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lorasvet [3.4K]
2 years ago
13

The line perpendicular to y=3/4x+7 containing (3,-4)

Mathematics
1 answer:
Ainat [17]2 years ago
8 0

Answer:

<em>y = - </em>\frac{4}{3}<em> x </em>

Step-by-step explanation:

1). y_{1} = m_{1} x_{1} + b_{1}  

y_{2} = m_{2} x_{2} + b_{2}

y_{1} ⊥ y_{2}  if  m_{2} = - \frac{1}{m_{1} }

2). ( x_{3} , y_{3} )

y - y_{3} = m( x - x_{3} )

~~~~~~~~~~~~~~~~~~

y = \frac{3}{4} x + 7

m_{1} = \frac{3}{4}

m_{2} = - \frac{4}{3}

( 3, - 4 )

y - ( - 4) = - \frac{4}{3} ( x - 3 )

y + 4 = - \frac{4}{3} x + 4

<em>y = - </em>\frac{4}{3}<em> x </em>

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Given that x=3sin​​θ-2 and y=3cos​​​θ+4.Show that (x+2)²+ (y-4)²=9​​​​​​
asambeis [7]

Answer:

First, plug-in x and y as 3sin​​θ-2 and 3cos​​​θ+4 into the equation, respectively:

((3\sin (\theta)-2)+2)^2 + ((3\cos (\theta)+4)-4)^2 = 9

Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:

(3\sin(\theta))^2+(3\cos(\theta))^2=9

We can factor out 3^2 = 9 from both equations:

9(\sin(\theta)^2+cos(\theta)^2) = 9

We know from a trigonometric identity that \sin(\theta)^2+cos(\theta)^2 = 1, meaning we can reduce the equation to:

9(1) = 9

9=9

And therefore, we have shown that (x+2)^2 + (y-4)^2 = 9, if x=3sin​​θ-2 and y=3cos​​​θ+4.

Hope this helped you.

7 0
3 years ago
I need help with these two problems please
Debora [2.8K]

Problem 2

Plot point L anywhere that isn't on segment JK. Draw a line through point L. I find it helps to make the lines parallel.

Next, use a compass to measure the width of segment JK. Keeping this same width, transfer the nonpencil end of the compass to point L. Draw an arc that crosses the line through L.

Mark this intersection point M. Lastly, use a pen or marker to form segment LM and erase everything else of that line.

======================================================

Problem 3

The ideas of the previous problem will be used here. We copied segment JK to form congruent segment LM. So JK = LM.

The same steps will be used to form segment GN where GN = EF. In other words, segment GN is a perfect copy of segment EF.

If you repeat these steps again, you'll get another segment of the same length. This segment goes from point N to point H. So NH = GN = EF

Then we can say,

GH = GN + NH

GH = EF + EF

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7 0
3 years ago
Help me please I don’t understand this and it is due tonight
andreyandreev [35.5K]

Answer:

y = 5/3x + 31/3

=

5

3

x

+

31

3

Step-by-step explanation:

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3 years ago
How to solve (2.31*10^-6)+(5.87*10^-4)
S_A_V [24]

We want to calculate the following

2.31\cdot10^{-6}+5.87\cdot10^{-4}

Using the properties of exponents, we have that

10^{-6}=10^{-4}\cdot10^{-2}

So we have

2.31\cdot10^{-6}+5.87\cdot10^{-4}=2.31\cdot10^{-2}\cdot10^{-4}+5.87\cdot10^{-4}

So, if factor 10^-4 on the right side, we have

10^{-4}(2.31\cdot10^{-2}+5.87)

Note that

2.31\cdot10^{-2}=0.0231

Then,

5.87+2.31\cdot10^{-2}=5.87+0.0231=5.8931^{}

So we have that

2.31\cdot10^{-6}+5.87\cdot10^{-4}=5.8931\cdot10^{-4}

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