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3 years ago

F(-4)=8 and f(-1)=4 write the linear equation

Mathematics

1 answer:

kobusy [5.1K]3 years ago

7 0

$f(-4)=8\to(-4,\ 8)\\\\f(-1)=4\to(-1,\ 4)$

The point-slope formula of a line:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute:

$m=\dfrac{4-8}{-1-(-4)}=\dfrac{-4}{3}=-\dfrac{4}{3}\\\\y-8=-\dfrac{4}{3}(x-(-4))\\\\y-8=-\dfrac{4}{3}x-\dfrac{16}{3}\ \ \ \ |+8\\\\y=-\dfrac{4}{3}x-\dfrac{16}{3}+\dfrac{24}{3}\\\\y=-\dfrac{4}{3}x+\dfrac{8}{3}\ \ \ |\cdot3\\\\3y=-4x+8\ \ \ |+4x\\\\4x+3y=8$

The slope-intercept form: $y=-\dfrac{4}{3}x+\dfrac{8}{3}$

The standard form: $4x+3y=8$

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Read 2 more answers

You don't need to construct a Venn Diagram, it is just part of the instruction. Just determine whether or not the argument is va

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Answer:

It is valid.

Venn Diagram is attached.

I also provided a truth table.

I also provided a couple of names this argument could be called.

Please let me know if you have any questions about this question.

Thank you kindly.

Step-by-step explanation:

If a person is a poet, then that person is a loner.

If a person is a loner, then that person is a taxi driver.

If a person is a poet, then that person is a taxi drive.

This is in the form:

p->q

q->r

Therefore, p->r.

This is an example of a hypothetical syllogism.

The first thing my mind goes to when seeing this is the transitive property which says if A is related to B and B is related to C then A is related to C.

So this syllogism also has another name and it is called the principle of transitivity of implication.

Let p=person is a poet, q=person is a loner, and r=person is a taxi driver.

I'm going to make a truth table and compare the truth values of the propositions to the conclusion.

Since we have 3 variables, we are going to need 2^3=8 rows.

p q r p->q q->r (p->q) and (q->r) conclusion=(p->r)

T T T T T T T

T T F T F F F

T F T F T F T

T F F F T F F

F F F T T T T

F F T T T T T

F T F T F F T

F T T T T T T

So we are trying to see if we ever have the preposition part true and the conclusion false.

That doesn't happen so the argument is valid.

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3 years ago

In quadrilateral ABCD, AD is congruent to BC, and AD is parallel to BC. Andre has written a

Dahasolnce [82]

Answer:

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I tried hard to sketch out what the shape looked like based on the information given, and that's because I need a visual of what the shape looks like. Sorry, this took so long to answer.

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1 year ago

I'm supposed to answer this word problem "Martin bought a television for $225. It had been on sale for 25% off. How much money d

garik1379 [7]

Answer:

Martin saved $75 on the television because of the sale

Step-by-step explanation:

Equations

Let's call x=the original price of the television (before discount).

The television had been on sale for 25% off, this means the discount was:

25% of x = $\frac{25}{100}.x$ = 0.25x

The sale price was the original price minus the discount:

x - 0.25x = 0.75x

This is what Martin paid, thus:

0.75x = 225

Dividing by 0.75:

x = 225 / 0.75

x = $300

The original price of the television was $300, and the discount was:

0.25*$300 = $75

Martin saved $75 on the television because of the sale

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3 years ago