Round 14.568 to the nearest hundredth.

There are no horses in the stables. There are 3 stables in all. How many horses are in each stable?

ddd [48]

There are no horses in any of the stables. It says so at the beginning of the question

5 0

4 years ago

What reasoning and explanations can be used when solving radical equations and how do extraneous solutions arise from radical eq

Mkey [24]

Answer:

We know that, a 'radical equation' is an equation that contains radical expressions, which further are the expressions containing radicals ( square roots and other roots of numbers ).

In order to solve radical equations, we use the rules of exponents and basic algebraic properties.

The common reasoning to use while solving a radical equation is:

1. Isolate the radical expression.

2. Square both sides of the equation to remove radical.

3. After removing the radical, solve the equation to find the unkown variable

4. Check the answer for the errors occurred by removing the radicals.

For e.g. $\sqrt{x}-3=5$

i.e. $\sqrt{x}-3+3=5+3$ ( Adding 3 on both sides )

i.e. $\sqrt{x}=8$

i.e. $(\sqrt{x})^{2} =8^{2}$

i.e. $x=64$ .

So, the solution the the radical equation $\sqrt{x}-3=5$ is x = 64.

Further, we know that an 'extraneous solution' is that root of the radical equation which is not a root of the original equation and is excluded from the domain.

for e.g. Take $\sqrt{x+4} =x-2$

i.e. $(\sqrt{x+4})^{2} =(x-2)^2$

i.e. $x+4=x^2+4-4x$

i.e. $0=x^2-5x$

i.e. $0=x(x-5)$

i.e. x = 0 and x = 5.

Substituting x = 0 in $\sqrt{x+4} =x-2$ , gives $\sqrt{0+4} =0-2$ i.e. $\sqrt{4} =-2$ i.e. $2=-2$ , which is not possible.

So, x = 0 is a solution that does not satisfy the equation.

Hence, x = 0 is an extraneous solution.

7 0

4 years ago

Consider a civilization broadcasting a signal with a power of 2.0×104 watts. The Arecibo radio telescope, which is about 300 met

Vitek1552 [10]

For light: Inverse Square Law

The signal is weaken by the inverse square of the difference of distances this means that one over the square of the difference.

Therefore, 70000LY / 141 LY =496.45 and that squared =246462.602 times less signal, or 1/246462.602.

2 For a circular telescope like the Arecibo radio telescope that equals Pi times the radius squared. Sensitivity of the telescope depends on its area.
The new telescope needs 246462.60 times that area to have enough sensitivity

(150 x 150 x Pi) = 70 685 sq m area for the Arecibo telescope and that times 246462.60
= 1.74212 x 10^10

What is the diameter of a circle with that area?

1. Divide the area by Pi = 5.548156 x 10^9
2. Take the square root of the result to find the radius = 74485.94293

3. Multiply by 2 to find the diameter = 148971.886

7 0

3 years ago

A bottle contains 30 fluid ounces of orange juice and 18 fluid ounces of pineapple juice. Which graph has a slope that best repr

mojhsa [17]

Answer:

option B. G

Step-by-step explanation:

Let

y ---->ounces of orange juice

x ---> ounces of pineapple juice

we know that

The ratio of orange juice to pineapple juice is equal to

$ratio=\frac{y}{x}$

substitute the given values

$ratio=\frac{30}{18}$

simplify

$ratio=\frac{5}{3}=1.67$

Verify each graph

Remember that the formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

we have

$ratio=\frac{5}{3}$