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Arturiano [62]
2 years ago
14

a line has a slope of -3, so it's equation has the form y= -3x + b. the line passes through the point (1, -2). what is the y-int

ercept, b, of the line? ​
Mathematics
1 answer:
grin007 [14]2 years ago
7 0

Answer:

y-intercept = 1

Step-by-step explanation:

y = -3x + b

(1 , -2)

Plugin the equation

-2 = -3*1 + b

-2 = -3 + b

-2 + 3 = b

1 = b

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olchik [2.2K]

4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 4, the last two terms vanish and we're left with

x\equiv63\equiv64-1\equiv-1\equiv3\pmod4

We have 3^2\equiv9\equiv1\pmod4, so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 7, the first and last terms vanish and we're left with

x\equiv72\equiv2\pmod7

which is what we want, so no adjustments needed here.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 9, the first two terms vanish and we're left with

x\equiv140\equiv5\pmod9

so we don't need to make any adjustments here, and we end up with x=401.

By the Chinese remainder theorem, we find that any x such that

x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}

is a solution to this system, i.e. x=149+252n for any integer n, the smallest and positive of which is 149.

3 0
2 years ago
Does this graph represent a function? Why or why not?
Lunna [17]

Answer:

Step-by-step explanation:

B. Yes, because it passes the vertical line test, is the answer.

6 0
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In right triangle ABC, A=28º, b= 7, and ZC is the right angle. Solve the triangle.
sweet-ann [11.9K]

Answer:

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Step-by-step explanation:

5 0
2 years ago
12/13 divided by 3/15<br> write your answer as a simplified fraction
Agata [3.3K]

Answer:

\frac{60}{13}

[improper fraction]

4 \frac{8}{13}

[mixed fraction]

4.\overline{615384}

[decimal]

Explanation:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b}       × \frac{d}{c} = \frac{ad}{bc}

12/13 divided by 3/15 →

\frac{\frac{12}{13}}{\frac{3}{15}} →

\frac{12}{13} × \frac{15}{3} →

\frac{12}{13} × 5 →

\frac{60}{13}

________________________________

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3 years ago
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Answer:

Step-by-step explanation:

Graph the absolute value function y = |x|.  This is v-shaped and opens up.

Now translate the entire graph 2 units to the left.  You will then have the graph of y=|x+2|​.

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