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3 years ago

A youth chorus has 30 members. There are 14 boys in the chorus.

2 answers:

4 0

The ratio of boys to girls in simplest form is
14:16
14/16
Divide through by 2
7/8
So the ratio of boys to girls in simplest form is 7/8

tiny-mole [99]3 years ago

4 0

Answer:

your answer is 7/8

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Completing the square

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4 years ago

In a right triangle the leg opposite to the acute angle of 30° is 7 in. Find the hypotenuse and other leg.

Maksim231197 [3]

This is a 30-60-90 triangle.
Therefore,
7 is A
the other leg is A√3
And the hypotenuse is 2A
So the other leg is 7√3 and the hypotenuse is 14

5 0

3 years ago

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20 POINTS!!

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3 years ago

How do you solve these equations? I don't want you to answer all of them, just tell me how to solve each type of equation on the

miss Akunina [59]

Answer:

8. Identify the common denominator; express each fraction using that denominator; combine the numerators of those rewritten fractions and express the result over the common denominator. Factor out any common factors from numerator and denominator in your result. (It's exactly the same set of instructions that apply for completely numerical fractions.)

9. As with numerical fractions, multiply the numerator by the inverse of the denominator; cancel common factors from numerator and denominator.

10. The method often recommended is to multiply the equation by a common denominator to eliminate the fractions. Then solve in the usual way. Check all answers. If one of the answers makes your multiplier (common denominator) be zero, it is extraneous. (10a cannot have extraneous solutions; 10b might)

Step-by-step explanation:

For a couple of these, it is helpful to remember that (a-b) = -(b-a).

$\dfrac{5}{x+2}+\dfrac{25-x}{x^2-3x-10}=\dfrac{5(x-5)}{(x+2)(x-5)}+\dfrac{25-x}{(x+2)(x-5)}\\\\=\dfrac{5x-25+25-x}{(x+2)(x-5)}=\dfrac{4x}{x^2-3x-10}$

___

$\displaystyle\frac{\left(\frac{x}{x-2}\right)}{\left(\frac{2x}{2-x}\right)}=\frac{x}{x-2}\cdot\frac{-(x-2)}{2x}=\frac{-x(x-2)}{2x(x-2)}=-\frac{1}{2}$

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$\dfrac{3}{x-1}+\dfrac{6}{x^2-3x+2}=2\\\\\dfrac{3(x-2)}{(x-1)(x-2)}+\dfrac{6}{(x-1)(x-2)}=\dfrac{2(x-1)(x-2)}{(x-1)(x-2)}\\\\3x-6+6=2(x^2-3x+2) \qquad\text{multiply by the denominator}\\\\2x^2-9x+4=0 \qquad\text{subtract 3x}\\\\(2x-1)(x-4)=0 \qquad\text{factor; x=1/2, x=4}$

Neither solution makes any denominator be zero, so both are good solutions.

8 0

3 years ago

Now there is a door whose height is more than its width by 6 chi 8 cun. The distance between the [opposite] corners is 1 zhang.

Kaylis [27]

Answer:

height: 9 chi 6 cun
width: 2 chi 8 cun

Step-by-step explanation:

The factor-of-ten relationship between the different units means we can combine the numbers in decimal fashion. If 1 unit is 1 zhang, then 1 chi is 0.1 zhang and 1 cun is 0.01 zhang. Hence 6 chi 8 cun is 0.68 zhang.

Let x and y represent the width and height, respectively. In terms of zhang, we have ...

y - x = 0.68

x^2 +y^2 = 1^2

Substituting y = 0.68 +x into the second equation gives ...

x^2 + (x +0.68)^2 = 1

2x^2 +1.36x - 0.5376 = 0 . . . . . eliminate parentheses, subtract 1

Using the quadratic formula, we have ...

x = (-1.36 ±√(1.36^2 -4(2)(-0.5376)))/(2·2) = (-1.36 ±√6.1504)/4

x = 0.28 . . . . . the negative root is of no interest

y = 0.28 +0.68 = 0.96

In units of chi and cun, the dimensions are ...

height: 9 chi 6 cun

width: 2 chi 8 cun

6 0

4 years ago

Read 2 more answers