The trumpet player in a jazz band receives $64 in tips and a portion of the band's

If (9x − 4)(9x + 4) = ax² − b, what is the value of a? (5 points)

lions [1.4K]

Given, (9x - 4)(9x + 4) = ax² - b

From algebraic identities:

We know, (a + b)(a - b) = a² - b²

Now, 81x² + 36x - 36x - 16 = ax² - b

81x² - 16 = axis² - b

So ax² = 81x²

a = 81

-b = -16

b = 16

Solution

Therefore, the value of a is 81.

<h2>MyHeritage</h2>

8 0

2 years ago

Read 2 more answers

Line m and point P are shown below. Part A: Using a compass and straightedge, construct line n parallel to line m and passing th

Morgarella [4.7K]

Answer:

The steps to construct a a line parallel to another line from a point includes

1) From the given line draw a transversal through the point

2) With the compass, copy the angle formed between the transversal and the given line to the point P

3) Draw a line through the intersection of the arcs of the angle construction to get the parallel line through the point P

Step-by-step explanation:

8 0

2 years ago

The original price of a shirt is increased by $15. Patrick buys two of the shirts. The total price before sales tax is added is

kotegsom [21]

1. 86/2=43/new price of one shirt
2. 43-15=28/original price of one shirt

Your answer would be $28.

8 0

2 years ago

Read 2 more answers

Megan has practiced the piano for 7.5 hours over the course of this week. She practices on Tuesdays, Thursdays, and Saturdays. H

gulaghasi [49]

Answer:

150

Step-by-step explanation:

you have three days and 7.5 so decide 7.5 by 3 it equals 2.5 which in minutes is 150

7 0

2 years ago

Several years ago, 50% of parents who had children in grades K-12 were satisfied with the quality of education the students r

galina1969 [7]

Answer:

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

We have to see if 50% = 0.5 is part of the confidence interval.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1095, \pi = \frac{478}{1095} = 0.4365$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 - 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4118$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 + 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4612$

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

5 0

2 years ago