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2 years ago

A driveway is in the shape of a rectangle 20 feet wide by 25 feet long.

1 answer:

7 0

A= 20x25 so the area is 500
To find the perimeter you have to add both the width and length x2 so it’s 20+25 =45
45x2=90

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Perform the indicated operation. (2a2 - 8)(4a4 + 16a2 + 64)

padilas [110]

We have the following expression:

$(2a^2 - 8)(4a^4 + 16a^2 + 64)$

So let's solve this problem step by step.

1st. Applying distributive property:

$(2a^2)(4a^4+16a^2+64)-8(4a^4+16a^2+64)$

2st. Applying distributive property again:

$8a^6+32a^4+128a^2-32a^4-128a^2-512$

3st. Grouping terms with the same base:

$8a^6+(32a^4-32a^4)+(128a^2-128a^2)-512$

4st. Solving, the result is:

$8a^6-512$

7 0

3 years ago

Which transformations can be used to carry ABCD onto itself? The point of rotation is (3, 2). Check all that apply.

gavmur [86]

Answer:

The correct answer for this question is Reflection across the line x=3 and Reflection across the line y=2.

Step-by-step explanation:

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Cfrac%7Bx%5E%7B3-8%7D%20%7D%7Bx%5E%7B2%7D%20-6x%2B8%7D" id="TexFormula1" ti

Firlakuza [10]

Answer:

Domain: All the real values except x = 2 and x = 4: R - {2, 4}
Holes: x = 2
VA, vertical asymptores: x = 4
HA: horizontal asymptotes: there are not horizontal asymptotes
OA: oblique asymptotes: x + 6 [note that OH does not stand for any known feature, and so it is understood that it was intended to write OA]
Roots: x = 2
Y-intercept: -1

Step-by-step explanation:

1. Given:

$f(x)=\frac{x^3-8}{x^2-6x+8}$

Note that the number 8 in the numerator is not part of the power.

Type of function: rational function

2. Domain: is the set of x-values for which the function is defined.

The given function is defined for all x except those for which the denominator equals 0.

Denominator: x² -6x + 8 = 0

Solve for x:

Factor. (x - 4 )(x - 2) = 0

Zero product property: (x - 4) = 0 or (x - 2) = 0

x - 4 = 0 ⇒ x = 4

x - 2 = 0 ⇒ x = 2

Domain:

All the real values except x = 2 and x = 4: x ∈ R / x ≠ 2 and x ≠ 4.

3. Holes:

The holes on the graph of a rational function are at those x-values for which both the numerator and denominator are zero.

Find the values for which the numerator is zero:

Numerator: x³ - 8 = 0

Factor using difference of cubes property:

a³ - b³ = (a - b)(a² + ab + b²)

x³ - 8 = (x - 2)(x² + 2x + 4) = 0

Zero product property: (x - 2)(x² + 2x + 4) = 0

x - 2 = 0 ⇒ x = 2

x² + 2x + 4 = 0 (this has not real solution)

The values for which the denominator is zero were determined above: x = 2 and x = 4.

Conclusion: for x = 2 both numerator and denominator equal 0, so this is a hole.

4. VA: Vertical asymptotes.

The vertical asymptotes on the graph of a rational function are the vertical lines for which only the denominator (and not the numerator) equals zero.

In the previous part it was determined that happens when x = 4.

5. HA: Horizontal asymptotes.

In rational functions, if the numerator is a higher degree polynomial than the denominator, there is no horizontal asymptote.

6. OA: oblique asymptotes

Find the quotient and the remainder.

x + 6

_______________

x² - 6x + 8 ) x³ + 0x² + 0x - 8

- x³ + 6x² - 8x

___________

6 x² - 8x - 8

- 6x² + 36x - 48

_____________

28x - 56

Result: (x + 6) + (28x - 56) / (x² - 6x + 8)

Find limit x → ∞

$\lim_{x \to \infty}(x + 6) + \frac{28x-56}{x^2-6x+8}=x+6$

7. Roots:

Roots are the values for which f(x) = 0.

That happens when the numerator equals 0, and the denominator is not 0.

As determined earlier: x³ - 8 = 0 ⇒ x = 2.

8. Y-Intercept

The y-intercepts of any function are the y-values when x = 0

Substitute x = 0 into the function:

$f(x)=\frac{x^3-8}{x^2-6x+8}=\frac{0^3-8}{0^2-6(0)+8}}=\frac{-8}{8} =-1$

3 0

3 years ago

Sierra borrows $310 from her brother to buy a lawnmower. She will repay $85 to

Ivanshal [37]

310-85=225
225/25=9
Therefore it will take her 9 weeks

8 0

2 years ago

Video games sold: x

Nata [24]

Answer:

The correct answer is D. 53x - 12

Step-by-step explanation:

Let's find P(x), this way:

Profits = Revenue - Cost

Profit function = Revenue function - Cost function

P (x) = R (x) - C (x)

Replacing with the real values we have:

P (x) = 60x - (12 + 7x)

P (x) = 60x - 12 - 7x

P (x) = 53x - 12

The correct answer is D. 53x - 12

6 0

2 years ago