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2 years ago

Use y = mx + b to determine the equation of a line that passes through the point A(-1, 4) and is

Mathematics

1 answer:

Shalnov [3]2 years ago

4 0

Answer:

Step-by-step explanation:

If we are looking for a line parallel to the given line, we need to find the slope of the given line, since parallel lines have the exact same slope. That means that we need to solve this equation for y, which naturally puts the line into slope-intercept form. Solving for y:

-2y = -4x - 8 and

2y = 4x + 8 so

y = 2x + 4 and the slope, we see here, is 2. Use that slope and the given point of (-1, 4) to write the new equation we need.

In point-slope form, the line will be

y - 4 = 2(x - (-1)) which simplifies a bit to

y - 4 = 2(x + 1). That's point-slope form. Putting it into slope-intercept just requires that we solve this equation for y:

y - 4 = 2x + 2 and

y = 2x + 6. That's slope-intercept form of the same line. The last form is standard, which looks like this:

-2x + y = 6 or, if you don't like to lead with a negative,

2x - y = -6

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Answer:

SSS, SAS, ASA, AAS, HL

Step-by-step explanation:

1. SSS (side side side) says if 3 sides of one triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent.

2. SAS (side angle side) says if 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.

3. ASA (angle side angle) says if 2 angles and the included side of a triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.

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2 years ago

A manager bought 12 pounds of peanuts for $30. He wants to mix $5 per pound cashews with the peanuts to get a batch of mixed nut

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Answer:

18 pounds of cashews are needed.

Step-by-step explanation:

Given;

A manager bought 12 pounds of peanuts for $30.

Price of peanut per pound P = $30/12 = $2.5

Price of cashew per pound C = $5

Price of mixed nut per pound M = $4

Let x represent the proportion of peanut in the mixed nut.

The proportion of cashew will then be y = (1-x), so;

xP + (1-x)C = M

Substituting the values;

x(2.5) + (1-x)5 = 4

2.5x + 5 -5x = 4

2.5x - 5x = 4 -5

-2.5x = -1

x = 1/2.5 = 0.4

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y = 1-x = 1-0.4 = 0.6

For 12 pounds of peanut the corresponding pounds of cashew needed is;

A = 12/x × y

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18 pounds of cashews are needed.

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