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3 years ago

What is an equation of the line that is parallel to y=3x-8 and passes through (1,8)

Mathematics

1 answer:

Alla [95]3 years ago

4 0

Answer:

y = 3x + 5

Step-by-step explanation:

Two lines which are parallel have the same gradient. This means that the parallel line must have a gradient of 3x

y = 3x + c

To figure out c you substitute in the given coordinate for the x and y values

8 = 3(1) + c

c = 5

y = 3x + 5

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2 years ago

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3 years ago

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How do you solve sin (5pi/3) without a calculator?

Savatey [412]

very simple, we use the formula sin(a+b)=sinacosb + sinbcosa and sin(20)=2sinacosa

5pi = 2pi/3+3pi/3,

First, we use sin(a+b)=sinacosb + sinbcosa

sin(5pi/3)=sin(2pi/3+3pi/3)= sin(2pi/3+pi)= sin(2pi/3)cos(pi) +sin(pi)cos(2pi/3)

but we know that sin(pi)= 0, and cos (pi) = -1, so sin(5pi/3)= - sin(2pi/3)

now, use sin(2a)=2sinacosa, sin(5pi/3)= - sin(2pi/3)= -2sin(pi/3)cos(pi/3)

sin(5pi/3)= -2sin(pi/3)cos(pi/3)

sin(pi/3)= 0.86, cos(pi/3)=0.5, finally we have sin(5pi/3)= -0.86 x 0.5= -0.43

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3 years ago

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System of equations by substitution how do this? y= x+2 y= -4x+7

jekas [21]

Equations are given,
y= x+2

y= -4x+7

As you can see both the expressions, x+2 and -4x+7 are equal to "y". That means they are equal to each other too.

So let's equal them and solve it.

 $x+2=-4x+7\\ \\ x+2+4x=7\\ \\ x+4x+2=7\\ \\ 5x+2=7\\ \\ 5x=7-2\\ \\ 5x=5\\ \\ x=\frac { 5 }{ 5 } \\ \\ x=1$

Now we have x's value we will plug it in the first equation to find "y".

 $x=1\\ \\ y=x+2\\ \\ y=1+2\\ \\ y=3$

(1,3)

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3 years ago