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3 years ago

Which property justifies the fact that 5(x-2) is equivalent to 5x-10

Mathematics

2 answers:

zaharov [31]3 years ago

8 0

The distributive property of multiplication over addition allows you do write that equivalence.

Brilliant_brown [7]3 years ago

8 0

The distributive property

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PLSSS HELP IF YOU TURLY KNOW THISS

Eduardwww [97]

Answer:

Step-by-step explanation:

3² * 5³ = 3*3 * 5*5*5

= 9 * 125

= 1125

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3 years ago

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Graph y=-5x Help please

wariber [46]

Hopefully, this helps.

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3 years ago

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Math homework help exponents

Len [333]

Answer + Step-by-step explanation:

$\frac{5^{10}}{5^{5}} =5^{10-5} = 5^5$

$\text{used property :} \ \ \ \frac{a^{m}}{a^{n}} =a^{m-n}$

_______________________

$(4^8)^3 = a^{8 \times 3}=a^{24}$

$\text{used property :} \ \ \ (a^n)^m = a^{n \times m}$

_______________________

$10^{-4}=\frac{1}{10^{4}} \ \text{not} \ \frac{1}{4^{10}}$

_______________________

15⁶ × 15³ = 15⁶⁺³ = 15⁹

_______________________

Recall : If a ≠0 ⇒ a⁰ = 1

Then

Since 6⁸ ≠ 0 ⇒ (6⁸)⁰ = 1

6 0

2 years ago

Select all the correct graphs. Which graphs are the graphs of even functions?

natali 33 [55]

Answer:

I think it the first one is

7 0

2 years ago

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

3 years ago