MATHEMATICS HIGH SCHOOL

Which expression is irrational? 8 over 5. square root of 4 square root of 10. square root of 64

Answers

Answer 1

Answer:

The expression which is irrational is √10. Also, 8/5 is rational. √4 is rational. √64 is rational.

What are rational numbers and irrational numbers?

Rational numbers are numbers that can be written in the form of $(a)/(b)$ where a and b are integers.

Example: 1/2, 3.5 (which is writable as 7/5), etc.

Irrational numbers are those real numbers that are not rational numbers.

Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.

8/5 is rational. It is expressed in the form of $(a)/(b)$ .

√4 = 2 = 2/1 . This is rational because it is expressed as the ratio of two integers.

√64 = 8. This is rational because it is expressed as the ratio of two integers.

√10 = 3.16227..... The decimal part does not end and it is irrational because it can not be expressed in the form of $(a)/(b)$ .

Therefore √10 is irrational.

Learn more about rational number here;

brainly.com/question/14261303

#SPJ2

Answer 2

Answer: 8/5 is rational. It is expressed as a ratio of two integers.

√4 = 2 = 2/1 . This is rational because it expressed as ratio of two integers.

√64 = 8. This is rational because it expressed as ratio of two integers.

√10 = 3.16227..... The decimal part does not end and it is irrational because it can not be expressed as ratio of two integers.

Therefore √10 is irrational.

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I need this TONIGHT!!! Three years ago, Jolene bought $750 worth of stock in a software company. Since then the value of her purchase has been increasing at an average rate of 5 1/2% per year. How much is the stock worth now? (Round each money calculation you make to the nearest cent.) The stock is worth $ now.

Answers

Answer:

$A\approx\$880.68$

Step-by-step explanation:

So, we know that Jolene bought an initial $750.

We also know that the purchase is increasing at an average rate of 5 1/2 %or 5.5%. In other words, this is being compounded.

So, we can use the compound interest formula, which is:

$A=P(1+(r)/(n))^(nt)$

Where A is the total amount, P is the principal value, r is the rate and n is the number of times compounded per year, and t is the amount of years.

So, substitute 750 for P. 5 1/2% is the same as 5.5% or 0.055 (you move the decimal two places to the left and remove the percent symbol) so substitute this for r. Since it's increasing yearly, n is 1. So, our formula is:

$A=750(1+0.055)^t$

Add:

$A=750(1.055)^t$

Since the stock was bought 3 years ago, the value now is t=3. So, substitute 3 for t and evaluate:

$A=750(1.055)^3$

Evaluate. Use a calculator:

$A\approx\$880.68$

And we're done!

Formula: A = P(1 + r/n)^t

We have these variables:

P = 750

r/n = 0.055

t = 3

Substitute and simplify:

A = 750(1 + 0.055)^3

A = 750(1.055)^3

A = 880.68

Best of Luck!

14.88 to 12.32 find the ratio

Answers

14.88 to 12.32

14.88 : 12.32. 2 into 14.88 is 7.44, 2 into 12.32 is 6.16

7.44 : 6.16    2 into 7.44 is 3.72, 2 into 6.16 is 3.08

3.72 : 3.08            2 into 3.72 is 1.86, 2 into 3.08 is 1.54

1.86 : 1.54    2 into 1.86 is 0.93, 2 into 1.54 is 0.77

0.93 : 0.77

You can multiply both numbers by 100 to change it whole numbers.

0.93*100 : 0.77*100

93 : 77

In sunlight, a vertical stick 7 ft tall casts a shadow 3 ft long. At the same time a nearby tree casts a shadow 11 ft long. How tall is the tree? Round to the nearest tenth.

Answers

Answer:

25.7 feet.

Step-by-step explanation:

Let x be the actual length of tree.

We have been given that in sunlight, a vertical stick 7 ft tall casts a shadow 3 ft long. We are asked to find the actual length of tree casting a 11 ft long shadow.

We will use proportions to solve our given problem.

$(x)/(11)=(7)/(3)$

Upon multiplying both sides of our equation by 11, we will get:

$(x)/(11)*11=(7)/(3)*11$

$x=(77)/(3)$

$x=25.6666666\approx 25.7$

Therefore, the tree is 25.7 feet tall.

$look\ at\ the\ picture\n\n\Delta ABC\sim\Delta D EF\n\n(|ED|)/(|EF|)=(|AB|)/(|BC|)\n\n(|ED|)/(11)=(7)/(3)\ \ \ \ /\cdot11\n\n|ED|=(77)/(3)\n\n|ED|\approx25.7\ (ft)\leftarrow Answer$

In New York, state sales tax rates vary by county. In Allegany County, the sales tax rate is 8 1 2 %. a. A book costs $12.99, and a video game costs $39.99. Rounded to the nearest cent, how much more is the tax on the video game than the tax on the book?

Answers

Answer:

$ 2.30

Step-by-step explanation:

Given that the sales tax rate $= 8(1)/(2)\%=8.5\%$

The cost of the book is $ 12.99.

So, the tax on the book= 8.5% of 12.99

$= \frac {8.5}{100}* 12.99$

=1.10

So, the sales tax on the book is $ 1.10.

The cost of the video game is $ 39.99.

So, the tax on the book= 8.5% of 39.99

$= \frac {8.5}{100}* 39.99$

=3.30

So, the sales tax on the book is $ 3.40.

The difference of taxes on both the items = $ 3.40-$ 1.10=$ 2.30

So, the tax on the video game is $ 2.30 more than then tax on the book.

Given the following functions, find g(f(x)). f(x) = 2x + 1 g(x) = x2 + 6

Answers

Answer:

Step-by-step explanation:

g(x) = x^2 + 6

f(x^2 + 6) = 2(x^2 + 6) + 1 = 2x^2 + 12 + 1 = 2x^2 + 13

Find domain and range