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3 years ago

Which of the following is the graph of f(x) = -0.5|x+3| -2?

Mathematics

2 answers:

Tcecarenko [31]3 years ago

7 0

Answer:

The last graph

Step-by-step explanation:

We transform functions in the following ways:

multiplying the function by a number to stretch or shrink it
multiplying by a negative to flip the orientation of the function
adding/subtracting a value to the input x to shift it horizontally
adding/subtracting a value to the output (or outside the function operation) to shift it vertically or horizontally.

Looking at the equation we can see $f(x)=-0.5\left|x+3\right|-2$

Vertically shrunk by 0.5
Negative leading coefficient to flip the graph's orientation
Horizontal shift of the vertex of 3 units to the left from (0,-2) to (-3,-2)
Vertical shift of the vertex of 2 units downward (-3,0) to (-3,-2)

The last graph has vertex (-3,-2) and satisfies the the equation.

emmasim [6.3K]3 years ago

5 0

Answer: first one

Step-by-step explanation:

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Point B has coordinates (3,2). The x-coordinate of point A is −6. The distance between point A and point B is 15 units. What

xxTIMURxx [149]

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2 years ago

the half-life of strontium-90 is approximately 29 years. how much of a 500 g sample of strontium-90 will remain after 58 years

Yuliya22 [10]

Answer: 125 g

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

$A = P_o\cdot e^{kt}\\\\\text{First, use the given information to find k:}\\\\\bullet A=\dfrac{1}{2}P_o\\\\\bullet k = unknown\\\\\bullet t=29\text{ years}\\\\\dfrac{1}{2}P_o=P_o\cdot e^{k(29)}\\\\\\\dfrac{1}{2}=e^{k(29)}\qquad divided\ both\ sides\ by\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=ln\bigg(e^{k(29)}\bigg)\qquad applied\ ln\ to\ both\ sides\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=29k\qquad simplified-ln\ and\ e\ cancel\ out\\\\\\\dfrac{ln\bigg(\dfrac{1}{2}\bigg)}{29}=k\qquad divided\ 29\ from\ both\ sides\\\\\\-0.0239=k$

$\text{Now, use the following in the equation to solve for A:}\\\\\bullet A=unknown\\\bullet P_o=500\\\bullet k=-0.0239\\\bullet t=58\text{ years}\\\\A=500\cdot e^{(-0.0239)(58)}\\\\.\quad=500\cdot e^{-1.386}\\\\.\quad=125$

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