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Gennadij [26K]
3 years ago
15

Find the value of r so that the line through (4,5) and (r,3) has a slope of 2/3

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
3 0

Answer:

The value of r is 1

(1,3)

Step-by-step explanation:

First you have to plot (4,5)

Then you do rise over run

you go you 2 and then to the left 3

Hope this helps

Stay safe:)

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What value of x makes the equation 3(x - 6) - 8x = -2 + 5(2x + 1) true ?
Romashka-Z-Leto [24]

Answer:

x = -3

Step-by-step explanation:

3(x - 6)= -2 + 5(2x + 1)

= 3x - 18 = -2 + 10x + 5

= -18 = -2 + 7x + 5

= -18 = 7x + 3

= -21 = 7x

= -3 = x

= x = -3

5 0
2 years ago
Find the midpoint of line AB.<br> A(-4,2) B(0,-4)
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Answer:

Dilate circle A by a scale factor of 4.

Step-by-step explanation:

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2 years ago
Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)
zubka84 [21]
\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } &#10;

This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

\frac{ \sqrt{-49}}{7-2i-4-9i}

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result: 

\frac{ \sqrt{-49} }{3-11i}

Now, the \sqrt{-49} must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to \sqrt{49}  \sqrt{-1}
This means that we get the result 7i for the numerator.

\frac{7i}{3-11i}

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: x^2 - y^2 =(x+y)(x-y)
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

\frac{7i (3+11i)}{(3-11i)(3+11i)}

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how (3-11i)(3+11i)= 3^2 -(11i)^2 therefore, we can finally write:

\frac{7i(3+11i)}{3^2 - (11i)^2 }

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product 7i(3+11i) = 21i+77i^2.
You should know from your classes that i^2 = -1, thefore the numerator simplifies to -77+21i
You can do it as a curious thing, but simplifying yields the result:
\frac{-77+21i}{130}
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Bumek [7]
12. The answer is 12 because two x 6 is twelve awesome
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3 years ago
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