Answer:
- The two solutions are:
- The next and every step are below.
Explanation:
1. 
: Given (addition property / add - 3 to both sides)
2. 
: Given (commom factor - 2)
3. 
To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.
Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.
4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:
5. Divide both sides by - 2 to get the next expression:
6. The last step is to extract squere root from both sides of the equality:
Answer:
C
Step-by-step explanation:
The line crosses the y-axis at 3, and has a slope of -1/5. You can use the formula y=mx+b where m represents the slope and b is the point at which the line crosses the y-axis.
Answer:
Step-by-step explanation:
I'll show you how to do the first one; the other are exactly the same, so pay attention.
The formula for arc length is
where θ is the central angle's measure. It just so happens that the measure of the central angle is the same as the measure of the arc it intercepts. Our arc shows a measure of 40°; this measure is NOT the same as the length. Measures are in degrees while length is in inches, or cm, or meters, etc. Going off that info, our central angle measures 40°. Filling in the formula and using 3.1415 for π:
. I'm going to reduce that fraction a bit (and I'll use the same reduction in the Area of a sector coming up next):
which makes
AL = 2.09 units. Now for Area of the Sector. The formula is almost identical, but instead uses the idea that the area of a circle is πr²:
where θ is, again, the measure of the central angle (which is the same as the measure of the arc it intercepts). Filling in:
which simplifies a bit to
. As you can see, the 9's cancel each other out, leaving you with
units²
Answer:
2
Step-by-step explanation:
Well knowing that the terminal arm of the standard position angle is in quadrant 2, we can determine the reference angle, in quadrant 2, by simply taking the difference between 180 and whatever the angle is.
So ø reference = 180 - ø in standard position.
Regardless, the reference angle is in quadrant 2, we need to then label the sides of the reference triangle based on the opposite and hypotenuse.
Solve for adjacent side using Pythagoras theorem.
A^2 = C^2 - B^2
A^2 = 3^2 - 2^2
A^2 = 9 - 4
A^2 =5
A = sq root of 5.
Then write the cos ratio using the new side.
Cos ø =✔️5/3. Place a negative in front of cos ø as cos is negative in second quadrant.
