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2 years ago

Work out x when the area is root 4 2^2 and angle C is 45 and ab are (x+2)(2x-3)

Mathematics

1 answer:

aleksandrvk [35]2 years ago

7 0

Answer:

x = 2.41

Step-by-step explanation:

<u>Area formula:</u>

A = 1/2bh

<u>The height is:</u>

h = (x + 2)sin 45° = √2(x + 2)/2

<u>Substitute the area value an set an equation:</u>

4√2 = (2x - 3)√2(x + 2)/2
(2x - 3)(x + 2) = 8
2x² + x - 6 = 8
2x² + x - 14 = 0
D = 1 + 4*2*14 = 113
x = (-1 + √113)/4 = 2.41 (rounded)

Note. the second root ignored as negative

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Is (0.3) the solution to the equation y=x+3

Goryan [66]

Answer:-3

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2 years ago

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A room has a rectangular floor that is 15 feet by 21 feet. What is the area of the floor in square yards ?

Soloha48 [4]

Answer:

Hey There!

Let's solve...

Here it is a rectangular floor with length =21 cm and width =15cm

$area = l \times w \\ = 21 \times 15 \\ = 315 {ft}^{2} \\ \\$

So now We need to convert it to yards square

$315ft^{2} \times \frac{ {1yd}^{2} }{ {9ft}^{2} } \\ \\ = \cancel{315ft^{2}} \: ^{35} \times \frac{ {1yd}^{2} }{ \cancel{9 {ft}^{2} }} \\ \\ = 35 {yd}^{2}$

So how this 9 ft^2 came??

Let's know

$ft \to \: yards \\ \\ 3ft = 1yd \\ \\ {3ft}^{2} = {1yd}^{2} \\ \\ \boxed{ {9ft}^{2} = {1yd}^{2}}$

<h2>I hope it is helpful to you...</h2><h3>Cheers!_______</h3>

8 0

2 years ago

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Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

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3 years ago

Which statement best describes the decimal equivalent of 5/9?

padilas [110]

The answer is c

Explanation:
A repeating decimal continues to go with the same number pattern. The terminating decimal stops the number pattern and does not keep repeating. The decimal for 5/9 is 0.5555... and it will keep repeating the number five.

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2 years ago

What is the highest multiple of 2 and 3?

zubka84 [21]

2 and 3 are prime numbers, so it means that the greatest common factor is:

G.C.M(2;3)=2*3=6

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3 years ago