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2 years ago

What is the vertex of the graph of the quadratic function f(x) = x2 + 6x +10?

Mathematics

1 answer:

mr Goodwill [35]2 years ago

4 0

Answer:

(-3, 1) (Answer H)

Step-by-step explanation:

f(x) = x^2 + 6x +10 can be rewritten by "completing the square" as

f(x) = (x + 3)^2 + 1, and by comparing this to y = (x - h)^2 + k, we see that h is -3, k is 1, so the vertex, (h, k), is at (-3, 1) (Answer H)

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Answer:

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2 years ago

We measure the diameters for a random sample of 25 oak trees in a neighbourhood. Diameters of oak trees in the neighbourhood fol

jarptica [38.1K]

Answer:

The required confidence inteval = 94.9%.

Step-by-step explanation:

Confidence interval: Mean ± Margin of error

Given: A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969).

i.e. Mean + Margin of error = 42.969 (i)

Mean - Margin of error = 36.191 (ii)

Adding (i) and (ii), we get

$2Mean =79.16\\\\\Rightarrow\ Mean= 39.58$

Margin of error = 42.969-39.58 [from (i)]

= 3.389

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here n= 25 $, \ \sigma=8.25$

i.e.

$3.389=t^*\dfrac{8.25}{5}\\\\\Rightarrow\ t^* = \dfrac{3.389}{1.65}\\\\\Rightarrow\ t^* =2.0539 \$

Using excel function 1-TDIST.2T(2.054,24)

The required confidence inteval = 94.9%.

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2 years ago