Answer:
Step-by-step explanation:
The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:
The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:
The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.
and on the right we will just add 10 and 2:
Now we move the 12 back over by subtracting and set the quadratic back to equal y:
From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}
Answer:
B, C, and E
Step-by-step explanation:
<u>Simplify all answer choices:</u>
A.
5(2x+10)+1=
10x+50+1=
10x+51
B.
7(x+2)+3x-3=
7x+14+3x-3=
10x+11
C.
3(3x+4)+x-1=
9x+12+x-1=
10x+11
D.
2(6x+4)+2x+5=
12x+8+2x+5=
14x+13
E.
2(6x+5)-2x+1=
12x+10-2x+1=
10x+11
Answer choices B, C, and E simplify to 10x+11
Answer:
a = jd
Step-by-step explanation:
We want to solve for a given that a/d = j
To do so we want to isolate a (get a by itself )
We can do this by using inverse operations.
We would want to get rid of the d
A is being divided by d.
The inverse of division is multiplication so to get rid of the d we multiply a/d by d but whatever we do to one side we must do to the other so we multiply both sides by d
a/d * d = a
j * d = jd
we are then left with a = jd
And we are done!
Answer:
y = 2x+8
Step-by-Step Explanation:
The equation should be in the form of y=mx+b
So you already know it's not A. Also you already know it's not D because the line goes at an angle, if "m"(slope) was 0 then the line would be straight horizontal or straight vertical. So that leaves B and C. And finally you know it's not B because the line is going in the positive direction not negative, so the slope has to be positive, also "b" in the equation is the y-intercept, and that's where the line intersects with the y-axis, and you can see that the line intersects at 8 on the graph. Therefore, the answer is C, y=2x+8
Hope this helps!! :)
Step-by-step explanation:
Given,
Side of a square = 4xy
Therefore, area of the square = side × side
= 4xy × 4xy
