How many whole numbers between 1 and 150 have exactly 3 different factors?

2x+y=3<br>x-y= 1<br><br>solve the equation

svetlana [45]

Answer:

x = 4/3

y = 1/3

Step-by-step explanation:

System of equations! This is set up really well to make the second equation equal x then substitute.

x - y = 1

x = 1 + y

and then our substitution:

2 (1+y) + y = 3

and solve:

2 + 2y + y = 3

3y + 2 = 3

3y = 1

y = 1/3

And now we can substitute that value into one of our equations:

x - (1/3) = 1

x = 4/3

Next we should check by substituting these values into both of our equations:

2 (4/3) + (1/3) = 3

9 / 3 does equal 3 !

(4/3) - (1/3) does equal 1 !

Therefore, x = 4/3 , and y = 1/3

4 0

3 years ago

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The digit in the tens place of a two digit number is three times that in the units place. If the digits are reversed the new num

S_A_V [24]

We could do it with algebra. But we can also do it the long way, which is
shorter than the algebraic way.

The digit in the tens place is 3 times the digit in the units place.
So the number MUST be
31, or
62, or
93 .
It can't be anything else.

Now here they are again, with the reverse of each one:

31 . . . 13 The new number is 18 less.
62 . . . 26 The new number is 36 less.
93 . . . 39 The new number is 54 less.

Obviously, the original number is 62.

4 0

3 years ago

In each situation, write a recurrence relation, including base case(s), for the given function. briefly explain in words why thi

vova2212 [387]

A thumb-wrestling match requires two thumbs, so we can either suppose that we need at least two people $(n\ge2)$ , or allow one to thumb-wrestle one's self. In either case, we'd have $t(1)=t(2)=1$ , so let's just say we need a minimum of two players.

If we add one more person to the set of players, then the first two people would need to play 1 additional match each. So $t(3)=t(2)+2$ .

If we add one more person, then the first three people would again each have to play 1 more match with the new person. So $t(4)=t(3)+3$ .

And so on, so that in general, the number of games needed for everyone to play exactly one match with everyone else is given recursively by

$\begin{cases}t(2)=1\\t(n+1)=t(n)+n&\text{for }n\ge2\end{cases}$

6 0

3 years ago

n a cookie recipe, there are 3 parts ugar and 2 parts flour. For every cup of our, how much sugar do you need?

Nina [5.8K]

Answer: For every cup of flour we need 2/3 cups of sugar.

For every cup of sugar you need 3/2 cups of flour.

Step-by-step explanation:

4 0

3 years ago

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The slope of the line below is ___.

worty [1.4K]