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3 years ago

Which statement is NOT true about Rational Numbers? *

Mathematics

1 answer:

serg [7]3 years ago

3 0

Answer:

Integers, Whole Numbers, and Natural Numbers are Rational Numbers

Step-by-step explanation:

Hope it helps :3

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Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches

Mamont248 [21]

Answer:

6 in

Step-by-step explanation:

Let x = the side length of the original square.

They removed 3 in from each side of the original square, so the side lengths of the remaining square are x - 3 in.

The area of the smaller square is (x - 3)².

The area of the original square is x²

I assume the area of the smaller square is ¼ that of the original square. Then

1. Solve for x

$\begin{array}{rcl}\frac{1}{4}x^{2} & = & (x - 3)^{2}\\x^{2} & = & 4(x - 3)^{2}\\& = & 4(x^{2} - 6x + 9)\\x^{2}& = & 4x^{2} - 24x + 36\\3x^{2} - 24x + 36 & = & 0\\x^{2} - 8x + 12 & = & 0\\(x - 2)(x - 6) & = & 0\\x - 2 = 0& \qquad &x - 6 = 0\\x = 2& \qquad &x = 6\\\end{array}$

2. Calculate the side length of the smaller square

(a) x = 2

Side length = x - 3 = 2 - 3 = -1 in.

IMPOSSIBLE. You can't have a negative side length.

(b) x = 6

Side length of smaller square = 6 - 3 = 3 in.

Side length of original square = x = 6 in

Check:

$\begin{array}{rcl}\frac{1}{4}(6)^{2} & = & (6 - 3)^{2}\\\frac{1}{4}\times 36 & = & 3^{2}\\9 & = & 9\\\end{array}$

OK.

3 0

3 years ago

Which of the following equations is the result of completing the square on x^2 - 6x - 9 = 0?

lina2011 [118]

X² - 6x - 9 = 0
x² - 3x - 3x - 9 = 0
x (x-3) -3(x + 3) = 0
(x - 3)² = 0

In short, Your Answer would be Option A

Hope this helps!

6 0

3 years ago

Read 2 more answers

Graph f(x)=log 1/2 (x+1)

iVinArrow [24]

Please keep in mind that f(x)=log 1/2 (x+1) can also be written as:

f(x)=log ((x+1)/2)

6 0

4 years ago

Consider the following vector function. R(t) = 9 2 t, e9t, e−9t (a) find the unit tangent and unit normal vectors t(t) and n(t)

garik1379 [7]

The unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.

<h3>What is vector?</h3>

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

We have vectored function:

$\rm R(t) = (9\sqrt{2t}, e^{9t}, e^{-9t})$

Find its derivative:

$\rm R'(t) = (9\sqrt{2}, 9e^{9t}, -9e^{-9t})$

Now its magnitude:

$\rm |R'(t) |= \sqrt{(9\sqrt{2})^2+ (9e^{9t})^2+ (-9e^{-9t})^2}$

After simplifying:

$\rm R'(t) = 9 \dfrac{e^{18t}+1}{e^{9t}}$

Now the unit tangent is:

$\rm T(u) = \dfrac{R'(t)}{|R'(t)|}$

After dividing and simplifying, we get:

$\rm T(u) = \dfrac{1}{e^{18t}+1} (\sqrt{2}e^{9t}, e^{18t}, -1)$

Now, finding the derivative of T(u), we get:

$\rm T'(u) = \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t}), 18e^{18t}, 18e^{18t})$

Now finding its magnitude:

$\rm |T'(u) |= \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t})^2+ (18e^{18t})^2+( 18e^{18t})^2)$

After simplifying, we get:

$\rm |T'(u)|= \dfrac{9\sqrt{2}e^{9t}}{e^{18t}+1}$

Now for the normal vector:

Divide T'(u) and |T'(u)|

We get:

$\rm N(t) = \dfrac{1}{e^{18t}+1} ( 1-e^{18t}, \sqrt{2}e^{9t}, \sqrt{2}e^{9t})$

Thus, the unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.

Learn more about the vector here:

brainly.com/question/8607618

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3 0

2 years ago

What is two times three

Lapatulllka [165]

Answer:

Step-by-step explanation:

Because you are adding 2, 3 times.

4 0

4 years ago

Read 2 more answers