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2 years ago

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Which expressions below equal a rational number? Choose all that apply. 4/5 + 3/8; sqrt(100) + sqrt(5); 7sqrt(5) - sqrt(245); (4

sqrt(7))(2sqrt(7)); pi * sqrt(36)

1 answer:

masha68 [24]2 years ago

8 0

Answer:

Step-by-step explanation:

<h3>Rational number</h3>

$1) \dfrac{4}{5}+\dfrac{3}{8}\\\\\dfrac{4}{5} \ \text{is a rational number} \ and \ \dfrac{3}{8} \ \text{is a rational number}\\\\\dfrac{4}{5}+\dfrac{3}{8} \ \text{is also a rational number}$

$b) \sqrt{100}+\sqrt{5} = 10+\sqrt{5}\\\\\sqrt{5} \ \text{is a irrational number}. \\\\ \text{Rational number added to irrational number will result in an irrational number}\\\\10 + \sqrt{5} \ is \ not \ a \ rational \ number.$

c)

$7\sqrt{5}-\sqrt{245}=7\sqrt{5}-\sqrt{7*7*5}$

$= 7\sqrt{5}-7\sqrt{5}\\\\=0\\\\\text{\bf $ 7\sqrt{5}-\sqrt{245}$ ia a rational number}$

d)

$(4\sqrt{7})*(2\sqrt{7})=4*2*\sqrt{7*7}\\$

= 4*2*7

= 56

$4\sqrt{7}*2\sqrt{7} \ \text{\bf is a rational number}$

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Answer:

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c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

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Let us convert our given rate in decimal form.

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Therefore, the exponential model $y=830*(0.87)^x$ represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

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Let us take natural log of both sides of our equation.

$ln(0.5)=ln(0.87^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.5)=x*ln(0.87)$

$\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}$

$\frac{ln(0.5)}{ln(0.87)}=x$

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$x=4.977286\approx 4.98$

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