All categories

3 years ago

What is the distance between 3x - 5y + 3 =0 and 6x - 10y -12 =0

Mathematics

1 answer:

pogonyaev3 years ago

5 0

9514 1404 393

Answer:

(9/34)√34 ≈ 1.543

Step-by-step explanation:

The second equation can be rewritten as ...

6x -10y -12 = 0

3x -5y -6 = 0

3x -5y = 6

The formula for the distance from point (x, y) to line ax+by+c=0 is ...

d = |ax+by+c|/√(a²+b²)

Then the distance from a point to the first line is ...

d = |3x -5y +3|/√(3² +(-5)²)

We know from the rearrangement of the second equation that points on its line satisfy (3x-5y) = 6. Substituting this value for (3x -5y) in the distance formula gives ...

d = |6 +3|/√34

Simplifying and rationalizing the denominator gives a distance of ...

d = (9/34)√34 ≈ 1.543

You might be interested in

How do I rewrite statement using associative property -6+(-3/7+1/7)

Paladinen [302]

(-6 + -3/7) +1/7 this is because the associative property is a+(b+c)= (a+b)+c

4 0

3 years ago

What does the greater than and less than signs look like

sdas [7]

This: >(Greater than) and <(less than)

6 0

3 years ago

Read 2 more answers

if £2000 is placed into a bank account the pays 3percent compound interest per year, how much will be in the account after 2 yea

Nastasia [14]

Answer:

£2,120.00

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year.

Solving our equation:

A = 2000(1 + (0.03 × 2)) = 2120

A = $2,120.00

The total amount accrued, principal plus interest, from simple interest on a principal of £2,000.00 at a rate of 3% per year for 2 years is £2,120.00.

8 0

3 years ago

The polynomial p(x)=x^3-6x^2+32p(x)=x 3 −6x 2 +32p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 6, x, squar

STatiana [176]

Answer:

<h3>The remainder is zero</h3>

Step-by-step explanation:

Given the polynomial function p(x)=x^3-6x^2+32, if x-4 is a factor, then <u>we can find the remainder if the polynomial is divided by x -4.</u>

First we need to equate the function x - 4 to zero and find x;

x - 4 = 0

x= 0+4

x = 4

Next is to substitute x = 4 into the expression p(x)=x^3-6x^2+32

p(x)=x^3-6x^2+32

p(4)=(4)^3-6(4)^2+32

p(4) = 64 - 96 + 32

p(4) = 0

Hence the remainder when x-4 is divided by the polynomial is zero

7 0

3 years ago

Need help please 9× > 108

butalik [34]

Answer:

x > 12

Step-by-step explanation:

9x>108

x> 108/9

x > 12

8 0

3 years ago

Read 2 more answers