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3 years ago

11. The rectangle has a width of 8 in, a length of x-5 in, and an area of 16 in). Solve for x.

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

3 0

Use the area of rectangle formula which is:

$\displaystyle \large \tt{A = width \times length}$

Given that:

area of rectangle = 16
width = 8
length = x-5

Substitute in the formula:

$\displaystyle \large{16 = 8 \times (x - 5)} \\ \displaystyle \large{16 = 8(x - 5)}$

Distribute 8 in the expression:

$\displaystyle \large{16 = (8 \times x) + (8 \times ( - 5))} \\ \displaystyle \large{16 = 8x - 40}$

Move -40 to another side and change from -40 to 40.

$\displaystyle \large{16 + 40 = 8x} \\ \displaystyle \large{56= 8x} \\$

Then move 8 to divide 56, leaving only x.

$\displaystyle \large{ \frac{56}{8} = x} \\ \displaystyle \large{7 = x} \\$

Hence, the answer is:

$\displaystyle \large \boxed{x = 7} \\$

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Tomas buys a bag of 5 peaches for $3.55. Write and solve an equation to find how much money, m, Tomas paid for each peach

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3 years ago

Twenty-seven is % of 60 help mee asap

jok3333 [9.3K]

Answer: The answer is: " 45 % " .

________________________________________________

→ " Twenty-seven is 45 % of 60. "

________________________________________________

Step-by-step explanation:

________________________________________________

The question asks:

" 27 is what % {percentage] of 60 " ? ;

________________________

So: " 27 = (n/100) * 60 " ; Solve for "n" ;

________________________________________________

Method 1:

________________________________________________

→ (n/100) * 60 = 27 ;

Divide each side by 60 :

→ [ (n/100) * 60 ] / 60 = 27 /60 ;

to get:

→ (n/100) = 27/60 ;

Now: Cross-factor multiply:

→ 60n = (27)*(100) ;

to get:

→ 60n = 2700 ;

Divide each side by "60" ;

→ 60n = 2700/ 60 ;

to get: n = 45 ;

________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Method 2:

________________________________________________

The question asks:

" 27 is what % {percentage] of 60 " ?

________________________

To solve this problem:

Rephrase this question as:

________________________

" 27 is 60% of what number ? "

→ The answer will be the same!

________________________

→ 27 = (60/100)* n ; Solve for "n" ;

Multiply each side of the equation by "100" ; to eliminate the fraction:

→ 100 * 27 = 100 * [ (60/100)* n ] ;

to get:

→ 2700 = 60n ;

↔ 60n = 2700 ;

Divide Each Side of the equation by "60" ;

→ 60n/60 = 2700 / 60 ;

to get: n = 45 ;

________________________________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Method 2: Variant 1 of 2:

________________________________________________

When we have:

→ 27 = (60/100)* n ; Solve for "n" ;

________________________

Note that: "(60/100) = (60÷ 100) = (6 ÷ 10)" ; since: in "(60/100)" ; the "zero" from the "numerator" cancels out; And: the "last zero" in "100" — from the "denominator" cancels out; since we are dividing "each side" of the fraction by "10" ;

→ "(60÷10) / (600÷10)" = " 6/10 " ;

→ " (6/10)" ; that is; "six-tenths"} ;

→ can be represented by: " 0.6 " ;

→ {by convention; but specifically, here is the explanation} — as follows:

________________________

→ "(6/10)" = " (6 ÷ 10) " ;

Note: When dividing a number by "10" ; we take the original number; and move the decimal point to the left; & then we rewrite that number as the "answer".

Note: When multiplying or dividing by a positive, non-zero integer factor of "10" that has at least 1 (one) "zero" after that particular factor of "10". We can get the answer by taking the original number & moving the decimal point the number of spaces as designated by the number of zeros following the particular [aforementioned factor of "10".].

We move the decimal point to the right if we are multiplying; and to the left if we are dividing. In this case, we are dividing "6" by "10 " :

→ " 6 ÷ 10 = ? " ;

→ " 6. ÷ 10 = ? " ;

We take the: " 6. " ; and move the decimal point "one space backward [i.e. "to the left"]; since we are dividing by "10" ;

→ to get: " .6 " ; & we rewrite this value as "0.6" in a rewritten equation:

________________________

So; we take our equation:

→ 27 = (60/100)*n ; And rewrite—substituting "0.6" for

"(60/100)"— as follows:

________________________

→ 27 = (0.6)n ; ↔ (0.6) n = 27 ;

Multiply each side of the equation by "10" ; to eliminate the decimal:

→ 10 * [ (0.6)n ] = 27 * 10 ;

to get:

→ 6n = 270 ;

Divide each side of the equation by "6" ; to isolate "n" on one side of the equation; & to solve for "n" ;

→ 6n / 6 = 270 / 6 ;

to get: n = 45 ;

________________________________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Method 2 (variant 2 of 2):

________________________________________________

We have the equation: 27 = (60/100)* n ; Solve for "n" ;

________________________

Note: From Method 2 (variant) 1 of 2— see above):

________________________

Note: Refer to the point at which we have:

________________________

→ " { (60÷10) / (600÷10)" = " (6/10) " ; that is; "six-tenths"} ;

________________________

Note that the fraction— "(6/10)" ; can be further simplified:

→ "(6/10)" = "(6÷2) / (10÷2)" = "(3/5)" ;

Now, we can rewrite the equation;

→ We replace "(60/100)" ; with: "(3/5)" :

→ 27 = (3/5)* n ; Solve for "n" ;

↔ (3/5)* n = 27 ;

↔ (3n/5) = 27 ;

Multiply Each Side of the equation by "5" ;

→ 5* (3n/5) = 27 * 5 ;

to get:

→ 3n = 135 ;

Divide Each side of the equation by "3" ; to isolate "n" on one side of the equation; & to solve for "n" ;

→ 3n / 3 = 135 / 3 ;

to get: n = 45 ;

________________________________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Hope this answer is helpful!

Wishing you the best in your academic endeavors

— and within the "Brainly" community!

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ira [324]

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