The question does not present the options, but this does not interfere with the resolution
we have that
y=3(x-2)²-(x-5)²
y=3(x²-4x+4)-(x²-10x+25)
y=3x²-12x+12-x²+10x-25
y=(3x²-x²)+(-12x+10x)+(12-25)
y=2x²-2x-13
y+13=2x²-2x
y+13=2(x²-x)
y+13+0.50=2(x²-x+0.25)
y+13.50=2(x-0.5)²------> this is the equation in the vertex form
the vertex is the point (0.5,-13.50)
The Law of Sines may be written as
b/sin(B) = c/sin(C)
Multiply each side by sin(B).
b = (c*sin(B))/sin(C)
The correct answer is C.
Answer: C. (c*sin B)/sin C
Complete Question
The complete qustion is shown on the first uploaded image
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The sample size is 
The mean is 
The standard deviation is 
Generally the standard error of this measurement is mathematically represented as
substituting values
ppb
Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )
Next is to find the z value


Now checking the z-table for the z-score of -1 we have

Given the function 
1. Translation to the right 1 unit changes the function
into the function 
2. Translation 2 units down changes the function
into the function 
3. Two translations change the funcion
into the function 
4. The graph of the final function you can see in attached diagram.
Answer:
Correct option: third one -> 11.5 m3
Step-by-step explanation:
To find the volume of the ramp, first we need to find the volume of the rectangular prism and the volume of the triangular prism:
V_rectangular = 4m * 2m * 1m = 8 m3
V_triangular = (2m * 3.5m * 1m) / 2 = 3.5 m3
Now, to find the volume of the ramp, we just need to sum both volumes:
V_total = V_rectangular + V_triangular = 8 + 3.5 = 11.5 m3
Correct option: third one.