Answer:
C. (16y + 7z)
Step-by-step explanation:
9y + 11z + 7y - 4z
1. Simplify the y's: 9y + 7y = 16y
16y + 11z - 4z
2. Simplify the x's: 11z - 4z = 7z
16y + 7z
Answer:
y = 6
Step-by-step explanation:
We have to consider the equation of a line ( in slope - intercept form ) that is parallel to y = 3, and passes through the point ( 0, 6 ). Now y = 3 can be plotted as a horizontal line that passes through the point ( 0, 3 ). If we want a line that is parallel to this, it must be horizontal as well;
Let us consider the second point now. This line must pass through the point ( 0, 6 ). We can conclude that the line must be 1. Horizontal, and 2. Pass through point ( 0, 6 );
Equation - y = 6
Given:
Scott can run 20 km in 85 minutes.
To find:
How long will it take Scott to run 52 km?
Solution:
Let x be the number of minutes it will take him to run 52 km.
We know that,
Using this formula, we get
...(i)
...(ii)
Equating (i) and (ii), we get
Divide both sides by 20.
Therefore, it will take 221 minutes to run 52 km.
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:
3,984,896 rounded to the nearest hundred is 3,984,900
