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3 years ago

Can someone help me out with these equations? 1. (5+ √3)^2 2. (√6-5√3)^2 3. (6+3√2)^2

Mathematics

1 answer:

Aloiza [94]3 years ago

6 0

9514 1404 393

Answer:

28 +10√3
81 -30√2
54 +36√2

Step-by-step explanation:

It is useful to remember the form for the square of a binomial.

(a +b)² = a² +2ab +b²

(a -b)² = a² -2ab +b²

1. (5 +√3)² = 5² +2·5·√3 +(√3)² = 25 +10√3 +3

= 28 +10√3

2. (√6 -5√3)² = (√6)² -2·√6·5√3 +(5√3)² = 6 -30√2 +75

= 81 -30√2

3. (6 +3√2)² = 6² +2·6·3√2 +(3√2)² = 36 +36√2 +18

= 54 +36√2

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At a hockey game, a vender sold a combined total of 176 sodas and hot dogs. The number of sodas sold was three times the number

goldfiish [28.3K]

Answer:

Hot dogs sold: 44

Sodas sold: 132

Step-by-step explanation:

This is is a problem of a system of two equations with two unknowns. This can be solved in multiple ways (the substitution method, the elimination method, the equalization method, the graphic method...) . I will resolve it using the equalization method that is a little bit more practical from my point of view.

First, we have to determine the system by the data we are given:

$\left \{ {{y+x=176} \atop {y=3x}} \right.$

Where:

$y=sodas sold\\x=hot dogs sold$

Secondly, we are going to isolate any variable from both equations. I chose to isolate Y.

$\left \{ {{y=176-x} \atop {y=3x}} \right.$

Thirdly, we equalizate both equations.

$Y= Y$

So we get:

$176-x=3x$

Then we isolate X.

$-x-3x=-176$

$-4x=-176$

$x=-176:(-4)$

$x=44$

So now we know that the number of hot dogs sold was 44! If the sodas sold were three times the number of hot dogs sold, then we know that there were 132 sodas sold at the hockey game!

8 0

3 years ago

Choose whether the expression is a result of multiplying

vladimir1956 [14]

Answer:

neither

Step-by-step explanation:

Take out 5 as a common factor. It will be easier to look at.

5(5c^2 + 11c + 6)

5(5C +6 )(c + 1 )

Now you can put the 5 inside.

(25c + 30)(c + 1) is one answer.

(5c + 6)(5c + 5) is another.

The answer is multiplying binomials. There is nothing that that is squared and the answers are not conjugates. They are two binomials multiplied together.

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3 years ago

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Answer:

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Step-by-step explanation:

Xi:"i-th Signal"

Xi=1, False alarm

Xi=0, True error

$Y=\sum ^{10}_{i=1}Xi$

X=Ber(p=0.07)

Y=Bin(n=10, p=0.07)

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4 years ago

Write the equation of the hyperbola with foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5).

mash [69]

If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down. We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively. Also, the equation looks like this when it is horizontal: $\frac{(x-h) ^{2} }{ a^{2} } - \frac{(y-k) ^{2} }{ b^{2} } =1$ . a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3. We need to find b now, using Pythagorean's theorem. $( 2)^{2} + b^{2} =( 3)^{2}$ and $b= \sqrt{5}$ . Now we have everything we need to rewrite the equation: $\frac{(x-4) ^{2} }{4} - \frac{(y-5) ^{2} }{5} =1$

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3 years ago

Given 3x^2+x-4/x-1 what are the domain and range

Katarina [22]

Answer:

doman: x ≠ 1
range: y ≠ 7

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

<h3>Simplified</h3>

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

$\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1$

<h3>Domain</h3>

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

x ≠ 1

In interval notation, this is ...

(-∞, 1) ∪ (1, ∞)

<h3>Range</h3>

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

y ≠ 7

In interval notation, this is ...

(-∞, 7) ∪ (7, ∞)

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2 years ago