Find an equation of the line that is perpendicular to the line y=5x+6 and passes through the point (-2,5)

Mathematics

1 answer:

DaniilM [7]3 years ago

5 0

Answer:

$5y=-x+23\\$

Step-by-step explanation:

Since the equation of the line is perpendicular to the line y = 5x +6

we can use the formula:

$m_1m_2=-1\\$

where m1 is the slope of the line we have and,

m2 is the slope of the line we need

so here m1 is 5 as we compare it with the slope-intercept form our slope is:

$y=5x+6\\y=mx+b$

our m1 is 5 but we need m2 so plugging in the value we get m2 to be:

$m_1m_2=-1\\5m_2=-1\\m_2=-1/5\\$

and now we have our m2, now furthermore since the line passes through the point (-2 , 5) it means the point must lie on the line and satisfy it. We can use this point and the slope m2 and find out the equation by the point-slope form equation:

$y-y_1=m(x-x_1)\\y-5=-\frac{1}{5}(x-(-2))\\\\5(y-5)=(-1)(x+2)\\5y-25=-x-2\\5y=-x-2+25\\5y=-x+23\\$

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How many different 4 digit even numbers can be written using 0,5,6,3,8,7?

kherson [118]

Step-by-step explanation:

I assume the digits cannot be repeated in the numbers.

and that we don't want any numbers that start with 0, as that would be considered a 3- digit number, right ?

so, under these assumptions we have the question of in how many ways can we pull 4 digits out of 6.

if the sequence of the pulled digits would not matter, it would be combinations C(6, 4).

but because we are building actual numbers, the sequence does matter, and we use permutations P(6, 4).

P(6, 4) = 6!/(6-4)! = 6!/2! = 6×5×4×3 = 360

so, we can create 360 different numbers.

but not all of them are wanted.

we don't want the ones that start with 0. how many are those ?

since we are handling all digits in the same way and priority, there are an equal amount of numbers that start with a 0, or a 5, or a 6, or a 3, or a 8, or a 7.

so, 1/6 of the 360 numbers start with a 0, and we need to subtract them :

360 - 60 = 300 really 4-digit numbers

and from these 300 we only want even numbers. that means they can only end with 0, 6 or 8.

in the same way as for the first position, we have 1/6 of the more 300 numbers that end with one of these digits.

we allow 3 digits, so we have

3×1/6 × 300 = 1/2 × 300 = 150

that means we can write 150 different 4-digit even numbers out of these 6 digits.

6 0

2 years ago

How many pounds are there in 2 and 1 over 4 tons? (1 ton = 2000 pounds)

madam [21]

2 tons = 4000 pounds and so 1/4 ton = 500 pounds, so the answer is 4500 pounds