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3 years ago

Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8.

Mathematics

1 answer:

AlladinOne [14]3 years ago

8 0

Answer:

(1,6) & (7,0)

Step-by-step explanation:

y = -x + 7

y = -0.5(x - 3)² + 8

To solve the system, solve these two equations simultaneously

-x + 7 = -0.5(x - 3)² + 8

-x + 7 = -0.5(x² - 6x + 9) + 8

-x + 7 = -0.5x² + 3x - 4.5 + 8

0.5x² - 4x + 3.5 = 0

x² - 8x + 7 = 0

x² - 7x - x + 7 = 0

x(x - 7) - (x - 7) = 0

(x - 1)(x - 7) = 0

x = 1, 7

y = -1 + 7 = 6

y = -7 + 7 = 0

(1,6) (7,0)

Since the system has two distinct solutions, the line and the curve meet at two distinct poibts9: (1,6) & (7,0)

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Bob cycles 5.4 km every morning.how many feet are in 5.4 km, given that 1 mile=1.609 km and 1 mile=5,280 feet?

creativ13 [48]

Answer:

17,720 ft

Step-by-step explanation:

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3 years ago

On Texas Avenue between University Drive and George Bush Drive, accidents occur according to a Poisson process at a rate of thre

Zarrin [17]

Answer:

(a) The probability is 0.6514

(b) The probability is 0.7769

Step-by-step explanation:

If the number of accidents occur according to a poisson process, the probability that x accidents occurs on a given day is:

$P(x)=\frac{e^{-at}*(at)^{x} }{x!}$

Where a is the mean number of accidents per day and t is the number of days.

So, for part (a), a is equal to 3/7 and t is equal to 1 day, because there is a rate of 3 accidents every 7 days.

Then, the probability that a given day has no accidents is calculated as:

$P(x)=\frac{e^{-3/7}*(3/7)^{x}}{x!}$

$P(0)=\frac{e^{-3/7}*(3/7)^{0}}{0!}=0.6514$

On the other hand the probability that February has at least one accident with a personal injury is calculated as:

P(x≥1)=1 - P(0)

Where P(0) is calculated as:

$P(x)=\frac{e^{-at}*(at)^{x} }{x!}$

Where a is equivalent to (3/7)(1/8) because that is the mean number of accidents with personal injury per day, and t is equal to 28 because 4 weeks has 28 days, so:

$P(x)=\frac{e^{-(3/7)(1/8)(28)}*((3/7)(1/8)(28))^{x}}{x!}$

$P(0)=\frac{e^{-(3/7)(1/8)(28)}*((3/7)(1/8)(28))^{0}}{0!}=0.2231$

Finally, P(x≥1) is:

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3 0

3 years ago

There are 42. Children in the classroom each student will get 28 pictures and 46 erasers how many pictures with the teacher had

Stella [2.4K]

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7 0

3 years ago

Read 2 more answers

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Sidana [21]

Answer:

231 miles.

Step-by-step explanation:

Tom rented a truck with a base fee of 19.95. You will subtract this from the total since you just want to get the mileage.

Tom is getting charged .85 cents per mile driven.

Tom payed 216.30 subtotal minus the 19.95 base fee since we are trying to only see how many miles he drove.

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4 0

3 years ago

I need help please. The question is already there. Tysm. 20 points.

Bess [88]

Answer:

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5 0

3 years ago