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Elan Coil [88]
3 years ago
5

How to find the vertex of a parabola given a quadratic equation?

Mathematics
1 answer:
Nat2105 [25]3 years ago
8 0
let \: f(x) = ax {}^{2} + bx + c \\ thus \: f(x) \: represents \: a \: parabola \: whose \: axis \: is \: parallel \: to \: the \: y \: axis \: and \: vertex \: is \: \frac{ - b}{2a} ,\frac{ - d}{4a} \\

At the respective max and min values

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Which of the following best describes the perpendicular lines?
AysviL [449]

Answer:

A perpendicular line is a line that meets a 90 degree angle.

Step-by-step explanation:

Think of the letter L

the top stick of the letter is perpendicular to the bottom stick and it makes a 90 degree angle.

Thats the best way I can explain it.

Hope this helps and please mark me brainliest if it did :)

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3 years ago
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Use properties of equality to solve the equation for w. You must show your work. 2(w+3) = −2(w−21)
natta225 [31]

Answer:

9

Step-by-step explanation:

2w+6=-2w+42

4w+6=42

4w=36

w=9

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two-eighths of the students are boys. If there are 13 boys in the class, how many students are there in all?​
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Answer:

52 students

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1/8 is 6.5

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Solve 6( x + 20) = 168
Licemer1 [7]

Answer: X=8

Step-by-step explanation:

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3 years ago
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A data set lists earthquake depths. The summary statistics are nequals300​, x overbarequals5.89 ​km, sequals4.44 km. Use a 0.01
kirza4 [7]

Answer:

Null hypothesis H_0:\mu=5.00km

Alternative hypothesis H_1:\mu\neq 5.00km

The p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.

Step-by-step explanation:

It is given that a data set lists earthquake depths. The summary statistics are

n=300

\overline{x}=5.89km

s=4.44km

Level of significance = 0.01

We need to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00.

Null hypothesis H_0:\mu=5.00km

Alternative hypothesis H_1:\mu\neq 5.00km

The formula for z-value is

z=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}

z=\frac{5.89-5.00}{\frac{4.44}{\sqrt{300}}}

z=\frac{0.89}{0.25634351952}

z=3.4719

The p-value for z=3.4719 is 0.000517.

Since the p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.

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