All categories

3 years ago

2²×2⁴÷2³ can you help me out and please add explanations it would be very helpful.

Mathematics

2 answers:

aalyn [17]3 years ago

8 0

Answer:

Step-by-step explanation:

$2^{2}$ × $2^{4}$ ÷ $2^{3}$

simplifies to $2^{3}$

then evaluate the power to 8 as the solution

Oxana [17]3 years ago

4 0

Answer:

Step-by-step explanation:

2²×2⁴÷2³

=2^2x2^{4-3}

=2^{2+4-3}

=2^3

I hope this helps!

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2 years ago

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What are the side lengths of a rectangle if the area = 40 in and the perimeter = 48 in

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the 11th term in a geometric sequence is 48 and the common ratio is 4. the 12th term is 192 and the 10th term is what?

Soloha48 [4]

Given:

The 11th term in a geometric sequence is 48.

The 12th term in the sequence is 192.

The common ratio is 4.

We need to determine the 10th term of the sequence.

General term:

The general term of the geometric sequence is given by

$a_n=a(r)^{n-1}$

where a is the first term and r is the common ratio.

The 11th term is given is

$a_{11}=a(4)^{11-1}$

$48=a(4)^{10}$ ------- (1)

The 12th term is given by

$192=a(4)^{11}$ ------- (2)

Value of a:

The value of a can be determined by solving any one of the two equations.

Hence, let us solve the equation (1) to determine the value of a.

Thus, we have;

$48=a(1048576)$

Dividing both sides by 1048576, we get;

$\frac{3}{65536}=a$

Thus, the value of a is $\frac{3}{65536}$

Value of the 10th term:

The 10th term of the sequence can be determined by substituting the values a and the common ratio r in the general term $a_n=a(r)^{n-1}$ , we get;

$a_{10}=\frac{3}{65536}(4)^{10-1}$

$a_{10}=\frac{3}{65536}(4)^{9}$

$a_{10}=\frac{3}{65536}(262144)$

$a_{10}=\frac{786432}{65536}$

$a_{10}=12$

Thus, the 10th term of the sequence is 12.

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2 years ago