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Radda [10]
2 years ago
13

What is the vertex form of Y = x2 - 6x + 6?

Mathematics
1 answer:
ahrayia [7]2 years ago
7 0

Answer:

\large\boxed{y=(x-3)^2-3}

Step-by-step explanation:

The vertex form of a quadratic equation <em>y = ax² + bx + c:</em>

<em>y = a(x - h)² + k</em>

(h, k) - coordinates of a vertex

We have the equation <em>y = x² - 6x + 6</em>.

Convert to the vertex form:

y=x^2-2(x)(3)+6\\\\y=\underbrace{x^2-2(x)(3)+3^2}_{(*)}-3^2+6\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\y=(x-3)^2-9+6\\\\y=(x-3)^2-3\to h=3,\ k=-3

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Crystal has exactly $2.40 in quarters, dimes, and nickers. She has the same number of each type of coin. What is the number?​
Nadya [2.5K]

Answer:

6 quarters, 6 dimes, and 6 nickels

Step-by-step explanation:

6 quarters=1.50

6 dimes=0.6

6 nickels=0.3

1.5+0.6+0.3=2.40

8 0
3 years ago
John goes running every morning. He can run 3 miles in 1 hour. How many miles would he be able to run in 1 and ½ hours?
sp2606 [1]

Answer:

4.5 or 4 1/2 miles

Step-by-step explanation:

\dfrac{3\text{ miles}}{\text{hour}}\cdot 1.5 \text{ hours}= 3\cdot 1.5=4.5

Hope this helps!

5 0
3 years ago
5/8 brainliest im giving if u get it right :D
blondinia [14]

Well basically if they lost 8 points and gained 6, they have -2 points.

3 0
2 years ago
Read 2 more answers
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorab
Katyanochek1 [597]

Answer:

(a) Customer will not purchase the light bulbs at significance level of 0.05

(b) Customer will purchase the light bulbs at significance level of 0.01 .

Step-by-step explanation:

We are given that Light bulbs of a certain type are advertised as having an average lifetime of 750 hours. A random sample of 50 bulbs was selected,  and the following information obtained:

Average lifetime = 738.44 hours and a standard deviation of lifetimes = 38.2 hours.

Let Null hypothesis, H_0 : \mu = 750 {means that the true average lifetime is same as what is advertised}

Alternate Hypothesis, H_1 : \mu < 750 {means that the true average lifetime is smaller than what is advertised}

Now, the test statistics is given by;

       T.S. = \frac{Xbar-\mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, X bar = sample mean = 738.44 hours

               s  = sample standard deviation = 38.2 hours

               n = sample size = 50

So, test statistics = \frac{738.44-750}{\frac{38.2}{\sqrt{50} } } ~ t_4_9

                            = -2.14

(a) Now, at 5% significance level, t table gives critical value of -1.6768 at 49 degree of freedom. Since our test statistics is less than the critical value of t, so which means our test statistics will lie in the rejection region and we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is smaller than what is advertised and so consumer will not purchase the light bulbs.

(b) Now, at 1% significance level, t table gives critical value of -2.405 at 49 degree of freedom. Since our test statistics is higher than the critical value of t, so which means our test statistics will not lie in the rejection region and we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is same as what it has been advertised and so consumer will purchase the light bulbs.

6 0
3 years ago
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yaroslaw [1]

Here, to make your day a little better<3

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