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3 years ago

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In a particular year, a total 44,064 of students studied in two of the most popular host countries when traveling abroad. If 83

82 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were ____ students who studied abroad in the most popular host country.

1 answer:

zaharov [31]3 years ago

6 0

Step-by-step explanation:

Total=44,064

Host countries= 2

2nd most popular country= x

Popular country=x+8382

x+x+8,382=44,064

2x=44,064-8,382=35,682

2x=35,682

x=17,842

2nd most popular=17,842

Popular=17,842+8,382=26,224

Answer=26,224

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A candidate took a phone poll of 110 people. Of the 110 people polled, 87 said they would vote for the other person. There are 9

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Option B

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<em><u>Solution:</u></em>

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Let "x" be the number of people who would vote for the other candidate

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Answer:

Part 1) $2(x-3)^{2}-17=0$ (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

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Step-by-step explanation:

Part 1) we have

$2x^{2} -12x+1=0$

Convert to vertex form

step 1

Factor the leading coefficient and complete the square

$2(x^{2} -6x)+1=0$

$2(x^{2} -6x+9)+1-18=0$

step 2

$2(x^{2} -6x+9)+1-18=0$

$2(x^{2} -6x+9)-17=0$

step 3

Rewrite as perfect squares

$2(x-3)^{2}-17=0$

Part 3) we have

$f(x)=-x^{2}+16x-60$

we know that

This is the equation of a vertical parabola open downward

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Convert to vertex form

$f(x)+60=-x^{2}+16x$

Factor the leading coefficient

$f(x)+60=-(x^{2}-16x)$

Complete the squares

$f(x)+60-64=-(x^{2}-16x+64)$

$f(x)-4=-(x^{2}-16x+64)$

Rewrite as perfect squares

$f(x)-4=-(x-8)^{2}$

$f(x)=-(x-8)^{2}+4$

The vertex is the point (8,4)

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Part 4) Solve for x

we have

$-2(x-2)^{2}+5=0$

$-2(x-2)^{2}=-5$

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square root both sides

$(x-2)=(+/-)1.58$

$x=2(+/-)1.58$

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Part 5) we have

$f(x)=-x^{2}+50x-264$

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The zeros or x-intercepts are the value of x when the value of the function is equal to zero

so

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To find the zeros equate the function to zero

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$-x^{2}+50x=264$

Factor -1 of the leading coefficient

$-(x^{2}-50x)=264$

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$-(x^{2}-50x+625)=264-625$

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Factor the leading coefficient

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Rewrite as perfect square

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$f(x)=-x^{2}+8x-10$

Convert to vertex form

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Factor -1 the leading coefficient

$f(x)+10=-(x^{2}-8x)$

Complete the square

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Rewrite as perfect square

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Convert to vertex form

Group terms

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Rewrite as perfect squares

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