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Liula [17]
3 years ago
14

Multiply (5x-1)(6x^2+3x+7) SHOW WORK

Mathematics
2 answers:
kykrilka [37]3 years ago
8 0

Answer:

30x³ + 9x² + 32x - 7

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

5x(6x² + 3x + 7) - 1 (6x² + 3x + 7) ← distribute both sets of parenthesis

= 30x³ + 15x² + 35x - 6x² - 3x - 7 ← collect like terms

= 30x³ + 9x² + 32x - 7

notsponge [240]3 years ago
4 0

sorry for using printed paper, I tried my best to avoid the lines

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2 years ago
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Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84
guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

x²(1 + k²) + x(20k - 10) = 0

using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

20k - 10 = 0 and 20k - 10 = 0

add 10 on both sides

20k = 10 and 20k = 10

divide 20 on both sides

k = 10/20 and k = 10/20 which are both the same

10/20 is simplified to 1/2

k = 1/2

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2 years ago
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9514 1404 393

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