math

posted by .

a) What is the area of the tri-angle determined by the lines y= − 1/ 2x + 5,y =6x and they-axis?

(b) If b > 0 and m < 0, then the line y = mx +b cuts off a triangle from the first quadrant. Express the area of that tri-angle in terms ofm andb.

(c) The lines y = mx +5, y = x and the y-axis form a triangle in the first quadrant. Suppose this triangle has an area of 10 square units. Findm.

  • math -

    a)
    Find where the two slanting lines intersect:
    -x/2 + 5 = 6x
    x = 10/13
    That's the height of a triangle with base on the y-axis, length 5.
    Area = 5 * 10/13 = 50/13

    b)
    the height = b
    the width is where y=0: x = -b/m
    Area = b * -b/m = -b^2/m

    c)
    where do they intersect?
    mx+5 = x
    x = 5/(1-m)
    That's the height of the triangle with base on the y-axis, length 5
    Area = 5/(1-m) * 5 = 25/(1-m)

    25/(1-m) = 10
    25 = 10m - 10
    m = 35/10 = 3.5

  • math -

    a) -x/2 +5 = 6x
    x=10/13
    A= 1/2 (b)(h)
    A= 1/2 (10/13)(5)= 25/13

    b) height=b
    width= x =-b/m
    A= 1/2 (-b/m)(b)= -b^2/2m

    c) x=5/(1-m)
    10=1/2 (5) (5/(1-m))
    m= -1/4

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. maths geometry

    Find and write down a proof that the product of the gradients of two perpendicular lines is -1 Use trigonometry. Let the slope of a line from A to B be m1. Let the slope of a perpendicular line from A to C be m2. The tangent (or slope) …
  2. Math

    This question concerns the straight line that passes through the points (−1, 3) and (2, −6). Choose the three true statements from the following. Options A The gradient of the line is 3. B The gradient of the line is −3. …
  3. Mathamatics

    This question concerns the straight line that passes through the points (−1, 3) and (2, −6). Choose the three true statements from the following. Options A) The gradient of the line is 3. B) The gradient of the line is …
  4. Calculus

    1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
  5. Trigonometry

    Let è be the angle between the x-axis and the line connecting the origin O(0,0) and the point P(−3,−4) , where 180<è<270. Given that sinè+cosè+tanè=−a/b, where a and b are coprime positive integers. What …
  6. Geometry

    I have four questions: 1. The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid. 2. In trapezoid ABCD, line BC is parallel …
  7. algebra

    Two lines, C and D, are represented by the following equations: Line C: y = x + 5 Line D: y = −2x − 1 Which of the following options shows the solution to the system of equations and explains why?
  8. Math; Solve by Graphing

    Which description best describes the solution to the following system of equations?
  9. Math

    Line a intersects line b, forming angles of 135 degrees and 45 degrees. A third line,line c, is perpendicular to line a and forms triangle ABC. What is the measure of the angle between lines b and c?
  10. brief calc

    Calculate the total area of the region described. Do not count area beneath the x-axis as negative.Bounded by the line y = 6x, the x-axis, and the lines x = 4 and x = 5

More Similar Questions