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ANEK [815]
3 years ago
12

Megan paid $2.52 in sales tax on an item that cost $36.00 before tax. At that rate, how much would she pay in sales tax for an i

tem that costs $40.00 before tax? ​
Mathematics
1 answer:
jeyben [28]3 years ago
7 0

Answer:

She would pay $2.80 in sales tax.

Step-by-step explanation:

This question can be solved by proportions, using a rule of three.

Megan paid $2.52 in sales tax on an item that cost $36.00 before tax. How much in taxes for $40.00 before taxes?

$2.52 - $36.00

x - $40.00

Applying cross multiplication

36x = 40*2.52

x = \frac{40*2.52}{36}

x = 2.8

She would pay $2.80 in sales tax.

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Simplify u^2+3u/u^2-9<br> A.u/u-3, =/ -3, and u=/3<br> B. u/u-3, u=/-3
VashaNatasha [74]
  The correct answer is:  Answer choice:  [A]:
__________________________________________________________
→  "\frac{u}{u-3} " ;  " { u \neq ± 3 } " ; 

          →  or, write as:  " u / (u − 3) " ;  {" u ≠ 3 "}  AND:  {" u ≠ -3 "} ; 
__________________________________________________________
Explanation:
__________________________________________________________
 We are asked to simplify:
  
  \frac{(u^2+3u)}{(u^2-9)} ;  


Note that the "numerator" —which is:  "(u² + 3u)" — can be factored into:
                                                      →  " u(u + 3) " ;

And that the "denominator" —which is:  "(u² − 9)" — can be factored into:
                                                      →   "(u − 3) (u + 3)" ;
___________________________________________________________
Let us rewrite as:
___________________________________________________________

→    \frac{u(u+3)}{(u-3)(u+3)}  ;

___________________________________________________________

→  We can simplify by "canceling out" BOTH the "(u + 3)" values; in BOTH the "numerator" AND the "denominator" ;  since:

" \frac{(u+3)}{(u+3)} = 1 "  ;

→  And we have:
_________________________________________________________

→  " \frac{u}{u-3} " ;   that is:  " u / (u − 3) " ;  { u\neq 3 } .
                                                                                and:  { u\neq-3 } .

→ which is:  "Answer choice:  [A] " .
_________________________________________________________

NOTE:  The "denominator" cannot equal "0" ; since one cannot "divide by "0" ; 

and if the denominator is "(u − 3)" ;  the denominator equals "0" when "u = -3" ;  as such:

"u\neq3" ; 

→ Note:  To solve:  "u + 3 = 0" ; 

 Subtract "3" from each side of the equation; 

                       →  " u + 3 − 3 = 0 − 3 " ; 

                       → u =  -3 (when the "denominator" equals "0") ; 
 
                       → As such:  " u \neq -3 " ; 

Furthermore, consider the initial (unsimplified) given expression:

→  \frac{(u^2+3u)}{(u^2-9)} ;  

Note:  The denominator is:  "(u²  − 9)" . 

The "denominator" cannot be "0" ; because one cannot "divide" by "0" ; 

As such, solve for values of "u" when the "denominator" equals "0" ; that is:
_______________________________________________________ 

→  " u² − 9 = 0 " ; 

 →  Add "9" to each side of the equation ; 

 →  u² − 9 + 9 = 0 + 9 ; 

 →  u² = 9 ; 

Take the square root of each side of the equation; 
 to isolate "u" on one side of the equation; & to solve for ALL VALUES of "u" ; 

→ √(u²) = √9 ; 

→ | u | = 3 ; 

→  " u = 3" ; AND;  "u = -3 " ; 

We already have:  "u = -3" (a value at which the "denominator equals "0") ; 

We now have "u = 3" ; as a value at which the "denominator equals "0"); 

→ As such: " u\neq 3" ; "u \neq -3 " ;  

or, write as:  " { u \neq ± 3 } " .

_________________________________________________________
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Mrs. Hartill drove 3.1 miles to the grocery store, then 4.25 miles to the salon, and 10.8 miles to her sons house. How many mile
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Answer: 18.15 miles

Step-by-step explanation:

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Answer:

The answer is 37.68 I just took the test.

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What is the number between 8 and 21
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Answer:

9,10,11,12,13,14,15,16,17,18,19 and 29

Step-by-step explanation:

Hope this help!!

3 0
2 years ago
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Please help me this is due in less than 45 minutes!
Natasha_Volkova [10]

Answer:

1.) It's 20th century painting

2.) 0.5 probability

Step-by-step explanation:

If the universal = 60

We need to first get the value of X. That is,

x (x - 2) + x + 2x + 8 + 10 = 60

First open the bracket

x^2 - 2x + x + 2x + 8 + 10 = 60

x^2 + x + 18 = 60

x^2 + x - 42 = 0

Factorise the above equation

x^2 + 7x - 6x - 42 = 0

x (x + 7) -6(x + 7) = 0

x = 6 or - 7

Since x can't be negative, so we will ignore -7

The value for T = 6(6 - 2) = 6×4 = 24

The value for B = 2(6) + 8 = 12 + 8 = 20

If a painting is chosen from random,

If it's from 20th century, the probability will be 34/60 = 0.567

If it's from British painting, the probability will be 30/60 = 0.5

We can therefore conclude that it's from 20th century painting since it has higher value of probability.

The the probability of choosing a British painting will be 30/60 = 0.5

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