Answer:
Step-by-step explanation:
X=9
The boundary of the lawn in front of a building is represented by the parabola
y = (x^2) /16 + x - 2
And you have three questions which require to find the focus, the vertex and the directrix of the parabola.
Note that it is a regular parabola (its symmetry axis is paralell to the y-axis).
1) Focus:
It is a point on the symmetry axis => x = the x-component of the vertex) at a distance equal to the distance between the directrix and the vertex).
In a regular parabola, the y - coordinate of the focus is p units from the y-coordinate of the focus, and p is equal to 1/(4a), where a is the coefficient that appears in this form of the parabola's equation: y = a(x - h)^2 + k (this is called the vertex form)
Then we will rearrange the standard form, (x^2)/16 + x - 2 fo find the vertex form y = a(x-h)^2 + k
What we need is to complete a square. You can follow these steps.
1) Extract common factor 1/16 => (1/16) [ (x^2) + 16x - 32]
2) Add (and subtract) the square of the half value of the coefficent ot the term on x =>
16/2 = 8 => add and subtract 8^2 => (1/16) [ (x^2) + 16 x + 8^2 - 32 - 8^2]
3) The three first terms inside the square brackets are a perfect square trinomial: =>
(1/16) [ (x+8)^2 - 32 - 64] = (1/16) [ (x+8)^2 - 96] =>
(1/16) [(x+8)^2 ] - 96/16 =>
(1/16) (x +8)^2 - 6
Which is now in the form a(x - h)^2 + k, where:
a = 1/16 , h = - 8, and k = -6
(h,k) is the vertex: h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
=> a = 1/16 => p =1/4a = 16/4 = 4
y-componente of the focus = -6 + 4 = -2
x-component of the focus = h = - 8
=> focus = (-8, -2)
2) Vertex
We found it above, vertex = (h,k) = (-8,-6)
3) Directrix
It is the line y = p units below the vertex = > y = -6 - 4 = -10
y = -10
Answer:
32x-24y-7
Step-by-step explanation:
Use the distributive property and multiply 4 by each term in the parentheses. 4 times 8x = 32x and 4 times -6y = -24y.
Answer:
y=-7
Step-by-step explanation:
y-3=-2(x+5)
distribute the -2 into the ( )
y -3= -2x -10
cancel to -2x
y- 3 = -2(0) -10
y-3 = -10
+3 +3
y= -7
Hope this helps!!
To find an average you take the numbers to be averaged and add them together then You take the number and divide it by the number of numbers, in this case 4, and that gives you the average.
on this problem you want to do the opposite. you know the average she wants, an 87, so you multiply it by 4. 87*4=348. then you add the three numbers you have (88,81 and 87) and you get 256.
then you subtract 256 from 348 and you get 92. 92 is your answer to check just add 87+81+88+92=348
348/4=87
87 was the average she wanted.
Hope this helped! good luck :)
