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timofeeve [1]
3 years ago
7

The function g is defined by:

Mathematics
1 answer:
Alisiya [41]3 years ago
6 0

<em>g(x)</em> = <em>x</em>² - <em>x</em> - 6

so

<em>g</em> (-4) = (-4)² - (-4) - 6 = 16 + 4 - 6 = 14

When <em>g(x)</em> = 6, we have

6 = <em>x</em>² - <em>x</em> - 6

<em>x</em>² - <em>x</em> - 12 = 0

Solve for <em>x</em>. We factorize this easily as

(<em>x</em> - 4) (<em>x</em> + 3) = 0

which gives

<em>x</em> - 4 = 0   <u>or</u>   <em>x</em> + 3 = 0

<em>x</em> = 4   <u>or</u>   <em>x</em> = -3

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Answer:

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Step-by-step explanation:

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2 years ago
Which properties of logarithms help you simplify log 200 + log 5 - log 100? (Select all that apply.)
bearhunter [10]

Answer:quotient property

Product property

Step-by-step explanation:

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5 0
3 years ago
Write an absolute value inequality for the graph below GRAPH ADDED. Please reply with correct answer 1/3
Mama L [17]

The absolute value inequality for the graph is given as |x| < 4

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

The absolute value is given by:

|x - average| = distance to midpoint

From the graph:

x > -4 and x < 4

The midpoint is 0, hence Distance between -4 or 4 to midpoint (0) is 4

Average = (-4 + 4)/2 = 0

Hence:

|x - 0| = 4

|x| < 4

The absolute value inequality for the graph is given as |x| < 4

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3 0
2 years ago
Your company is planning to air a number of television commercials during a television network's presentation of the an awards s
Sunny_sXe [5.5K]

This question is incomplete, the complete question is;

Your company is planning to air a number of television commercials during a television network's presentation of the an awards show. The network is charging your company $1.9 million per 30-second spot. Additional fixed costs (development and personnel costs) amount to $500,000, and the network has agreed to provide a discount of $160,000√x for x television spots.  

Required:

Write down the cost function C, marginal cost function C’, and average cost function

Answer:

- The  the cost function is 500,000 + 1,900,000x - 160,000√x

- the marginal cost function is 1,900,000 - (80000 /√x  )

- The  average cost function is 1,900,000 + [ 500,000 / x ] - [ 160,000 / √x ]

Step-by-step explanation:

Given the data in the question;

cost per spot = $1.9 million

Additional cost =  $500,000

discount = $160,000√x

 Let C(x) represent the cost ;

Cost x television spot = cost per spot × Number pf spots

Cost x television spot = $1.9 million × x

Cost x television spot = $1,900,000x

Now, the television set total cost will be;

C(x) = television cost + additional cost - discount  

C(x) = 500,000 + 1,900,000x - 160,000√x

Therefore, The  the cost function is 500,000 + 1,900,000x - 160,000√x

Marginal Cost Function;

Cost function C(x) = 500,000 + 1,900,000x - 160,000√x

we differentiate with respect to x

C'(x) = d/dx( 500,000 + 1,900,000x - 160,000√x )

= d/dx( 500000 ) + 1,900,000d/dx -160,000 d/d( √x )

= 0+ 1,900,000(1) -160,000( 1 / 2√x )

= 1,900,000 - (160,000 / 2√x  )

= 1,900,000 - (80000 /√x  )

Therefore, the marginal cost function is 1,900,000 - (80000 /√x  )

Average cost function;

Average cost function = C(x) / x

we substitute

Average cost function = [500,000 + 1,900,000x - 160,000√x] / x

=  [500,000 / x ] + [1,900,000x / x ]  - [ 160,000√x / x ]

=  [ 500,000 / x ] + 1,900,000 - [ 160,000√x / x ]

=  1,900,000 + [ 500,000 / x ] - [ 160,000 / √x ]

Therefore, The average cost function is 1,900,000 + [ 500,000 / x ] - [ 160,000 / √x ]

5 0
3 years ago
The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price
iren [92.7K]
Part A.

1) Function given:

f(x)=0.69(1.03)^x

2) Interpretation:

initial value: => x = 0 => f(x) = 0.69

table:

x                f(x)
year          price

0              0.69

1             0.69 * 1.03 = 0.7107 => increase = 3%

2             0.69 * (1.03)^2 = 0.732021 => increase = 3%

So, the answer is that the function is increasing at 3% per year.

Part B.

3) table

<span> t (number of years)      1             2              3                  4
f(t) (price in dollars)     10,100    10,201     10,303.01   10,406.04

Percent change:

Year 2: 10,201 / 10,100 = 1.01 => 1% increase

Year 3: 10,303.01 / 10,201 = 1.01 => 1% increase

Year 4: 10,406.04 / 10,303.01 = 1.01 => 1% increase.

Answer: the </span><span>product of the part A recorded a greater percentage change in price over the previous year (3% vs 1%).</span>
5 0
4 years ago
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