All categories

2 years ago

Expand and reduce (2+√3)^2

Mathematics

1 answer:

nasty-shy [4]2 years ago

6 0

Answer:

7 + 4 $\sqrt{3}$

Step-by-step explanation:

note that $\sqrt{a}$ × $\sqrt{a}$ = a

Given

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

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

2(2 + $\sqrt{3}$ ) + $\sqrt{3}$ (2 + $\sqrt{3}$ ) ← distribute both parenthesis

= 4 + 2 $\sqrt{3}$ + 2 $\sqrt{3}$ + 3 ← collect like terms

= 7 + 4 $\sqrt{3}$

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Using the given information, give the vertex form equation of each parabola.

Amanda [17]

Answer:

The equation of parabola is given by : $(x-4) = \frac{-1}{3}(y+3)^{2}$

Step-by-step explanation:

Given that vertex and focus of parabola are

Vertex: (4,-3)

Focus:( $\frac{47}{12}$ ,-3)

The general equation of parabola is given by.

$(x-h)^{2} = 4p(y-k)$ , When x-componet of focus and Vertex is same

$(x-h) = 4p(y-k)^{2}$ , When y-componet of focus and Vertex is same

where Vertex: (h,k)

and p is distance between vertex and focus

The distance between two points is given by :

L= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

For value of p:

p= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

p= $\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}$

p= $\sqrt{(\frac{1}{12})^{2}}$

p= $\frac{1}{12}$ and p= $\frac{-1}{12}$

Since, Focus is left side of the vertex,

p= $\frac{-1}{12}$ is required value

Replacing value in general equation of parabola,

Vertex: (h,k)=(4,-3)

p= $\frac{-1}{12}$

$(x-h) = 4p(y-k)^{2}$

$(x-4) = 4(\frac{-1}{12})(y+3)^{2}$

$(x-4) = \frac{-1}{3}(y+3)^{2}$

8 0

2 years ago

PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!! I NEED TO FINISH THESE QUESTIONS BEFORE MIDNIGHT TONIGHT.

Natali [406]

Yo sup??

To solve this question we have to apply trigonometric ratios

sin31=UT/TV

TV=UT/sin31

=7.76

=7.8

Hope this helps.

6 0

2 years ago

VERY IMPORTANT I NEED HELP!!!

Advocard [28]

Answer:

2√3

Step by step Explanation:

$= > \frac{ \sqrt{96} }{ \sqrt{8} } \\ \\ = > \frac{ \sqrt{12 \times 8} }{ \sqrt{8} } \\ \\ = > \frac{ \sqrt{12} \times \sqrt{8} }{ \sqrt{8} } \\ \\ = > \sqrt{12} \\ \\ = > \sqrt{4 \times 3} \\ \\ = > \sqrt{2 \times 2 \times 3} \\ \\ = > 2 \sqrt{3}$

3 0

2 years ago

What is 3/5 divided by 7/9

Daniel [21]

3/5(divided)9/7
3/5x7/9
27/35

6 0

2 years ago

Find each quotient. Write in simplest form. keep answer as fraction - not decimal

kirill [66]

So we are given the expression:

$\frac{mn^{2}}{4}$ ÷ $\frac{m^{2}n}{8}$

When we divide fractions, we must flip the second term and change the sign to multiplication:

$\frac{mn^{2}}{4} *\frac{8}{m^{2}n}$

And then we multiply across:

$\frac{mn^{2}}{4} *\frac{8}{m^{2}n}= \frac{8mn^{2}}{4m^{2}n}$

Then we can break apart all of the like variables for simplification:

$\frac{8mn^{2}}{4m^{2}n}=\frac{8}{4} * \frac{m}{m^{2}} *\frac{n^{2}}{n}$

When we simplify variables through division, we subtract the exponent of the numerator from the exponent of the denominator. So we then have:

$\frac{8}{4} =2$

$\frac{m}{m^{2}}=m^{-1} =\frac{1}{m}$

$\frac{n^{2}}{n}=n^{1}=\frac{n}{1}$

So then we multiply all of these simplified parts together:

$\frac{2}{1}*\frac{1}{m}*\frac{n}{1} =\frac{2n}{m}$

So now we know that the simplified form of the initial expression is: $\frac{2n}{m}$ .

3 0

2 years ago