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Katarina [22]
3 years ago
8

Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6

Mathematics
1 answer:
Zinaida [17]3 years ago
6 0
We will find the numerator step by step for each expression:
 For 10/15 = x / 60
 x = (10/15) * (60)
 x = 40

 For  x / 108 = 4/9
 x = (4/9) * (108)
 x = 48

 For  7/11 = x / 121
 x = (7/11) * (121)
 x = 77

 For  x / 144 = 2/6
 x = (2/6) * (144)
 x = 48
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Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function f(
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Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function ()=−(+)^−

<em><u>Answer:</u></em>

vertex = (-4, -5)

Axis of symmetry = -4

use the (-4, -5) to find the minimum value

Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5

<em><u>Solution:</u></em>

Given function is:

f(x) = (x+4)^2 - 5

The equation in vertex form is given as:

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Where, (h, k) is constant

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h = -4

k = -5

Vertex is (-4 , -5)

Axis of symmetry : x co-ordinate of vertex

Thus, axis of symmetry = -4

The coefficient of x^2 is positive in given function.

Thus the vertex point will be a minimum

Minimum\ value = f(\frac{-b}{a})

f(x) = x^2 + 8x + 16 - 5\\\\f(x) = x^2 + 8x + 11

f(x) = ax^2+bx+c

On comparing,

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x = \frac{-b}{2a} = \frac{-8}{2 \times 1} = -4

f(-4) = (-4)^2 + 8(-4) + 11 = 16 - 32 + 11 = -5

Thus, use the (-4, -5) to find the minimum value

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f(x) = (x+4)^2 - 5

The domain is the input values shown on the x-axis

The range is the set of possible output values f(x)

Therefore,

Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5

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