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3 years ago

PLEASE HELP, GIVING 25 POINTS!!!! Fill in the blank. (5x)^2 = ___ x^2

Mathematics

1 answer:

Dimas [21]3 years ago

3 0

Answer:

The answer is 25

Step-by-step explanation:

(5x)^2=25^2

5x times 5x is 25x^2

25^2 divided by 5x is 5x

The two x's become x^2 and the two 5's just multiply to 25

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The map shows the length (in miles) of shoreline along the Gulf of Mexica for each state that borders the body of water. What is

Jet001 [13]

Answer:

TX: 0.23

LA: 0.24

MS: 0.03

AL: 0.03

FL: 0.47

Step-by-step explanation:

In the figure attached, the map is shown.

Total length of the shoreline: 367 + 397 + 44 + 53 + 770 = 1631 miles

probability of the ship landing in Texas: 367/1631 = 0.23

probability of the ship landing in Louisiana: 397/1631 = 0.24

probability of the ship landing in Mississippi: 44/1631 = 0.03

probability of the ship landing in Alabama: 53/1631 = 0.03

probability of the ship landing in Florida: 770/1631 = 0.47

8 0

4 years ago

Please help me out with this question

Liono4ka [1.6K]

It is not continuous at x=3

6 0

4 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:

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

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4 years ago

Can someone help me with this???

Veseljchak [2.6K]

The awnser would be 210 because 7 times 10 times 3 is 210

8 0

3 years ago

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will

AfilCa [17]

I'm guessing the % of syrup refers to the % of sugar it has, therefore:

50% = 50 / 100 = 0.5

0.5 * x = 0.5

x = 0.5/0.5

x = 1

She will have 1 lbs of syrup

3 0

3 years ago