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2 years ago

Identify the correct slope and y intercept of the equation 2x + 4y = 12.

1 answer:

7 0

The standard form of a line is an easy way to solve for the properties of a line, such as slope and the intercepts. Take a line with the equation in standard form,

Ax + By = C

The slope here is given by y = -A/B.
The x-intercept here is given by (C/A, 0).
The y-intercept here is given by (0, C/B).

For this problem, the equation is 2x + 4y = 12. Thus,
slope = -2/4 = -1/2
y-intercept = (0, 12/4) = (0, 3)

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2 years ago

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Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, and C = {1, 2, 4, 5, 8, 9}. List the element

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$C\ n\ C^c = \{ \}$

$(A\ n\ C)^c = \{2,3,4,6,7,8,10\}$

$A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}$

Step-by-step explanation:

Required

Determine

$C\ n\ C^c$

$(A\ n\ C)^c$

$A\ u\ (B\ n\ C)$

Solving $C\ n\ C^c$

$C^c$ implies that elements in U but not in C

Since

$C = \{1, 2, 4, 5, 8, 9\}$

$C^c = \{3, 6, 7, 10\}$

$C\ n\ C^c = \{1, 2, 4, 5, 8, 9\}\ n\ \{3, 6, 7, 10\}$

$C\ n\ C^c = \{ \}$

<em>Because there's no intersection between both</em>

Solving $(A\ n\ C)^c$

First, we need to determine A n C

$A\ n\ C = \{1, 3, 5, 7, 9\}\ n\ \{1, 2, 4, 5, 8, 9\}$

$A\ n\ C = \{1, 5, 9\}$

$(A\ n\ C)^c = (\{1, 5, 9\})^c$

$(A\ n\ C)^c = \{2,3,4,6,7,8,10\}$

Solving $A\ u\ (B\ n\ C)$

First, we need to determine B n C

$B\ n\ C = \{2, 4, 6, 8, 10\}\ n\ \{1, 2, 4, 5, 8, 9\}$

$B\ n\ C = \{2, 4, 8\}$

So:

$A\ u\ (B\ n\ C) = \{1, 3, 5, 7, 9\}\ u\ \{2,4,8\}$

$A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}$

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3 years ago

Martin bought a new carpet to cover a room. The carpet is in the shape of a square and it covers an area of 200 ft2. How long is

svlad2 [7]

Answer:

14.14 ft long

Step-by-step explanation:

Martin bought a new carpet to cover a room. The carpet is in the shape of a square and it covers an area of 200 ft². How long is the side length of the carpet?

The Area the carpet covers is a square.

Hence, the Area of a square = (Side length)²

From the question, we are given the Area of the square = 200 ft²

Hence:

200 ft² = (Side length)²

We square root both sides.

√200 ft² = √(Side length)²

Side length = 14.142135624 ft

Approximately = 14.14 ft

The side length of the carpet is 14.14 ft long

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