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3 years ago

What property is used to find a product

1 answer:

3 0

The distributive property tells us how to solve equations in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division.
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Plz help me with this

Aleks04 [339]

Answer: FALSE

Step-by-step explanation:

x⁵ + 0x⁴ - 4x³ + 2x² - 4x + 1

If x - 2 is a factor, then x =2 should result in a remainder of 0 when using synthetic division.

2 | 1 0 -4 2 -4 1

| ↓ 2 4 0 4 0

1 2 0 2 0 1 ← Remainder ≠ 0 so x - 2 is NOT a factor

3 0

3 years ago

Use the numbers 6 2 9 5 2 3 to make 36.

VashaNatasha [74]

Answer:

6+2+9+5+2+3+6+3 = 36

Step-by-step explanation:

If you like my answer than please mark me brainliest

5 0

3 years ago

A researcher wants to estimate the mean commute time of residents in Westchester County. The researcher samples 40 commuters and

Ksenya-84 [330]

Answer:

21.759

Step-by-step explanation:

Given that :

Mean (m) = 25

Standard deviation (s) = 12.5

Sample size (n) = 40

α = 90%

The confidence interval is obtained using the relation:

Mean ± Zcritical * s/sqrt(n)

Zcritical at 90% confidence interval = 1.64

25 ± 1.64 * (12.5/sqrt(40))

Lower boundary : 25 - 1.64(1.9764235) = 21.75866546

Upper boundary : 25 + 1.64(1.9764235) = 28.24133454

(21.759, 28.241)

Hence, lower bound of confidence interval is : 21.759

4 0

3 years ago

The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

3 0

3 years ago

Find the slope of the line. -4,1 1,-2

const2013 [10]

Answer: finding slope (-4, 1), (1,-2) : m= -3/5

6 0

3 years ago