Rewrite the equation y – 4x = –9 in slope-intercept form. simple explanation and proof

Mathematics

2 answers:

Strike441 [17]2 years ago

7 0

Answer:

The slope-intercept form of this equation would be y = 4x - 9.

(For explanation look down below)

Step-by-step explanation:

Slope-intercept form would be an equation that would look like...

y = mx + b

Where m is the slope and b is the intercept. From this form, we can understand that all we need to do is rearange the formula in a way that positive y would be on its left side. And so we get...

y - 4x = - 9

y - 4x + 4x = - 9 + 4x

y = 4x - 9

dusya [7]2 years ago

4 0

Answer:

y=4x-9

Step-by-step explanation:

add 4x to both sides to isolate y

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In a shipment of 56 vials, only 13 do not have hairline cracks. If you randomly select 3 vials from the shipment, in how many wa

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Answer: 27434

Step-by-step explanation:

Given : Total number of vials = 56

Number of vials that do not have hairline cracks = 13

Then, Number of vials that have hairline cracks =56-13=43

Since , order of selection is not mattering here , so we combinations to find the number of ways.

The number of combinations of m thing r things at a time is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Now, the number of ways to select at least one out of 3 vials have a hairline crack will be :-

$^{13}C_2\cdot ^{43}C_{1}+^{13}C_{1}\cdot ^{43}C_{2}+^{13}C_0\cdot ^{43}C_{3}\\\\=\dfrac{13!}{2!(13-2)!}\cdot\dfrac{43!}{1!(42)!}+\dfrac{13!}{1!(12)!}\cdot\dfrac{43!}{2!(41)!}+\dfrac{13!}{0!(13)!}\cdot\dfrac{43!}{3!(40)!}\\\\=\dfrac{13\times12\times11!}{2\times11!}\cdot (43)+(13)\cdot\dfrac{43\times42\times41!}{2\times41!}+(1)\dfrac{43\times42\times41\times40!}{6\times40!}\\\\=3354+11739+12341=27434$