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Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

7 0

Answer:

1. 617.5 cm³

2. 335.6 in³

3. 151.6 m³

4. 3479.1 ft³

Step-by-step explanation:

B1: 19.5 × 9 = 175.5

B2: 6 × 13 = 78

sqrt(B1 ×B2) = 117

h = 5

Volume = ⅓ × 5 × [175.5 + 78 + 117]

617.5

B1: 3.14 × 4.5² = 63.585

B2: 3.14 × 3² = 28.26

sqrt(B1 ×B2) = 42.39

h = 7.5

Volume = ⅓ × 7.5 × [63.585 + 28.26 + 42.39]

335.5875

B1: ½(8+12) × 6 = 60

B2: ½(3+4.5) × 2.25 = 8.4375

sqrt(B1 ×B2) = 22.5

h = 5

Volume = ⅓ × 5 × [60 + 8.4364 + 22.5]

151.5625

B1: 3.14 × 12² = 452.16

B2: 3.14 × 7² = 153.86

sqrt(B1 ×B2) = 263.76

h² = 13² - (12-7)²

h² = 13² - 5²

h² = 144

h = 12

Volume = ⅓ × 12 × [452.16 + 153.86 + 263.76]

3479.12

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Which expression is equivalent to the following complex fraction?

marta [7]

Answer:

$\dfrac{-4x+7}{2(x-2)}$

Step-by-step explanation:

The first step is to combine the parts of the numerator and denominator into one rational expression each. Those will have the same denominator, so their ratio is the ratio of their numerators.

$\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\left(\dfrac{3-4(x-1)}{x-1}\right)}{\left(\dfrac{2(x-1)-2}{x-1}\right)}=\dfrac{3-4(x-1)}{2(x-1)-2}\\\\=\dfrac{3-4x+4}{2x-2-2}=\boxed{\dfrac{-4x+7}{2(x-2)}}$