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3 years ago

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Mathematics

1 answer:

vfiekz [6]3 years ago

5 0

Answer:

45% of the students prefer biology

Step-by-step explanation:

Let's read and write all the data from the question.

100 students are interviewed to see which of biology, chemistry and physics they prefer.

Therefore, we have three categories to classify the students :

A student that prefers biology

A student that prefers chemistry

And a student that prefers physics

52 of the students are girls. Therefore,

students are boys.

29 of the girls like biology best. In order to answer the question, we will only need the amount of boys that prefer biology and sum them to the amount of girls that like biology best.

24 of the boys prefer physics. Therefore,

is the sum of the boys that prefer chemistry and biology.

If 24 is the sum of the boys that prefer chemistry and biology ⇒

are boys that prefer biology.

If we sum is the number of students that prefer biology.

If we want to calculate the percentage we need to divide the amount of students that prefer biology by the total of students interviewed and then multiply that number by 100 :

45 % of the students prefer biology.

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<h2>Perfect Squares</h2>

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$a^2+2ab+b^2=(a+b)^2$
$a^2-2ab+b^2=(a-b)^2$

Trinomials are often organized like $ax^2+bx+c$ .

The <em>b</em> value in this case is <em>c</em>, and it will always equal the square of half of the <em>b</em> value.

Perfect square trinomial: $ax^2+bx+(\dfrac{b}{2})^2$
or $ax^2-bx+(\dfrac{b}{2})^2$

<h2>Solving the Question</h2>

We're given:

$c^2-4c$

In a trinomial, we're given the $ax^2$ and $bx$ values. <em>a</em> in this case is 1 and <em>b</em> in this case is 4. To find the third value by dividing 4 by 2 and squaring the quotient:

4 ÷ 2 = 2
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Therefore, the term that we can add is + 4.

$c^2-4c+4$

To write this as the square of a bracketed expression, we can follow the rule $a^2-2ab+b^2=(a-b)^2$ :

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<h2>Answer</h2>

$c^2-4c+4$

$(c-2)^2$

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