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Katarina [22]
3 years ago
12

If four times a whole number is subtracted from three times the square of the number, the result 15 is obtained. Find the number

Mathematics
1 answer:
Novay_Z [31]3 years ago
4 0
See attached picture for answer:

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The boundary of the lawn in front of a building is represented by the parabola . The parabola is represented on the coordinate p
Colt1911 [192]
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   

 


4 0
3 years ago
Rewrite the expression −7/8 − 2 1/4 ​as the sum of two numbers.
pychu [463]

Answer:

-3 1/8.

Step-by-step explanation:

−7/8 − 2 1/4

= -7/8 + -9/4

= -7/8 - 18/8

= -25/8

= -3 1/8.

4 0
3 years ago
I have free points to give. If you want points, I will give them away for free. I give points daily. My only request is to give
Pie

Answer:

ok!

Step-by-step explanation:

3 0
3 years ago
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What is the domain and range of this map?
uranmaximum [27]

The domain and the range is [-6 to +inf)


7 0
3 years ago
Greg deposits $500 into an account that pays simple interest at a rate of % 3 per year. How much interest will he be paid in the
Klio2033 [76]

Answer: 90 dollars

Work Shown:

i = p*r*t

i = 500*0.03*6

i = 90

6 0
2 years ago
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