What is the equation of the line in slope- intercept form

What are the zeros of the quadratic function f(x) equals 6X squared +12 X -7

tamaranim1 [39]

The zeroes of the function will be $\rm -1 \pm \dfrac{\sqrt{78}}{6}}$

<h3>What is a Quadratic Function ?</h3>

A quadratic function is given by ax² +bx+c = f(x)

The given quadratic function is

f(x) = 6x² +12x - 7

The zeroes of the function will be given by

f(0) = 0

6x² +12x - 7 = 0

The zeroes are given by

$\rm \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}$

here

a = 6

b = 12

c = -7

Therefore the zeroes of the function will be

$\rm \dfrac {-12 \pm \sqrt{12^2 -4*6*(-7)}}{2 *6}$

$\rm \dfrac {-12 \pm \sqrt{312}}{12}$

$\rm -1 \pm \dfrac{\sqrt{78}}{6}}$

Therefore these are the two zeroes of the function.

To know more about Quadratic Function

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7 0

2 years ago

A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 100 hou

hodyreva [135]

Answer:

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645*\frac{600}{\sqrt{100}} = 98.7$

The lower end of the interval is the sample mean subtracted by M. So it is 4500 - 98.7 = 4401.3 gallons

The upper end of the interval is the sample mean added to M. So it is 4500 + 98.7 = 4598.7 gallons

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

4 0

3 years ago

Explorers on a planet with a thin atmosphere want to measure the acceleration of gravity at its surface. So they use a spring gu

Murljashka [212]

Answer:

The value of $g_s$ is $g_s=\frac{30}{21} \:\frac{m}{s^2}$ .

Step-by-step explanation:

We know that the position function is given by

$s(t)=30t-\frac{g_s}{2} t^2$

Velocity is defined as the rate of change of position. Therefore,

$v(t)=\frac{d}{dt}(s(t))$

So, the velocity function is

$v(t)=\frac{d}{dt}(s(t))\\\\v(t)=\frac{d}{dt}(30t-\frac{g_s}{2} t^2)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(30t\right)-\frac{d}{dt}\left(\frac{g_s}{2}t^2\right)\\\\v(t)=30-g_st$

When a body reaches a vertical velocity of zero, this is the maximum height of the body and then gravity will take over and accelerate the object downward. Thus,

$v(t)=30-g_st=0\\\\g_s=\frac{30}{t}$

We know that the ball bearing reaches its maximum height 21 seconds after being launched (t = 21 s).

So, the value of $g_s$ is $g_s=\frac{30}{21} \:\frac{m}{s^2}$ .

5 0

3 years ago

From a group of 8 people, you randomly select 3 of them.

Vanyuwa [196]

Answer:

3/8

Step-by-step explanation:

You don't know whether they are young or old and your not replacing them so your best answer is 3/8.

6 0

3 years ago

Read 2 more answers

The population of two different cities are modeled by the equations shown below. The population (in thousands) is represented by

lesya [120]

Answer: years of equal population are 1995 and 2022.

in 1995, population was 425,000 people and in 2022, population was 1,910,000 people.

Step-by-step explanation: Baskinville: y = x2 - 22x + 350

Cryersport: y = 55x - 950

Note that x2 is xsquare not x2

Resolving the quadratic equations carefully will give the values of y and x which represent the population and years.

7 0

3 years ago