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andrew11 [14]
3 years ago
14

Find the vertex of y = x^2 – 2x – 15

Mathematics
2 answers:
svet-max [94.6K]3 years ago
7 0
The vertex is ( 1, -16 ).
solong [7]3 years ago
7 0

Answer:

The vertex is at (h, k), which here is (1, -16).

Step-by-step explanation:

One of the quicker ways to approach this proplem is to "complete the square," which puts the equation into "vertex form."

Starting with y = x^2 – 2x – 15, add 1 to, and then subtract 1 from,  x^2 – 2x :

y = x^2 – 2x + 1 - 1– 15

Now re-write   x^2 – 2x   as (x - 1)^2 - 1:

y = (x - 1)^2 - 1 – 15. or  y = (x - 1)^2 - 16, which has the form y = (x - h)^2 + k.  Comparing these two equations, we see that h = 1 and k = -16.

The vertex is at (h, k), which here is (1, -16).

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Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95​%of all males.​ (Accommodating 100%
Anarel [89]

Answer:

Upper P95 = 16.21in

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 14.4, \sigma = 1.1

Upper P 95

This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

Then

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 14.4}{1.1}

X - 14.4 = 1.1*1.645

X = 16.21

Upper P95 = 16.21in

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3 years ago
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melisa1 [442]

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6 0
3 years ago
What is -24/-11 simplified?
Kisachek [45]

Answer:

2.18 repeating.

Step-by-step explanation:

So it will be 24/11 because the negatives cancel out each other. So the answer is 2.18 repeating.

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Salsk061 [2.6K]

Answer:

1/4

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15/60 = 1/4

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