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alexdok [17]
2 years ago
9

Donna's company reimburses her expenses on food, lodging, and conveyance during business trips. The company pays $50 a day for f

ood and lodging and $0.60 for each mile traveled. Donna drove 200 miles and was reimbursed $1,620.
Part A: Create an equation that will determine the number of days x on the trip. (3 points)

Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points)

Part C: How many days did Donna spend on this trip? (1 point)
Mathematics
1 answer:
Maksim231197 [3]2 years ago
3 0

A.

Multiply the number of days, x by 50 per day to get 50x.

Next multiply the number of miles driven to the amount she gets per mile: 0.60 x 200 = $120

Now add both together to equal the total of 1620.

The equation becomes: 50x +120 = 1620

B.

50x +120 = 1620

Step 1: subtract 120 from both sides ( subtraction property of equality):

50x = 1500

Step 2: Divide both sides by 50 ( division property of equality):

x = 1500 / 50

x = 30

C.

The trip lasted 30 days.

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Step-by-step explanation:

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v(t)=4t²-24t-28

1) To write the expression in a factored form, we need to factorize the equation given;

v(t)=4t²-24t-28

divide through by 4

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2) To know the number of months after the company creation that the company reaches its lowest value, we will substitute v(t) = 0 into the factored form of the expression as shown;

v(t)= (t+1)(t-7)

0 = (t+1)(t-7)

(t+1)(t-7) = 0

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8 0
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Mya is a performance athlete. She wants to use a function to represent the number of calories that she burns while training, whe
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We have an exponential function that is the best fit for the number of calories Mya burns, in function of time (minutes).

The function is:

y=45.3e^{0.0548x}

Where y: calories burned, and x: training time.

Whenever we use regression models, we have a real value and a predicted value. The difference between them, the measure we want to minimize when we adjust with this typo of models, is called residual.

In the table is shown as one of the columns.

For example, for x=10 minutes, we have a real value of 30 and a predicted value of 78.36, so the residual becomes e=30-78.36=-48.36.

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For x=30 minutes, we have only the residual, that has a value of 5.53. That means that the predicted value, which we can calculate, is 5.53 below the real value.

The predicted value for x=30 is:

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Using the equation for the residual e, we can calcualte the actual number of calories that Mya burned in 30 minutes:

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