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Rudiy27
3 years ago
13

∠DGC and ∠CGB are □ angles. Adjacent Complementary Supplementary Vertical

Mathematics
1 answer:
Usimov [2.4K]3 years ago
4 0

Answer:

angle DGC and angle CGB are adjacent angles

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Which statement best describes the graphs of the lines
adoni [48]

Answer:

A

Step-by-step explanation:

Since they have the same slope and have different y-intercept they're parallel

3 0
3 years ago
Integral of 17/(x^3-125)
daser333 [38]

Answer:

17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

Step-by-step explanation:

∫ 17 / (x³ − 125) dx

= 17 ∫ 1 / (x³ − 125) dx

= 17 ∫ 1 / ((x − 5) (x² + 5x + 25)) dx

Use partial fraction decomposition:

= 17 ∫ [ A / (x − 5) + (Bx + C) / (x² + 5x + 25) ] dx

Use common denominator to find the missing coefficients.

A (x² + 5x + 25) + (Bx + C) (x − 5) = 1

Ax² + 5Ax + 25A + Bx² − 5Bx + Cx − 5C = 1

(A + B) x² + (5A − 5B + C) x + 25A − 5C = 1

Match the coefficients and solve the system of equations.

A + B = 0

5A − 5B + C = 0

25A − 5C = 1

A = 1/75

B = -1/75

C = -2/15

So the integral is:

= 17 ∫ [ 1/75 / (x − 5) + (-1/75 x − 2/15) / (x² + 5x + 25) ] dx

Simplify:

= 17/75 ∫ [ 1 / (x − 5) − (x + 10) / (x² + 5x + 25) ] dx

Factor ½ from the numerator of the second fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 20) / (x² + 5x + 25) ] dx

Split the fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − ½ (15) / (x² + 5x + 25) ] dx

Multiply the last fraction by 4/4:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 30 / (4x² + 20x + 100) ] dx

Complete the square:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 15 / ((2x + 5)² + 75) ] dx

Split the integral:

= 17/75 ∫ 1 / (x − 5) dx − 17/150 ∫ (2x + 5) / (x² + 5x + 25) dx − 17/5 ∫ 1 / ((2x + 5)² + 75) dx

The first integral is:

∫ 1 / (x − 5) dx = ln│x − 5│

The second integral is:

∫ (2x + 5) / (x² + 5x + 25) dx = ln(x² + 5x + 25)

The third integral is:

∫ 1 / ((2x + 5)² + 75) dx = 1/√75 tan⁻¹((2x + 5) / √75)

Plug in:

= 17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

4 0
3 years ago
What is 257,650 rounded to nearest hundred
Elza [17]
257,650 rounded to the nearest hundred is 257,700 because it is right at the border (50) we have to round up.
7 0
3 years ago
Read 2 more answers
Kendall is making greeting cards, which she will sell by the box at an arts fair. She paid $40
natta225 [31]

Answer:

9

Step-by-step explanation:

40 dollars due up front

10 dollars made per sale

5 dollars lost per creation

Realistically speaking she is only making a $5 profit per box she sells;

<em>$5 used up for material cost, $10 made from sales </em><em>-5+10= 5</em>

To pay the $40 dollar for the booth she would need to make 9 sales with her current profit

<em>40/5 = 9</em>

5 0
3 years ago
A triangle has sides xcm, (x + 4) cm and 11cm, where x is a whole number of cm. if the perimeter of the triangle is less than 32
NARA [144]

9514 1404 393

Answer:

  {4, 5, 6, 7, 8}

Step-by-step explanation:

The inequality related to the perimeter is ...

  x +(x +4) +11 < 32

  2x < 17 . . . . . . . . . . . . subtract 15

  x < 8.5

The inequality related to the triangle inequality is ...

  (x) +(x +4) > 11

  2x > 7

  x > 3.5

Then possible whole-number values of x are ...

  {4, 5, 6, 7, 8}

6 0
3 years ago
Read 2 more answers
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