A closed plane figure with all sides congruent is called a

professor190 [17]

The formula for the area of the triangles is base x hight divided by 2 (bh/2)
The formula for the square is length times width (l x w)

therefore...

bh/2 = (12)(6) / 2 = 36 (this is the area of one triangle)

then you need to times 36 by 4 because you have 4 triangles.
36 x 4 = 144

l x w = 12 x 12 = 144 (this is the area of the square)

last you need to add the area of the triangles (144) and the area of the square (144) because that will give you the total surface area of the shape.

144+144= 288

so your answer is 288cm squared (288cm2)

6 0

3 years ago

Read 2 more answers

David is making patterns using these rules. Rule for Pattern A: start with 20 and subtract 2 Rule for Pattern B: start with 10 a

pochemuha

Answer:

20,18,16,14,12,10,8,6,4,2

10,9,8,7,6,5,4,3,2,1

Step-by-step explanation:

Pattern A:

Rule : start with 20 and subtract 2

Pattern B:

Rule : Start with 10 and subtract 1

Pattern 1:

20 - 2 = 18

18 - 2 = 16

16 - 2 = 14

14 - 2 = 12

12 - 2 = 10

10 - 2 = 8

8 - 2 = 6

6 - 2 = 4

4 - 2 = 2

20,18,16,14,12,10,8,6,4,2

Pattern 2:

10 - 1 = 9

9 - 1 = 8

8 - 1 = 7

7 - 1 = 6

6 - 1 = 5

5 - 1 = 4

4 - 1 = 3

3 - 1 = 2

2 - 1 = 1

10,9,8,7,6,5,4,3,2,1

5 0

2 years ago

2. A bank representative studies compound interest, so she can better serve

Kaylis [27]

Answer:

Step-by-step explanation:

Given that a bank representative studies compound interest, so she can better serve customers. She analyzes what happens when $2,000 earns interest several different ways at a rate of 2% for 3 years.

a) the interest if it is computed using simple interest. 12.00

= $\frac{2000(3)(12)}{100} \\=720$ dollars

b) the interest if it is compounded annually.

= $2000(1.12)^3-2000\\= 809.86$ dollars

c) the interest if it is compounded semiannually

= $2000(1.06)^6 -2000\\= 837.04$

d) the interest if it is compounded quarterly.

= $2000(1.03)^12 -2000\\= 851.52$

e) the interest if it is compounded monthly.

= $2000(1.01)^24 -2000\\= 861.54$

4 0

3 years ago

In the derivation of Newton’s method, to determine the formula for xi+1, the function f(x) is approximated using a first-order T

dimaraw [331]

Answer:

Part A.

Let f(x) = 0;

suppose x= a+h

such that f(x) =f(a+h) = 0

By second order Taylor approximation, we get

f(a) + hf'±(a) + $\frac{h^{2} }{2!}$ f''(a) = 0

$h = \frac{-f'(a) }{f''(a)}$ ± $\frac{\sqrt[]{(f'(a))^{2}-2f(a)f''(a) } }{f''(a)}$

So, we get the succeeding equation for Newton's method as

$x_{i+1} = x_{i} + \frac{1}{f''x_{i}} [-f'(x_{i})$ ± $\sqrt{f(x_{i})^{2}-2fx_{i}f''x_{i} } ]$

Part B.

It is evident that Newton's method fails in two cases, as:

1. if f''(x) = 0

2. if f'(x)² is less than 2f(x)f''(x)

Part C.

In case $x_{i+1}$ is close to $x_{i}$ , the choice that shouldbe made instead of ± in part A is:

f'(x) = $\sqrt{f'(x)^{2} - 2f(x)f''(x)}$ ⇔ $x_{i+1} = x_{i}$

Part D.

As given $x_{i+1}$ = $x_{i}$ = h

or h = $x_{i+1}$ - $x_{i}$

We get,

f(a) + hf'(a) +(h²/2)f''(a) = 0

or h² = -hf(a)/f'(a)

Also, ( $x_{i+1}$ - $x_{i}$ )² = -( $x_{i+1}$ - $x_{i}$ )(f( $x_{i}$ )/f'( $x_{i}$ ))

So, f(a) + hf'(a) - (f''(a)/2)(hf(a)/f'(a)) = 0

It becomes h = -f(a)/f'(a) + (h/2)[f''(a)f(a)/(f(a))²]

Also, $x_{i+1}$ = $x_{i}$ -f( $x_{i}$ )/f'( $x_{i}$ ) + [( $x_{i+1}$ - $x_{i}$ )f''( $x_{i}$ )f( $x_{i}$ )]/[2(f'( $x_{i}$ ))²]

6 0

3 years ago

Which fraction is larger 7/16 or 51/100?

zaharov [31]

51/100 would be larger
From the first look, I already know half of 100 is fifty and 51 is greater than that
So when I looked at 7/16, I was looking for something greater than half, but 7 is greater than half of 16.
51/100 is your answer

5 0

3 years ago

Read 2 more answers