Square of which of the following numbers would be odd numbers? 257, 324, 560, 491 , 662.

257 and 491

Step-by-step explanation:

There are two methods you could use to solve this.

Whether a number is odd or even relies on whether its last digit is odd or even, that is, if its last digit is divisible by 2 or not.

The first method would be to just calculate it and see if the last digit is an even or odd number. This method can be simplified by using the rule that the last digit of the whole number squared is the last digit of its last digit squared. For example, 257, the last digit is 7. 7x7 is 49. 9 is the last digit of 49, therefore the last digit of 257x257 is 9. (257x257=66049). We can use this strategy to work out each number:

257: Last digit is 7, 7x7 = 49, last digit of the square of the whole number will be 9 which is an odd number, therefore 257 squared is an odd number.

324: Last digit is 4, 4x4 = 16, 6 is even, therefore 324 squared is even.

560: Last digit is 0, 0x0 = 0, 0 is even, therefore 560 squared is even.

491: Last digit is 1, 1x1 = 1, 1 is odd, therefore 491 squared is odd.

662: Last digit is 2, 2x2 = 4, 4 is even, therefore 662 squared is even.

The second strategy would be to use the rules of multiplication:

An even number multiplied by an even number = even number

Even number multiplied by odd number = even number

Odd number x odd number always = odd number

257 is an odd number so if it is squared, then it is an odd number x an odd number which according to the rules, always makes an odd number.

You can use this strategy for all of the other numbers too.

Hope this helped!

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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