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3 years ago

What type of number is -1/3

Mathematics

1 answer:

KonstantinChe [14]3 years ago

6 0

Answer:

a rational number

Step-by-step explanation:

Rational number are numbers that can be written as a fraction where both the numerator and denominator are integers. This means that both the top and bottom of the fraction are whole numbers.

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Use Pascal's Triangle to determine the second term of the expansion of (x - 2)^5

goldfiish [28.3K]

Pascal's triangle up to the 5th iteration is

$\begin{array}{cccccc}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\\1&5&10&10&5&1\end{array}$

This tells us

$(x-2)^5=\boxed{1}x^5(-2)^0+\boxed{5}x^4(-2)^1+\boxed{10}x^3(-2)^2+\boxed{10}x^2(-2)^3+\boxed{5}x^1(-2)^4+\boxed{1}x^0(-2)^5$

so the second term in the expansion is

$5x^4(-2)^1=\boxed{-10x^4}$

8 0

3 years ago

A coordinate grid is placed over a college Station map. Tiger Stadium is located at (-3,2)

Olin [163]

Answer:

$4.61\ units$

Step-by-step explanation:

The complete question is

A coordinate grid is placed over a College Station map. Tiger Stadium is located at (-3, 2) and Kyle Field is located at (4, 8). If a shuttle bus stop is at the midpoint between Tiger Field and Kyle Field, which is the closest to the distance in coordinate units from Tiger Field to the shuttle bus stop?

Options

4.61 units

6.52 units

9.22 units

21.25 units

step 1

Find the midpoint between Tiger Field and Kyle Field ( shuttle bus stop)

we know that

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have the points

(-3, 2) and (4, 8)

substitute in the formula

$M=(\frac{-3+4}{2},\frac{2+8}{2})$

$M=(0.5,5)$

step 2

Find the distance from Tiger Field to the shuttle bus stop

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the points

(-3,2) and (0.5,5)

substitute in the formula

$d=\sqrt{(5-2)^{2}+(0.5+3)^{2}}$

$d=\sqrt{(3)^{2}+(3.5)^{2}}$

$d=\sqrt{21.25}\ units$

$d=4.61\ units$

6 0

3 years ago

A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness L and index of refraction n=1.5

boyakko [2]

Additional information to complete the question:

How long does it take for a short pulse of light to travel from one end of the glass to the other?

Express your answer in terms of some or all of the variables f and L. Use the numeric value given for n in the introduction.

T = ___________ s

Answer:

$T = \frac{15}{f}$

Step-by-step explanation:

Given:

Thickness og glass = L

Index of refraction n=1.5

Frequency = f

$Wavelength = \frac{L}{10}$

λ(air) $= \frac{L}{10}$

λ(glass) = λ(air) / n

= $\frac{\frac{L}{10}}{1.5}$

= $\frac{L}{10} * \frac{1}{1.5}$

= $\frac{L}{15}$

V(glass) = fλ(glass)

$= f * \frac{L}{15}$

$T = \frac{L}{V_{glass}} = \frac{15}{f}$

7 0

3 years ago

Simplify the algebraic expression 3x^2 + 8x - 6x^2 + 2x

OverLord2011 [107]

-3x^2 +10x
All you have to do is combine like terms!

8 0

3 years ago

Read 2 more answers

What's a simplified form of x-1+4+7x-3

Dovator [93]

Ok so right now leave the x's alone. Now add/subtract the numbers without variables which would equal to 0 since -1+4 = 3 and 3-3 =0

now 7x+x =8x so 8x is answer

8 0

3 years ago