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2 years ago

What is the factored form of x^6-9?

Mathematics

2 answers:

taurus [48]2 years ago

7 0

It is the last one: (x^3 + 3(x^3 -3)

avanturin [10]2 years ago

6 0

Answer: (x³ + 3)(x³ - 3)

Explanation: A variable taken to any even power is a perfect square. Its factors will have exponents equal to one-half the original power.

In this case, x⁶ would therefore be a perfect square.

Since 9 is also a perfect square,

what we have here is the difference of two squares.

That can be factored as the product of two binomials,

one with a plus and one with a minus.

So we have ( + )( - ).

Now ask yourself "what are the factors of x⁶ that are the same?"

Remember the rule is that those factors will use

one-half the exponent on the original.

So the factors of x⁶ that are the same are x³ and x³.

The factors of 9 that are the same are 3 and 3.

So our answer is (x³ + 3)(x³ - 3) and that's all there is to it.

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#10 i The table shows the admission costs (in dollars) and the average number of daily visitors at an amusement park each the pa

lions [1.4K]

The line of best fit is a straight line that can be used to predict the

average daily attendance for a given admission cost.

Correct responses:

The equation of best fit is; $\underline{ \hat Y = 1,042 - 4.9 \cdot X_i}$

The correlation coefficient is; r ≈<u> -0.969</u>

<h3>Methods by which the line of best fit is found</h3>

The given data is presented in the following tabular format;

$\begin{tabular}{|c|c|c|c|c|c|c|c|c|}Cost, (dollars), x&20&21&22&24&25&27&28&30\\Daily attendance, y&940&935&940&925&920&905&910&890\end{array}\right]$

The equation of the line of best fit is given by the regression line

equation as follows;

$\hat Y = \mathbf{b_0 + b_1 \cdot X_i}$

Where;

$\hat Y$ = Predicted value of the<em> i</em>th observation

b₀ = Estimated regression equation intercept

b₁ = The estimate of the slope regression equation

$X_i$ = The <em>i</em>th observed value

$b_1 = \mathbf{\dfrac{\sum (X - \overline X) \cdot (Y - \overline Y) }{\sum \left(X - \overline X \right)^2}}$

$\overline X$ = 24.625

$\overline Y$ = 960.625

$\mathbf{\sum(X - \overline X) \cdot (Y - \overline Y)} = -433.125$

$\mathbf{\sum(X - \overline X)^2} = 87.875$

Therefore;

$b_1 = \mathbf{\dfrac{-433.125}{87.875}} \approx -4.9289$

Therefore;

The slope given to the nearest tenth is b₁ ≈ -4.9

$b_0 = \mathbf{\dfrac{\left(\sum Y \right) \cdot \left(\sum X^2 \right) - \left(\sum X \right) \cdot \left(\sum X \cdot Y\right)} {n \cdot \left(\sum X^2\right) - \left(\sum X \right)^2}}$

By using MS Excel, we have;

n = 8

∑X = 197

∑Y = 7365

∑X² = 4939

∑Y² = 6782675

∑X·Y = 180930

(∑X)² = 38809

Therefore;

$b_0 = \dfrac{7365 \times 4939-197 \times 180930}{8 \times 4939 - 38809} \approx \mathbf{1041.9986}$

The y-intercept given to the nearest tenth is b₀ ≈ 1,042

The equation of the line of best fit is therefore;

$\underline{\hat Y = 1042 - 4.9 \cdot X_i}$

The correlation coefficient is given by the formula;

$\displaystyle r = \mathbf{\dfrac{\sum \left(X_i - \overline X) \cdot \left(Y - \overline Y \right)}{ \sqrt{\sum \left(X_i - \overline X \right)^2 \cdot \sum \left(Y_i - \overline Y \right)^2} }}$

Where;

$\sqrt{\sum \left(X - \overline X \right)^2 \times \sum \left(Y - \overline Y \right)^2} = \mathbf{446.8121}$

$\sum \left(X_i - \overline X \right) \times \left(Y - \overline Y\right) = \mathbf{-433.125}$

Which gives;

$r = \dfrac{-433.125}{446.8121} \approx \mathbf{-0.969367213}$

The correlation coefficient given to the nearest thousandth is therefore;

<u>Correlation coefficient, r ≈ -0.969</u>

Learn more about regression analysis here:

brainly.com/question/14279500

7 0

2 years ago

Triangle ABC is transformed to obtain triangle A′B′C′:

Lisa [10]

Answer:

Option C is right.

Step-by-step explanation:

Given is a graph with two triangles marked on it.

Triangle ABC is in the I quadrant with vertices (2,2) (2,10) and (8,12)

Triange A'B'C' is in the III quadrant with vertices (-1,-1), (-1,-5) and (-4,-6)

On comparison we find corresponding side of AB is A'B'

Length of AB = 8 and Length of A'B' = 4.

Hence A'B'C' is obtained by dilating ABC by a scale factor of 1/2.

Now since moved to III quadrant from I quadrant we find that there is a rotation of triangle ABC about the origin. The degree of rotation is 180 degrees.

Hence A'B'C' is obtained by dilating ABC by a scale factor of 1/2 and then rotating it about the origin by 180 degrees

8 0

2 years ago

A right rectanular prism has a length of 2 a width of 4 and a height of 5. How many unit cubes can fit in the prism

-Dominant- [34]

Answer:

Step-by-step explanation:

4 x 2 = 8 x 5

l x w x h

Bxh

7 0

1 year ago

Consider the following function.

shtirl [24]

Help ASAP only right answers only no spam don’t answer if you don’t know

3 0

2 years ago

7. Write the slope-intercept form of the equation of the line graphed below.

Stels [109]

Answer:

The answer to your question is $y = \frac{-1}{2} x - 1$

Step-by-step explanation:

Process

1.- Get to points of the line

A (-2, 0)

B (0, -1)

2.- Find the slope of the line

Slope = m = $\frac{y2 - y1}{x2 - x1}$

Substitution

m = $\frac{-1 - 0}{0 + 2} = \frac{-1}{2}$

3.- Find the equation of the line

y - y1 = m(x - x1)

Substitution

y - 0 = -1/2(x + 2)

Simplification

y = -1/2x - 1

3 0

2 years ago