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Dimas [21]
3 years ago
7

\sqrt[]{2} ) {}^{2} " alt="(3 + \sqrt[]{2} ) {}^{2} " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Vesnalui [34]3 years ago
6 0

Answer:

11 + 6\sqrt{2}

Step-by-step explanation:

(3 + \sqrt{2} )²

= (3 + \sqrt{2} )( 3 + \sqrt{2} )

Each term in the second factor is multiplied by each term in the first factor

= 3( 3 + \sqrt{2} ) + \sqrt{2} ( 3 + \sqrt{2} )

Distribute each parenthesis noting that \sqrt{2} × \sqrt{2} = 2

= 9 + 3\sqrt{2} + 3\sqrt{2} + 2 ← collect like terms

= 11 + 6\sqrt{2}

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matilda is considering getting a credit card and using it instead of cash. which of these is good reason for her to do so?
IrinaK [193]
She will be able to keep track of her purchases easier.
8 0
3 years ago
Read 2 more answers
Convert the following radian angle into degrees.
NeTakaya

The degree of the radian angle 0.11 is 6.3^{\circ}

Explanation:

It is given that the radian angle is 0.11

We need to determine the degrees of the radian angle.

To convert the radian into degrees, let us multiply the radian with \left(\frac{180}{\pi}\right)

Thus, we have,

0.11\times\left(\frac{180}{\pi}\right)=\frac{19.8}{\pi}

It is given that \pi=3.14

Substituting \pi=3.14 in the above expression, we have,

\frac{19.8}{3.14} =6.303...

Rounding off to the nearest tenth, we have,

6.3^{\circ}

Thus, the degree of the radian angle 0.11 is 6.3^{\circ}

4 0
3 years ago
Please help asap!!!!!!!!!!!
mars1129 [50]
X = 59, y = 44

2x + 18 + x - 15 = 180
3x + 3 = 180
3x = 177
x = 59

x - 15 = y
59 - 15 = y
44 = y
6 0
3 years ago
Read 2 more answers
Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.
gladu [14]

Answer:

Vertical asymptote: x=3

Horizontal asymptote: f(x) =2

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

f (x) = -\dfrac{1 }{ x-3} +2

One root, x = 3.5

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

<em>Roots of f(x) means the value of x where f(x) = 0</em>

0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5

One root, x = 3.5

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) \rightarrow \infty

For all, other values of x , f(x) is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is \frac{1}{x-3}.

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) \rightarrow \infty.

-\dfrac{1 }{ x-3} +2 \rightarrow \infty

It is possible only when

x-3=0\\\Rightarrow x=3

\therefore vertical asymptote: x=3

Horizontal Asymptote is the value of f(x) , where value of x \rightarrow \infty.

x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2

\therefore Horizontal asymptote: f(x) =2

Please refer to the graph of given function as shown in the attached image.

5 0
3 years ago
Express x% of 4 plus y% of 5 as a percentage of 11
djverab [1.8K]
X% of 4 = x*4/100 = 0.04x

y% of 5 = x*5/100 = 0.05y

x% of 4 + y% of 5 = 0.04x + 0.05y

How you express a number, n, as percentage of 11?: [n/11]*100= 9.10n %

Then make n = 0.04x + 0.05y

9.10n %= 9.10[0.04x + 0.05y] %= (0.3656x + 0.455y)%

.


 



4 0
4 years ago
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