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marin [14]
3 years ago
11

X/6 = 10/9 improper fraction in its simplified form

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0

Answer:

\frac{x}{6}  =  \frac{10}{9}  \\   \therefore \: 9 \times x = 6 \times 10 \\ \therefore \:9x = 60 \\ \therefore \:x =  \frac{60}{9}  \\ \therefore \:x =  \frac{20}{3}  \\   \:  \:  \:  \:  \:  \: \huge \red{ \boxed{\therefore \:x =  6\frac{2}{3} }}

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To travel 105 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 64 miles riding a bicycle. S
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<span>Let t=time Doreen travels; let r=rate of Doreen

                RATE * TIME = DIST.
        Sue | r+13      t-3       105
   Doreen |   r           t          64
 
Now solve the system:
(r+13)(t-3)=105
</span>r*t=64<span>
 
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Doreen: rate = 8 mph, time = 8 hours
Sue:  </span>rate = 21 mph, time = 5 hours<span>


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8 0
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4 0
3 years ago
a square garden has a diagonal of 12 m. What is the perimeter of the garden? Express in simplest radical form
lianna [129]

Answer:

The perimeter of the garden, in meters, is 24\sqrt{2}

Step-by-step explanation:

Diagonal of a square:

The diagonal of a square is found applying the Pythagorean Theorem.

The diagonal of the square is the hypothenuse, while we have two sides.

Diagonal of 12m:

This means that d = 12, side s. So

s^2 + s^2 = 12^2

2s^2 = 144

s^2 = \frac{144}{2}

s^2 = 72

s = \sqrt{72}

Factoring 72:

Factoring 72 into prime factors, we have that:

72|2

36|2

18|2

9|3

3|3

1

So

72 = 2^{3}*3^{2}

So, in simplest radical form:

s = \sqrt{72} = \sqrt{2^{3}*3^{2}} = \sqrt{2^3}*\sqrt{3^2} = 2\sqrt{2}*3 = 6\sqrt{2}

Perimeter of the garden:

The perimeter of a square with side of s units is given by:

P = 4s

In this question, since s = 6\sqrt{2}

P = 4s = 4*6\sqrt{2} = 24\sqrt{2}

The perimeter of the garden, in meters, is 24\sqrt{2}

5 0
2 years ago
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