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3 years ago

Polygon H is a scaled copy of Polygon G using a scale factor of 1/4

Mathematics

1 answer:

boyakko [2]3 years ago

3 0

Answer:

Consider polygon G as a triangle or any quadrilateral, pentagon, Hexagon, Heptagon, Decagon,....

Now Polygon H is scaled copy of Polygon G by a scale factor of 1/4, it means

If the length of sides of triangle are a,b,c then scaled copy of triangle by using

1/4 means the new sides of polygon which is triangle will be a/4,b/4,c/4.

For example consider a parallelogram having sides 12 cm and 8 cm respectively.The scaled copy of parallelogram by a scale factor of 1/4 will be of length 1/4×12,1/4×8 which is parallelogram having sides 3 cm and 2 cm respectively.

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Given f'(x) = (x-4)(4-2x), find the x-coordinate for relative maximum on the graph of f(x)

antiseptic1488 [7]

Answer:

The coordinate of the relative maximum is x=4.

Step-by-step explanation:

Given that the derivative of the function $f(x)$ is $f'(x) = (x-4)(4-2x)$ , the maxima and minima or the critical points can be found where $f'(x)=0,$ that is:

$f'(x) = (x-4)(4-2x)=0.$

The solutions to this equation are $x=4$ and $x=2.$

Now, if the second derivative $f''(x)$ for a function $f(x)$ is negative at a critical point, then the critical point is the relative maximum.

Therefore we want to see at which of the two critical points is $f''(x)$ negative. The second derivative is:

$\frac{\mathrm{d f'(x)}}{\mathrm{d}x}=f''(x)=-4(x-3).$

Now $f''(4)$ is $-4$ , and $f''(2)$ is $+4$ , therefore we deduce that the relative maxium is located at $x=4$ , because there the second derivative $f''(x)$ is negative.

4 0

3 years ago

Two sides of a rectangle are 10 and 6cm each. Calculate the area of a square with the same perimeter as that of the rectangle

KengaRu [80]

Answer: 64 cm ²

Step-by-step explanation:

The perimeter of this rectangle will be:

= 2 * Length + 2 * Width

= 2 * 10 + 2 * 6

= 20 + 12

= 32 cm

The square has the same perimeter. Squares have 4 equal sides so each side of the square must be:

= 32 / 4

= 8 cm

Area = Length * Width

= 8 * 8

= 64 cm ²

4 0

3 years ago

Maria makes a quilt. The main design is 5 feet long on each side. Then she adds a

fenix001 [56]

Answer:

1. 6 feet

2. 1 ft

0.5 ft

Step-by-step explanation:

The given dimensions for the quilt are;

The length of each sides of the quilt = 5 feet long, therefore, the shape of the quilt is a square

The area, A, of the finished quilt plus the border = 36 ft²

1. Given that the quilt's shape is that of a square, we have;

A = (side length)²

Side length = √A = √36 = 6 feet

2. Given that the initial length of the sides of the quilt are 5 feet, we have;

Increase in total length by border = Final length of quilt - Initial length of quilt

Increase in total length by border = 6 ft - 5 ft = 1 ft

The increase in total length of the quilt by the border = 1 ft

3) Given that the increase in the length by the border = 1 ft

The sum of the width of the border on both sides = 1 ft

Border width on one side + Border width on the other side = 1 ft

Since there is equal border width on each side of the quilt, we have;

2 × Border width = 1 ft

Border width = width of the border = 1 ft/2 = 0.5 ft.

7 0

3 years ago

A runner warmed up for 10 minutes and then takes seven minutes to run each mile. The total time after r miles is 45 minutes how

scoundrel [369]

So our equation to find this can be represented by 7x + 10 = 45.
(x representing miles run)
Just solve for x!

Subtract the 10 from both sides, you've got
7x = 35
And now to isolate the x, we divide both sides by 7.
Now we're left with just
x = 5!

We can check this by substituting 5 as x in our equation.
7x x 5 + 10 = 45
45 = 45
It's right!

So the runner ran 5 miles total.

Hope this helps!
If I skimmed over this too much, let me know and I'll try to explain the best that I can.

7 0

3 years ago

What number is 12 less than 43

OlgaM077 [116]

Well 43 - 12 = 31 so the answer is 31

4 0

3 years ago

Read 2 more answers