Plz answer it’s easy giving brainliest

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andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

Definition of the identity property of addition and the commutative property of addition

Novay_Z [31]

Let x, y be numbers.
The addition identity property states that 0 + x = x.
The commutative property states that x + y = y + x

6 0

2 years ago

Read 2 more answers

The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units

nydimaria [60]

Answer:

The volume of the prism is equal to the volume of the cylinder

Step-by-step explanation:

For each solid figure, the volume formula is ...

V = Bh

where B is the cross-sectional area and h is the height. The problem statement tells us B and h have the same values for both figures. Hence their volumes are the same.

5 0

2 years ago

Mr. Hernandez's backyard is shaped like a trapezoid with a height of 10 m, a top base of 15 m, and a bottom base of 19 m. In his

Zolol [24]

The area of the trapezoid is calculated through the equation,
A = 0.5(b₁ + b₂)h
where A is area, b₁ and b₂ are the lengths of the bases and h is the height. Substituting the known values,
A = 0.5(15 m + 19 m)(10 m)
A = 170 m²
The area of the garden is 170 m².

7 0

2 years ago

Read 2 more answers

NO LINKS!! Please help me with this problem

iogann1982 [59]

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