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sergeinik [125]
2 years ago
8

Mike earns $15 for each hour he works plus a $25 bonus. Represent this story in function notation

Mathematics
2 answers:
Brrunno [24]2 years ago
6 0
<h3>Hello there!</h3>

In this question, we have to turn the given information into function notation.

Function notation is f(x) = (expression)

From the information given, we know that:

  • Earns $15 each hour
  • Gets a $25 bonus

Now, we turn it into an equation.

We would write the equation as y = mx + b

m = rate

x = hours

b = bonus

This means that our equation would be:

y = 15x + 25

Now, we can write it as a function notation.

f(x) = 15x + 25

<h3>Answer: f(x) = 15x + 25</h3><h3>I hope this helps!</h3><h3>Best regards,</h3><h3>MasterInvestor</h3>
Kitty [74]2 years ago
4 0

Answer:

y=15x +25

Step-by-step explanation:

Every hour he works, he get 15 dollars in addition to his bonus of 25 dollars

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Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?
Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

sec^4 x + sec^2 x tan^2 x - 2 tan^4 x

Required

Simplify

(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2

Represent sec^2x with a

Represent tan^2x with b

The expression becomes

a^2 + ab- 2 b^2

Factorize

a^2 + 2ab -ab- 2 b^2

a(a + 2b) -b(a+ 2 b)

(a -b) (a+ 2 b)

Recall that

a = sec^2x

b = tan^2x

The expression (a -b) (a+ 2 b) becomes

(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

..............................................................................................................................

In trigonometry

sec^2x =1  +tan^2x

Subtract tan^2x from both sides

sec^2x - tan^2x =1  +tan^2x - tan^2x

sec^2x - tan^2x =1

..............................................................................................................................

Substitute 1 for sec^2x - tan^2x in (sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

(1) (sec^2x+ 2 tan^2x)

Open Bracket

sec^2x+ 2 tan^2x ------------------This is an equivalence

(secx)^2+ 2 (tanx)^2

Solving further;

................................................................................................................................

In trigonometry

secx = \frac{1}{cosx}

tanx = \frac{sinx}{cosx}

Substitute the expressions for secx and tanx

................................................................................................................................

(secx)^2+ 2 (tanx)^2 becomes

(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2

Open bracket

\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})

\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}

Add Fraction

\frac{1 + 2sin^2x}{cos^2x} ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

sin^2x + cos^2x= 1

Make sin^2x the subject of formula

sin^2x= 1  - cos^2x

................................................................................................................................

Substitute the expressions for 1  - cos^2x for sin^2x

\frac{1 + 2(1  - cos^2x)}{cos^2x}

Open bracket

\frac{1 + 2  - 2cos^2x}{cos^2x}

\frac{3  - 2cos^2x}{cos^2x} ---------------------- This is another equivalence

8 0
3 years ago
What is the value of x in 34 + 2x = 40
alekssr [168]

Hello from MrBillDoesMath!

Answer:

3

Discussion:

34           + 2x = 40             => subtract 34 from both sides

(34-34)   + 2x = 40 - 34     => as (34-34) = 0 and 40-34 = 6

2x                   = 6               => divide both sides by 2

x = 6/2 = 3

Check the answer:

Does 34 + 2x = 40 if x = 3 ?

Does 34 + 2(3) = 40 ?

Does 34 + 6      = 40 ?  YES! so the answer checks.

Thank you,

MrB

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Step-by-step explanation:

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Answer:

<u>4</u>

Step-by-step explanation:

Hi so basically you just convert the inches to decimals so

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Then multiply \frac{1}{16} by \frac{1}{64} = 4

Soo that was probably very confusing, but I hope it helps! :)

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