Mathematics, 14.09.2020 19:01 jennsou

What is the square root of 129

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Answer from: gstevens

If you are allowed to use a calculator then you only need to press the buttons.

Assuming you cannot use a calculator you need to use approximation techniques. First let us begin by finding the two closest numbers that are perfect squares. In this case 11^2 and 12^2 are the closest square numbers to 129.

11^2 = 121
12^2 = 144
We can already tell that the square root of 129 is closer to 11 than to 12.
Now we need to get even closer.
If you try squaring a number like 11.5 then you can get even closer to 129. When you square 11.5 you get 132.25. Already you can tell that the square root of 129 is close to the square root of 132.25 or 11.5
Now we can get even closer square the number 11.25 and keep on going until one of these numbers when squared is almost or exactly 129. I hope I helped, there really isn't a great way to do this without a calculator, or by using the graph of y=x^2

Answer from: Quest

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2 polynomial long division

dividing : x4+5x3-4x2-8x+6

("dividend")

by : x-1 ("divisor")

dividend x4 + 5x3 - 4x2 - 8x + 6

- divisor * x3 x4 - x3

remainder 6x3 - 4x2 - 8x + 6

- divisor * 6x2 6x3 - 6x2

remainder 2x2 - 8x + 6

- divisor * 2x1 2x2 - 2x

remainder - 6x + 6

- divisor * -6x0 - 6x + 6

remainder 0

quotient : x3+6x2+2x-6 remainder: 0

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

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