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3 years ago

Rewrite the expression with the given base.

Mathematics

2 answers:

ASHA 777 [7]3 years ago

8 0

The expression given to us is: 64^2x and we have to rewrite it with a base of 8 .

We know that 64 can be written in terms of 8 as the squared of 8 as: $64=8^2$ .

Thus, the expression, $64^{2x}$ can be rewritten as:

$64^{2x}=(8^2)^{2x}$

Now, using the rules of exponents we get:

$(8^2)^{2x}=8^{2\times 2x}=8^{4x}$

$\therefore 64^{2x}=8^{4x}$

Thus, out of the given options, <u>option C is the correct option</u>.

satela [25.4K]3 years ago

3 0

C. 8^4x
64^2x = 4096x
8^4x= 4096x

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Rewrite 9 to the 3rd power divided by 9 to the 9th power using a single, positive exponent

Brums [2.3K]

Answer:

$\dfrac{1}{9^6}$

Step-by-step explanation:

$\dfrac{9^3}{9^9} = 9^{3 - 9} = 9^{-6} = \dfrac{1}{9^6}$

8 0

2 years ago

The temperature is 60°F. The temperature will decrease by 3°F each hours. Let h be the number of hours. When will the temperatur

lisabon 2012 [21]

Answer:

For the temperature to be below 32 F, following inequality must be met,

$h\geq 9.333$

Step-by-step explanation:

Let "t" be the temperature at any time.

General format of a linear equation can be given as,

y= mx + c

Where,

y ⇒ dependent variable ( in this case temperature t)

m⇒ Gradient ( the rate at which the temperature drops)

x⇒ independent variable ( hours )

c⇒ intercept ( this is the starting temperature)

Now we can substitute the given values to the above format to arrive at the equation,

$t=-3h+60$

We can re-arrange the equations as ,

$3h=60-t$

= $h=20-\frac{t}{3}$

We can write this as an inequality when t = 32 F

$h\geq 20-\frac{32}{3}$

= $h\geq \frac{28}{3}$

= $h\geq 9.333$

7 0

3 years ago

Find the value of b. Express the answer as a simplified radical.

Mama L [17]

Here three sides of a right angled triangle given.

The three sides are b, 8 and 14.

The side with length 14 is the hypotenuse here. We have to find the side of length b.

To get b, we will use Pythagoras theorem here.

By using Pythagoras theorem we can write,

$c^2=a^2+b^2$ , where c is the hypotenuse.

So here we can write,

$14^2=8^2+b^2$

$196 = 8^2+b^2$

$196=64+b^2$

To solve it for b, now we have to move 64 to the left side by subtracting it from both sides.

$196-64 = 64+b^2-64$

$196-64 = b^2$

$132=b^2$

Now to find b, we have to take square root to both sides. We will get,

$\sqrt{132}= \sqrt{b^2}$

$\sqrt{132} =b$

$b= \sqrt{(4)(33)}$

$b= (\sqrt{4})(\sqrt{33})$

$b= 2\sqrt{33}$

We have got the required answer for the side b.

6 0

3 years ago

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Answer:

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