X2 +8x+16=0 in factoring algorithm

Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Sel

baherus [9]

Option D: $20 \div 6-4$ is the correct solution to the equation $6(x+4)=20$

Option E: $\frac{1}{6} (20-24)$ is the correct solution to the equation $6(x+4)=20$

Option F: $(20-24) \div 6$ is the correct solution to the equation $6(x+4)=20$

Explanation:

The expression is $6(x+4)=20$

Let us find the value of x.

$\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}$

Now, we shall find the expression that is equivalent to the value $x=-\frac{2}{3}$

Option A: $(20-4) \div 6$

Simplifying the expression, we have,

$\frac{16}{6}=\frac{8}{3}$

Since, $\frac{8}{3}$ is not equivalent to $x=-\frac{2}{3}$ , the expression $(20-4) \div 6$ is not equivalent to the equation $6(x+4)=20$

Hence, Option A is not the correct answer.

Option B: $16(20-4)$

Simplifying the expression, we have,

$16(16)=256$

Since, 256 is not equivalent to $x=-\frac{2}{3}$ , the expression $16(20-4)$ is not equivalent to the equation $6(x+4)=20$

Hence, Option B is not the correct answer.

Option C: $20-6-4$

Simplifying the expression, we have,

$20-10=10$

Since, 10 is not equivalent to $x=-\frac{2}{3}$ , the expression $20-6-4$ is not equivalent to the equation $6(x+4)=20$

Hence, Option C is not the correct answer.

Option D: $20 \div 6-4$

Using PEMDAS and simplifying the expression, we have,

$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$ , the expression $20 \div 6-4$ is equivalent to the equation $6(x+4)=20$

Hence, Option D is the correct answer.

Option E: $\frac{1}{6} (20-24)$

Simplifying the expression, we have,

$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$ , the expression $\frac{1}{6} (20-24)$ is equivalent to the equation $6(x+4)=20$

Hence, Option E is the correct answer.

Option F: $(20-24) \div 6$

Simplifying the expression, we have,

$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$ , the expression $(20-24) \div 6$ is equivalent to the equation $6(x+4)=20$

Hence, Option F is the correct answer.

6 0

4 years ago

The national average for the number of students per teacher for all U.S. public schools in 15.9. A random sample of 12 school di

Nady [450]

Answer:

The 95% confidence interval for the true mean number of students per teacher is (17.9, 20.5). The lower bound of the interval is above the national average, which means that this estimate is higher than the national average.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 12 - 1 = 11

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2.201

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.201\frac{\sqrt{4.41}}{\sqrt{12}} = 1.3$

In which s is the standard deviation of the sample(square root of the variance) and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 19.2 - 1.3 = 17.9 students.

The upper end of the interval is the sample mean added to M. So it is 19.2 + 1.3 = 20.5 students

The 95% confidence interval for the true mean number of students per teacher is (17.9, 20.5). The lower bound of the interval is above the national average, which means that this estimate is higher than the national average.

5 0

3 years ago

What factors of 32 add up to -12

irakobra [83]

Answer: -8 and -4

This is something you do through trial and error. Making a list or a table like shown below might help.

8 0

3 years ago

What are the solutions on the following system?

Oksana_A [137]

2x+y = -5. Solve this for y. We get y = -2x - 5. Find y^2: 4x^2 + 20x + 25. Substitute 4x^2 + 20x + 25 for y^2 in the first equation:

x^2 + 4x^2 + 20x + 25 = 25

Then 5x^2 + 20x = 0, so that x = 0. Subst. 0 for x in the 2nd eqn and find the value of y. Write your solutions as shown above: ( , ) and ( , ).

3 0

4 years ago

12 Terrel says 5x = 5x + 0. Johnny says 5x = 5x .0. Which person is correct?

Galina-37 [17]

Answer:

c

5x=5x so when five Cross the=sign

5x-5x=0

5 0

3 years ago