Answer:
Third option
Step-by-step explanation:
We can't factor this so we need to use the quadratic formula which states that when ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / 2a. However, we notice that b (which is 6) is even, so we can use the special quadratic formula which states that when ax² + bx + c = 0 and b is even, x = (-b' ± √(b'² - ac)) / a where b' = b / 2. In this case, a = 1, b' = 3 and c = 7 so:
x = (-3 ± √(3² - 1 * 7)) / 1 = -3 ± √2
Answer:
RT=75/4= 18.75
Step-by-step explanation:
RS+ST=RT
x+6+8=5x-5
4x=19
x=19/4
RT=5x-5
RT=5(19/4)-5
RT=95/4-20/4
RT=75/4= 18.75
Length × width × height
2×2×2= 8 meters cubed
Answer:
2 to the 20th power over 3 to the 12th power
Step-by-step explanation:
Numerator: base = 2. Power=5*4=20
Denominator :base 3 Power=3*4=12
Answer:
![2\Bigl[(x+\frac{3}{4} )^2-\frac{25}{16} \Bigr]](https://tex.z-dn.net/?f=2%5CBigl%5B%28x%2B%5Cfrac%7B3%7D%7B4%7D%20%29%5E2-%5Cfrac%7B25%7D%7B16%7D%20%5CBigr%5D)
Step-by-step explanation:
Step 1
We factor out 2 so that the coefficient of the quadratic term is 1.
Step 2
In this step we add and subtract the square of the coefficient of the x term, this term is 
. This is the step where we complete the square.
![f(x)=2\Bigl[x^2+\frac{3}{2}x+(\frac{3}{4})^2-(\tfrac{3}{4})^2 -1 \Bigr]\\f(x)=2\Bigl[x^2+\frac{3}{2}x+(\frac{3}{4})^2-\frac{25}{16} \Bigr]](https://tex.z-dn.net/?f=f%28x%29%3D2%5CBigl%5Bx%5E2%2B%5Cfrac%7B3%7D%7B2%7Dx%2B%28%5Cfrac%7B3%7D%7B4%7D%29%5E2-%28%5Ctfrac%7B3%7D%7B4%7D%29%5E2%20-1%20%5CBigr%5D%5C%5Cf%28x%29%3D2%5CBigl%5Bx%5E2%2B%5Cfrac%7B3%7D%7B2%7Dx%2B%28%5Cfrac%7B3%7D%7B4%7D%29%5E2-%5Cfrac%7B25%7D%7B16%7D%20%5CBigr%5D)
Step 3
In this step we factor out the perfect square tri-nomial formed by the first 3 terms in last line of step 2. This calculation is shown below,
![f(x)=2\Bigl[\bigl(x+\frac{3}{4} \bigr)^2-\frac{25}{16} \Bigr]](https://tex.z-dn.net/?f=f%28x%29%3D2%5CBigl%5B%5Cbigl%28x%2B%5Cfrac%7B3%7D%7B4%7D%20%5Cbigr%29%5E2-%5Cfrac%7B25%7D%7B16%7D%20%5CBigr%5D)
