What is the following product?

<img src="https://tex.z-dn.net/?f=%20%5Cbigstar%20%5C%3A%20%5Cunderline%7B%20%5Cunderline%7B%20%5Ctt%7BQuestion%7D%7D%7D%20%3A%2

Fittoniya [83]

Answer:

See Below.

Step-by-step explanation:

We are given two intersecting circles with centers M and N.

And we want to prove that: I) PQ ⊥ MN and that II) PR = RQ.

Since MP and MQ are radii of the same circle:

$MP\cong MQ$

Likewise, since NP and NQ are radii of the same circle:

$NP\cong NQ$

And by the Reflexive Property:

$PQ\cong PQ$

Therefore, by SSS Congruence:

$\Delta MPN\cong \Delta MQN$

By CPCTC:

$\displaystyle \angle PMN\cong \angle QMN$

And by the Reflexive Property:

$MR\cong MR$

And since they are the radii of the same circle:

$MP\cong MQ$

Therefore, by SAS Congruence:

$\Delta MPR\cong \Delta MQR$

Therefore, by CPCTC:

$PR\cong RQ$

Note that PQ is a chord in Circle M.

Therefore:

$\text{Segment $MN$ bisects chord $PQ$}$

In a circle, a segment that passes through the center of the circle that is perpendicular to a chord also bisects the chord.

And conversely, a segment that passes through the center of a circle that bisects a chord in the circle is also perpendicular to the chord.

So:

$\displaystyle PQ\perp MN$

4 0

3 years ago

Read 2 more answers

One of the parallel sides of a trapezium is 5cm longer than the other. If the

Citrus2011 [14]

The area of a trapezium is the product of height and average base length. The average base length is
(126 cm^2)/(9 cm) = 14 cm

One base is half the difference longer than this, 16.5 cm; the other is half the difference shorter, 11.5 cm.

8 0

3 years ago

Sarah and Joe are seeking to join a gym. Sarah saw on television that Great Gym is offering membership at $19.50 per month, plus

inna [77]

Set up an equation for both Sarah and Joe.

Sarah's equation would be 59+19.50x=y

Joe's Equation would be 149+9.50x=y

The goal is to get y to equal the lowest number. If we plug in 1 for x for both equations we get:

59+19.50(1)=y for sarah and Joes would be 149+9.50(1)=y.

Sarah would pay $78.50 for her 1st month and Joe would pay $158.5 for his 1st month. Sarah pays much less than joe but over a few months Sarah would pay more eventually. Hope I helped and if you have any questions, just leave a comment.

7 0

3 years ago

Juarez scored 32 points in a basketball game. He scored twice as many baskets worth 3 points than baskets worth 2 points. How ma

Ksju [112]

Answer:

8 baskets worth 3 points each and 4 baskets worth 2 points each

Step-by-step explanation:

It is 8 baskets worth 3 points each and 4 baskets worth 2 points each because it says Juarez scored twice as many baskets worth 3 points than the baskets worth 2 points. 4 x 2 = 8

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6 baskets worth 3 points each and 7 baskets worth 2 points each : wrong because 7 x 2 = 14.

10 baskets worth 3 points each and 1 basket worth 2 points : wrong because 1 x 2 = 2.

4 baskets worth 3 points each and 10 baskets worth 2 points each: wrong because 10 x 2 = 40.

3 0

4 years ago

Read 2 more answers

A 9 cm tall cone shaped paper cup can hold up to 58.9 cm3 of water. What is the minimum amount of paper needed to make the paper

IgorC [24]

Volume of cone is given by:
V=1/3πr²h
thus the radius of the cone will be:
58.9=1/3×3.14×r²×9
r²=6.25265
r~2.5 cm
thus the area of the cone will be:
A=πr(r+√(h²+r²))
A=3.14×2.5(2.5+√(2.5²+9²))
A=92.9500 cm²
Thus the area of material needed to make the cup is 92.95 cm²

8 0

3 years ago

Read 2 more answers