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docker41 [41]
3 years ago
6

The graph of a quadratic function has roots at -3 and -7 and a vertex at (-5, 4). What is the equation of the function in vertex

form?
Mathematics
1 answer:
melomori [17]3 years ago
3 0

Answer:

y = -(x + 5)² + 4

Step-by-step explanation:

The roots are -3 and -7, so:

y = a (x + 3) (x + 7)

Distribute and complete the square:

y = a (x² + 10x + 21)

y = a (x² + 10x + 25 − 4)

y = a (x² + 10x + 25) − 4a

y = a (x + 5)² − 4a

The vertex is (-5, 4), so a = -1.

y = -(x + 5)² + 4

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Johns collection contains US, Indian and British stamos. If the stamps ratios of US to Indian stamps is 5 to 2, and the ratio of
NARA [144]
<span>Figure out what is the commonality for each ratio.
There are India stamps in each ratio, so India is the commonality.

Now you simply take the two ratios and multiply them until India has the same amount.

So, Multiply the first by 5 to get a ratio of 25 US to 10 Indian
Multiply the second by 2 to get a ratio of 10 Indian to 2 British

Now that you have "10 Indian" in both ratios, they match up
You have 25 US : 10 Indian : 2 British.

Since the answer is only asking for US and British, you only need 25 US : 2 British</span>
8 0
3 years ago
In September 2011, Gallup surveyed 1,004 American adults and asked them whether they blamed Barack Obama a great deal, a moderat
Alexus [3.1K]

Answer:

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 1004, \pi = 0.53

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.4894

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.5706

The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..

3 0
3 years ago
Wat is the sign of the product of three integers with the same positive sign
Otrada [13]
The sign of the product would be the postitive sign because all three integers have the same sign.
4 0
3 years ago
Read 2 more answers
Surface area helpp needed
Firlakuza [10]

Answer:

144 un²

Step-by-step explanation:

Front Parallelogram = 5 x 11 = 55

Two triangles = 3 x 4 = 12

Back Parallelogram = 3 x 11 = 33

Bottom rectangle = 4 x 11 = 44

Total =

55 + 12 + 33 + 44 = 144

units = un²

144 un²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

5 0
3 years ago
Ethan is responsible to write the minutes for the meeting. During the meeting, he finished writing of the minutes. Before gettin
dolphi86 [110]
11/24
1. 3/8 = 9/24
2. 1/6 = 4/24
3. 9/24 + 4/24 = 13/24
4. 1- 13/24 = 11/24

And that’s if! Hoped this helped :)
These are all the correct steps to get the answer to this problem
7 0
3 years ago
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