Ask question

Ask question

All categories

3 years ago

11

Find the zeros in the function 3x2+ 6 = 0

1 answer:

sattari [20]3 years ago

5 0

Answer:

x = ± i $\sqrt{2}$

Step-by-step explanation:

Given

3x² + 6 = 0 ( subtract 6 from both sides )

3x² = - 6 ( divide both sides by 3 )

x² = - 2 ( take the square root of both sides )

x = ± $\sqrt{-2}$

= ± $\sqrt{2(-1)}$

= ± ( $\sqrt{2}$ × $\sqrt{-1}$ ) → $\sqrt{-1}$ = i

= ± i $\sqrt{2}$

You might be interested in

saw5 [17]

The above expression is not in its simplest form, and we need to simplify it, that is what asked in the question.

Given equation,

$(9 {x}^{2} - 3x + 7) + ( - 3 {x}^{2} + 2)$

First of all, let's open the parentheses to combine the like terms for simplifying.

$9 {x}^{2} - 3x + 7 - 3 {x}^{2} + 2$

Arranging the like terms, x² with x², x with x and constant terms near to each other.

$9 {x}^{2} - 3 {x}^{2} - 3x + 7 + 2$

Simplying further,

$(9 - 3) {x}^{2} - 3x + 9$

$6 {x}^{2} - 3x + 9$

So, the correct option is C

<u>━━━━━━━━━━━━━━━━━━━━</u>

8 0

3 years ago

A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce th

ivolga24 [154]

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\$

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

$H_0: \mu=500\\\\H_a:\mu< 500$

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1$

The degrees of freedom for this sample size are:

$df=n-1=5-1=4$

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

4 0

3 years ago

Find the conjugate of the complex number, use division:<br> 2+i<br> ——<br> 1+i

Fittoniya [83]

I assume you mean divide using the conjugate to rationalize the denominator and express the result in standard rectangular form.

$\dfrac{2+i}{1+i} = \dfrac{2+i}{1+i} \cdot \dfrac{1-i}{1-i} = \dfrac{2(1)-i^2-2i+i}{1^2+1^2} = \frac 3 2 - \frac 1 2 i$

4 0

3 years ago

Write an equation of a circle with a center at (2, - 4) and a radius of 4.

fgiga [73]

9514 1404 393

Answer:

(x -2)^2 +(y +4)^2 = 16

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is ...

(x -h)^2 +(y -k)^2 = r^2

You have (h, k) = (2, -4) and r = 4, so your equation is ...

(x -2)^2 +(y -(-4))^2 = 4^2

(x -2)^2 +(y +4)^2 = 16

6 0

3 years ago

I WILL GAVE BRAINLIEST

Arte-miy333 [17]

Answer:

x < -14

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

$-3x+6-6 > 48-6$
$-3x > 42$

Step 2: Divide both sides by -3 and flip the inequality sign.

$-3x/-3 > 42/-3$
$x < -14$

Therefore, the answer is x < -14.

4 0

2 years ago

Read 2 more answers