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2 years ago

What is an equation of the line that is perpendicular to -x+3y=9 and passes through the point (-3,2)

Mathematics

1 answer:

erastovalidia [21]2 years ago

5 0

Answer:

y=-3x-7

Step-by-step explanation:

the line is currently in standard form (ax+by=c). Let's put it into slope-intercept form (y=mx+b)

-x+3y=9

add x to both sides

3y=x+9

divide by 3

y=1/3x+3

perpendicular lines have slopes that when multiplied, equal -1.

to find the slope (m) of our new line:

1/3m=-1

multiply by 3

m=-3

the slope of the new line is -3

here's our equation so far:

y=-3x+b

we need to find b (y intecept)

since the line passes through the point (-3,2), it should be a solution in the equation (plug it in, and the result is a true statement). We can also use it to find b

so, substitute the pointt into the equation:

2=-3(-3)+b

multiply

2=9+b

subtract

-7=b

so the equation of the line is y=-3x-7

Hope this helps!

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Help!!!!!!!!!find the equation of the linear function q(16)=1 that is parralel to f(x)=1/3x+39

kkurt [141]

Answer:

$q(x)= \frac{1}{3} x -\frac{13}{3}$

Step-by-step explanation:

So you have (16, 1)

When two linear functions are parallel, they have the same slope.

So function q also has a slope of 1/3x. You have a set of points so you can plug them in a slope intercept equation to find b.

y= mx+b

m= slope

y= y-intercept

1= 1/3(16) +b

1 - (16/3) = b

b= -13/3

so then, $y= \frac{1}{3} x -\frac{13}{3}$

6 0

2 years ago

The mass of a bacteria culture doubles every four days. If the initial sample is 5mg: a) how much will you have after one week (

maks197457 [2]

Answer:

a) 16.82 mg

b) 24 days

Step-by-step explanation:

Formula for exponential growth is given as:

$A=A_0b^{\frac{t}{c}}$

Where A is the final population

$A_0$ is the initial population

b is the growth factor

c is the time taken for the growth 'b'

t is the amount of time

Here, We are given the following:

$A_0$ = 5 mg

b = 2 (Given because it doubles)

c = 4 days

a) A = ?

Using the formula:

$A=5 \times 2^{\frac{7}{4}}\\\Rightarrow A=5 \times 2^{1.75} \\\Rightarrow A = \bold{16.82\ mg}$

b) Given

A = 320 mg

t = ?

Using the above formula again:

$320 = 5 \times 2^{\frac{t}{4}}\\\Rightarrow \dfrac{320} 5= 2^{\frac{t}{4}}\\\Rightarrow 2^{\frac{t}{4}} = 64\\\Rightarrow 2^{\frac{t}{4}} = 2^6\\\Rightarrow \dfrac{t}{4} = 6\\\Rightarrow t = 6 \times 4\\\Rightarrow \bold{t = 24\ days}$