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inna [77]
3 years ago
14

A and b are positive integers and a–b = 3. Evaluate the following:

Mathematics
1 answer:
yulyashka [42]3 years ago
6 0

1/27

1/27

125

Step-by-step explanation:

Given that,

a - b = 3

9^(1/2b) /3^a = 3^(2/2b) /3^a

= 3^b/3^a

= 3^(b-a)

= 3^(-3)

= 27^(-1)

= 1/27

27^(1/3b) /9^(1/2a) = 3^(3/3b) /3^(2/2a)

= 3^b/3^a

= 3^(b-a)

= 3^(-3)

= 27^(-1)

= 1/27

125^(1/3a) /25^(1/2b) = 5^(3/3a) /5^(2/2b)

= 5^a/5^b

= 5^(a- b)

= 5^3

= 125

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2 years ago
What is the solution to log (9x)-log 3 = 3?
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Answer:

The solution x = \frac{e^{3} }{3}

Step-by-step explanation:

<u>Step 1</u>:-

Given log(9 x) -log 3 =3

we have to use formula  log a-log b=log\frac{a}{b}

log(9 x)- log 3 = log(\frac{9 x}{3} ) =3

Again by using formula log a =b

                                       a = e^{b}

so \frac{9 x}{3} =e^{3}

<u>step 2:</u>-

   3 x = e^{3}

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3 years ago
write the equation in slope intercept form of the line that passes through -1, 11 and is parallel to the graph of y = -8x + 3
lawyer [7]
<h2>Answer: The line from the question [ y = -8x + 3 ] passes through the point ( -1, 11 ). </h2>

<h3 /><h3>Step-by-step explanation: </h3>

<u>Find the slope of the parallel line</u>

When two lines are parallel, they have the same slope.

                 ⇒  if the slope of this line = - 8

                      then the slope of the parallel line (m) = - 8

<u>Determine the equation</u>

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:  

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We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

                      since   y - 11  = - 8 (x + 1)

                                        y  = - 8 x  + 3

The line from the question [ y = -8x + 3 ] passes through the point ( -1, 11 ).

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