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4 years ago

Create the linear equation from the points (3,3) and (1,-5).

Mathematics

1 answer:

Kisachek [45]4 years ago

7 0

Answer:

$-4x + y = -9\:or\:y = 4x - 9$

Step-by-step explanation:

First, find the rate of change [slope]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-3 - 5}{-3 + 1} = \frac{-8}{-2} = 4$

Then, plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly that way. It does not matter which ordered pair you choose::

−5 = 4 + b

$\displaystyle -9 = b \\ \\ y = 4x - 9$

If you want it in Standard Form:

y = 4x - 9

- 4x - 4x

_________

$\displaystyle -4x + y = -9$

_______________________________________________

3 = 4[3] + b

$\displaystyle -9 = b \\ \\ y = 4x - 9$

y = 4x - 9

- 4x - 4x

_________

$\displaystyle -4x + y = -9$

** You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.

I am joyous to assist you anytime.

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3 years ago

Read 2 more answers

If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these

Vikki [24]

Answer:

if the 5 numbers are different, the maximum difference is 64

Step-by-step explanation:

We have 5 positive (different) integers, a, b, c, d and e (suppose that are ordered from least to largest, so a is the smallest and b is the largest.

The mean will be:

M = (a + b + c + d + e)/5 = 15.

Now, if we want to find the largest difference between a and e, then we must first select the first 4 numbers as the smallest numbers possible, this is:

a = 1, b = 2, c = 3 and d = 4

M = (1 + 2 + 3 + 4 + d)/5 = 15

M = (10 + d)/5 = 15

10 + d = 15*5 = 75

d = 75 - 10 = 65

then the difference between a and d is = 65 - 1 = 64.

Now, if we take any of the first 4 numbers a little bit bigger, then we will see that the value of d must be smaller, and the difference between d and a will be smaller.

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3 years ago

Let p, q, and r represent the following statements"

Nitella [24]

In logic, own symbols are used in order to be able to represent the relations between propositions in a general and independent way to the proposition, in order to be able to find the relationship process that operates in the communicated message, the propositional logic.

For this purpose there are, among others, the following logical operators: conjunction (and) ∧, disjunction (or) ∨, denial (not) ¬, conditional (if - then) ⇒ and double conditional (if and only if, iff) ⇔.

So for this case we have:

Answer

a) Sam had pizza last night if and only if Chris finished her homework.

p⇔q

b) Pat watched the news this morning iff Sam did not have pizza last night.

r⇔¬p

c) Pat watched the news this morning if and only if Chris finished her homework and Sam did not have pizza last night.

r⇔(q∧¬p)

d) In order for Pat to watch the news this morning, it is necessary and sufficient that Sam had pizza last night and Chris finished her homework.

r⇔(p∧q)

e) q ⇔ r

Chris finished his homework if and only if Pat watched the news this morning

f) p ⇔ (q ∧ r)

Sam had pizza last night if and only if Chris finished his homework and Pat watched the news this morning

g) (¬p) ⇔ (q ∨ r)

Sam didn't have pizza last night if and only if Chris finished his homework or Pat watched the news this morning

h) r ⇔ (p ∨ q)

Pat watched the news this morning if Sam had pizza last night or Chris finished his homework

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3 years ago

What is 80 in its simplest form as a fraction?

Ann [662]

I believe the correct given problem is:

“What is 80% in its simplest form as a fraction?”

Take note that you missed to place the percent sign which is very important.

Now to solve this, 80% when converted to decimal form is 0.80 which means that you have 80 parts per 100 parts. Therefore the fraction form of this would be 80 / 100.

fraction = 80 / 100

However this fraction is not yet the answer because we can still simplify this further. First step in simplifying is to divide both the numerator and denominator by 10 so that we are left with:

8 / 10

Next step is to divide by 2:

4 / 5

Now we can see that we can no longer divide this (numbers should be whole number). Therefore the simplest form as a fraction is 4/5

Answer:

4/5

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3 years ago

Please help me:) i will give brainliest to the right answer<3

erik [133]

Answer:

It does

Step-by-step explanation:

It does have a proportional relationship because if you try to find the relationship between the first two inputs and outputs, you can find that it is 21 (1 to 21, 21 divided by 1 would be 21) then if you use that relationship with the other numbers (times 21) you would get the same answer. For example in the second one, the two numbers are 2 and 42, 2 times 21 would equal 42. The next one would be 3 times 21 to equal 63 and etc.

Hope this Helps!!

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3 years ago