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2 years ago

How to describe a transformation?

Mathematics

1 answer:

svet-max [94.6K]2 years ago

6 0

The horizontal shift depends on the value of h . The horizontal shift is described as: g(x)=f(x+h) g ( x ) = f ( x + h ) - The graph is shifted to the left h units. g(x)=f(x−h) g ( x ) = f ( x - h ) - The graph is shifted to the right h units.

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if a point on the graph of a proportional relationship is located at 3,4, can you determine the constant of proportionality? exp

Mashutka [201]

The answer is: No, because we also need to know the type of proportionality

In mathematics, we talk about proportionality when two variables are related and this relationship is that there is a constant ratio between them. There are two types of proportionality.

1. Direct Proportionality:

If there are two variables x and y, we can write the relationship between them as follows:

$y=kx$

So, by substituting the point in this equation we have that the constant of proportionality is:

$4=k(3) \\ \\ \therefore \boxed{k=\frac{4}{3}}$

2. Inverse Proportionality:

In this case, the relationship is:

$y=\frac{k}{x}$

So, the constant of proportionality is:

$4=\frac{k}{3} \\ \\ \therefore \boxed{k=12}$

As you can see, we have found two different values of the constant of proportionality. So, it is necessary to know the type of proportionality.

7 0

3 years ago

What's the input lol *photo attatched*

marishachu [46]

-20+1= -19
-19/2= -9.5

Check:
-9.5x2= -19
-19-1= -20

3 0

2 years ago

An unopened cereal box contains `15/28` cubic foot of cereal. If the box is full, and the length and height of the box are `5/7`

VikaD [51]

Answer:

1/2ft

Step-by-step explanation:

15/28=(5/7)(1 1/2)(w)

15/28=(5/7)(3/2)w

15/28=(15/14)w

(15/28)/(15/14)=w

(15/28)*(14/15)=w

w=14/28

w=1/2 ft

4 0

3 years ago

Simplify the expression state any excluded values<br> 2a^2-4a+2<br> ---------------<br> 3a^2-3

chubhunter [2.5K]

Answer:

The simplified form is $\dfrac{2(x-1)}{3(x+1)}$ .

$x =1$ is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

$\dfrac{2a^2-4a+2}{3a^2-3}$

Let us simplify the numerator and denominator separately.

The numerator is given as $2a^2-4a+2$

2 is a common factor in all the three terms. So, we factor it out. This gives,

$=2(a^2-2a+1)$

Now, $a^2-2a+1=(a-1)(a-1)$

Therefore, the numerator becomes $2(a-1)(a-1)$

The denominator is given as: $3a^2-3$

Factoring out 3, we get

$3(a^2-1)$

Now, $a^2-1$ is of the form $a^2-b^2=(a-b)(a+b)$

So, $a^2-1=(a-1)(a+1)$

Therefore, the denominator becomes $3(a-1)(a+1)$

Now, the given expression is simplified to:

$\frac{2a^2-4a+2}{3a^2-3}=\frac{2(x-1)(x-1)}{3(x-1)(x+1)}$

There is $(x-1)$ in the numerator and denominator. We can cancel them only if $x\ne1$ as for $x=1$ , the given expression is undefined.

Now, cancelling the like terms considering $x\ne1$ , we get:

$\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}$

Therefore, the simplified form is $\dfrac{2(x-1)}{3(x+1)}$

The simplification is true only if $x\ne1$ . So, $x =1$ is the excluded value for the given expression.

8 0

3 years ago

Please help!!! Verify which of the following are identities.

Ierofanga [76]

Answer:

First one

Step-by-step explanation:

None of the equations are identities

4 0

2 years ago