Write an expression you could use to convert 2.5 gallons to quaRTS. PLZ ANSWER. THANKS. IM GIVING 24 POINTS AWAY FOR THIS QUESTION

Answers

Answer 1

Answer: well, there are 4 quarts in a gallon, so 2.5*4 would give you 10 quarts

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Imagine you are an engineer for a soda company, and you must find the most economical shape for its aluminum cans. You are given this set of constraints. The can must hold a volume, V, of liquid and be a cylindrical shape of height h and radius r, and you need to minimize the cost of the metal required to make the can. a) First, ignore any waste material discarded during the manufacturing process and just minimize the total surface area for a given volume, V. Using this constraint, show that the optimal dimensions are achieved when h = 2r. The formula for the volume of a cylinder is V = πr 2h. The formula for the lateral area of a cylinder is L = 2πrh. b) Next, consider the manufacturing process. Materials for the cans are cut from flat sheets of metal. The cylindrical sides are made from curved rectangles, and rectangles can be cut from sheets of metal leaving virtually no waste material. However, the process of cutting disks for the tops and bottoms of the cans from flat sheets of metal leaves significant waste material. Assume that the disks are cut from squares with side lengths of 2r, so that one disk is cut out of each square in a grid. Show that, in this case, the amount of material needed is minimized when: h/r = 8/π ≈ 2.55 c) It is far more efficient to cut the disks from a tiling of hexagons than from a tiling of squares, as the former leaves far less waste material. Show that if the disks for the lids and bases of the cans are cut from a tiling of hexagons, the optimal ratio is h/r = 4√3/π ≈ 2.21. Hint: The formula for the area of a hexagon circumscribing a circle of radius r is A = 6r/2 √3 . d) Look for different-sized aluminum cans from the supermarket. Which models from problems a–c best approximate the shapes of the cans? Are the cans actually perfect cylinders? Are there other assumptions about the manufacture of the cans that we should consider? Do a little bit of research, and write a one-page response to answer some of these questions by comparing our models to the actual dimensions used.
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Any number that is divisible by 3 is also divisible by 6.Find a counterexample to show that the conjecture is false.
21
18
24
12

Answers

21/3 = 7 21/6 = 3.5
18/3 = 6 18/6 = 3
24/3 = 8 24/6 = 4
12/3 = 4 12/6 = 2

Each can be divided to obtain an integer, except:

21/6 = 3.5

So, while 21 can be divided by 3, it cannot be divided by 6 (for an integer anyway)

21/3=7
but
21/6=3.5
.......

Answer this in pattern,show the solutionCube of Binomial

1.) (x+4)³
2.) (x-4)³
3.) (7m-3n)³
4.) (3xy+1)

Factoring:Factor the ff. Trinomials

1.) 6m³-9m²
2.) 6m²-12mn²+3n

Factor the difference of two square

1.) 9x²-25y²
2.)36x²-49y²
3.)32m²-98n²
4.)36p²-25

Answers

Cube of Binomial
1. $(x + 4)^(3)$
   $(x + 4)(x + 4)(x + 4)$
   $(x(x + 4) + 4(x + 4))(x + 4)$
   $(x(x) + x(4) + 4(x) + 4(4))(x + 4)$
   $(x^(2) + 4x + 4x + 16)(x + 4)$
   $(x^(2) + 8x + 16)(x + 4)$
   $x^(2)(x + 4) + 8x(x + 4) + 16(x + 4)$
   $x^(2)(x) + x^(2)(4) + 8x(x) + 8x(4) + 16(x) + 16(4)$
   $x^(3) + 4x^(2) + 8x^(2) + 32x + 16x + 64$
   $x^(3) + 12x^(2) + 48x+ 64$

2. $(x - 4)^(3)$
   $(x - 4)(x - 4)(x - 4)$
   $(x(x - 4) - 4(x - 4))(x - 4)$
   $(x(x) - x(4) - 4(x) + 4(4))(x - 4)$
   $(x^(2) - 4x - 4x + 16)(x - 4)$
   $(x^(2) - 8x + 16)(x - 4)$
   $x^(2)(x - 4) - 8x(x - 4) + 16(x - 4)$
   $x^(2)(x) - x^(2)(4) - 8x(x) + 8x(4) + 16(x) - 16(4)$
   $x^(3) - 4x^(2) - 8x^(2) + 32x + 16x - 64$
   $x^(3) - 12x^(2) + 48x - 64$

