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Svetllana [295]
3 years ago
6

What is the area of the composite figure below?

Mathematics
1 answer:
musickatia [10]3 years ago
3 0

Answer:

33 sq cm.

Step-by-step explanation:

Let's calculate each shape serperately,

--------

For the square, the area is 25 since

5 × 5 = 25

-------

For the rectangle, the area is 8:

4 × 2 = 8

-----

Add these together to get 33 sq cm

Have a good day :)

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The parabola with equation $y=ax^2+bx+c$ is graphed below:
Mashutka [201]

Answer:

m-n=2

Step-by-step explanation:

Instead of using the standard form, we can use the vertex form of a quadratic equation:

f(x)=a(x-h)^2+k

Where a is the leading coefficient, and (h, k) is our vertex.

Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:

f(x)=a(x-2)^2-4

Now, we need to determine a.

We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:

12=a((4)-2)^2-4

Solve for a. Subtract within the parentheses:

12=a(2)^2-4

Add 4 to both sides:

16=a(2)^2

Square:

16=4a

Solve:

a=4

Thererfore, the value of a is 4.

So, our function is:

f(x)=4(x-2)^2-4

Now, let’s find our roots. Set the equation to 0 and solve for x:

0=4(x-2)^2-4

4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1

So, our roots are 1 and 3.

The greater root is 3 and the lesser root is 1.

Therefore, m-n, where m>n, is 3-1 or 2.

Our final answer is 2.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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