Multiply<span> by </span><span><span>(7−4i)/</span><span>(7−4i)</span></span><span> to make the </span>denominator<span> of </span><span><span>(4−7i)/</span><span>(7+4i)</span></span><span> real.
</span><span>(<span><span>4−7i/</span><span>7+4i</span></span>)(<span><span>7−4i/</span><span>7−4i</span></span>)
</span>Expand <span>(7+4i)(7−4i)</span><span> using the </span>FOIL<span> Method.
</span><span>(4−7i)(7−4i)/</span><span>7(7)+7(−4i)+4i(7)+4i(−4i<span>)
</span></span><span>Simplify.
</span><span><span>(4−7i)(7−4i)/</span>65
</span>Expand <span>(4−7i)(7−4i)</span><span> using the </span>FOIL<span> Method.
</span><span><span>4(7)+4(−4i)−7i(7)−7i(−4i)/</span>65
</span>Simplify each term<span>.
</span><span><span>28−16i−49i−28/</span>65
Simplify
</span><span><span>−65i/</span>65
</span><span>−i</span>
This is true.
It comes from the same side interior angles theorem which says that same side interior angles are supplementary, only if the lines are parallel.
Answer:
See below.
Step-by-step explanation:
x^2 = y + 16
4y - 1 = 7x
are the 2 equations. (answer)
From the second equation
4y = 7x + 1
y = 7/4 x + 1/4
Substituting in the first equation:
7/4x + 1/4 + 16 = x^2
x^2 - 7/4 x - 16 - 1/4 = 0
x^2 - 7/4 x - 16 1/4 = 0
Multiplying though by 4
4x^2 - 7x - 65 = 0
Using the ac method to solve this 4 * -65 = -260 and we need factors of this to add up to -7. -20 and 13 look good so we write:
4x^2 - 20x + 13x - 65 = 0
Fatcor by grouping:
4x(x - 5) + 13(x - 5) = 0
(4x + 13)(x - 5) = 0
So the the roots are 5, -3.25
To find the values of y we substitute these values of x into the second equation:
x = 5: 4y - 1 = 7*542y = 36
y = 9.
x = -3.25:
4y - 1 = 7*-3.25
4y = (7 * -3.25) + 1
y = -5.44.
So the solutions are (5, 9) and (-3.25, -5.44) (Answer)
