May anyone HELP ME please

Mathematics

1 answer:

Vladimir79 [104]3 years ago

5 0

1a. 64*10^6 +5.4*10^6 = 69.4*10^6 = 6.94*10^7 . . . . square miles

1b. 6.4*10^7 +0.54*10^7 = 6.94*10^7 . . . . square miles
.. yes, we can find the same answer this way

2. The ratio of areas is 6.4*10^7/(5.4*10^6) ≈ 11.85
The Pacific Ocean is about 12 times the size of the Arctic Ocean.

The difference of areas is 6.4*10^7 -0.54*10^7 = 5.86*10^7
The Pacific Ocean is 5.86*10^7 square miles larger than the Arctic Ocean.

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Solve the equation; 3a/4-2a/3=7/4

DiKsa [7]

Answer: " a = 21 " .

_____________________

Step-by-step explanation:

Given: 3a/4-2a/3 = 7/4 ; Solve for "a" ;

Rewrite as: (3a/4) - (2a/3) = (7/4) ;

Now, for each of the three (3) "denominator values" in "fraction form" within the equation given:

→ Find the "LCD" ["Least Common Denominator"]:
The denominators are: 4, 3, and 4 ;

that is: "3" and "4" ;
____

To find the LCD: First; multiply the denominators: "4 * 3 = 12" .
So; the value "12" could be the LCD; so, the value for the LCD is no greater than "12" ; however, there could be a smaller value.
To determine the LCD:
List the multiples of the given denominators:
____
3: 3, 6, 9, 12, 15 .... ;
4: 4, 8, 12, 16... ;
____
We find that "12" is, in fact, the LCD of "3" and 4:
____
We can multiply each side of the equation by "12" ; to eliminate the "fractional values" :
____
$12*[\frac{3a}{4} - \frac{2a}{3}] = 12*[{\frac{7}{4}]$
____
Note the "distributive property" of multiplication:
→ a(b+c) = ab + ac ;

____

As such:
$12*[\frac{3a}{4} - \frac{2a}{3}] = 12*[{\frac{7}{4}]$ ;

____
Let us start with the "left-hand side" of the equation:
____
$12*[\frac{3a}{4} - \frac{2a}{3}]$ ;

= $[12*\frac{3a}{4}] + [-12 * \frac{2a}{3}]$ ;
= $[12*\frac{3a}{4}] - [12 * \frac{2a}{3}] ;$
____
Note: " $[12*\frac{3a}{4}]$ " ;

$= \frac{12}{1} * \frac{3a}{4}$ ;

→ The "12" cancels to a "3" ; and the "4" cancels to a "1" ;
since: "12÷4 = 3" ; and since: "4÷4 = 1" ;
→ and we can rewrite the "left-hand-side" expression as:
→ " $\frac{3}{1} * \frac{3a}{1}$ " ; which we can simplify as:

→ "3 * 3a" ; which we can simplify as: " 9a " .
then we have: " [12 * $\frac{2a}{3}$ ] " ;

which equals:
= " $\frac{12}{1} * \frac{2a}{3}$ " ;
Note: The "12" cancels out to a "4"; & the "3" cancels out to a "1" ;

→ {since: "(12 ÷ 3 = 4)"; & since: "(3 ÷ 3 = 1)" ;
____
→ And we can rewrite the expression as:
→ " $\frac{4}{1} *\frac{2a}{1}$ " ; which we can simplify as:
→ " 4 * 2a " ; which we can simplify/calculation as: " 8a " ;
Now, we can rewrite the expression of the "left-hand side"
of the equation as:
____
→ " [9a] − [8a] " ; (don't forget to carry down the "minus sign"!) ;
which we can simplify/calculate to get:
→ " [9a − 8a] " ; which we can further simplify/calculate;

→ to get:
→ " 1a " ; or: "a" —the value for which we wish to solve!
____
Now, let us examine the "right-hand side" of the equation:
____

→ " $\frac{12}{1} * \frac{7}{4}$ " ;
Note: The "12" cancels out to a "3" ; & the "4" cancels out to a "1" ;
→ {Since: "12 ÷4 = 3 " ; & since: "4 ÷ 4 = 1 "} ;

And we can rewrite the expression as:
→ " $\frac{3}{1} * \frac{7}{1}$ " ; which we can simplify as:
→ " 3 * 7 " ; which can simplify/calculate to get: " 21" ;
⇒ Now, let us rewrite the equation; by using our simplified values for both the "left-hand side" and the "right-hand side" of the equation; to solve for "a" :
⇒ a = 21 ;