Which of the following expressions is equivalent to 4y + z + y − 8 + 6z

Sonbull [250]

The equation is $y=(x-7)^2+7$ .

We are looking for a function with a vertex above the x-axis and a function that opens upward (has coefficient a > 0).

The first function opens downward and intersects the x-axis. The second function has a vertex below the x-axis. The third function satisfies our requirements. The fourth function has a vertex on the x-axis.

We can solve this algebraically with the knowledge that the real solutions of a quadratic are its x-intercepts. If there are no x-intercepts (because it lies entirely above or below the x-axis), then there are no real solutions. This is true when the discriminant $b^2-4ac \ \textless \ 0$ . You can see that from the quadratic formula. This holds true for both answers A and C, so to find the correct one, we remember that when the coefficient a of the $x^2$ term is positive, the graph opens upwards, so we choose C.

5 0

3 years ago

Read 2 more answers

Find the perimeter of a rectangle with 33 inches for a width and 75 inches for the length. Have the perimeter in YARDS.

juin [17]

The answer is 72
the formula is (width+length)*2

7 0

3 years ago

A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed

Anuta_ua [19.1K]

Answer:

$t=\frac{370.69-360}{\frac{24.36}{\sqrt{26}}}=2.238$

The degrees of freedom are given by:

$df = n-1= 26-1=25$

And the p value would be:

$p_v =P(t_{25}>2.238)=0.0172$

If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change

Step-by-step explanation:

Information given

$\bar X=370.69$ represent the sample mean

$s=24.36$ represent the sample standard deviation

$n=26$ sample size

$\mu_o =6*60 =360 s$ represent the value to verify

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to check if the true mean is at most 360 seconds, the system of hypothesis would be:

Null hypothesis: $\mu \leq 360$

Alternative hypothesis: $\mu > 360$

The statistic for this case would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

We can replace in formula (1) the info given like this:

$t=\frac{370.69-360}{\frac{24.36}{\sqrt{26}}}=2.238$

The degrees of freedom are given by:

$df = n-1= 26-1=25$

And the p value would be:

$p_v =P(t_{25}>2.238)=0.0172$

If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change

4 0

3 years ago

In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches. Find the measure of ∠P to the nearest degree.

Sophie [7]

Given:

In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches.

To find:

The measure of ∠P to the nearest degree.

Solution:

According to the law of cosine:

$\cos A=\dfrac{b^2+c^2-a^2}{2bc}$