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3 years ago

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Mathematics

1 answer:

ohaa [14]3 years ago

6 0

Answer:

Step-by-step explanation:

the sample space is the set that contain all possible outcomes

B-blue, R-red, G-green

sample space is {B,B,B,R,R,G,G,G,G}

so there are 9 possible outcomes

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What is the value of 6 2/3 + 1 7/12?

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Answer:

Im not sure but i think the answer is 7 9/15

Step-by-step explanation:

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3 years ago

...................................................................

Genrish500 [490]

Answer:

12 cm

Step-by-step explanation:

The Pythagorean Theorem is as follows:

$a^{2} +b^{2} =c^{2}$

A and B represent the side lengths (legs) and C represents the hypotenuse.

The length of one leg equals 5cm. (This can be represented by either a or b)

The hypotenuse equals 13 cm.

Plug these into the equation from above:

$a^{2} + (5^{2}) = (13^{2})$

Solve for the other leg:

$a^{2} + 25 = 169$ Square what's in the parentheses from above

$a^{2} = 144\\$ Subtract 25 from 169

$\sqrt{a^{2} } = \sqrt{144}$ Square root both sides

a = 12 cm

Thus, the length of the other leg is 12 cm.

Let's check our answer:

$12^{2} +5^{2} =13^{2}$ Square everything

144 + 25 = 169 Add

169 = 169

Because both sides are equal it means that 12 cm is the correct answer.

Hope this helps!!

3 0

2 years ago

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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vekshin1

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