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3 years ago

What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=|4+x|?

Mathematics

2 answers:

ivolga24 [154]3 years ago

4 0

Translation to the left by 4 units

ss7ja [257]3 years ago

4 0

Answer:

horizontal translation of 4 units left

Step-by-step explanation:

the graph of f(x)=|x| to the graph of g(x)=|4+x|

In g(x) , 4 is added with x

The rule of transformation is

f(x) -> f(x-a), horizontal translation of 'a' units right

f(x) -> f(x+a), horizontal translation of 'a' units left

f(x) -> f(x)+a, Vertical translation of 'a' units up

f(x) -> f(x)-a, Vertical translation of 'a' units down

When we compare f(x) and g(x), 4 is added with x

f(x) -> f(x+a), horizontal translation of 'a' units left

So its a horizontal translation of 4 units left

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2 years ago

Read 2 more answers

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KonstantinChe [14]

Given:

In triangle $ABC,m\angle A=138^\circ,c=19,a=29$ .

To find:

The $m\angle C$ .

Solution:

According to the law of sines:

$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

Taking $\dfrac{\sin A}{a}=\dfrac{\sin C}{c}$ , we get

$\dfrac{\sin 138^\circ}{29}=\dfrac{\sin C}{19}$

$\dfrac{0.66913}{29}\times 19=\sin C$

$0.4383959=\sin C$

Taking sin inverse on both sides, we get

$\sin{-1}0.4383959=C$

$26.001577^\circ=C$

$C\approx 26^\circ$

Therefore, the correct option is b.

6 0

3 years ago

g If the economy improves, a certain stock stock will have a return of 23.4 percent. If the economy declines, the stock will hav

dusya [7]

Answer:

$E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%$

Now we can find the second central moment with this formula:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965$

And the variance is given by:

$Var(X) = E(X^2) - [E(X)]^2$

And replacing we got:

$Var(X) = 413.5965 -(11.759)^2 =275.5105$

And finally the deviation would be:

$Sd(X) = \sqrt{275.5105}= 16.599 \%$

Step-by-step explanation:

We can define the random variable of interest X as the return from a stock and we know the following conditions:

$X_1 = 23.4 , P(X_1) =0.67$ represent the result if the economy improves

$X_2 = -11.9 , P(X_1) =0.33$ represent the result if we have a recession

We want to find the standard deviation for the returns on the stock. We need to begin finding the mean with this formula:

$E(X) = \sum_{i=1}^n X_i P(X_i)$

And replacing the data given we got:

$E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%$

Now we can find the second central moment with this formula:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965$

And the variance is given by:

$Var(X) = E(X^2) - [E(X)]^2$

And replacing we got:

$Var(X) = 413.5965 -(11.759)^2 =275.5105$

And finally the deviation would be:

$Sd(X) = \sqrt{275.5105}= 16.599 \%$

7 0

2 years ago

Complete the following:

Svetlanka [38]

1) A mathematical ratio is known as the golden ratio. It is frequently found in nature, and when employed in a design, it encourages compositions that look organic and natural and are visually appealing.

2) The algebraic form of golden ratio is root of x2-x-1 = 0

3) The golden ratio number is approximately equal to 1.618

4) When a line is split into two equal sections, the sum of the two parts, (a) + (b), divided by (a), equals 1.618, and this is known as the Golden Ratio

5) When designing forms, logos, layouts, and other things, this formula might be useful. By dividing each number in the Fibonacci series by its direct predecessor, the golden ratio is obtained. Mathematically speaking, the quotient F(n)/F(n-1) will become closer to the limit 1.618 for rising values of n if F(n) describes the nth Fibonacci number. The golden ratio is a more popular name for this restriction.

Learn more about golden ratio here: brainly.com/question/2263789

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1 year ago