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LenKa [72]
3 years ago
14

Write the equation of a straight line passing through the point (1,8) and perpendicular to y=3x+2

Mathematics
1 answer:
Neko [114]3 years ago
5 0
Hello there!

The first thing you must do is to find the slope of the line. To do this, find the negative reciprocal of your current equation. Since your current slope is 3, the negative reciprocal of that would be -1/3, which would be your slope.

Now that you have your slope, plug it into the slope intercept equation as well as your known points:
(1,8)  m(slope)=-1/3
8=1(-1/3)+b

Now, solve for b:
8=1(-1/3)+b
8=-1/3+b
b=25/3

Now that you have the slope and the b value, you can conclude that your equation would be:
y=-1/3x+25/3
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Perform the indicated operations. Write the answer in standard form, a+bi.<br> 5-3i / -2-9i
Vsevolod [243]

\huge \boxed{\mathfrak{Answer} \downarrow}

\large \bf\frac { 5 - 3 i } { - 2 - 9 i } \\

Multiply both numerator and denominator of \sf \frac{5-3i}{-2-9i} \\ by the complex conjugate of the denominator, -2+9i.

\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2-9i\right)\left(-2+9i\right)})  \\

Multiplication can be transformed into difference of squares using the rule: \sf\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2\right)^{2}-9^{2}i^{2}})  \\

By definition, i² is -1. Calculate the denominator.

\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{85})  \\

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

\large \bf \: Re(\frac{5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9i^{2}}{85})  \\

Do the multiplications in \sf5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9\left(-1\right).

\large \bf \: Re(\frac{-10+45i+6i+27}{85})  \\

Combine the real and imaginary parts in -10+45i+6i+27.

\large \bf \: Re(\frac{-10+27+\left(45+6\right)i}{85})  \\

Do the additions in \sf-10+27+\left(45+6\right)i.

\large \bf Re(\frac{17+51i}{85})  \\

Divide 17+51i by 85 to get \sf\frac{1}{5}+\frac{3}{5}i \\.

\large \bf \: Re(\frac{1}{5}+\frac{3}{5}i)  \\

The real part of \sf \frac{1}{5}+\frac{3}{5}i \\ is \sf \frac{1}{5} \\.

\large  \boxed{\bf\frac{1}{5} = 0.2} \\

3 0
3 years ago
The monthly fees for the local pool are $8 per month
Liono4ka [1.6K]

Given:

Monthly fees for the local pool are $8 per month  and $2 per visit.

Hector pays $34 in pool fees total for  the month.

To find:

The number of times he visit the pool.

Solution:

We have,

Monthly fee of pool = $8

Additional fee = $2 per visit

Let Hector visit x times.

Additional fee for x times = $2x

Total fee = Monthly fee + Additional fee

34=8+2x

34-8=2x

26=2x

Divide both sides by 2.

\dfrac{26}{2}=x

13=x

Therefore, Hector visit the pool 13 times.

3 0
3 years ago
-4(y+1)+2 <br> help i am very confused
likoan [24]

Answer:

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4 0
3 years ago
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DaniilM [7]

Answer:

what is this

Step-by-step explanation:

7 0
3 years ago
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xxTIMURxx [149]

Answer:

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Example-

2:4

4:8

6:12

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        Turn one into a fraction

4/8

       Simplify

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7 0
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