Answer:
32.02
Step-by-step explanation:
The number that is in the hundredths place is five. You can remember this by knowing that the decimal point counts as one and all the number to the right of the decimal point count as zero. So 0 is in the tenths place, 1 is in the hundredths place, 5 is in the thousandths place, 6 is in the ten thousandths place and so on. So if you round this number to the nearest hundredth, you'll get 32.02 because if you're rounding a number and the number you're rounding with (knowing that the number you're rounding will always be rounded with the number to the right of it) is 5 or greater than 5, that number that you have to round will go up one unit.
I hope this helped!
Answer:
The two roots of the quadratic equation are
![x_1= - \frac{1}{3} \text{ and } x_2= \frac{2}{3}](https://tex.z-dn.net/?f=x_1%3D%20-%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctext%7B%20and%20%7D%20x_2%3D%20%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
Original quadratic equation is ![9x^{2}-3x-2=0](https://tex.z-dn.net/?f=9x%5E%7B2%7D-3x-2%3D0)
Divide both sides by 9:
![x^{2} - \frac{x}{3} - \frac{2}{9}=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%20%5Cfrac%7Bx%7D%7B3%7D%20-%20%5Cfrac%7B2%7D%7B9%7D%3D0)
Add
to both sides to get rid of the constant on the LHS
==> ![x^{2} - \frac{x}{3}=\frac{2}{9}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%20%5Cfrac%7Bx%7D%7B3%7D%3D%5Cfrac%7B2%7D%7B9%7D)
Add
to both sides
![x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{2}{9} +\frac{1}{36}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%20%5Cfrac%7Bx%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B36%7D%3D%5Cfrac%7B2%7D%7B9%7D%20%2B%5Cfrac%7B1%7D%7B36%7D)
This simplifies to
![x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{1}{4}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%20%5Cfrac%7Bx%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B36%7D%3D%5Cfrac%7B1%7D%7B4%7D)
Noting that (a + b)² = a² + 2ab + b²
If we set a = x and b =
we can see that
= ![x^2 - 2.x. (-\frac{1}{6}) + \frac{1}{36} = x^{2} - \frac{x}{3}+\frac{1}{36}](https://tex.z-dn.net/?f=x%5E2%20-%202.x.%20%28-%5Cfrac%7B1%7D%7B6%7D%29%20%2B%20%5Cfrac%7B1%7D%7B36%7D%20%3D%20x%5E%7B2%7D%20-%20%5Cfrac%7Bx%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B36%7D)
So
![\left(x - \frac{1}{6}\right)^2=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cleft%28x%20-%20%5Cfrac%7B1%7D%7B6%7D%5Cright%29%5E2%3D%5Cfrac%7B1%7D%7B4%7D)
Taking square roots on both sides
![\left(x - \frac{1}{6}\right)^2= \pm\frac{1}{4}](https://tex.z-dn.net/?f=%5Cleft%28x%20-%20%5Cfrac%7B1%7D%7B6%7D%5Cright%29%5E2%3D%20%5Cpm%5Cfrac%7B1%7D%7B4%7D)
So the two roots or solutions of the equation are
and ![x - \frac{1}{6}=\sqrt{\frac{1}{4}}](https://tex.z-dn.net/?f=x%20-%20%5Cfrac%7B1%7D%7B6%7D%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%7D)
![\sqrt{\frac{1}{4}} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
So the two roots are
![x_1=\frac{1}{6} - \frac{1}{2} = -\frac{1}{3}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B1%7D%7B6%7D%20-%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20-%5Cfrac%7B1%7D%7B3%7D)
and
![x_2=\frac{1}{6} + \frac{1}{2} = \frac{2}{3}](https://tex.z-dn.net/?f=x_2%3D%5Cfrac%7B1%7D%7B6%7D%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
Answer:
Ok what you can try to do is multiply, then, subtract, add , or do division to see what you get. So try doing all of that then see what you're answer is.
Step-by-step explanation:
Answer:
The measure of angle a is of 140º.
Step-by-step explanation:
Supplementary angles:
If two angles are supplementary, their measures add to 180º.
Angle a and angle b are supplemetary angles.
This means that
<a + <b = 180º.
m angle a = (5x+25) and m angle b = (x+17)
So
![5x + 25 + x + 17 = 180](https://tex.z-dn.net/?f=5x%20%2B%2025%20%2B%20x%20%2B%2017%20%3D%20180)
![6x + 42 = 180](https://tex.z-dn.net/?f=6x%20%2B%2042%20%3D%20180)
![6x = 138](https://tex.z-dn.net/?f=6x%20%3D%20138)
![x = \frac{138}{6}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B138%7D%7B6%7D)
![x = 23](https://tex.z-dn.net/?f=x%20%3D%2023)
Measure of angle a:
![](https://tex.z-dn.net/?f=%3Ca%20%3D%205x%20%2B%2025%20%3D%205%2823%29%20%2B%2025%20%3D%20140)
The measure of angle a is of 140º.