 − 1/ 5 + 4y
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Please please help!!
Answers
x must be different to zero, then x=0 is an asymptote
When x tends to -infinite or x tends to + Infinite, the function f(x) tends to zero, then y=0 is an asymptote.
In g(x):
x-1 must be different to zero, then x=1 is an asymptote
When x tends to -infinite or x tends to + Infinite, the function g(x) tends to zero, then y=0 is an asymptote.
Answers:
Third option: y=0
x=0 is an asymptote
The answer for the question is the 3rd option y= 0
5,895÷36
show all your work
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____
The calculator is certainly faster.
hey can you please help me posted picture of question
Answers
There are 50 total patrons. 16 like lattes, 12 like espressos, and 8 like both drinks.
Add the two totals for patrons that like either lattes or espressos:
[tex] 16 + 12 = 28 [/tex]
8 patrons like both drinks, so subtract this from the amount of patrons that like either drink:
[tex] 28 - 8 = 20 [/tex]
20 patrons like at least one drink.
Subtract the amount of patrons that like a drink from the total amount of patrons:
[tex] 50 - 20 = \boxed{30} [/tex]
30 patrons like neither drink.
n(L) = 16
n(E) = 12
n(L and E) = 8
n(L or E) = n(L) + n(E) - n(L and E)
n(L or E) = 16 + 12 - 8 = 20
Thus 20 like Either of the coffee drinks.
The patrons don't like either of the drinks will be = 50 - 20 = 30
So, option D gives the correct answer
In a class, 12 out of 25 students are female. what percent of students are female?
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12 females
25 total students
12 / 25 = 0.48 = 48%
What is the surface area of a cylinder with a radius of 5 ft and a height of 2 ft?
Answers
Answer:
Its B.
Have a great day! OwO
A bookstore costs $90 a day to keep open, and spends $12 for each book it sells. the store charges $18 for each book it sells. If n represents the number of books sold, which equation represents the revenue function for this bookstore?
Answers
Answer:
[tex]R=6n-90[/tex]
Step-by-step explanation:
Let
R------> the revenue function
n------> the number of books sold per day
we know that
In this problem
[tex]18n[/tex] -----> represent the profit
[tex](12n+90)[/tex] -----> represent the cost
so
The revenue is equal to the profit minus the cost
[tex]R=18n-(12n+90)[/tex]
[tex]R=n(18-12)-90[/tex] ------> equation that represent the revenue function
Simplify
[tex]R=6n-90[/tex]