All categories

2 years ago

A^2+14a-51=0 solve the quadratic by completing the square.

2 answers:

8 0

A^2+14a-51=0
Add 51 to both sides
a^2+14a-51+51=0+51
a^2+14a=51
add (14/2)^2
a^2+14a+(14/2)^2=100
Solve a+7=+sqrt 100: a=3
Solve a-7 = -sqrt 100: a=-17
a=3 a=-17

ehidna [41]2 years ago

7 0

Steps if you have ax^2+bx+c=0
1. put vairable on other side (-c from both sides)
2. make sure that leading term is 1 (ax^2+bx+c=0 where a=1)
3. take half of b and square it

so
a^2+14a-51=0
move c to other side
add 51 to both sides
a^2+14a=51
leading term is 1
take 1/2 of b and square
14/2=7, 7^2=49
add that to both sides
a^2+14a+49=51+49
factor perfect square
(a+7)^2=100
square root both sides
a+7=+/-10

a+7=10
a+7=-10

a+7=10
minus 7
a=3

a+7=-10
subtract 7
a=-17

a=3 or -17

You might be interested in

Find the remainder when $3 \times 13 \times 23 \times 33 \times \ldots \times 183 \times 193$ is divided by $5$.

Trava [24]

209.095.543and 8 tenths

5 0

3 years ago

There were 624 envelopes to be sorted into 8 different mail bags. if the same number of envelopes will be in each bag how many e

pickupchik [31]

Answer:

I think it is 710

Step-by-step explanation:

8 0

3 years ago

Carson purchased supplies for his computer for $64. The sales tax was $4.16. He gave the salesperson $80. How much change did he

krek1111 [17]

To work this out you need to do 80 - 64 - 4.16 = 11.48

he received $11.48 change

3 0

2 years ago

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA ba

PSYCHO15rus [73]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA basketball tournament (not all private schools report their coach's salaries). Consider these 62 salaries to be a sample from the population of salaries of all 346 NCAA Division I basketball coaches.

Question 1. Use the 62 salaries from the TOTAL PAY column to construct a 95% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

xbar = $1,465,752

SD = $1,346,046.2

lower bound of confidence interval ________

upper bound of confidence interval _______

Question 2. Coach Mike Krzyzewski's high salary is an outlier and could be significantly affecting the confidence interval results. Remove Coach Krzyzewski's salary from the data and recalculate the 95% confidence interval using the remaining 61 salaries.

xbar = $1,371,191

SD = $1,130,666.5

lower bound of confidence interval _________

upper bound of confidence interval. ________

Answer:

Question 1:

lower bound of confidence interval = $1,124,027

upper bound of confidence interval = $1,807,477

Question 2:

lower bound of confidence interval = $1,081,512

upper bound of confidence interval = $1,660,870

Step-by-step explanation:

Question 1:

The sample mean salary of 62 couches is

$\bar{x} = 1,465,752$

The standard deviation of mean salary is

$s = 1,346,046.2$

The confidence interval for the mean salary of all basketball coaches is given by

$CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } )$

Where $\bar{x}$ is the sample mean, n is the sample size, s is the sample standard deviation and $t_{\alpha/2}$ is the t-score corresponding to a 95% confidence level.

The t-score corresponding to a 95% confidence level is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 62 - 1 = 61

From the t-table at α = 0.025 and DoF = 61

t-score = 1.999

So the required 95% confidence interval is

$CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (\frac{1,346,046.2}{\sqrt{62} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (170948.04 ) \\\\CI = 1,465,752 \pm 341,725 \\\\LCI = 1,465,752 - 341,725 = 1,124,027 \\\\UCI = 1,465,752 + 341,725 = 1,807,477\\\\$

Question 2:

After removing the Coach Krzyzewski's salary from the data

The sample mean salary of 61 couches is

$\bar{x} = 1,371,191$

The standard deviation of the mean salary is

$s = 1,130,666.5$

The t-score corresponding to a 95% confidence level is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 61 - 1 = 60

From the t-table at α = 0.025 and DoF = 60

t-score = 2.001

So the required 95% confidence interval is

$CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (\frac{1,130,666.5}{\sqrt{61} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (144767 ) \\\\CI = 1,371,191 \pm 289,678.8 \\\\LCI = 1,371,191 - 289,678.8 = 1,081,512 \\\\UCI = 1,371,191 + 289,678.8 = 1,660,870\\\\$

6 0

3 years ago

0.029 g in Scientific notation

Kay [80]

0.029= 2.9 x 10 power of negative 2

4 0

3 years ago