How do you graph: y≤−4x+40 and y≤10

Mathematics

1 answer:

Arturiano [62]3 years ago

7 0

Answer:

See attached picture.

Step-by-step explanation:

To graph linear inequalities, use the y=mx + b form to graph using the slope and y-intercept.

y ≤ -4x + 40 has slope -4 and y-intercept (0,40).

Start at (0,40) and mark it. Then move down 4 units and to the right 1. Mark this point at (1,36). Connect the points with a solid line since the inequality has equal to. Substitute a point like (0,0) to test where the solution set is.

0 ≤ -4(0) + 40

0 ≤ 0 + 40

0 ≤ 40

This is true so shade to the left of the line.

To graph y ≤ 10 mark a point on the y-axis at (0,10). Draw a horizontal solid line through the point. Then shade below the line.

You might be interested in

Bearings Problem Solving Question:

Lynna [10]

9514 1404 393

Answer:

a) 123.4°

b) 3.3 km

Step-by-step explanation:

In (N, E) coordinates, Boat 1 is located relative to the lighthouse at ...

2(cos(60°), sin(60°)) = (1.0, 1.732) . . . . . km

Boat 2 is located at ...

3(cost(340°), sin(340°)) = (2.819, -1.026) . . . . . km

So, relative to Boat 2, Boat 1 is located at ...

(1, 1.732) -(2.819, -1.026) = (-1.819, 2.758) . . . . . km

This is at a bearing of ...

arctan(2.758/-1.819) = 123.4°

and a distance of ...

√(1.819² +2.758²) ≈ 3.304 . . . . . km

a) Boat 2 would need to travel on a bearing of 123.4°.

b) Boat 2 would need to travel 3.3 km.

_____

<em>Additional comment</em>

We use (North, East) coordinates so we don't have to do the mental gyrations necessary to translate to and from (E, N) coordinates. The latter would correctly orient a map relative to the X-Y Cartesian plane. The former are equivalent to flipping the map over and looking at it from the back side. This is a "rigid transformation", so angles and distances remain unchanged.