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Assoli18 [71]
3 years ago
5

Which points satisfy this linear-quadratic system of equations? x + y = 1 y = 4x − 3 − x2

Mathematics
1 answer:
zhenek [66]3 years ago
8 0
Y = 4x - 3 - x^2
now sub that in for y in the other equation
x + y = 1
x + 4x - 3 - x^2 = 1
-x^2 + 5x - 4 = 0
(-x + 1)(x - 4) = 0

-x + 1 = 0       y = 4x - 3 - x^2
-x = -1            y = 4(1) - 3 - 1^2
x = 1              y = 4 - 3 - 1 = 0

x - 4 = 0        y = 4x - 3 - x^2
x = 4             y = 4(4) - 3 - 4^2
                     y = 16 - 3 - 16
                      y = -3

points that satisfy this are : (1,0) and (4,-3)
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Solve 3/4x+1/4y=5 for y
Hitman42 [59]

Answer:

y=-3x+20

Step-by-step explanation:

3/4x+1/4y=5

-3/4x           -3/4x

1/4y=5-3/4x

divide the whole entire equation by 1/4 like this: (4)1/4y=4(5-3/4x)

Your answer is y=-3x+20

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6 0
2 years ago
You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received
Alexus [3.1K]

Money received in tenth month: $104

Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.

<h3>What is arithmetic progression?</h3>

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

  • Money received in first four months: $50, $52, $55, %59.

To find: Money received in tenth month.

Finding:

As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.

That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.

Thus, for the tenth month, we can use the formula of recursion, given by: a_n=a_{n-1}+n, n ≥ 1.

For a₁ = 50, a₂ = a₁ + 2

=> a₂ = 50 + 2

This way, a₅ = a₄ + 5

=> a₅ = 59 + 5 = 64

a₆ = a₅ + 6

=> a₆ = 64 + 6 = 70

a₇ = a₆ + 7

=> a₇ = 70 + 7 = 77

a₈ = a₇ + 8

=> a₈ = 77 + 8 = 85

a₉ = a₈ + 9

=> a₉ = 85 + 9 = 94

a₁₀ = a₉ + 10

=> a₁₀ = 94 + 10 = 104

Thus, the payment received in tenth month will be $104.

(b) Difference between explicit formula and recursive formula of an arithmetic progression:

  • The first term of a recursive formula is a₁ and the formula for the nth term uses the first term and the common difference, d. One example of a recursive formula is a_n=a_{n-1}+d.
  • A formula for the nth term in an explicit formula would include the initial term a₁, the common difference d, and the term number, n. The equation a_n = a_1 + (n-1)d.

To learn more about arithmetic Progressions, refer to the link: brainly.com/question/6561461

#SPJ4

6 0
1 year ago
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