How do you find the area above the x-axis, to the left of #x=8#, to the right of #x=5# and below #y=2x+4#?

Answer 1

You can first plot your area:

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the area above the x-axis, to the left of ( x = 8 ), to the right of ( x = 5 ), and below ( y = 2x + 4 ), you first need to find the points of intersection between the given lines and then calculate the area of the region bounded by these lines.

  1. Find the points of intersection:

    • Set ( y = 2x + 4 ) equal to ( y = 0 ) to find where it intersects the x-axis: ( 0 = 2x + 4 ), which gives ( x = -2 ).
    • At ( x = 5 ), ( y = 2(5) + 4 = 14 ).
    • At ( x = 8 ), ( y = 2(8) + 4 = 20 ).
  2. Calculate the area of the region:

    • The area can be divided into two regions: a triangle and a trapezoid.
    • Triangle: base = ( 8 - 5 = 3 ), height = ( 14 - 0 = 14 ).
    • Trapezoid: bases = ( 20 ) and ( 14 ), height = ( 8 - (-2) = 10 ).
  3. Calculate the area of each shape:

    • Area of triangle = ( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 14 = 21 ).
    • Area of trapezoid = ( \frac{1}{2} \times (\text{sum of bases}) \times \text{height} = \frac{1}{2} \times (20 + 14) \times 10 = 170 ).
  4. Add the areas together:

    • Total area = ( 21 + 170 = 191 ).

Thus, the area above the x-axis, to the left of ( x = 8 ), to the right of ( x = 5 ), and below ( y = 2x + 4 ) is ( 191 ) square units.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7