3. $(7m - 3n)^(3)$
   $(7m - 3n)(7m - 3n)(7m - 3n)$
   $(7m(7m - 3n) - 3n(7m - 3n))(7m - 3n)$
   $(7m(7m) - 7m(3n) - 3n(7m) + 3n(3n))(7m - 3n)$
   $(49m^(2) - 21mn - 21mn + 9n^(2))(7m - 3n)$
   $(49m^(2) - 42mn + 9n^(2))(7m - 3n)$
   $49m^(2)(7m - 3n) - 42mn(7m - 3n) + 9n^(2)(7m - 3n)$
   $49m^(2)(7m) - 49m^(2)(3n) - 42mn(7m) + 42mn(3n) + 9n^(2)(7m) - 9n^(2)(3n)$
   $343m^(3) - 147m^(2)n - 294m^(2)n + 126mn^(2) + 63mn^(2) - 27n^(3)$
   $343m^(3) - 441m^(2)n + 189mn^(2) - 27n^(3)$

4. $(3xy + 1)^(3)$
   $(3xy + 1)(3xy + 1)(3xy + 1)$
   $(3xy(3xy + 1) + 1(3xy + 1))(3xy + 1)$
   $(3xy(3xy) + 3xy(1) + 1(3xy) + 1(1))(3xy + 1)$
   $(9x^(2)y^(2) + 3xy + 3xy + 1)(3xy + 1)$
   $(9x^(2)y^(2) + 6xy + 1)(3xy + 1)$
   $9x^(2)y^(2)(3xy + 1) + 6xy(3xy + 1) + 1(3xy + 1)$
   $9x^(2)y^(2)(3xy) + 9x^(2)y^(2)(1) + 6xy(3xy) + 6xy(1) + 1(3xy) + 1(1)$
   $27x^(3)y^(3) + 9x^(2)y^(2) + 18x^(2)y^(2) + 6xy + 3xy + 1$
   $27x^(3)y^(3) + 27x^(2)y^(2) + 9xy + 1$

Factoring Trinomials
1. $6m^(3) - 9m^(2)$
   $3m^(2)(2m) + 3m^(2)(3)$
   $3m^(2)(2m + 3)$

2. $6m^(2) - 12mn^(2) + 3n$
   $3(2m^(2)) - 3(4mn^(2)) + 3(n)$
   $3(2m^(2) - 4mn^(2) + n)$

Factoring the Difference of Two Squares
1. $9x^(2) - 25y^(2)$
   $9x^(2) + 15xy - 15xy - 25y^(2)$
   $3x(3x) + 3x(5y) - 5y(3x) - 5y(5y)$
   $3x(3x + 5y) - 5y(3x + 5y)$
   $(3x - 5y)(3x + 5y)$

2. $36x^(2) - 49y^(2)$
   $36x^(2) - 42xy + 42xy - 49y^(2)$
   $6x(6x) - 6x(7y) + 7y(6x) - 7y(7x)$
   $6x(6x - 7y) + 7y(6x - 7y)$
   $(6x + 7y)(6x - 7y)$

3. $32m^(2) - 98n^(2)$
   $2(16m^(2)) - 2(49n^(2))$
   $2(16m^(2) - 49n^(2))$
   $2(16m^(2) - 28mn + 28mn - 49n^(2))$
   $2(4m(4m) - 4m(7n) + 7n(4m) - 7n(7n))$
   $2(4m(4m - 7n) + 7n(4m - 7n))$
   $2(4m + 7n)(4m - 7n)$

4. $36p^(2) - 25$
   $36p^(2) - 30p + 30p - 25$
   $6p(6p) - 6p(5) + 5(6p) - 5(5)$
   $6p(6p - 5) + 5(6p - 5)$
   $(6p + 5)(6p - 5)$

At a cost of $2.50 per square yard, what would be the price of carpeting a rectangular ﬂoor, 18 ft x 24 ft?

Answers

Answer is: $120

(18ft x 24ft) = 432 square feet

1 yard = 3 feet
1 square yard = (1yd * 1yd) =(3ft * 3ft) = 9 square feet

(432 ft^2)/(9 ft^2 per yard) = 48 square yards

(48 square yards)*($2.50 per yard) = $120

Frank runs 3 miles in 25 minutes. At the same rate, how many miles would he run in 20 minutes?n milos

Answers

2.4 miles

cross multiple 3/25 x x/20
25x=60
x = 60/25 simplified is 2 2/5 or 2.4 miles

What is the slope of the line passing through the points (-3, 4) and (2, - 1)? A -1B 1
C 3/5
D - 5/3

Answers

Answer:

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $(y_(2)-y_(1) )/(x_(2)-x_(1) )$

with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (2, - 1 )

m = $(-1-4)/(2-(-3))$ = $(-5)/(2+3)$ = $(-5)/(5)$ = - 1 → A

Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2f(x) = x3 – x2 – 4x + 4
f(x) = x4 – 3x2 – 4
f(x) = x4 + 3x2 – 4
f(x) = x3 + x2 – 4x – 4

Answers

Hello,

ANSWER B (x^4-3x²-4) [roots are i,-i,2,-2]

Your answer is f(x) = x4 – 3x2 – 4

Hope this helps.

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Which expression is equivalent to x^4-y^4?