Answer this for branlist if get right

Determine whether each expression is equivalent to 49^2t – 0.5.

vampirchik [111]

Answer:

None of the expression are equivalent to $49^{(2t - 0.5)}$

Step-by-step explanation:

Given

$49^{(2t - 0.5)}$

Required

Find its equivalents

We start by expanding the given expression

$49^{(2t - 0.5)}$

Expand 49

$(7^2)^{(2t - 0.5)}$

$7^2^{(2t - 0.5)}$

Using laws of indices: $(a^m)^n = a^{mn}$

$7^{(2*2t - 2*0.5)}$

$7^{(4t - 1)}$

This implies that; each of the following options A,B and C must be equivalent to $49^{(2t - 0.5)}$ or alternatively, $7^{(4t - 1)}$

A. $\frac{7^{2t}}{49^{0.5}}$

Using law of indices which states;

$a^{mn} = (a^m)^n$

Applying this law to the numerator; we have

$\frac{(7^{2})^{t}}{49^{0.5}}$

Expand expression in bracket

$\frac{(7 * 7)^{t}}{49^{0.5}}$

$\frac{49^{t}}{49^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{49^{t}}{49^{0.5}}$ becomes

$49^{t-0.5}}$

This is not equivalent to $49^{(2t - 0.5)}$

B. $\frac{49^{2t}}{7^{0.5}}$

Expand numerator

$\frac{(7*7)^{2t}}{7^{0.5}}$

$\frac{(7^2)^{2t}}{7^{0.5}}$

Using law of indices which states;

$(a^m)^n = a^{mn}$

Applying this law to the numerator; we have

$\frac{7^{2*2t}}{7^{0.5}}$

$\frac{7^{4t}}{7^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{7^{4t}}{7^{0.5}}$ = $7^{4t - 0.5}$

This is also not equivalent to $49^{(2t - 0.5)}$

C. $7^{2t}\ *\ 49^{0.5}$

$7^{2t}\ *\ (7^2)^{0.5}$

$7^{2t}\ *\ 7^{2*0.5}$

$7^{2t}\ *\ 7^{1}$

Using law of indices which states;

$a^m*a^n = a^{m+n}$

$7^{2t+ 1}$

This is also not equivalent to $49^{(2t - 0.5)}$

6 0

3 years ago

The first step in the process for factoring the trinomial x^2-3x-40 is to

jenyasd209 [6]

(x-8)(x+5)

First thing you do is put the X's into the parentheticals because it is x^2 meaning there are 2 factors with x's. Then, you wonder what factors of -40 could add to get -3. In this case, they are -8 and 5. -8 times 5 is -40 and -8 +5 is -3. Then, you just add -8 and 5 beside the x's in the parentheticals.

5 0

3 years ago

Read 2 more answers

M∠GHI = 3x° and m∠LMN = 17x°. If ∠GHI and ∠LMN are supplementary, find the measure of each angle.

Savatey [412]

If they are supplementary then 3x + 17x = 180

20x = 180

x = 9
m<GHI = 27 degrees
m < LMN = 153 degrees

3 0

3 years ago

Read 2 more answers

Simplify this expression.<br> 2x/12(x + y)

Ymorist [56]

Answer: = 1 /6 x^2+ 1 /6 xy

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Consider the sequence 3, 6, 12, 24, 48, .... (a) Write a recursive rule to represent the sequence. (b) Write an explicit rule to

saveliy_v [14]

Answer:

a. a[1] = 3; a[n] = 2a[n-1]

b. a[n] = 3·2^(n-1)

c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

The recursive rule is ...

a[1] = 3

a[n] = 2×a[n-1]

__

The explicit rule is ...

a[n] = a[1]×r^(n-1)

a[n] = 3×2^(n-1)

__

The 15th term is ...

a[15] = 3×2^(15-1) = 3×2^14

a[15] = 49,152

5 0

2 years ago