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3 years ago

Point P is the midpoint of both MR and NQ, which are on the same line. If MN=26, NP=3x+4, and QR=6x+2, find NP.

Mathematics

1 answer:

sammy [17]3 years ago

7 0

Answer: NP= 16 cm

Explanation:

As we shown in the figure below :

Since P is the midpoint of MN and NQ

So, We consider ΔMNP and ΔPQR,

∠MPN=∠QPR (∵ Vertically opposite angles are equal)

MP=PR (∵ P is the mid point of MR)

NP=PQ (∵P is the midpoint of NQ)

So, ΔMNQ ≅ ΔPQR (∵By SAS congruence )

∴ $26=6x+2 \text{(By CPCT )}\\26-2=6x\\24=6x\\\frac{24}{6}=x\\4=x$

So, NP $=3x+4=3\times 4+4=12+4=16 cm$

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Option (b) is correct.

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Step-by-step explanation:

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c) There is a 82% probability that between two and five students, inclusive, use credit cards because of the rewards program.

Step-by-step explanation:

There are only two possible outcomes. Either the student use credit cards because of the rewards program, or they use for other reason. So, we can solve this problem by the binomial distribution.

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$P(X > 2) = 1 - P(X \leq 2)$

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