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2 years ago

Factor problems 9 - 12 by using the difference of squares method.

Mathematics

1 answer:

Grace [21]2 years ago

4 0

Answer: 9) D 10) E 11) E 12) D

<u>Step-by-step explanation:</u>

Notes: The difference of squares is a² - b² = (a - b)(a + b)

To solve, take the square root of the first term and the square root of the last term. The factors are the sum and difference of those values.

9) x² - 4

a = √x² = x

b = √4 = 2

Factors: (x - 2)(x + 2)

Answer: D

10) x² - 25

a = √x² = x

b = √25 = 5

Factors: (x - 5)(x + 5)

Answer: E

11) 36x⁴ - 4x²

Factor out the common term (4x²) --> 4x²(9x² - 1)

a = √9x² = 3x

b = √1 = 1

Factors: 4x²(3x - 1)(3x + 1)

Answer: E

12) x² + 100

The plus (+) sign means this is not in the form of a² - b²

so it cannot be factored over the Real #s using this method

Answer: D

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Step-by-step explanation:

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2 years ago

The diagram below shows a shaded parallelogram drawn inside a rectangle. Using Pythagoras, find the hypotenuse of triangle A and

Julli [10]

Answer: 5.9 cm for both triangles.

Step-by-step explanation:

Hi, since the situation forms 2 right triangles we have to apply the Pythagorean Theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse of a triangle (the longest side of the triangle) and a and b are the other sides.

Replacing with the values given:

c^2 = 3^2 + 5^2

c^2 = 9+25

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c = 5.9 cm

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2 years ago

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3 years ago

The Patronete Winery's tastiest wine must have a 12% alcohol content. How many gallons of wine with a 9% alcohol content must be

erik [133]

Answer: 3000 gallon

Step-by-step explanation:

Here, The total quantity of 15% alcohol content = 3000 gallon

And, in which quantity of alcohol = 15% of 3000 gallon = 450 gallon.

Let the total quantity of 9% alcohol content = x

In which quantity of alcohol = 9% of x gallon= 9x/100 gallon

Now, according to the question, The wine with a 9% alcohol content will be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content.

Thus, the total quantity of mixture of 12% alcohol content = The total quantity of 15% alcohol content + total quantity of 9% alcohol content

= 3000 + x

In which quantity of alcohol = 12 % of ( 3000+x) = (360 + 12x/100) gallon ---(1)

But, the quantity of alcohol in 12 % of alcohol content = quantity of alcohol in 15% of alcohol content + quantity of alcohol in 9% of alcohol content

The quantity of alcohol in 12 % of alcohol content = (450 + 9x/100) gallon ---(2)

On equating equation (1) and (2)

We get, 360 + 12x/100 = 450 + 9x/100

⇒ 3x/100 = 90

⇒ x = 3000

Therefore, The total quantity of the mixture of 9% alcohol content = 3000

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3 years ago