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denis23 [38]
3 years ago
12

The positive integer k has exactly two positive prime factors, 3 and 7. if k has a total of 6 positive factors, including 1 and

k, what is the value of k ?
Mathematics
1 answer:
Sav [38]3 years ago
5 0
I think there are two solutions, 63 or 147:

63 = 3² x 7, factors  1 | 3 | 7 | 9 | 21 | 63<span>
147 = 3 x 7</span>², factors 1 | 3 | 7 | 21 | 49 | 147
You might be interested in
A train leaves at 08.43 and arrives at its destination at 09.23. If the train travelled 73 km, what was it's average speed in km
serg [7]

Answer: 109.5 km/ hr

Step-by-step explanation:

Distance = 73 km

Time = 40 minutes = 40/60 = 2/3 hours

Speed = Distance / time

= 73 / 2/3

= 73 x 3/2 = 219 / 2 = 109.5 km/hr

5 0
3 years ago
Kristen is 64 inches tall, and she stands 12 feet away from a streetlight. If she casts an 82-inch-long shadow, how tall is the
o-na [289]

Answer:

176.39 inches or

14.70 feet

Step-by-step explanation:

Consider the right triangle made by Kristen, ground and shadow.

This triangle has one leg as 64 inches.

Next consider the right triangle formed by street light, ground upto shadow tip.

The two triangles have common angle of elevation and also another angle as 90 degrees.

Hence the two triangles would be similar

Also if A is the angle made by hypotenuse of both triangles with the ground we have

tanx=\frac{64}{82}

This value also equals by bigger triangle as

tanx=\frac{h}{82+12(12)}=\frac{h}{226}

From these two we get

h = height of street light =\frac{226(64)}{82} =176.39

6 0
3 years ago
The two men measure the angle of elevation to the highest point on the rock to be 22.6°. They
IgorC [24]

Answer:

  • 15 m

Step-by-step explanation:

<em>Refer to attached picture</em>

  • The height  = h
  • Angles of elevation 22.6° and 38.3°
  • Closer distance  = d

<u>Use tangent to solve</u>

  • tan 22.6° = h/(d + 17) ⇒ h = (d + 17) tan 22.6° ⇒ h = 0.42(d + 17)
  • tan 38.3° = h/d          ⇒ h = d tan 38.3°           ⇒ h = 0.79d

<u>Compare the equations above and find the value of d:</u>

  • 0.42(d + 17) = 0.79d
  • 0.42d + 7.14 = 0.79d
  • 0.79d - 0.42d = 7.14
  • 0.37 d = 7.14
  • d = 7.14/0.37
  • d = 19.3 m

<u>Now find the value of h:</u>

  • h = 0.79d
  • h = 0.79*19.3
  • h = 15

Wave Rock is 15 m tall

3 0
3 years ago
In a geometric sequence, a2=108 and as 256. Write the explicit formula for this sequence.
torisob [31]

Answer:

The first choice is correct.

Step-by-step explanation:

First work out the common ratio r:-

a2 = a1r and a5 = a1 r^4

So r^3 = a1r^4 / a1r = 256/ 108

r = cube root (256/-108) =  4/3

So the explicit formula is 108(4/3)^(n-1)

8 0
3 years ago
Read 2 more answers
What is the answer to this problem-k-6-7k+20=-2
STatiana [176]

Answer:

K=2 that is the answer

6 0
3 years ago
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