First, we are going to find the vertex of our quadratic. Remember that to find the vertex
of a quadratic equation of the form
, we use the vertex formula
, and then, we evaluate our equation at
to find
.
We now from our quadratic that
and
, so lets use our formula:
Now we can evaluate our quadratic at 8 to find
:
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is
The x-coordinate of the minimum is 8
Answer:
AB ║ CD. (Proved)
Step-by-step explanation:
See the attached diagram of the triangle.
It is given that Δ ACD is an isosceles triangle.
Therefore, AC = AD and ∠ ACD = ∠ ADC, ⇒ ∠ 3 = ∠ 4 .......... (1)
Again, given that ∠ 1 = ∠ 3 ........... (2)
Now, from equations (1) and (2) we can write, ∠ 1 = ∠ 4
Now, AB and CD are two straight lines and AD is the transverse line and hence, ∠ 1 and ∠ 4 are alternate angles that are equal.
Therefore, AB and CD are parallel straight lines and AB ║ CD. (Proved)
The goal is to construct a triangle. If you choose A) you will only have two lines connecting, with an angle of 90°. If you choose B) you cannot have a triangle also with 2 lines only. Neither D). So choose C) construct an angle congruent to a given one-- connect the lines and produce a perfect triangle.
Answer:
5, 17
Step-by-step explanation:
For this problem, you need to create a system of equations.
We can name one number x and the other y.
First equation: 2x + 7 = y
Second equation: x + y - 10 = 12, or x + y = 22.
We know y = 2x + 7, so we can substitute that into the second equation.
x + 2x + 7 = 22.
3x = 15
x = 5.
Plug x back into the first equation:
2 · 5 + 7 = y.
y = 10 + 7
y = 17.
Answer: The missing coordinate R is 5.
Step-by-step explanation:
11=1/2(-4) + B
11=-2 +B
B= 13
B represents the y-intercept
so we will use the equation y=mx + B and we know the slope and y intercept.
r= 1/2(-16) + 13
r= 5
