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Arada [10]
3 years ago
10

What is the are of the following figure if AC = 12, AD = 16.

Mathematics
1 answer:
Degger [83]3 years ago
7 0

Answer:

116

Step-by-step explanation:

∆ABC

A = ½bh = ½ × 12 × 6 = 36

∆ACD

A = ½bh = ½ × 16 × 7 = 56

∆ADE

A = ½bh = ½ × 16 × 3 = 24

ABCDE  

A = ∆ABC + ∆ACD +∆ADE = 36 + 56 + 24 = 116

The area of the figure is 116 square units.

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I don’t understand need it by tomorrow!
snow_tiger [21]

Explanation:

It can help to draw your own figure with the right angles better represented. You will notice that right triangles PQR and PRS share side RS. PQ is the hypotenuse of one of them; RS is the hypotenuse of the other.

We can write two equations that make use of the Pythagorean theorem:

  PQ² = PR² +RQ²

  RS² = QS² +RQ²

Then we can swap sides of the first equation and subtract the second equation. This gives ...

  (PR² +RQ²) -(RS²) = (PQ²) -(QS² +RQ²)

Adding RQ², we can write this as ...

  PR² -RS² +2RQ² = PQ² -QS²

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The given relationship PR > RS means that PR² -RS² will be positive, so the left side of this equation must be positive.

Since PQ² - QS² is a positive number, PQ > QS.

6 0
4 years ago
Read 2 more answers
Please help with my algebra homework and explain if you can : v= pi/3 rsquared h
Tanzania [10]

To isolate the variable means to have it by itself on one side of the equation, where the variable equals an expression.

To isolate h, we will need to remove the variables and other terms "connected" to the h variable:

V = \dfrac{\pi}{3}r^2h

\dfrac{V}{r^2} = \dfrac{\pi}{3}h

\boxed{\dfrac{3V}{r^2\pi} = h}

By dividing terms "connected" to our h variable, we have isolated it one side of the equation.

6 0
3 years ago
Write the equation of the line parallel to the given line and passing through the given point. y= 1/2 x+2 through (0,4)
marshall27 [118]

Parallel lines have the same slope, so the slope of the new line is 1/2.

The line passes through (0,4), and this gives the y-intercept, which would equal 4.

The equation now would be: y = 1/2x + 4

3 0
3 years ago
A rancher has 400 feet of fencing to put around a rectangular field and then subdivide the field into 22 identical smaller recta
Fudgin [204]

Answer:

Overall rectangle: 100 ft × 8 16/23 ft ≈ 100 ft × 8.696 ft

Individual pen: 8 16/23 ft × 4 6/11 ft ≈ 8.696 ft × 4.545 ft

Step-by-step explanation:

Half the fence will be used in each of the orthogonal directions to make the pen. That is, the long side of the overall rectangle will be (400 ft/2)/2 = 100 ft. The short side of the overall rectangle will be (400 ft/2)/23 = 8 16/23 ft. (There are 21 partitions between the 22 pens, and 2 end fences, for a total of 23 fence segments of the short length.)

The long (100 ft) side of the overall rectangle is divided into 22 parts by the internal partitions, so each pen will have a short dimension of 100 ft/22 = 4 6/11 ft.

_____

We know half the fence will be used in each direction because we know the total area is a quadratic function of the side length. If the long side of the overall pen is x, then the short side is (400 ft -2x)/23, and the overall area is ...

... A = x(400 ft -2x)/23

The vertex of this quadratic function is halfway between the zeros, at x = 100 ft. That is, the two long sides of the pen total 200 ft, or half the overall length of fence.

3 0
3 years ago
The sum of two numbers is 65. One number is 4 times as large as the other. What are the numbers?
Cloud [144]

Answer:

Large number =52

small number =13

Step-by-step explanation:

4x + x =65

5x=65

x=13

4x=52

7 0
3 years ago
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