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2 years ago

Determine the solution to the system of equations graphed below and explain

Mathematics

1 answer:

lawyer [7]2 years ago

7 0

If x - 4 ≥ 0, then |x - 4| = x - 4, so

G(x) = F(x) ⇒ 3x + 2 = (x - 4) + 2

⇒ 3x + 2 = x - 2

⇒ 2x = -4

⇒ x = -2

Otherwise, if x - 4 < 0, then |x - 4| = -(x - 4), so

G(x) = F(x) ⇒ 3x + 2 = -(x - 4) + 2

⇒ 3x + 2 = -x + 6

⇒ 4x = 4

⇒ x = 1

However,

• when x = -2, we have

G(-2) = 3(-2) + 2 = -4

F(-2) = |-2 - 4| + 2 = 8

• when x = 1, we have

G(1) = 3(1) + 2 = 5

F(1) = |1 - 4| + 2 = 5

so only x = 1 is a solution to G(x) = F(x).

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3 years ago

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Kate is a wage earner. One year she earned $72 000. She works 36 hours/week.

Lemur [1.5K]

Answer:

Kate's possible hourly rate of pay: $34.75

Hours of overtime: 100

Step-by-step explanation:

In order to find Kate's hourly wage, we can set up an equation based on the number of hours she works per week and the estimated number of overtime hours to equal her total pay for the year. If Kate works 36 hours/week and there are 52 weeks in a year, her total hours for one year are: 36 x 52 = 1872. Setting up an equation based on her total earnings of $72,000:

1872x + 100(2x) = 72000, where 'x' is the hourly rate and '2x' is her overtime rate which is double time.

Combine like terms: 1872x + 200x = 72000 or 2072x = 72000

Divide both sides by 2072: 2072x/2072 = 72000/2072

Solve for x: x = $34.75

Kate's hourly rate is estimated at $34.75. We can check to see if this is correct by putting this value back into our original equation:

1872(34.75) + 100(2)(34.75) = 65052 + 6950 = 72002

The answer of $72,002 is very close to $72,000 and the best estimate of Kate's hourly wage and overtime hours.

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3 years ago

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3 years ago

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Situation:A researcher in North America discoversa fossile that contains 65% of its originalamount of C-14..-ktN=NoeNo inital am

zheka24 [161]

SOLUTION

We have been given the equation of the decay as

$\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}$

So we are looking for the time

Plugging the values into the equation, we have

$\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}$

Taking Ln of both sides, we have

$\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}$

Hence the answer is 4308 to the nearest year

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1 year ago

Michael writes down 4 different factors of 60

Marizza181 [45]

Answer:

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3 years ago