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4 years ago

What is the factored form of the expression? t2 – 81

1 answer:

6 0

We have that
t² – 81

we know that
A difference of two perfect squares, (A² - B²) can be factored into (A+B) • (A-B)
 let
A²-------> t²
B²-------> 9²
then
(t² – 9²)------->(t+9)*(t-9)

the answer is
(t+9)*(t-9)

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A child lets go of a balloon that rises at a constant rate. 5 seconds after it was released, the balloon is at a height of 16 fe

Mama L [17]

Answer:

1. h = 2.4t + 4

2. 4 feet

3. 220 feet

Step-by-step explanation:

1. Write a linear model for the height, h, of the balloon as a function of the number of seconds, s that it has been raising.

Since the balloon rises at a constant rate, we find this rate by using the initial and final values of height and time at 5 seconds and 20 seconds respectively which are 12 feet and 52 feet respectively.

So, rate = gradient of line

= change in height/change in time

= (52 ft - 16 ft)/(20 s - 5 s)

= 36 ft/15 s

= 2.4 ft/s

Now the equation of the line which shows the height is gotten from

(h - h')/(t - t') = rate

Using h'= 16 feet and t' = 5 s, we have

(h - 16)/(t - 5) = 2.4

h - 16 = 2.4(t - 5)

h - 16 = 2.4t - 12

h = 2.4t - 12 + 16

h = 2.4t + 4

where h is the height of the balloon above the ground and t is the time spent in the air in seconds.

2. What was the height of the balloon initially before the child let it go?

We obtain the initial height of the balloon before the child let go at time, t = 0 the time before the child let go.

So, substituting t = 0 into the equation for h, we have

h = 2.4t + 4

h = 2.4(0) + 4

h = 0 + 4

h = 4 feet

So, the height of the balloon before the child let go is 4 feet above the ground.

3. Use your model to predict the height of the balloon after 90 seconds.

We insert t = 90 s into the equation for h. So,

h = 2.4t + 4

h = 2.4(90) + 4

h = 216 + 4

h = 220 feet

So, the height of the balloon after 90 s is 220 feet above the ground.

8 0

3 years ago

Solve the following system by elimination: 4x+3y=2 5x + 4y = 3

MAXImum [283]

Answer:

5x+4y=3

- 4x+3y=2

-----------------

x+y=1

5 0

3 years ago

You received a $178 per month raise. That was a 5% increase. What was your monthly salary before the increase? Show work please

zzz [600]

Answer: 169.52

Step-by-step explanation

%increase which is 5% =100 x final - initial

---------------------

initial

the initial is $169.52

and the final $178

3 0

3 years ago

What is the median of the data set?

Artist 52 [7]

Answer:

11.7

Step-by-step explanation:

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3 years ago

Read 2 more answers

A car company is going to issue new ID codes to its employees. Each code will have one digit followed by four letters. The lette

scoray [572]

2734375 employee ID codes can be generated

Solution:

Given that Each code will have one digit followed by four letters

The letter V and the digits 3, 4, and 5 will not be used

So, there are 25 letters and 7 digits that will be used

Assume that the letters can be repeated

Each code = 1 digit + four letters

digits 3 , 4 , 5 cannot be used

Therefore, the remaining digits are 1, 2, 6, 7, 8 , 9, 0

7 digits that will be used

One digit can be chosen from 7 digits in 7 ways

The first letter can be chosen from 25 letters in 25 ways

Since given that letters can be repeated

The second letter can be chosen from 25 letters in 25 ways

Similarly, the third letter can be chosen from 25 letters in 25 ways

Similarly, the fourth letter can be chosen from 25 letters in 25 ways

Therefore, the total number of ways are:

$\rightarrow 7 \times 25 \times 25 \times 25 \times 25 = 7 \times 25^4\\\\ \rightarrow 2734375$

Thus 2734375 employee ID codes can be generated

3 0

3 years ago