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Dmitry_Shevchenko [17]

3 years ago

5

Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0,

negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).

2 answers:

masha68 [24]3 years ago

6 0

Answer:

last graph is correct

Step-by-step explanation:

zavuch27 [327]3 years ago

5 0

Answer:

A line passing through the points (-1,-4),(0,0) and (1,4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

<u><em>Verify each case</em></u>

Part 1) A line passing through the points (-4,0) and (0,-2)

This line not represent a direct variation, because the line not passes through the origin.

Part 2) A line passing through the points (-5,4) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 3) A line passing through the points (-4,-6) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 4) A line passing through the points (-1,-4),(0,0) and (1,4)

The line passes through the origin

Find out the value of k

$k=y/x$

For the point (-1,-4)

substitute

$k=-4/-1=4$

For the point (1,4)

substitute

$k=4/1=4$

The linear equation is $y=4x$

This line represent a direct variation

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Step-by-step explanation:

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Answer:

(a) Shown below.

(b) Shown below.

(c) The probability that a person does not learn Spanish is 0.18.

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Step-by-step explanation:

(a)

Consider the provided data.

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Then the probability of not learning Spanish using the respective methods are:

$P(L'|A)=1-P(L|A)=1-0.70=0.30\\\\P(L'|B)=1-P(L|B)=1-0.70=0.15$

(b)

The Probability Tree representing each of the probabilities mentioned above is attached below.

(c)

Compute the probability that a person does not learn Spanish as follows:

$P(L')=P(L'|A)P(A)+P(L'|B)P(B)$

$=(0.30\times 0.20)+(0.15\times 0.80)\\\\=0.06+0.12\\\\=0.18$

Thus, the probability that a person does not learn Spanish is 0.18.

(d)

Compute the probability that method B was used given that a student learned the Spanish successfully as follows:

$P(B|L)=\frac{P(L|B)P(B)}{P(L|A)P(A)+P(L|B)P(B)}$

$=\frac{(0.85\times 0.80)}{(0.70\times 0.20)+(0.85\times 0.80)}\\\\=\frac{0.68}{0.14+0.68}\\\\=0.82927\\\\\approx 0.83$

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Step-by-step explanation:

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So if we flipped x and y's for f(x). We would see that our output or y of g(x) is -3 when x = 2, or in other words g(2) = -3. This means that we are now going to solve for when f(-3). So now lets look at the table and find the value at x = -3 for f(x). This value is 2, so the value of f(g(2)) = 2.

*In the future*

When you have a composite function of two inverses they essentially cancel out and would leave whatever the value of x is. So if we know f(x) and g(x) were inverses the value of f(g(2)) would just be 2.

For example:

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