All categories

2 years ago

What is the answer / product of 8x2

Mathematics

1 answer:

Mademuasel [1]2 years ago

3 0

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

8*x^2-(8)=0

Step by step solution :

STEP

Equation at the end of step 1

23x2 - 8 = 0

STEP

Pulling out like terms

3.1 Pull out like factors :

8x2 - 8 = 8 • (x2 - 1)

Trying to factor as a Difference of Squares:

3.2 Factoring: x2 - 1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check : x2 is the square of x1

Factorization is : (x + 1) • (x - 1)

Equation at the end of step

8 • (x + 1) • (x - 1) = 0

STEP

Theory - Roots of a product

4.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Equations which are never true:

4.2 Solve : 8 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3 Solve : x+1 = 0

Subtract 1 from both sides of the equation :

x = -1

Solving a Single Variable Equation:

4.4 Solve : x-1 = 0

Add 1 to both sides of the equation :

x = 1

Two solutions were found :

x = 1

x = -1

You might be interested in

John runs a computer software store. Yesterday he counted 123 people who walked by the store, 56 of whom came into the store. Of

vaieri [72.5K]

Answer:

a) There is a 45.53% probability that a person who walks by the store will enter the store.

b) There is a 41.07% probability that a person who walks into the store will buy something.

c) There is a 18.70% probability that a person who walks by the store will come in and buy something.

d) There is a 58.93% probability that a person who comes into the store will buy nothing.

Step-by-step explanation:

This a probability problem.

The probability formula is given by:

$P = \frac{D}{T}$

In which P is the probability, D is the number of desired outcomes and T is the number of total outcomes.

The problem states that:

123 people walked by the store.

56 people came into the store.

23 bought something in the store.

(a) Estimate the probability that a person who walks by the store will enter the store.

123 people walked by the store and 56 entered the store, so $T = 123, D = 56$ .

$P = \frac{D}{T} = \frac{56}{123} = 0.4553$

There is a 45.53% probability that a person who walks by the store will enter the store.

(b) Estimate the probability that a person who walks into the store will buy something.

56 people came into the store and 23 bought something, so $T = 56, D = 23$ .

$P = \frac{D}{T} = \frac{23}{56} = 0.4107$

There is a 41.07% probability that a person who walks into the store will buy something.

(c) Estimate the probability that a person who walks by the store will come in and buy something.

123 people walked by the store and 23 came in and bought something, so $T = 123, D = 23$ .

$P = \frac{D}{T} = \frac{23}{123} = 0.1870$

There is a 18.70% probability that a person who walks by the store will come in and buy something.

(d) Estimate the probability that a person who comes into the store will buy nothing.

Of the 56 people whom came into the store, 23 bought something. This means that 56-23 = 33 of them did not buy anything. So:

$D = 33, T = 56$

$P = \frac{D}{T} = \frac{33}{56} = 0.5893$

There is a 58.93% probability that a person who comes into the store will buy nothing.

8 0

3 years ago

The owner of Mattâ€™s Gas Station wants to study gasoline purchases of customers at his station. In 2017, the mean amount of gas

gulaghasi [49]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 9

For the alternative hypothesis,

µ ≠ 9

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 9

x = 9.9

σ = 2.5

n = 50

z = (9.9 - 9)/(2.5/√50) = 2.55

Looking at the normal distribution table, the probability corresponding to the area above the z score is 1 - 0.99461 = 0.00539

Recall, population mean is 9

The difference between sample sample mean and population mean is 9.9 - 9 = 0.9

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 9 - 0.9 = 8.1

the x value for the right tail is 9 + 0.9 = 9.9

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area above the z score as z = 0.00539

We would double this area to include the area in the left tail of z = - 2.55. Thus

p = 0.00539 × 2 = 0.01078

Since alpha, 0.01 < 0.01078, we would reject the null hypothesis

But we are told to use the critical value approach, then

Since α = 0.01, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.01/2 = 0.005

The z score for an area to the left of 0.005 is - 2.575

For the right, α/2 = 1 - 0.005 = 0.995

The z score for an area to the right of 0.995 is 2.575

In order to reject the null hypothesis, the test statistic must be smaller than - 2.575 or greater than 2.575

Since - 2.55 > - 2.575 and 2.55 < 2.575, we would reject the null hypothesis. This corresponds to our previous decision.

b) we would assume normal distribution because the sample size is sufficiently large and the population standard deviation is known.

c) Confidence interval is written in the form,

(Sample mean ± margin of error)

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

The z score for confidence level of 99% is 2.58

Margin of error = 2.58 × 2.5/√50 = 0.91

Confidence interval = 9.9 ± 0.91

The lower end of the confidence interval is

9.9 - 0.91 = 8.99

Therefore, p = 9 will be contained in the interval.

4 0

3 years ago

Today, both the soccer team and the basket ball team had games (starting on Monday). The soccer team plays every 3 days and the

yarga [219]

I think eight because if you add those days together they will play again in eight days so that they play on the same day.

Sorry if I got it wrong I tried and that's what counts, right?

3 0

3 years ago

Find the volume of the following solid figure. A rectangular solid has sides of 10.5 cm, 6.5 cm, and 8.5 cm. What is its volume?

Zolol [24]

580.125 cm3 is the answer.

6 0

3 years ago

Read 2 more answers

When using fraction strips ,how do you know that 2 fractions are equivalent

Zigmanuir [339]

When the longer strip is on top and the litter strips fit perfectly under the longer one. For example, the fraction 1/3 and 3/6. One longer strip will be on the top representing 6. Then 3 litter 3s will be under that perfectly

5 0

3 years ago