What 2 numbers can you multiply to get 31? can 31 get into smaller groups?

The roots of $3x^2 - 4x + 15 = 0$ are the same as the roots of $x^2 + bx + c = 0,$ for some constants $b$ and $c.$ Find the orde

Akimi4 [234]

we are given

quadratic equation as

$3x^2-4x+15=0$

now, we can find b and c from

$x^2+bx+c=0$

we can see that coefficient of x^2 is 1

so, we will have to make coefficient x^2 as 1

so, we divide both sides by 3

$3x^2-4x+15=0$

$\frac{3x^2-4x+15}{3}= \frac{0}{3}$

$\frac{3x^2}{3}-\frac{4x}{3}+\frac{15}{3}= \frac{0}{3}$

now, we can simplify it

$x^2-\frac{4}{3}x+5= 0$

now, we can compare it with

$x^2+bx+c=0$

we get

$b=-\frac{4}{3}$

$c=5$

so, we get order pair as

$(b,c)=(-\frac{4}{3} , 5)$ ..............Answer

6 0

3 years ago

Read 2 more answers

A G.P has its 3rd term and 7th term as 45 and 3645 respectively. what is the product of its 2nd and 4th

Ede4ka [16]

Answer:

2,025

Step-by-step explanation:

Given:

Third term ar² = 45

Seventh term ar⁶ = 3,645

Find:

ar x ar³

Computation:

From 7th term / 3rd term

ar⁶ / ar² = 3,645 / 45

r⁴ = 81

r = 3

So,

ar² = 45

a(3)² = 45

a = 5

So,

ar x ar³

(5)(3) x (5)(3)³

2,025

3 0

2 years ago

PLEASE ANSWER ILL MARK YOU AS THE BRAINLIEST

Solnce55 [7]

Answer:

63 i think

Step-by-step explanation:

7 0

2 years ago

Will mark brainliest! Problem is in pic below, no links please. Give explanation. Thanks.

sergey [27]

Answer:

2^12

Step-by-step explanation:

answer is in photo above

8 0

2 years ago

The standard deviation of math test scores at one high school is 16.1. A teacher claims that the standard deviation of the girls

Elanso [62]

Answer:

$\chi^2 =\frac{22-1}{259.21} 166.41 =13.482$

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(13.482,21,TRUE)"

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population deviation is not significantly lower than 16.1 at 1% of significance.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=22$ represent the sample size

$\alpha=0.01$ represent the confidence level

$s^2 =12.9^2=166.41$ represent the sample variance obtained

$\sigma^2_0 =16.1^2 =259.21$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population deviation is smaller than 16.1 (that's equivalent to check if the population variance is lower than 259.21:

Null Hypothesis: $\sigma^2 \geq 259.21$

Alternative hypothesis: $\sigma^2$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{22-1}{259.21} 166.41 =13.482$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 21. And since is a left tailed test the p value would be given by:

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(13.482,21,TRUE)"

Conclusion

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population deviation is not significantly lower than 16.1 at 1% of significance.

3 0

3 years ago