Please help with those two?

Mathematics

1 answer:

german2 years ago

6 0

First question:

When you bisect an angle, you create two new equal angles, both measuring half of the original angle. So, if the original angle was 52°, the two angles will be 52/2=26 degrees each.

Note: the picture is not very clear, and I'm not sure the original angle is 52°. It it's not, just divide by 2 whatever measure the angle is.

Second question:

Focus on triangles RQP and RSP:

They are both right, because Q and S are right angles
We are given QP=SP
They share the side RP

So, they are congruent. This implies that angle SRP is 50° as well, and then

QRS = QRP+SRP = 50°+50°=100°

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To rationalize the denominator of 2/square 13+ squared 11 , you should multiply the expression by which fraction?

eimsori [14]

Answer:

You should multiply the expression by $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}$

Explanation:

To rationalize any expression, you must multiply it by its conjugate. A conjugate is defined as a similar expression to the original one but with an opposite sign

This means that:

The conjugate of a + b would be a - b

Now, the given expression is $\frac{2}{\sqrt{13}+\sqrt{11}}$

Consider the denominator:

From the above, we can conclude that the conjugate of $\sqrt{13}+\sqrt{11}$ is $\sqrt{13}-\sqrt{11}$

And, remember that we need to keep the value of the expression unchanged. This means that we must multiply both the numerator and the denominator by the same value

Therefore:

You should multiply the expression by $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}$ in order to rationalize the denominator

Hope this helps :)

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