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Taya2010 [7]
2 years ago
5

A) Solve by determinant method: x - y = 2, 2x + 3y = 4​

Mathematics
1 answer:
grin007 [14]2 years ago
4 0

Answer:

x = 2

y = 0

Step-by-step explanation:

x - y = 2

2x + 3y = 4

Using creamers rule of determinants, we have;

D =

|1 1|

|2 3|

Thus; D = (1 × 3) - (1 × 2)

D = 1

Dx =

|2 1|

|4 3|

Dx = (2 × 3) - (1 × 4)

Dx = 2

Dy =

|1 2|

|2 4|

Dy = (1 × 4) - (2 × 2)

Dy = 0

Thus;

x = Dx/D = 2/1

x = 2

y = Dy/D = 0/1

y = 0

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The intersection of lines y=-14x+3 and y=-32x+3 is .
Kamila [148]

The intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

<h3>How to determine the intersection of the lines?</h3>

The lines are given as:

y = -14x + 3 and y = -32x+3

Substitute y = -32x+3 in

-32x+3 = -14x + 3

Evaluate the like terms

-18x = 0

Divide by -18

x = 0

Substitute x = 0 in y = -14x + 3

y = -14(0) + 3

Evaluate

y = 3

Hence, the intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

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2 years ago
Philip ran out of time while taking a multiple-choice test and plans to guess the last 4 questions. Each question has 5 possible
White raven [17]

Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
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Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:

n = 4, p = 1/5 = 0.2.

The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096

0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

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8 0
2 years ago
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goldenfox [79]

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<u>Step-by-step explanation:</u>

Step 1:

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f(x) = 9x - 8

g(x) = 2x + 4

f(x)g(x) = (9x - 8)(2x + 4)

= 18x² + 36x - 16x -32

= 18x² + 20x - 32

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