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2 years ago

How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Mathematics

1 answer:

Nina [5.8K]2 years ago

7 0

<h3>Explanation:</h3>

For a system of 2 equations in 2 unknowns, there are 3 cases:

slopes are different — one solution
slopes are the same and y-intercepts are different — no solutions
slopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at <em>one</em> point, the <em>solution</em>.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence <em>no solutions</em>. If the lines are the same line, they intersect at all points, so there are <em>infinitely many solutions</em>.

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What output corresponds with I2?

Sonbull [250]

Answer:

Solve for the input that corresponds to the given output value. (Round answers to three decimal places when appropriate. Enter your answers as a comma-separated list. Note: Even though the question may be completed without the use of technology, the authors intend for you to complete the activity using the technology you will be using.

Step-by-step explanation:

6 0

2 years ago

Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is f

pashok25 [27]

Answer:

0.999987

Step-by-step explanation:

Given that

The user is a legitimate one = E₁

The user is a fraudulent one = E₂

The same user originates calls from two metropolitan areas = A

Use Bay's Theorem to solve the problem

P(E₁) = 0.0131% = 0.000131

P(E₂) = 1 - P(E₁) = 0.999869

P(A/E₁) = 3% = 0.03

P(A/E₂) = 30% = 0.3

Given a randomly chosen user originates calls from two or more metropolitan, The probability that the user is fraudulent user is :

$P(E_2/A)=\frac{P(E_2)\times P(A/E_2)}{P(E_1)\times P(A/E_1)+P(E_2)\times P(A/E_2)}$

$=\frac{(0.999869)(0.3)}{(0.000131)(0.03)+(0.999869)(0.3)}$

$\frac{0.2999607}{0.00000393+0.2999607}$

$\frac{0.2999607}{0.29996463}$

= 0.999986898 ≈ 0.999987

6 0

3 years ago

June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as

mixer [17]

Answer:

The capacity of smaller cooler = 7.5 gallons

The capacity of bigger cooler = 37.5 gallons

Step-by-step explanation:

Let smaller cooler's capacity be x gallons

Hence

Larger cooler's capacity will be 5x gallons

Together, they will hold 45 gallons, thus we can write:

x + 5x = 45

Solving:

x + 5x = 45

6x = 45

x = 45/6 = 7.5

And 5x = 5(7.5) = 37.5

The capacity of smaller cooler = 7.5 gallons

The capacity of bigger cooler = 37.5 gallons

4 0

3 years ago

(5x^2 - 2x^3 + x) - (6x^3 - 8x^2 - x)

pashok25 [27]

Answer:

-8x^3+13x^2+2x

8 0

3 years ago

Read 2 more answers

Find the mean and standard deviation for the set of data.

dem82 [27]

The mean and standard deviation for the set of data will be 16 and 5.87. Then the correct option is A.

<h3>What is a standard deviation?</h3>

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

The set of data is given below.

16, 22, 8, 5, 20, 18, 14, 17, 24

The mean of the data set will be

μ = (16 + 22 + 8 + 5 + 20 + 18 + 14 + 17 + 24) / 9

μ = 144 / 9

μ = 16

Then the standard deviation of the data set will be

$\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}} \\\sigma = \sqrt{\dfrac{(16 - 16)^2 +(22 - 16)^2 + (8-16)^2 + ......+(24-16)^2 }{9}} \\\sigma = \sqrt{\dfrac{310}{9}}\\$

Simplify the expression further, then we have

σ = √34.44

σ = 5.87

The mean and standard deviation for the set of data will be 16 and 5.87.

Then the correct option is A.

More about the standard deviation link is given below.

brainly.com/question/12402189

#SPJ1

3 0

1 year ago