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ozzi
1 year ago
11

diagrams are not drawn to scale. do numbers 10 and 12. i only care about the answers & the steps to get the answers. pls don

’t take forever..

Mathematics
1 answer:
Stella [2.4K]1 year ago
3 0

10. from the question; the circle theorem obeyed is "angled formed by semi-circle"

The angle formed in a semicircle is 90 degrees, hence

m\angle XYZ=90^{\circ}

This gives

m\angle YXZ\text{ + m}\angle YZX\text{ = 90}

But

\begin{gathered} m\angle YXZ\text{ = 2x + 8} \\ m\angle YZX\text{ = 5X - 2} \end{gathered}

Substituting values we get

\begin{gathered} 2x\text{ + 8 + 5x - 2 = 90} \\ 2x\text{ + 5x + 8 - 2 = 90} \\ 7x\text{ + 6 = 90} \\ 7x\text{ = 90 -6} \\ 7x\text{ = 84} \\ \text{divide both sides by 7} \\ x\text{ = }\frac{84}{7} \\ x\text{ = 12} \end{gathered}

hence, x =12

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(X^2+ x– 12) (x^2+ 10x + 25)
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Solution:

  • (x² + x – 12)(x² + 10x + 25)
  • => (x⁴ + 10x³ + 25x²) + (x³ + 10x² + 25x) + (-12x² - 120x - 300)
  • => x⁴ + 10x³ + 25x² + x³ + 10x² + 25x - 12x² - 120x - 300
  • => x⁴ + (10x³ + x³) + (25x² + 10x² - 12x²) + (25x - 120x) - 300
  • => x⁴ + (11x³) + (23x²) + (-95x) - 300
  • => x⁴ + 11x³ + 23x² - 95x - 300

The only term that has a x-variable is "-95x".

The coefficient of x is -95.

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2 years ago
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According to a calculator, this is the answer: 0.1923076923. Hope this helped?
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Quanto fa 5+5<br><br> Quanto fa 5+5
Irina-Kira [14]

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Jake can cut and split a cord of firewood in 9 fewer hours than Dwight can. When they work together, it takes them 6 hours. How
Luba_88 [7]

Answer:

18 hours for Dwight, 9 hours for Jake

Step-by-step explanation:

If J is the time it takes for Jake working alone, and D is the time it takes for Dwight working alone, then:

J = D − 9

Working together, Jake's speed plus Dwight's speed equals 1 cord per 6 hours.

1 / J + 1 / D = 1 / 6

Solve the system of equations by substituting for J:

1 / (D − 9) + 1 / D = 1 / 6

Multiply both sides by D − 9.

1 + (D − 9) / D = (D − 9) / 6

Multiply both sides by D:

D + D − 9 = D (D − 9) / 6

Simplify and solve:

2D − 9 = (D² − 9D) / 6

12D − 54 = D² − 9D

0 = D² − 21D + 54

0 = (D − 3) (D − 18)

D = 3 or 18

Since J = D − 9, D must be greater than 9.  So D = 18 and J = 9.

That means it takes Dwight 18 hours working alone, and it takes Jake 9 hours working alone.

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