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sashaice [31]
3 years ago
6

Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
5 0

\text{Use:}(*)\ (a+b)^2=a^2+2ab+b^2\\\\2x^2+2x+1=0\ \ \ \ |:2\\\\x^2+x+0.5=0\\\\x^2+2\cdot x\cdot0.5+0.5=0\\\\\underbrace{x^2+2\cdot x\cdot0.5+0.5^2}_{(*)}-0.5^2+0.5=0\\\\(x+0.5)^2-0.25+0.5=0\\\\(x+0.5)^2+0.25=0\ \ \ \ |-0.25\\\\(x+0.5)^2=-0.25\to D)

Answer: D) (x + 0.5)2 = -0.25

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1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v
Ad libitum [116K]

Answer: (a) The ratio of spirit to varnish is 1 : 3

(b) You will need 80 ml of mineral spirits

(c) Ratio = 3 : 2

Step-by-step explanation: (a) If you have to mix 25% mineral spirit to the varnish as required in the question, then the whole solution would effectively contain 25 percent spirit and 75 percent varnish, giving you a hundred percent solution. To express both quantities in ratio can be done as follows;

Ratio = Spirit : Varnish

Ratio = 25 : 75

Ratio = 1 : 3

(b) Next, if you use 240 ml of varnish, this quantity would constitute 75 percent or ratio 3 out of 4 of your total solution. Therefore 240 ml of varnish can be expressed as follows;

240 : x = 3 : 4

Where x is the total solution and the right hand side (3 : 4) expresses the ratio of varnish in relation to the total solution. Hence,

240/x = 3/4

By cross multiplication you now have,

3x = 240 * 4

x = 960/3

x = 320

If x is the total solution which is 320 ml, and varnish constitutes 240 ml, then spirit equals,

Spirit = Total solution - varnish

Spirit = 320 - 240

Spirit = 80.

Therefore, you would need 80 ml of mineral spirits.

(c) Robson's tapestries all measure 1.5 m by 1 m. This can be expressed in whole numbers by first eliminating the decimal. Multiplying both dimensions by 10 results in,

1.5 (10) x 1 (10)

15 x 10

If both measurements can also be expressed as 15 m by 10 m, then reducing to the least terms would result in 3 by 2. That is,

15/5 by 10/5

3 by 2

Expressed as a ratio, this now becomes

Ratio = 3 : 2

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