Answer:
3/28
Step-by-step explanation:
Answer:
There are 1419.5 ml in 3 pints
Step-by-step explanation:
The pint is a unit used to measure volume. When measuring many cups of liquid all put together we might want to use quarts.
A quart (qt) is the same thing as 4 cups or 2 pints.
1 quart = 2 pints = 4 cups
Now we have to find how many ml in 3 pints.
1 pint = 473.17647 ml
Now multiply the quantity of pint given in the question by 473.17647 ml.
3 * 473.17647
= 1419.52941 ml
By rounding off we get:
=1419.5 ml
Thus there are 1419.5 ml in 3 pints....
Answer:
6.28 gallons
Step-by-step explanation:
first we need to find the area of a half sphere, and then find how much paint will be needed for that area.
The area of a sphere:
thus, the area of half a sphere is:
we know that the radius is:
we substitute this to find the area of the half sphere (the area they need to paint):
now the question is how many gallons of paint are needed to paint 2,513.27 square feet.
We are told that 1 gallon covers 400 square feet
thus, we must divide 2,513.27 by 400:
6.28 gallons of paint are needed.
Kilograms is used for metric units of measure
Answers:
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Part A) " (3x + 4) " units .
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Part B) "The dimensions of the rectangle are:
" (4x + 5y) " units ; <u>AND</u>: " (4x − 5y)" units."
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Explanation for Part A):
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Since each side length of a square is the same;
Area = Length * width = L * w ; L = w = s = s ;
in which: " s = side length" ;
So, the Area of a square, "A" = L * w = s * s = s² ;
{<u>Note</u>: A "square" is a rectangle with 4 (four) equal sides.}.
→ Each side length, "s", of a square is equal.
Given: s² = "(9x² + 24x + 16)" square units ;
Find "s" by factoring: "(9x² + 24x + 16)" completely:
→ " 9x² + 24x + 16 ";
Factor by "breaking into groups" :
"(9x² + 24x + 16)" =
→ "(9x² + 12x) (12x + 16)" ;
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Given: " (9x² + 24x + 16) " ;
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Let us start with the term:
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" (9x² + 12x) " ;
→ Factor out a "3x" ; → as follows:
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→ " 3x (3x + 4) " ;
Then, take the term:
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→ " (12x + 16) " ;
And factor out a "4" ; → as follows:
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→ " 4 (3x + 4) "
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We have:
" 9x² + 24x + 16 " ;
= " 3x (3x + 4) + 4(3x + 4) " ;
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Now, notice the term: "(3x + 4)" ;
We can "factor out" this term:
3x (3x + 4) + 4(3x + 4) =
→ " (3x + 4) (3x + 4) " . → which is the fully factored form of:
" 9x² + 24x + 16 " ;
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→ Or; write: " (3x + 4) (3x + 4)" ; as: " (3x + 4)² " .
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→ So, "s² = 9x² + 24x + 16 " ;
Rewrite as: " s² = (3x + 4)² " .
→ Solve for the "positive value of "s" ;
→ {since the "side length of a square" cannot be a "negative" value.}.
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→ Take the "positive square root of EACH SIDE of the equation;
to isolate "s" on one side of the equation; & to solve for "s" ;
→ ⁺√(s²) = ⁺√[(3x + 4)²] '
To get:
→ s = " (3x + 4)" units .
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Part A): The answer is: "(3x + 4)" units.
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Explanation for Part B):
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The area, "A" of a rectangle is:
A = L * w ;
in which "A" is the "area" of the rectangle;
"L" is the "length" of the rectangle;
"w" is the "width" of the rectangle;
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Given: " A = </span>(16x² − 25y²) square units" ;
→ We are asked to find the dimensions, "L" & "w" ;
→ by factoring the given "area" expression completely:
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→ Factor: " (16x² − 25y²) square units " completely '
Note that: "16" and: "25" are both "perfect squares" ;
We can rewrite: " (16x² − 25y²) " ; as:
= " (4²x²) − (5²y²) " ; and further rewrite the expression:
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Note:
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" (16x²) " ; can be written as: "(4x)² " ;
↔ " (4x)² = "(4²)(x²)" = 16x² "
Note: The following property of exponents:
→ (xy)ⁿ = xⁿ yⁿ ; → As such: " 16x² = (4²x²) = (4x)² " .
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Note:
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→ " (25x²) " ; can be written as: " (5x)² " ;
↔ "( 5x)² = "(5²)(x²)" = 25x² " ;
Note: The following property of exponents:
→ (xy)ⁿ = xⁿ yⁿ ; → As such: " 25x² = (5²x²) = (5x)² " .
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→ So, we can rewrite: " (16x² − 25y²) " ;
as: " (4x)² − (5y)² " ;
→ {Note: We substitute: "(4x)² " for "(16x²)" ; & "(5y)² " for "(25y²)" .} . ;
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→ We have: " (4x)² − (5y)² " ;
→ Note that we are asked to "factor completely" ;
→ Note that: " x² − y² = (x + y) (x − y) " ;
→ {This property is known as the "<u>difference of squares</u>".}.
→ As such: " (4x)² − (5y)² " = " (4x + 5y) (4x − 5y) " .
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Part B): The answer is: "The dimensions of the rectangle are:
" (4x + 5y) " units ; AND: " (4x − 5y)" units."
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