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Sladkaya [172]
3 years ago
13

What is the vertex form of f(x)=x^2+24x+138

Mathematics
2 answers:
Gre4nikov [31]3 years ago
8 0
F(x) = x^2 + 24x + 138
f(x) = x^2 + 24x + (24/2)^2 + 138 - (24/2)^2
f(x) = (x+12)^2 - 6
Veronika [31]3 years ago
6 0

Answer:

(x +12)^2 - 6

Step-by-step explanation:

d/dx x^2 + 24x + 138 = 2x + 24

when 2x + 24 = 0, the gradient = 0

x = -12

f(-12) = -6

therefore we have (x +12)^2 - 6.

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What are the solutions of the quadratic equation 4x^2-8x-12=0
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<h3>          x₁ = -1,   x₂ = 3</h3>

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4x^2-8x-12=0\\{}\qquad\qquad^{\div4\qquad\div4}\\x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\\\\x+1=0\quad\vee\quad x-3=0\\\\x=-1\quad\vee\quad x=3

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Of all of the individuals who develop a certain rash, suppose the mean recovery time for individuals who do not use any form of
VashaNatasha [74]

Answer:

z(s) is in the rejection  region. We reject  H₀. We dont have enought evidence to support that the cream has effect over the recovery time

Step-by-step explanation:

Sample information:

Size     n = 100

mean   x = 28,5

Population information

μ₀  =  30

Standard deviation  σ   = 8

Test Hypothesis

Null Hypothesis          H₀                x =  μ₀

Alternative Hypothesis   Hₐ           x <  μ₀

We assume CI = 95 %   then α = 5 %    α = 0,05

As the alternative hypothesis suggest we should develop a one tail-test on the left ( we need to find out if the cream have any effect on the rash), effects on the rash could be measured as days of recovery

A z(c) for 0,05 from z-table is:  z(c) = - 1,64

z(s) = ( x - μ₀ ) / σ/√n

z(s) = ( 28,5 - 30 ) / 8/√100

z(s) = - 1,5 * 10 / 8

z(s) =  - 1,875

Comparing z(s)  and z(c)

|z(s)| < |z(c)|        1,875  > 1,64

z(s) is in the rejection  region. We reject  H₀. We dont have enought evidence to support that the cream has effect over the recovery time

3 0
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