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3 years ago

8

Sam said the square root of a rational number must be a rational number. Jenna disagreed. She said that it is possible that the

square root of a rational number can be irrational. Who is correct and why?

1 answer:

ratelena [41]3 years ago

4 0

Jenna is correct because the square root of a rational number can still be irrational.

Take for example the square root of 2. It is an irrational number than goes 1.41421...

If you multiply just the first however many digits of the result by itself, you will never end up with a perfect 2, because the square root is irrational.

You might be interested in

math problem: Amanda worked 4.5 hours on Tuesday and 5.2 on Thursday. Her pay rate is $10.50 per hour. How much will Amanda get

kondor19780726 [428]

Answer:

$101.85

Step-by-step explanation:

Think of the two days as separate equations. They are added together to get a sum of the pay she will receive after the two days.

Equation

(4.5*10.5) + (5.2*10.5) = x (This just represents the unknown value)

Solve Through

(47.25) + (54.60) = x

47.25 + 54.60 = x

101.85 = x

Amanda will get paid $101.85 For her 2 days of work.

7 0

3 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

<em>Rough work</em>

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

------------------------------------------------------------------------------------

The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

<em>Solved</em>

7 0

3 years ago

Read 2 more answers

Amy, Bruce and Carlos collected a total of 168 pounds of cans to recycle. Bruce collected 1/3 the number of pounds of cans Carlo

disa [49]

A + b + c = 168
b = 1/3c
a = b + c....a = 1/3c + c = 4/3c

now we sub
4/3c + 1/3c + c = 168
8/3c = 168
c = 168 * 3/8
c = 504/8
c = 63 <=== Carlos collected 63 lbs

a = 4/3c
a = 4/3(63)
a = 252/3
a = 84 <== Amy collected 84 lbs

b = 1/3c
b = 1/3(63)
b = 63/3 <== Bruce collected 21 lbs
b = 21

3 0

3 years ago

What is the importance of polynomial functions and how this real life applications improve or contribute to the value of life

-Dominant- [34]

Answer:

<u><em>What is the importance of polynomial functions?</em></u>

<u><em> </em></u>Polynomials are an important part of the "language" of mathematics and algebra. They are used in nearly every field of mathematics to express numbers as a result of mathematical operations. Polynomials are also "building blocks" in other types of mathematical expressions, such as rational expressions.

<u><em /></u>

<u><em /></u>

<u><em /></u>

<u><em>How these real-life applications improve or contribute to the value of life?</em></u>

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Engineers use polynomials to graph the curves of roller coasters and bridges.

6 0

3 years ago

Suppose Quadrilaterals A and B are both squares. Are A and B necessarily scaled

nevsk [136]

Answer:

Yes

Step-by-step explanation:

A rectangle can be scaled into a square + rhombus. The difficult part is a trapezoid. If you can scale the sides, then the answer will remain yes because you would just make the top side longer both ways to straighten it and shorten the side lines.

8 0

2 years ago