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3 years ago

How to solve this pythagoras theorem

Mathematics

1 answer:

My name is Ann [436]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The hypotenuse is the longest side thus is (4x + 1)

The legs are 2x and (4x - 1)

Using Pythagoras' theorem, then

(4x + 1)² = (2x)² + (4x - 1)² ← expanding factors

16x² + 8x + 1 = 4x² + 16x² - 8x + 1 , that is

16x² + 8x + 1 = 20x² - 8x + 1 ( subtract 20x² - 8x + 1 from both sides )

- 4x² + 16x = 0 ( multiply through by - 1 )

4x² - 16x = 0 ← factor out 4x from each term

4x(x - 4) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x - 4 = 0 ⇒ x = 4

Now x > 0, thus x = 4

2x = 2(4) = 8

4x - 1 = 4(4) - 1 = 16 - 1 = 15

4x + 1 = 4(4) + 1 = 16 + 1 = 17

Thus

perimeter = 8 + 15 + 17 = 40 cm

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A store had 150 laptops in the month of January. Every month, 20% of the laptops were sold and 10 new laptops were stocked in th

Softa [21]

Answer-

$\boxed{\boxed{f(n)=0.8(f(n-1))+10,\ f(0)=150,\ \ n>0}}$

Solution-

Here, n represents the number of months and f(n) represents the number of laptops in the store after n months.

As the store had 150 laptops in the month of January or at the beginning.

So $f(0)=150$

Every month, 20% of the laptops were sold and 10 new laptops were stocked in the store.

As 20% of laptops were sold, so 80% were in the store.

So, after one month total number of laptops in the store,

$\Rightarrow f(1)=0.8(150)+10$

$\Rightarrow f(1)=0.8(f(0))+10$ $(\because f(0)=150)$

Again after one month total number of laptops in the store,

$\Rightarrow f(2)=0.8\times (0.8(150)+10)+10$

$\Rightarrow f(2)=0.8(f(1))+10$ $(\because f(1)=0.8(150)+10)$

Analyzing the pattern, the recursive function f(n) will be,

$f(n)=0.8(f(n-1))+10,\ f(0)=150,\ \ n>0$

3 0

3 years ago

Read 2 more answers

Find the area of the triangle below. Be sure to include the correct unit in your answer.

OleMash [197]

Answer:

area of triangle= 1/2*h*b

= 1/2*6*16

=3*16

= 48 yd²

This is your answer. If I'm right so,

Please mark me as brainliest. thanks!!!

5 0

3 years ago

In parallelogram ABCD, ∠A and ∠B are adjacent. The measure of ∠B is twice the measure of ∠A. Which equation gives the exact meas

viktelen [127]

The right answer to this problem is B

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3 years ago

What is the simplified answer of “One less than X is less than -1 OR 3 more than X is greater than or equal to 7.” This is solvi

blsea [12.9K]

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5 0

3 years ago

your gym membership cost $33 per month after an initial membership fee. you paid a total of $228 after 6 months. writer an equat

grin007 [14]

Answer:

what i did was multiply 33*6 and got 198 and then 228-198 to find out that the initial fee was 30 dollars. then multiply 33*9+30 to get a 9-month total cost of $327

Step-by-step explanation:

cost = $33 per month + fee

1. c(m) = 33m + f

33(6) + f = 228

198 + f = 228

f = $30 membership fee

c(m) = 33m + 30

2. at 9 months: 33(9) + 30 = $327

hopefully this helps :)

have a nice day !!

7 0

3 years ago