How many liters equal 1258 cm3 a 12.58 L b 125.8 L c 12,580 L d 1.258 L

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

Daniela is a stain glass artist; she created the window below for her living room. What is

OLga [1]

The window has a shape of a semi-circle (half of a circle).

We know the diameter d = 12 ft.

The area of a (complete) circle is given by the formula:
A = π × r²

The radius can be found by halving the diameter:
r = d ÷ 2
= 12 ÷ 2
= 6 ft

Therefore the area of the circle will be:
A = π × r²
= 3.14 × 6²
= 3.14 × 36
= 113.04 ft²

And the area of the semi-circle:
A = 113.04 ÷ 2
= 56.52 ft²

Hence, the area of the window will be 56.52 ft².

3 0

2 years ago

90 juniors took different SAT-II tests. 40% more students took the Chemistry test than took the History test, and 50% more stude

erastovalidia [21]

Answer:

Step-by-step explanation:

4.5x=90

x=20 history

28 chemistry

42 math

They add to 90.

History test=x

Chemistry test=1.4x

Math test=(1.5)(1.4)=2.1x

They add to 90

4 0

2 years ago

Diego pours 8 ounces of water from a full bottle of 36 ounces. What is the percent of decrease of water in the bottle?

Natali5045456 [20]

Answer:

The answer is 22%.

Step-by-step explanation:

All you need to do to figure this out is to divide 36 by 8.

8/36=.222222

Hope this helps!

4 0

2 years ago

A hotel house keeper cleaned 1/3 on

Aleksandr-060686 [28]

Answer:

dunno

Step-by-step explanation:

hope this helps has hdhd

3 0

2 years ago