MATHEMATICS MIDDLE SCHOOL

Simplify a squared x b x b four x b

Answers

Answer 1

Answer:

Answthat 16 is 42,

Step-by-step explanation:

Understand factoring. ...

Divide by the smallest prime number possible. ...

Rewrite the square root as a multiplication problem. ...

Repeat with one of the remaining numbers. ...

Finish simplifying by "pulling out" an integer. ...

Multiply integers together if there are more than one.

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The planet Mars could be a future destination for the U.S. space program. Assume that Mars is a perfect sphere. Its surface area is about 145 million square kilometers. What is the radius of Mars at its equator? Round to the hundreds place. ||| Answer choices:
A) 4,500 km
B) 2,200 km
C) 5,000 km
D) 3,400 km |||

Answers

surface area of a sphere is 4 times pi timers radius^2
aprox pi=3.14

so surface area=145,000,000

145,000,000=4 times 3.14 times rdaius^2
145,000,000=12.56 times radius^2
divide both sdies by 12.56
11544585.987=r^2
square root both sides
3397.73=radius

round to the hundreds
3397 rounded to the hundreds
3400

the answer is D 3,4000 km

In △ABC, point P∈AB so that AP:BP=1:2. Point R ∈ PB that PR:BR=1:2. Point Q∈BC so angle BQR = angle BCP. Find ratio of PQC to ABC.

Answers

Answer:

Ratio of PQC to ABC is 2:9.

Step-by-step explanation:

In ΔBRQ and ΔBPC

∠BQR = ∠BCP (given) and ∠B is common for both triangles, so from AAA similarity ΔBRQ and ΔBPC are similar.

⇒ BQ : QC = BR : RP = 2 : 1 →(1)

now draw perpendiculars from points A and P to BC line segment. Call the projected points as A' and P'.

It is clear that lines AA' and PP' are parallel. So in ΔBPP' and ΔBAA' we have AAA similarity with common angle at B.

⇒PP' : AA' = BP : BA = 2 : 3 →(2) (∵ AP : PB = 1 : 2)

area of ΔPQC = 0.5×PP'×QC

area of ΔABC = 0.5×AA'×BC

area of ΔPQC : area of ΔABC = (0.5×PP'×QC)/(0.5×AA'×BC)

=(PP'/AA')×(QC/BC)

=(2/3)×(1/3) (∵ from (1) and (2))

=2/9.

∴ Ratio of PQC to ABC is 2:9

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