What is the solution to the set? 1/2x -- 6.5

Racheal used a total of 5 1/6 gallons of gas while driving her car. Each hour she was driving, she used 5/9 gallons of gas. What

Andreyy89

Answer: The correct answer is: " 9.3 hours " .

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Step-by-step explanation:

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To calculate:

Let "gal" represent "gallons (of gas)" ;

Let "h" represent "hour(s)" ;

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5 $\frac{1}{6}$ gal * (  1 h  ) = ? h ;

( 5/9 gal ) ;

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Note: On the "left-hand side" of the equation;

The units of "gal" ["gallons"] — "cancel out" ;

→ {since: "gal/ gal = 1"} ;

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and we can rewrite our equation as:

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( 5 $\frac{1}{6}$ )

________ hours ;

( 5/9 )

______________________________ ;

To solve:

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5 1/6 ÷ (5/9) =

5 1/6 * (9/5) ;

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Note: Dividing by a fraction is the same as multiplying by that very fraction's reciprocal form.

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Now, let us convert "5 1/6" ; which is a "mixed fraction" ; into an

"Improper fraction" ;

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To do this, we can use the "MAD" method:

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M: Multiply the "denominator number" of the "fraction portion" [within the "mixed fraction"]—by the "whole number" [within the "mixed fraction" ; In this case: "6" , multiplied by "5" ; to get "30" ;

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Then:

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A: Add this obtained value; to the "numerator number" of the

"fraction portion" [within the "mixed fraction"] ;

In this case: "30" ; added to "1" ; to get 31:

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Then:

D: Divide this number by the "denominator number" of the "fraction portion" [within the "mixed fraction"] ; but instead of solving for the quotient—write in the format of a fraction:

In this case: " $\frac{31}{6}$ " .

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Now, substitute this "improper fraction" into our original problem; and rewrite:

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" $\frac{31}{6} * \frac{9}{5}$ " hours;

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We can reduce the "9" to "3" ; and the "6" to "2" ;

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{Since "9/6 = 3/2" };

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And rewrite as:

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" $\frac{31}{2} * \frac{3}{5}$ " hours ;

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Note: " \frac{31}{2} * \frac{3}{5} " ;

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= " $\frac{(31*3)}{(2*5)} = \frac{93}{10}$ " ;

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= 93 ÷ 10 ;

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= 9.3 hours.

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The answer is: " 9.3 hours " .

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Hope this explanation is helpful!

Best of luck to you in your academic pursuits!

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3 0

3 years ago

Quincy deposits $400 in a new bank account that earns 4 simple interest per year. What is the total amount in the account after

Kobotan [32]

Ÿū tj Yates tu hamase de Beas

6 0

3 years ago

5(2x + 6) + 4(4x + 6) + 2 = 26x + 57 What’s the answer

Rama09 [41]

Answer:

No solution

Step-by-step explanation:

10x + 30 +16 x +24 = 26 x + 57

26x + 56 = 26x + 57

56 ≠ 57

3 0

3 years ago

Read 2 more answers

50 POINTS + WILL MARK AS THE BRAINLIEST

Juli2301 [7.4K]

We can look at the graph

Vertex:

we know that vertex is the point where parabola changes it's shape

we can see that

vertex is at (0.5,-0.75)

Axis of symmetry:

we know that axis of symmetry of parabola is always x-value of vertex

we can see that

x-value of vertex is 0.5

so, axis of symmetry is

$x=0.5$

Formula for the function:

we know that this is graph of parabolas

so, we can use vertex formula of parabola

$y=a(x-h)^2+k$

where

(h,k) is vertex

Here , we got

vertex as (0.5 , -0.75)

h=0.5 and k=-0.75

now, we can plug these values

$y=a(x-0.5)^2-0.75$

now, we need to find 'a'

we can select any one point of parabola

and then we can find 'a'

We can see that one of point is (0,-1)

so, we can plug x=0 and y=-1

$-1=a(0-0.5)^2-0.75$

$-0.25=a(0-0.5)^2$

$-0.25=0.25a$

$a=-1$

now, we can plug it back

and we get

$y=-1(x-0.5)^2-0.75$

now, we can expand it

$y=-x^2+x-0.25-0.75$

$y=-x^2+x-1$

so, option-D..........Answer

4 0

3 years ago

Read 2 more answers

Find the distance between the points A (13,2) and B (7, 10)

VashaNatasha [74]

Answer:

8

Step-by-step explanation:

5 0

3 years ago

What is the solution to the set? 1/2x -- 6.5 > 12