MATHEMATICS HIGH SCHOOL

Find the 15th term in the geometric sequence below.20, 10, 5, 2.5, . . .
A.-25/4,096

B.-5/4,096

C.5/4,096

D.25/4,096

Answers

Answer 1
Answer: geo sequence
a_n=a_1r^(n-1)
an=nth term
a1=first term
r=common ratio
n=which term

10/20=1/2
r=1/2
20=a1

a_(15)=20(1/2)^(15-1)=
a_(15)=20(1/2)^(14)=
a_(15)=20( (1)/(16384) )=
a_(15)= (20)/(16384)=
a_(15)= (5)/(4096)




C is answer

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Brianna went to Los Angeles for a vacation. She spent 5 nights at a hotel and rented a car for 6 days. Justin stayed at the same hotel, but spent 7 nights and rented a car for 8 days from the same company. If Brianna paid $1170 and Justin paid $1610, how much did one night at the hotel cost?

Answers

$150 per night

Use a system of equations using x (cost of hotel) and y (cost of car): 

5x + 6y = 1170 

7x + 8y = 1610 

Solve for y in one of the equations and then use substitution to solve for x in the other: 

6y = 1170 - 5x 

y = (-5/6)x + 195 

7x + 8((-5/6)x + 195) = 1610 

7x + (-20/3)x + 1560 = 1610 

(1/3)x +1560 = 1610 

(1/3)x = 50 


x = $150 a night

Which amount is largest?

100 g
1 kg
1,000 mg
1 dg

Answers

The largest amount is B- 1 Kg.





Hope it is helpful :)

Eqyivalent expresion to 3√m^2n^5

Answers

The first step to solving this expression is to factor out the perfect cube
\sqrt[3]{m^(2) n^(3) X n^(2) }
The root of a product is equal to the product of the roots of each factor. This will make the expression look like the following:
\sqrt[3]{ n^(3) } \sqrt[3]{ m^(2) n^(2) }
Finally,, reduce the index of the radical and exponent with 3
n\sqrt[3]{ m^(2) n^(2) }
This means that the correct answer to your question is n\sqrt[3]{ m^(2) n^(2) } .
Let me know if you have any further questions
:)

Find the slope of the line passing through the points ( -9, 3) and (6, 3)

Answers

Answer:

M=0

Step-by-step explanation:
You want to use the formula (y2-y1)/(x2-x1). To do this, subtract 3-3/6- -9 and that is your slope. So the slope is 0/15.

the area of a rectangular field is x^2-x-72 m^2. The length of the field is x+8 cm. What is the width of the field meters.

Answers

Hello,


A(x)=x²-x-72 (m²)
L=(x+8) (cm)= (x+8)/100 (m)

We suppose here x≠-8
(in reality x²-x-72>0 ==>x<-8 or x>9
but x+8>0 ==> x>-8
 then
only x>9 are solutions)

W=A(x)/ ((x+8)/100 )=100*(x²-x-72)/(x+8)= 100*(x-9)(x+8)/(x+8)=100*(x-9)

It takes a motorboat 6 hours to travel 96 miles down a river, and 2 hours longer to make the return trip. Find the speed of the current.

Answers

Speed = distance / time
Down river------> 96/6 = 16 mph
up river<------ 96/(6+2) = 12 mph
difference of 4 mph or +- 2 mph
14 + 2 for down river or with the flow
14 - 2 for up river, against the flow
so the speed of the river is 2 mph
((16+12)/2)-12 = 2 or ((16+12)/2)-16 = -2 depending on which way you define to be positive -- Speed is scaler anyway so can only be positive
the speed of the boat in still water is 14 mph
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