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2 years ago

Determine the values of n and m so that the following system have infinite number of solutions

Mathematics

1 answer:

cupoosta [38]2 years ago

6 0

Answer:

n = 3

m = -1/2

Step-by-step explanation:

Multiply the second equation by 4

4(n - 2)x + y = 4(n + m) Y is now correct.

4(n - 2) = 4 Remove the brackets

4n - 8 = 4 Add 8 to both sides

4n = 8 + 4 Combine

4n = 12 Divide by 4

n = 3 x is now correct

4(n - 2) = 4

4(3 -2) = 4

4 = 4

Now you have to worry about m

4(n + m) = 10

n = 3

4(3 + m) = 10 Divide by 4

m + 3 = 10/4

m + 3 = 2.5 Subtract 3 from both sides.

m = 2.5 - 3

m = - 1/2

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2 years ago

Please help me find the total area of the composite figure below (geometry)

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Answer:

lw + $\frac{1}{2}$ × π × $(\frac{l}{2} )^{2}$ ⇒ Answer D is correct

Step-by-step explanation:

First, let us find the area of the semi-circle.

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2 years ago

Need to know the area of the composite figure.

Deffense [45]

Answer:

51 m^2

Step-by-step explanation:

The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.

The applicable formulas are ...

area of a triangle:

A = (1/2)bh

area of a rectangle:

A = bh

area of a trapezoid:

A = (1/2)(b1 +b2)h

___

We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...

A = (1/2)(16 m + 10 m)(5 m) = 65 m^2

The area of the white internal rectangle is ...

A = (2 m)(7 m) = 14 m^2

So, the shaded area is the difference:

65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure

_____

Alternate approach

Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...

(1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2

= 51 m^2

7 0

3 years ago