Whats the midpoint for (−3,5) and (0,−1)

Rewrite 4 1/2=2 <br> please

Luda [366]

The logarithmic expression of 4^(1/2) = 2 is $\log_4(2) = \frac 12$

<h3>How to rewrite the expression?</h3>

The expression is given as:

4^(1/2) = 2

Take the logarithm of both sides

log(4^(1/2)) = log(2)

Apply the change of base rule

1/2log(4) = log(2)

Divide both sides by log(4)

1/2 = log(2)/log(4)

Change the base

$\frac 12 =\log_4(2)$

Rewrite as:

$\log_4(2) = \frac 12$

Hence, the logarithmic expression of 4^(1/2) = 2 is $\log_4(2) = \frac 12$

Read more about logarithmic expression at:

brainly.com/question/24211708

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8 0

2 years ago

Which is equivalent to V180x11 after it has been simplified completely?

inna [77]

Question:

Which is equivalent to $\sqrt{180x^{11}}$ after it has been simplified completely?

Answer:

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

Step-by-step explanation:

Given

$\sqrt{180x^{11}}$

Required

Simplify

We start by splitting the square root

$\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}$

Replace 180 with 36 * 5

$\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}$

Further split the square roots

$\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}$

Replace power of x; 11 with 10 + 1

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}$

From laws of indices; $a^{m+n} = a^m * a^n$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}$

Further split the square roots

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}$

From laws of indices; $\sqrt{a} = a^{\frac{1}{2}}$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}$

Rearrange Expression

$\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}$

From laws of indices; $\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}$

So, we have

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}$

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

<em>The expression can no longer be simplified</em>

Hence, $\sqrt{180x^{11}}$ is equivalent to $6x^{5}\sqrt{5x}$

7 0

2 years ago

Read 2 more answers

Maria took out an unsubsidized Stafford loan of $6,925 to pay for college. She plans to graduate in 4 years. The loan had a dura

Finger [1]

Answer:

$144.70

Step-by-step explanation:

Calculation to determine how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization

First step is to determine the Interest only monthly repayments

Using this formula

I=Prt

where,

P=$6925

r=0.05/1

t=1

Let plug in the formula

I=6925*0.05/12

I= $28.854166666

Second step is to determine the amount she will owe after 4 years

Using this formula

S=P(1+r)n

Let plug in the formula

S=6925*(1+0.05/12)4*12

S=6925*(1+0.05/12)48

S=$8454.70

Third step is to determine the Interest part

Interest =8454.70 - 6925

Interest = $1529.70

Now let determine the how much greater will the amount of interest capitalized be

Interest capitalized=1529.70 - 1385.00

Interest capitalized =$144.70

Therefore how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization is $144.70

4 0

3 years ago

2. Given that the radius of the Earth is 6340 Km. calculate the Surface Acer of earth <br>

serious [3.7K]

Answer:

Step-by-step explanation:

The surface area of a sphere (which the earth is considered to be) = 4 pi r^2

pi = 3.14

r = 6340

Area = 4 * 3.14 * 6340 * 6340 = 504856736 square km.

You should either round this to 505,000,000 or express a value in scientific notation.

5.05 * 10^8

6 0

3 years ago

2qt= ?ml round to nearest hundredths

bezimeni [28]

Answer:

1982.71 mL

Step-by-step explanation:

1 qt = 946.353 mL

2 qt = 1982.71 mL

8 0

3 years ago