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pychu [463]
2 years ago
8

Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours,

the velocity of the car is 54 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equation obtained in Part A for the first seven hours? (5 points)
Mathematics
1 answer:
Eva8 [605]2 years ago
4 0
Let:
x = hours of travel
y = velocity

slope= rise/run slope=(y2-y1)/(x2-x1) 
(x1,y1) = (2,50) (x2,y2) = (6,54) 
sub values back into the equation m = (54-50)/(6-2) m = 1 
POINT SLOPE FORMy-y1 = m(x-x1) y-50= 1(x-2) y = x -2 +50
y = x + 48

B) 

the graph within the first seven hours can be obtained at point B

x = 7

y = 7+48 = 55
B(7,55)
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Helena uses a mixture of compost and topsoil in her garden. She purchased a total of 10 cubic yards of compost and topsoil for $
Annette [7]

Let C be the amount of compost

T be the amount of  topsoil

Each compost cost = $25

Cost of C compost = 25C

Each topsoil cost = $15

Cost of T topsoil = 15T

Amount of compost + amount of topsoil = 10

C + T = 10 -------> Equation 1

cost of C compost + cost of T topsoil = 180

25C + 15T = 180 --------> equation 2

Solve  the first equation for C

C + T = 10

C = 10 - T

Now plug it in second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

250 - 25T + 15T = 180 (combine like terms)

250 - 10 T = 180 (Subtract 250 on both sides)

-10T = 180 - 250

-10T = -70 ( divide by -10 on both sides)

T = 7

She purchased  7 cubic yards of topsoil .


4 0
2 years ago
Read 2 more answers
The function below represents the interest Kristina earns on an investment. Identify the term that represents the amount of mone
Elena-2011 [213]

Answer:

The amount of money originally invested which is the principal P = 5,000

Step-by-step explanation:

Using the compound interest formula, the return on investment can be represented on the interest function as;

f(x) = P(1+r)^x

Where

P is the principal which is the initial investment.

r = rate Proportion

x = time (number of years)

Comparing to the given function;

f(x) = 5,000(1 + 0.04)^x

We can see that;

Principal P = 5,000

Rate r = 0.04

time = x

The amount of money originally invested which is the principal P = 5,000

4 0
2 years ago
Orchids are a family of thousands of types of flowers that all share the same shape. Many gardening clubs are devoted to collect
irakobra [83]

Answer:

The correct options are;

1) Which type needs the highest temperature to grow

2) Do all of the types make food the same way

3) How long does it take for a specific type to make seeds

Step-by-step explanation:

The number of types of species in the orchid family = Several thousand

The tasks the gardening clubs are devoted to = Collecting, Studying, and growing of the orchids

The manner of the growth of the orchids = Difficulty observed in growing outside the orchid's natural habitat

Scientific questions are objective questions that are measurable, well defined about parameters that can be controlled which can be answered by means of an experiment and meant to provide a deeper understanding of the nature of the world around us

Therefore, the scientific questions that can be asked about a collection of different orchid types are;

1) Which type needs the highest temperature to grow

The above is a question that has a defined parameter (temperature) which is measurable and the answer can be provided by experimenting

2) Do all of the types make food the same way

An experiment with different orchid types will provide an answer to the above question

3) How long does it take for a specific type to make seeds

The length of time for it takes the seed to grow is measurable within an experiment.

8 0
1 year ago
Read 2 more answers
Discuss the validity of the following statement. If the statement is always​ true, explain why. If​ not, give a counterexample.
Zarrin [17]

Correction:

Because F is not present in the statement, instead of working on​P(E)P(F) = P(E∩F), I worked on

P(E∩E') = P(E)P(E').

Answer:

The case is not always true.

Step-by-step explanation:

Given that the odds for E equals the odds against E', then it is correct to say that the E and E' do not intersect.

And for any two mutually exclusive events, E and E',

P(E∩E') = 0

Suppose P(E) is not equal to zero, and P(E') is not equal to zero, then

P(E)P(E') cannot be equal to zero.

So

P(E)P(E') ≠ 0

This makes P(E∩E') different from P(E)P(E')

Therefore,

P(E∩E') ≠ P(E)P(E') in this case.

8 0
2 years ago
What is the balance on an amortized loan of $110,000 after the first payment if the interest rate is 5.5% with a monthly P&I
marishachu [46]
The interest due on the first payment is
.. I = Prt
.. I = 110,000*.055*(1/12)
.. I = 504.17

Then the decrease in principal resulting from the first payment is
.. 568.00 -504.17 = 63.83
and the new balance is
.. $110,000.00 -63.83 = $109,936.17
4 0
2 years ago
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