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Leno4ka [110]
3 years ago
15

At which root does the graph of f(x) = (x+4)6(x + 7)5 cross the x axis?

Mathematics
2 answers:
Licemer1 [7]3 years ago
5 0

Answer:

x = -7

Step-by-step explanation:

Our function is f(x) =(x+4)^6(x+7)^5. Notice that our possible roots are when x + 4 = 0 and when x + 7 = 0. So, our roots are -4 and -7.

However, the power above x + 4 is even, meaning the graph will simply <em>touch</em> the x-axis at x = -4, but not pass through. The power above x + 7, though, is odd, which means the graph will <em>cross</em> the x-axis.

Thus, the answer is x = -7.

devlian [24]3 years ago
3 0

Answer:

x = -7

Step-by-step explanation:

f(x) = (x+4)⁶(x + 7)⁵

The roots are when f(x) = 0

(x+4)⁶ = 0

x = -4 (multiplicity 6)

(x+7)⁵ = 0

x = -7 (multiplicity 5)

The graph is tangential to the x-axis on roots with even multiplicity, crosses tge x-axis at roots with odd multiplicity

This graph cuts/crosses the x-axis at x = -7

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How many solutions are there to this equation 3x(x-4)+5-x=2x-7
stich3 [128]

Answer:

  2 solutions

Step-by-step explanation:

I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...

  • x = 1
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To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:

  3x(x -4) +5 -x -(2x -7) = 0

  3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses

  3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms

  3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor

The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.

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<em>Alternate method</em>

Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...

  d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c

  d = (-15)^2 -4(3)(12) = 225 -144 = 81

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4 0
3 years ago
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3 years ago
Romb ma obwód równy 32 cm. Jakie jest pole tego rombu, jeżeli jego wysokość ma 3 cm?
Goshia [24]

Answer:

24 cm²

Step-by-step explanation:

Z zadanego powyżej pytania uzyskano następujące dane:

Obwód (obwód) = 32 cm

Wysokość (h) = 3 cm

Obszar rombu (A) =?

Następnie określimy długość boku rombu. Można to uzyskać w następujący sposób:

Obwód, czyli obwód (P) = 32 cm

Strona (y) =?

P = 4 s

32 = 4 s

Podziel obie strony przez 4

s = 32/4

s = 8 cm

Stąd długość boku rombu wynosi 8 cm

Na koniec określimy obszar rombu w następujący sposób:

Długość boków = 8 cm

Wysokość (h) = 3 cm

Obszar rombu (A) =?

A = sh

A = 8 × 3

A = 24 cm²

Dlatego obszar rombu jest

24 cm².

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