The answer is h(2k - 5) = -4 - 2k
Step-by-step explanation:
In a function f(x) = y, we can find the value of y for any given value of x
Examples:
- If f(x) = 2x - 3, and we need to find f(3), that means substitute x by 3 in f(x), so f(3) = 2(3) - 3 = 6 - 3 = 3, that means f(x) = 3 at x = 3
- If f(x) = 8 - 5x, and we need to find f(a - 2), substitute x by (a - 2) in f(x), so f(a - 2) = 8 - 5(a - 2) = 8 - 5a + 10 = 18 - 5a, that means f(a - 2) = 18 - 5a at x = a - 2
∵ h(x) = -9 - x
- We need to find h(2k - 5), that means substitute x by 2k - 5
∵ x = 2k - 5
∴ h(2k - 5) = -9 - (2k - 5)
- Simplify the right hand side
∴ h(2k - 5) = -9 - 2k - (-5)
- Remember (-)(-) = (+)
∴ h(2k - 5) = -9 - 2k + 5
- Add the like terms in the right hand side
∴ h(2k - 5) = (-9 + 5) - 2k
∴ h(2k - 5) = -4 - 2k
The answer is h(2k - 5) = -4 - 2k
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You can learn ore about the functions in brainly.com/question/5337932
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Answer:
area is 2 dimensional lika a carpet and a area rug. a parallelogram 4 sided-shape formed by 2 pairs of parrel lines. opposite sides are equal in lenght and opposite are equal in measure. to find the area of a parallegram, multiply the by the base by the height
Explanation:
Pls make me as brainliest and add as my friend i will check it.
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:
A's age = 6x = 6 × 5 = 30 years.
B's age = 5x = 5 × 5 = 25 years
Step-by-step explanation:
here's the solution : -
let their ages be 6x and 5x
and we know sum of their ages = 55
So, 6x + 5x = 55
=》11x = 55
=》x = 55 ÷ 11
=》x = 5
A's age = 6x = 6 × 5 = 30 years.
B's age = 5x = 5 × 5 = 25 years
Answer:
There is 170 cm³ free space in the container.
Step-by-step explanation:
Cylindrical container: height = 18 cm ; diameter = 6 cm.
3 balls each have a radius of 3 cm.
Volume of a cylinder = π r² h
V = 3.14 * (3cm)² * 18 cm
V = 508.68 cm³
Volume of rubber ball = 4/3 π r³
V = 4/3 * 3.14 * (3cm)³
V = 113.04 cm³
113.04 cm³ * 3 balls = 339.12 cm³
508.68 cm³ - 339.12 cm³ = 169.56 cm³ or 170 cm³
