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Sergio039 [100]
3 years ago
13

Solve for x: 12 = x - 5

Mathematics
1 answer:
musickatia [10]3 years ago
3 0

Answer:

x = 17

Step-by-step explanation:

12 + 5 = x - 5 + 5

x = 17

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Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivat
patriot [66]
The given function is f(x) = x⁶(x-1)⁵

The first derivative is
f'(x) = 6x⁵(x-1)⁵ + 5x⁶(x-1)⁴
       = x⁵(x-1)⁴(6x - 6 + 5x)
       = x⁵(x-1)⁴(11x - 6)
The critical values are the zeros of f'(x). They are
x = 0, 6/11, and 1.
The critical values indicate that turning points exist for f(x) at the critical points. However, we do not know the nature of the turning points.

Write the first derivative in the form f'(x) = (x-1)⁴(11x⁶ - 6x⁵).
The second derivative is
f''(x) = 4(x-1)³(11x⁶ - 6x⁵) + (x-1)⁴(66x⁵ - 30x⁴)
        = (x-1)³(44x⁶ - 24x⁵ + 66x⁶ - 30x⁵ - 66x⁵ + 30x⁴)
        = (x-1)³(110x⁶ - 120x⁵ + 30x⁴)
        = 10x⁴(x-1)³(11x² - 12x + 3)
The sign of f''(x) at the critical values tell us the nature of the turning point.

f''(0) = 0, therefore a point of inflection exists at x = 0.
f''(6/11) > 0, therefore a local minumum exists at x = 6/11.
f''(1) = 0, therefore a point of inflection exists at x=1.

The graphs shown below confirm these results.

8 0
3 years ago
PLZZZZZZ HELP I DON'T WANNA GET IT WRONG
prohojiy [21]

Answer:

She will save $5.25

Step-by-step explanation:

21 x 25% = 5.25

3 0
2 years ago
Read 2 more answers
a store is offering a 20% discount on all sales over $50. If you purchase a shirt and a pair of leans for $62.50, what is the am
vodomira [7]

Answer:

you would receive 12.5% of the discount

Step-by-step explanation:

20% off of 62.50 is 50; so you would pay $50

7 0
3 years ago
Match each description to its example.
kvv77 [185]

Answer:

if we have the point (x, y), a reflection over the x-axis give us the point (x, -y)

if we have the point (x, y), a reflection over the y-axis give us the point (-x, y)

if we have the point (x, y), a reflection across both axes give us the point (-x, -y)

1. (2, -3) → (-2, -3) -------  reflection across the y-axis

2. (2, -3) → (-3, 2) -------- not a reflection

3. (2, -3) → (-2, 3) ------ reflection across both axes

4.  (2, -3) → (2, 3)  -----   reflection across the x-axis

6 0
3 years ago
Jan's age is 3 years less than twice Tritt's age. The sum of their ages is 30. Find their ages.
AysviL [449]
J + t = 30
j = 2t - 3

sub eq 2 into eq 1
2t - 3 + t = 30...combine like terms
3t - 3 = 30...add 3 to both sides
3t = 30 + 3
3t = 33...divide both sides by 3
t = 33/3
t = 11 <=== Tritt is 11

j = 2t - 3
j = 2(11) - 3
j = 22 - 3
j = 19 <== Jan is 19
5 0
3 years ago
Read 2 more answers
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