Use substitution to solve the system

Mathematics

1 answer:

Doss [256]3 years ago

3 0

Answer:

x = 4, y = 16

Step-by-step explanation:

$y = 4x\\y = 2x + 8\\\\4x = 2x + 8\\2x = 8\\x = 4\\\\y = 4*4\\y = 16$

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Find the first five terms of each sequence. aₙ=5-a n₋₁ , where a₁ = 1

laila [671]

The first five terns of the sequence are - 1,4,1,4,1

<h3>What is a sequence?</h3>

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

an = 5 - a n-1

a1 = 1

a2 = 5 - (1) = 4

a3 = 5 - (4) = 1

a4 = 5 - (1) = 4

a5 = 5 - (4) = 1

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1 year ago

Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per we

Maru [420]

A) System of inequalities

Income from babysitting: 6x
Income from tutoring: 10y

Goal for this week: at least $ 75 => 6x + 10y ≥ 75
Number of hours: maximum $20 => x + y ≤ 20

x and y have to be zero or positvie => x≥0 and y ≥ 0

Answer of part A.

6x + 10y ≥ 75
x+y ≤ 20
x ≥ 0
y ≥ 0

Part B. Graph

The solution is a region closed by 4 lines and you can find it in the file attached.

In that graph:

1) the line x + y = 20 is the upper limit
2) the line 6x + 10 y = 75 is the lower incclined line
3) y = 0 is the botton horizontal line it is the x-axis
4) x = 0 is the left vertical line, in is the y-axis

Part C.

Use, for example the point (7,10).

It is in the region of the graph limited by the above equations.

It implies:

Number of hours worked = 7 + 10 = 17 which is less than 20.

Income: 6(7) + 10(10) = 42 + 100 = 142, which is greater than 75

Of course, both are greater than 0.

In this way we proved that the point (7,10) is a true solution for the model.

Download pdf

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3 years ago

Please help me with this homework

8090 [49]

Answer: The answer is 226.2

Step-by-step explanation: I got the answer from this website, its basically a volume calculator for any shape. https://www.omnicalculator.com/math/cylinder-volume

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3 years ago

The coach of the track and field team is putting together groups of runners to run relays. Each group will need to run a race th

andrew11 [14]

Answer:

16 runner

Step-by-step explanation:

It is given that,

Each group will need to run a race that is 1/2 of a mile long. Each runner has to run 1/8 of a mile in the race.

Let there are x no of runners. ATQ,

$\dfrac{1}{8}x=\dfrac{1}{2}\\\\x=\dfrac{(1/2)}{(1/8)}\\\\x=16$