Solve 2(x+3)=5(x-4) in pair of equation

Express 16 1/4in simplest radical form

elena-14-01-66 [18.8K]

Answer:

2

Step-by-step explanation:

${16}^{ \frac{1}{4} } \: can \: also \: be \: written \: as \: ( {{2}^{4})}^{ \frac{1}{4} }$

because ${2}^{4} = 16$

So,

${( {2}^{4} )}^{ \frac{1}{4} } = {(2)}^{4 \times \frac{1}{4} } = 2$

7 0

3 years ago

The length and width of a rectangle are measured as 55 cm and 49 cm, respectively, with an error in measurement of at most 0.1 c

valentina_108 [34]

Answer:

The maximum error in the calculated area of the rectangle is $10.4 \:cm^2$

Step-by-step explanation:

The area of a rectangle with length $L$ and width $W$ is $A= L\cdot W$ so the differential of A is

$dA=\frac{\partial A}{\partial L} \Delta L+\frac{\partial A}{\partial W} \Delta W$

$\frac{\partial A}{\partial L} = W\\\frac{\partial A}{\partial W}=L$ so

$dA=W\Delta L+L \Delta W$

We know that each error is at most 0.1 cm, we have $|\Delta L|\leq 0.1$ , $|\Delta W|\leq 0.1$ . To find the maximum error in the calculated area of the rectangle we take $\Delta L = 0.1$ , $\Delta W = 0.1$ and $L=55$ , $W=49$ . This gives

$dA=49\cdot 0.1+55 \cdot 0.1$

$dA=10.4$

Thus the maximum error in the calculated area of the rectangle is $10.4 \:cm^2$

4 0

3 years ago

PLEASE HELP WITH ALL!!!

rosijanka [135]

3/4. triangle FHE and triangle KMN; triangle GEH and triangle LNM

3 0

3 years ago

Read 2 more answers

Solve the equation 6.7x = 5.2x + 12.3

Anna [14]

Answer:

x = 8.2

Step-by-step explanation:

$6.7x = 5.2x + 12.3$

$6.7x - 5.2x = 12.3$

$1.5x = 12.3$

$x = 8.2 = \frac{41}{5} = 8 \frac{1}{5}$

7 0

3 years ago

BRAINLIESSTTTT ASAP !!!!!!!!!! 20 pointssss

Mars2501 [29]

Answers:
_____________________________________________________
Part A) " (3x + 4) " units .
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Part B) "The dimensions of the rectangle are:

" (4x + 5y) " units ; AND: " (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 ;

{Note: 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.}.
____________________________________________________
→ 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 .
_______________________________________________________

Part A): The answer is: "(3x + 4)" units.
____________________________________________________

Explanation for Part B):
_________________________________________________________

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;
_______________________________________________________
Given: " A = (16x² − 25y²) square units" ;

→ We are asked to find the dimensions, "L" & "w" ;
→ by factoring the given "area" expression completely:
____________________________________________________
→ 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:
_______________________________________________________

→ " (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 " .
______________________________________________________

→ So, we can rewrite: " (16x² − 25y²) " ;

as: " (4x)² − (5y)² " ;

→ {Note: We substitute: "(4x)² " for "(16x²)" ; & "(5y)² " for "(25y²)" .} . ;
_______________________________________________________
→ 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 "difference of squares".}.

→ As such: " (4x)² − (5y)² " = " (4x + 5y) (4x − 5y) " .
_______________________________________________________
Part B): The answer is: "The dimensions of the rectangle are:

" (4x + 5y) " units ; AND: " (4x − 5y)" units."
_______________________________________________________

7 0

3 years ago