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4 years ago

What is the value of the discriminant in the equation shown below? x^2 -6x +4 =0

Mathematics

1 answer:

irakobra [83]4 years ago

7 0

Answer:

Discriminant = 20

Step-by-step explanation:

We use formula to find the discriminant.

Discriminant (D) = b^2 - 4ac

The given equation is x^2 - 6x + 4 = 0.

Here the value of a = 1, b = -6 and c = 4.

Plug in the given values in the formula, we get

Discriminant (D) = (-6)^2 - 4*1*4

= 36 - 16

Discriminant = 20

Thank you.

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Find the product (8/6n-4)(9n^2-4)

Leokris [45]

Answer:

4(3n+2) or 12n+8

Step-by-step explanation:

Given expression is:

$(\frac{8}{6n-4})(9n^{2}-4)$

The numerator of the fraction will be multiplied with 9n^2- 4

So, Multiplication will give us:

$=\frac{8(9n^2-4)}{6n-4}$

We can simplify the expression before multiplication.

The numerator will be broken down using the formula:

$a^2 - b^2 = (a+b)(a-b)\\So,\\= \frac{8[(3n)^2 - (2)^2]}{6n-4}\\ = \frac{8(3n-2)(3n+2)}{6n-4}$

We can take 2 as common factor from denominator

$=\frac{8(3n-2)(3n+2)}{2(3n-2)}\\After\ cutting\\= 4(3n+2)$

Hence the product is 4(3n+2) or 12n+8 ..

6 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

Write an equation for the line on the graph below.

alukav5142 [94]

Answer:

A store ships cans by weight. A small box can hold 3 to 5 pounds. A medium box can hold 5 to 8 pounds. A large box can hold 8 to 10 pounds. The weights of the cans are given below.

Drag cans into each box to show what the box could contain.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Olivia wants to cut 3 3/4 inches from a piece of string.She has already cut off 2 9/16 inches from the piece of string.How much

Roman55 [17]

Answer: she still has to cut off 19/16 inches.

Step-by-step explanation:

Olivia wants to cut 3 3/4 inches from a piece of string. Converting 3 3/4 inches to improper fraction, it becomes 15/4 inches.

She has already cut off 2 9/16 inches from the piece of string. Converting 2 9/16 inches to improper fraction, it becomes 41/16 inches.

Therefore, the length of string that is left for her to cut off would be

15/4 - 41/16 = (60 - 41)/16

= 19/16 inches

6 0

4 years ago

HELP PLEASE Which expression is equivalent to:

mojhsa [17]

21 V³ 15- 9V³15

= (21-9)V³15

= 12V³15

4 0

3 years ago