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3 years ago

What is the equation of a line that passes thorough the point (9,-3) and is parallel yo the line whose equation is 2x-3y=6?

Mathematics

2 answers:

schepotkina [342]3 years ago

5 0

Answer:

y+3=2/3(x-9)

Step-by-step explanation:

2x-3y=6

-3y=-2x+6

y=2/3x-2

This means that any line parallel to it must have a slope of 2/3 as well. Therefore, the equation of this line, in point slope form, is:

y+3=2/3(x-9)

Hope this helps!

inysia [295]3 years ago

5 0

Answer:

y = 2/3 - 9

Step-by-step explanation:

1. rearrange the equation

-3y = -2x + 6

y = 2/3 - 2

2. because it is parallel, the gradient will be the same. substitute into y - y1 = m(x-x1)

y - (-3) = 2/3 (x - 9)

y + 3 = 2/3 - 6

y = 2/3 - 9

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2 years ago

Multiply 5x^2-6x+2 4x^2-3x

mixas84 [53]

Answer:

$20x^{4}-39x^{3} +26x^{2}-6x\\$

Step-by-step explanation:

Multiply the two polynomials by multiplying each term

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8 0

3 years ago

Read 2 more answers

Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv

Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number $x$ such that taking it mod 4, 5, and 7 leaves the desired remainders:

$x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6$

Taken mod 4, the last two terms vanish and we have

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4$

so we multiply the first term by 3.

Taken mod 5, the first and last terms vanish and we have

$x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5$

so we multiply the second term by 2.

Taken mod 7, the first two terms vanish and we have

$x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7$

so we multiply the last term by 7.

Now,

$x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147$

By the CRT, the system of congruences has a general solution

$n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}$

or all integers $27+140k$ , $k\in\mathbb Z$ , the least (and positive) of which is 27.

3 0

3 years ago

A square piece of fabric has an area of 595 cm2.

inna [77]

To find the length of the side, will take the under root of the area. So, the side will be :

c) 24.4 cm

8 0

3 years ago

Twice a number divid by 6 is 42

il63 [147K]

A number=x

2x/6=42
2x=252 by multiplying both sides by 6
x=126 by dividing both sides by 2 to isolate the variable

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3 years ago

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