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dybincka [34]
3 years ago
8

What is 13/169 in simplest form?

Mathematics
1 answer:
PolarNik [594]3 years ago
3 0
The answer is 1/13, because 13 goes into 169 13 times
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hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and
Mariulka [41]

Given:

The equation is,

2\log _3x-\log _3(x-2)=2

Explanation:

Simplify the equation by using logarthimic property.

\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{      \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}

Simplify further.

\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}

Solve the quadratic equation for x.

\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

\begin{gathered} x-6=0 \\ x=6 \end{gathered}

For (x - 3) = 0,

\begin{gathered} x-3=0 \\ x=3 \end{gathered}

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0
1 year ago
_ 2. (6 x 4)+ (6 x 11) = 6 x (4 + 11)<br> What is the property of this equation?
laiz [17]

Answer:

Distributive Property

Step-by-step explanation:

The distributive property of multiplication over addition can be used when you multiply a number by a sum.

4 0
3 years ago
when two lines intersect one of the angel formed is 82 degrees what would be the measure if the angle vertical to the 82 degree
babymother [125]

Answer:

it would be 98 degrees

Step-by-step explanation:

if 2 lines inersect it means you create 4 angles. 2 of those angles are the same as well as the other ones so if one is 82 then the angle that counters it is 98

82+98=180

180 degrees equals line

7 0
3 years ago
Anyone wanna help out? :’)
Sever21 [200]

Answer:

325 dollars

Step-by-step explanation:

find 10% of 39000 3900 then divide it by 12 months which is 325 every month

5 0
2 years ago
Read 2 more answers
An arched drainage culvert can be modelled by the function:
Zanzabum

Substitute 136.5 for y.

136.5=\frac{x(191-x)}{60}

8190=x(191-x)

8190=191x-x^{2}

x^{2} -191x+8190=0

Compare this equation with ax^{2} +bx+c=0

a = 1, b = - 191, c = 8190

x=\frac{-b+\sqrt{b^{2}-4ac } }{2} or

x=\frac{-b-\sqrt{b^{2}-4ac } }{2}

x=\frac{191+\sqrt{191^{2}-4(1)(8190) } }{2} or

x=\frac{191-\sqrt{191^{2}-4(1)(8190) } }{2}

x=\frac{191+\sqrt{36481-32760 } }{2} or

x=\frac{191-\sqrt{36481-32760 } }{2}

x=\frac{191+\sqrt{3721 } }{2} or

x=\frac{191-\sqrt{3721 } }{2}

x=\frac{191+61}{2} or

x=\frac{191-61}{2}

x=\frac{252}{2} or

x=\frac{130}{2}

x = 126 or x = 65

Hence, the points on the curve are (65, 136.5) and (126, 136.5).

The width of the air space is the distance between these points.

Width = \sqrt{(x_{2}- x_{1})^{2} +( y_{2}- y_{1}) ^{2}

= \sqrt{(126- 65)^{2} +(136.5-136.5) ^{2}

= 126 - 65

= 61

Hence, width of the air space is 61m.



5 0
3 years ago
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