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Nat2105 [25]
3 years ago
13

Layla and Sam are both dog sitters. Layla charges $2 per day plus a sign-up fee of $3. Sam charges a flat rate of $3 per day. Th

e system of linear equations below represents y, the total amount earned in dollars for x days of dog sitting.
1. Write the equation to represent Layla’s fees
2. Write the equation to represent Sam’s fees
3. After how many days do Layla and Sam earn the same amount for dog sitting?
What is that amount?

Mathematics
2 answers:
Stels [109]3 years ago
8 0

Answer:

Step-by-step explanation:

Let x represent the number of days of dog sitting.

1) Layla charges $2 per day plus a sign-up fee of $3. The equation representing Layla's charges for x days of dog sitting is

y = 2x + 3

2) Sam charges a flat rate of $3 per day. The equation representing Sam's charges for x days of dog sitting is 3x.

3)for Layla and Sam to earn the same amount, the number of days would be 3 as seen from the point of intersection on the graph. The corresponding amount would be $9

Nikolay [14]3 years ago
3 0

Answer:

Givens

  • Layla charges $2 per day, plus a sign-up fee of $3. Notice the sign-up fee represents a fixed value, that's gonna be the constant form of the function. And $2 is the ratio of change of the function, because it a cost per day.
  • Sam charges $3 per day, without extra fee. So, the ratio of change of this function is $3, and it doesn't have a constant term.

According to the given information, the linear function for Layla is:

f(x)=2x+3

Notice that the constant ratio of change is coefficient of the independent variable, that is, because that variable represents days, and each charges $2.

On the other hand, the linear function for Sam is:

g(x)=3x

As we said before, this expression doesn't have any constant term, because the charges are flate $3 per day, it's just that rate.

Now, to find the number of days needed to both Layla and Sam earn the same money, we just have to solve the equation f(x)=g(x)

2x+3=3x\\3=3x-2x\\x=3

Therefore, on day three they are gonna earn the same amount of money.

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The answer would be -7
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4 years ago
Factor completely: <br> x^3 - x^2 - 6x
PSYCHO15rus [73]

Answer:

x(x-3)(x+2)

Step-by-step explanation:

1. Find the GCF (Greatest Common Factor)

GCF=x

2. Factor out the GCF and simplify.

x(x^{2} -x-6)

3. Factor x^{2} -x-6.

Which two numbers add up to -1 and multiply to -6?

<u>-3 and 2</u>

Rewrite the expression using the numbers above.

(x-3)(x+2)

4. Done!

x(x-3)(x+2)

4 0
3 years ago
A bolt falls off an airplane at an altitude of 500 m. How long will it take the bolt to reach
Rudik [331]

Answer:

t = sqrt(500/4.9) =~ 10.1 seconds/ Answer: 10.1015 seconds (this is approximate)

Step-by-step explanation:

Use 4.9t^2 + v0t = s

a) A bolt falls off an airplane at an altitude of 500 m. Approximately how long does it take the bolt to reach the ground?

s = 4.9t^2 + v0t = 500

4.9t^2 = 500

t = sqrt(500/4.9) =~ 10.1 seconds

Part A)

v = initial velocity = 0

s = 500 = vertical distance the object travels (from plane to ground)  

Plug in the given values and solve for t

4.9t^2 + v*t = s

4.9t^2 + 0*t = 500

4.9t^2 + 0 = 500

4.9t^2 = 500

t^2 = 500/4.9

t^2 = 102.04081632653

t = sqrt(102.04081632653)

t = 10.101525445522

t = 10.1015

Answer: 10.1015 seconds (this is approximate)

8 0
3 years ago
Deb is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Boston was
Brilliant_brown [7]

Answer:

Percent increase = 60%

Percent increase with baggage = 83%

Step-by-step explanation:

Given that:

Old price of the ticket = $210

New price of the ticket = $335

Increase amount =335-210 = $125

Percent increase = \frac{Inrease\ amount}{Old\ price}*100

Percent increase = \frac{125}{210}*100 = 0.595*100

Percent increase = 59.52% = 60%

Additional charges = $125+$50 = $175

Percent increase = \frac{175}{210}*100

Percent increase = 83%

Hence,

Percent increase = 60%

Percent increase with baggage = 83%

4 0
3 years ago
Read 2 more answers
What are the solutions of 3(2m − 1) ≤ 6m − 2?
kaheart [24]

Hello from MrBillDoesMath!

Answer:

The solution set is the set all all real number m

 

Discussion:

3(2m-1) <= 6m-2       =>

3*2m - 3*1 <= 6m-2  =>

6m - 3 <.= 6m-2       =>   (Subtract 6m from both sides)

0-3 <= -2     =>

-3 < = -2      


As -3 <=-2 is always true the solution set is the set all all real number m

Regards,  

MrB


4 0
3 years ago
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