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3 years ago

Write all the possible two-digit numbers which can be formed using the digits 0,3,5

Mathematics

1 answer:

Leokris [45]3 years ago

8 0

Answer:

i) where the digits can repeat

1. 30

2. 50

3. 33

4. 55

5. 35

6. 53

ii) where the digits cannot be repeated

1. 30

2. 50

3. 35

4. 53

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Tickets to a movie cost $9.00 for adults and $5.50 for students. There were 150 tickets purchased for a total of $1,105.00. The

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Answer:

150a

Step-by-step explanation:

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3 years ago

A square patio has an area of 200 ft.² how long is each side of the patio to the nearest 0.05

kramer

14 multiplied by 14 equals 196 which is closer to 14.0 than to 14.5

4 0

3 years ago

Round 89,678 to the nearest hundred thousand

zmey [24]

Answer:

The nearest 100,000 of 89,678 would be 100,000.

Step-by-step explanation:

For me to simply put this, ignore the digits behind the commas.

You'll have 89, and imagine you have to get it to the nearest 100.

So when rounding / estimating, if the digit you're talking about is above 5, you round up. If it is below 5, you round down.

Since you have 89, you'd round up to a 100 because 89 is over 50.

Therefore you'd have 100,000 if you're rounding 89,678 to the nearest hundred thousand.

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3 years ago

An amount of 700 was invested at 7 percent for 7 months. What is the interest

sergeinik [125]

Answer:

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Step-by-step explanation:

700/7%

4 0

3 years ago

Read 2 more answers

Given that f(x) = √(ax + 1) , with x ≥ -1/a and a > 0

padilas [110]

Answer:

$\displaystyle 7$

Step-by-step explanation:

first thing I assume by f~¹ you meant $f^{-1}$ however

we want to find a²+3x-3 for the given condition. with the composite function condition we can do so

Finding the inverse of f(x):

$\displaystyle f(x) = \sqrt{ax + 1}$

substitute y for f(x):

$\displaystyle y= \sqrt{ax + 1}$

interchange:

$\displaystyle x= \sqrt{ay + 1}$

square both sides:

$\displaystyle ay + 1 = {x}^{2}$

cancel 1 from both sides:

$\displaystyle ay = {x}^{2} - 1$

divide both sides by a:

$\displaystyle y = \frac{{x}^{2} - 1 }{a}$

substitute f^-1 for y:

$\displaystyle f ^{ - 1} (x) = \frac{{x}^{2} - 1 }{a}$

finding the inverse of g(x):

$\displaystyle g(x) = \frac{x + 1}{x}$

substitute y for g(x)

$\displaystyle y= \frac{x + 1}{x}$

interchange:

$\displaystyle \frac{y + 1}{y} =x$

cross multiplication

$\displaystyle y + 1= xy$

cancel 1 from both sides

$\displaystyle y - xy= - 1$

factor out y:

$\displaystyle y(1 - x)= - 1$

divide both sides by 1-x:

$\displaystyle y= - \frac{1}{ 1 - x}$

substitute g^-1 for y:

$\displaystyle g ^{ - 1} (x)= - \frac{1}{ 1 - x}$

remember that

$\displaystyle (f \circ g)x = f(g(x))$

therefore we obtain:

$\rm \displaystyle (f ^{ - 1} \circ g ^{ - 1} ) (3) = \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a}$

since (f~¹•g~¹)(3)=-⅜ thus substitute:

$\rm \displaystyle \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify parentheses:

$\rm \displaystyle \frac{{ \bigg( \dfrac{1}{2} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify square:

$\rm \displaystyle \frac{{ \dfrac{1}{4} } - 1 }{a} = - \frac{3}{8}$

simplify substraction:

$\rm \displaystyle \frac{ - \dfrac{3}{4} }{ a}= - \frac{3}{8}$

simplify complex fraction:

$\rm \displaystyle - \dfrac{3}{4a} = - \frac{3}{8}$

get rid of - sign:

$\rm \displaystyle \dfrac{3}{4a} = \frac{3}{8}$

divide both sides by 3:

$\rm \displaystyle \dfrac{1}{4a} = \frac{1}{8}$

cross multiplication:

$\rm \displaystyle 4a= 8$

divide both sides by 4:

$\rm \displaystyle \boxed{ a= 2}$

as we want to find a²+3a-3 substitute the got value of a:

$\displaystyle {2}^{2} + 3.2 - 3$

simplify square:

$\displaystyle 4 + 3.2 - 3$

simplify multiplication:

$\displaystyle 4 +6 - 3$

simplify addition:

$\displaystyle 10 - 3$

simplify substraction:

$\displaystyle 7$

and we are done!

7 0

3 years ago