MATHEMATICS HIGH SCHOOL

A sequence has an initial value of 10 and each term is twice the previous.  Which function models this sequence?1. a(n)=10(2)"n
2. a(n)=10(2)n-1
3. a(n)=10+2n
4. a(n)=10+2(n-1)

Answers

Answer 1
Answer: 10,\ 20,\ 40,\ 80,\ ...\n\na_n=2\cdot a_(n-1)\ \ \ \Rightarrow\ \ \ q=2\n\ngeometric\ sequence \ \ \ \Rightarrow\ \ \ a_n=a_1\cdot q^(n-1)\n\na_1=10\ \ \ and\ \ \ q=2 \ \ \ \Rightarrow\ \ \ a_n=10\cdot 2^(n-1)\n\nAns.\ this\ sequence\ models:\ \ \ a_n=10\cdot 2^(n-1)

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The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 80 cm. What are the dimensions of the rectangle?length = 25 cm; width = 15 cm
length = 22 cm; width = 18 cm
length = 24 cm; width = 16 cm
length = 23 cm; width = 14 cm

Answers

Answer:

Length = 25 cm , Width = 15 cm.

Step-by-step explanation:

Given  : The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 80 cm.

To find : What are the dimensions of the rectangle.

Solution : We have given

Perimeter = 80 cm .

According to question :

Let width of rectangle = W .

Length is  twice its width.

L = 2W .

Length of a rectangle is 5 centimeters less than twice its width.

L = 2W - 5.

Then ,

Perimeter = 2 ( length + width).

Plug the values

80 = 2 ( 2W - 5 + W ) .

80 = 2( 3W -5) .

On dividing both sides by  2

40 = 3W - 5 .

On adding both sides by 5.

45 = 3 W .

On dividing both sides by 3.

W = 15 cm .

L = 2W -  5.

L = 2 ( 15) - 5 .

L = 30 -5 .

L = 25 cm .

Therefore, Length = 25 cm , Width = 15 cm.
Hello,

Answer A
Let's the width of the rectangle

2a-5 its length
Teh half perimeter is 80/2=40
a+2a-5=40 ==>3a=45==>a=15 and 2a-5=30-5=25

Mr. Lopez, Mrs. Manuel, Mrs. Manker and Mrs. Vo come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Mr. Lopez can cross the bridge in 1 minute,Mrs. Manker in 2 minutes, Mrs. Manuel in 5 minutes, and Mrs. Vo in 8 minutes. When two people cross the bridge together, they must move at the slower person's pace. The question is, can they all get across the bridge if the torch lasts only 15 minutes?[2]

Answers