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AlexFokin [52]
3 years ago
8

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of (f/g)(x)?

Mathematics
2 answers:
3241004551 [841]3 years ago
7 0

Answer:

b) all real values of x except x = 5

Step-by-step explanation:

Given functions,

f(x) = x^2 - 25

g(x) = x-5

(\frac{f}{g})(x)=\frac{f(x)}{g(x)}

By substituting the values,

(\frac{f}{g})(x)=\frac{x^2-25}{x-5}

Which is a rational function,

Since, a rational function is defined for all real values except those for which the denominator = 0,

That is,

x - 5 = 0

⇒ x = 5

Hence, the domain of (f/g)(x) are all real values of x except x = 5 ,

Option b) is correct.

Stels [109]3 years ago
5 0
Choice b. is right because for x=5 will result this fraction undefined bc than for x=5 the denominator will be equal zero
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An equilateral triangle with side length 7 cm is shown in the diagram, work out the area of the triangle.
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If a triangle has sides of 7 cm and it is an equilateral you can draw a line right down the middle to form two congruent triangles.

These smaller triangles have a hypotenuse of 7cm and a base of 3.5 cm (7/2)

To work out the height, use Pythagoras’ theorem.

a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides

7^2 - 3.5^2 = 36.75

Square root answer

= 6.06 cm

That’s the height of the triangle

Area of a triangle is base x height divided by 2

So 7 x 6.06 = 42.43…

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= 21.2 cm^2 to one d.p

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The solution of the system of equations is the point (-3,0)

Step-by-step explanation:

we have

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-3x+y=9\\2x-y=-6\\------\\-3x+2x=9-6\\-x=3\\x=-3

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Prove that an integer consisting of 3n ones is divisible by 3n (e.g. 111 is divisible by 3, 111,111,111 is divisible by 9, etc.)
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For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

<h3>Integers divisible by 3</h3>

The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.

<h3>Proof for the divisibility</h3>

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213 = 2 + 1 + 3 = 6 ( (the sum is multiple of 3 = 3 x 2)  (213/3 = 71)

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