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BlackZzzverrR [31]
1 year ago
5

How many positive three-digit numbers are evenly divisible by 33?

Mathematics
1 answer:
Sergio039 [100]1 year ago
7 0

Answer:

27

Step-by-step explanation:

smallest multiple of 33 that is 3 digits is 132 (33*4), and largest is 990 (33*30)

then all the numbers between 4 and 30 would also be 3 digits

including 4 and 30, that makes 27 number in total

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What are the solutions to the following system of equations? y = x2 + 3x − 7 3x − y = −2 (2 points) (3, 11) and (−3, −7) (11, 3)
Minchanka [31]
ANSWER

(3, 11) and (−3, −7)


EXPLANATION

The given system of equations are:


y =  {x}^{2}  + 3x - 7

and

3x - y =  - 2

or

y = 3x  + 2


We equate the two equations to obtain,



{x}^{2}  + 3x - 7 = 3x + 2

We rewrite in standard quadratic form to obtain,

{x}^{2}  + 3x  - 3x - 7 - 2 = 0


This simplifies to

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We solve for x to obtain,


{x}^{2}  = 9

x =  \pm \sqrt{9}

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x = 3 \: or \: x =  - 3

When
x = 3

y = 3(3) + 2 = 11

When x=-3,

y = 3(  - 3) + 2 =  - 7


Therefore the solution for the system is (3, 11) and (−3, −7).
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