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3 years ago

What is the vertex of the quadratic function below?

1 answer:

3 0

$y = - 3 {x}^{2} - 12x + 17 \\ x_0 = \frac{ - b}{2a } = \frac{12}{ - 6} = - 2 \\ y_0 = - 3 \times {( - 2)}^{2} - 12 \times ( - 2) + 17 = 29$

Maybe i did something wrong, maybe your question is incorrect, but the vertex is (-2; 29)

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Find the distance between the points. (Round your answer to two decimal places. (9.7, - 2.8), (- 3.2, 8.8)

Dmitry [639]

Answer:

Rounding it to two decimal places, we get distance, $d=17.35$

Step-by-step explanation:

Given:

The two points are $(9.7, -2.8)\textrm{ and }(-3.2, 8.8)$

The distance between the two points can be obtained using the distance formula which is given as:

$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Here, for the points, $(9.7, -2.8)\textrm{ and }(-3.2, 8.8)$

$x_{1}=9.7,x_{2}=-3.2,y_{1}=-2.8,y_{2}=8.8$

Therefore, the distance between the points is:

$d=\sqrt{(-3.2-9.7)^2+(8.8-(-2.8))^2}\\d=\sqrt{(-12.9)^2+(8.8+2.8)^2}\\d=\sqrt{(12.9)^2+(11.6)^2}\\d=\sqrt{166.41+134.56}\\d=\sqrt{300.97}=17.348$

Rounding it to two decimal places, we get $d=17.35$

7 0

3 years ago

Here goes problem 2 of three dimensional figures

Anna11 [10]

Well,

We would see the rectangular prism cut in half, which, if we looked from the top, would look like a rectangle. That is figure Z.

7 0

3 years ago

What is the value of f(7)

Lelu [443]

Answer:

7<em><u>f</u></em>

Step-by-step explanation:

You move 7 to the left of <em>f. </em>

This makes the exact value of <em>f</em>(7), 7<em>f</em>.

8 0

4 years ago

The two parallel chords in circle C have lengths of 8 and 12. The distance (BD) between the chords is 3. Find the radius.

aivan3 [116]

Answer:

i really like your oroile pic sorry for bothering you

Step-by-step explanation:

3 0

4 years ago

within a kiambu county,students were randomly assigned to one of two mathematics teachers.Mrs.Elite and Mrs. Bright. After the a

DerKrebs [107]

Using the t-distribution, as we have the standard deviation for the samples, it is found that since the absolute value of the test statistic is greater than the critical value, we reject the claim that Mrs.Elite and Mrs. Bright are equally effective teachers.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, we test if they are equally effective teachers, that is, the subtraction of their means is 0, hence:

$H_0: \mu_1 - \mu_2 = 0$

At the alternative hypothesis, we test if they are not equally effective teachers, that is, the subtraction of their means is not 0, hence:

$H_1: \mu_1 - \mu_2 \neq 0$

<h3>What is the distribution of the differences?</h3>

For Mrs. Elite, we have that:

$\mu_1 = 78, \sigma_1 = 10, n_1 = 30, s_1 = \frac{10}{\sqrt{30}} = 1.82574$

For Mrs. Bright, we have that:

$\mu_2 = 85, \sigma_2 = 15, n_2 = 25, s_2 = \frac{15}{\sqrt{25}} = 3$

For the distribution of differences, we have that:

$\overline{x} = \mu_1 - \mu_2 = 78 - 85 = -7$

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{1.82574^2 + 3^2} = 3.5119$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{-7 - 0}{3.5119}$

$t = -1.99$

Considering a<em> two-tailed test</em>, as we are testing if the mean is different of a value, with 30 + 25 - 2 = <em>53 df and a significance level of 0.1</em>, the critical value is of $|t^{\ast}| = 1.6741$ .

Since the absolute value of the test statistic is greater than the critical value, we reject the claim that Mrs.Elite and Mrs. Bright are equally effective teachers.

To learn more about the t-distribution, you can take a look at brainly.com/question/13873630

3 0

3 years ago