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Vlad1618 [11]
2 years ago
14

Can i get help? Don’t really understand.

Mathematics
1 answer:
Rufina [12.5K]2 years ago
4 0

First option: correct. This is because angles WOX and XOZ are supplementary, so

m\angle WOX=180^\circ-104^\circ=76^\circ

Second option: correct. By the inscribed angles theorem, we have

m\angle XWZ=m\angle XYZ=\dfrac{113^\circ}2=56.5^\circ

Angles WOX and YOZ are congruent because they form a vertical pair; they both have measure 76 degrees. This means angles WXY and WZY are also congruent, since the interior angles of any triangle sum to 180 degrees in measure. Therefore triangles WXO and YZO form a side-side-side pair, and all SSS triangles are similar.

Third option: not correct. There is a theorem (not sure what the name is) regarding intersecting chords that asserts the average of the measures of arcs WY and XZ is the same as the measure of angle XOZ. This means

\dfrac{m\widehat{WY}+113^\circ}2=104^\circ\implies m\widehat{WY}=95^\circ

Fourth option: not correct. This is because arcs WX and XZ are not "supplementary" in the sense that they do not form a semicircle and their measures do not add to 180 degrees. We know this because it's clear that point O is not the center of the circle. If it was, then angle XOZ would be a central angle and its measure would be the same as the arc XZ it subtends.

Fifth option: correct. The theorem mentioned in the assessment of the third option makes itself useful here. We have

\dfrac{m\widehat{WX}+m\widehat{YZ}}2=m\angle WOX\implies m\widehat{WX}+m\widehat{YZ}=2\cdot76^\circ=152^\circ

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Find the value of the variable and MN if N is between M and Q. Round to the nearest hundredth if necessary. 
Rudiy27
<em><u>Answer:</u></em>
MN = 4 units

<u><em>Explanation:</em></u>
<u>1- getting the value of m:</u>
<u>We are given that:</u>
NQ = 4m and NQ = 12
<u>This means that:</u>
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<u>2- getting MQ:</u>
<u>We are given that:</u>
MQ = 5m + 1
<u>We have calculated that:</u>
m = 3
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MQ = 5(3) + 1 = 15 + 1 = 16 units

<u>3- getting MN:</u>
We are given that point N is located somewhere between points M and Q.
<u>This means that:</u>
line MQ can be divided into two portions: MN and NQ
<u>This also means that:</u>
length of MQ = length of MN + length of NQ

<u>We have calculated that:</u>
MQ = 16 units
<u>We are given that:</u>
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Hope this helps :)
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Consider the given information that, Shishir bought 4000 orange at 70 paisa each.

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Thus, 70 paisa = 70/100 rupees = 0.70 rupees

Therefore, the cost price of 4000 oranges is:

4000×0.70 rupees = 2800 rupees

The selling price of 2000 oranges is:

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The number of oranges now Shishir have:

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He wants to make a profit of RS 200. Thus the selling price of 4000 oranges should be:

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He earned 1800 rupees by selling 2000 oranges at 90 paisa. So, the remaining amount that he needs to make with 1600 oranges is:

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