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3 years ago

Solve (x-2)^2-3=1 graphically.

Mathematics

1 answer:

zimovet [89]3 years ago

8 0

we are given

$(x-2)^2-3=1$

we can seperate them

First function is

$y=(x-2)^2-3$

second function is

$y=1$

now, we can draw graph

and find intersection points

so, we can see that

intersection points are

(0,1) and (4,1)

so, solutions are

$x=0,x=4$ ...........Answer

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Calculate the average rate of change for the given function, from x = 2 to x = 7.

Marina86 [1]

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\

\begin{array}{ccll}
x&f(x)\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
-2&0\\2&15\\7&30
\end{array}
\qquad 
\begin{cases}
x_1=2\\
x_2=7
\end{cases}\implies \cfrac{f(7)-f(2)}{7-2}\implies \cfrac{30-15}{5}
\\\\\\
\cfrac{15}{5}\implies 3$

5 0

3 years ago

The mathematics department sponsors Math Family Fun Night every year. In the first year, there were 35 participants. In the th

Korolek [52]

1,35 3,57

slope = (57 - 35)/(3 - 1) = 11

y = 11 x + b

35 = 11 (1) + b

b= 24

y = 11x + 24

y = 11(5) + 24 = 79

3 0

3 years ago

population growth problem: the deer population in georgia was 450,000 in 2010, and the population doubles every 5 years. in what

VikaD [51]

We know that in 2020 the population of deer will be 900,000 based on the given numbers. In another 5 years the population will be over 1 million (1,350,000) in order to calculate when it will reach 1 million we need to see how much growth is gained per year. I believe to obtain that information we will need to divide 450,000 by 5 that equals 90,000 a year. So if I’m 2020 the population of deer will be 900,000 than add 90,000 until you reach your 1 million marker. In this case 2021 would be 990,000 thousand so 2022 would be 1,080,000. So your answer should be year 2022. Hope that helps.

8 0

2 years ago

The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the numb

Bezzdna [24]

Answer:

Part A) The amplitude = 24

Part B) The period = 24

Part C) Vertical shift = 36

Step-by-step explanation:

The general equation of the sine function:

y = A sin (Bx) + C

Where A is the amplitude and B = 360°/Period and C is the vertical shift

See the attached figure which represents the graph of m and f(m)

So,

Part A:

The function has minimum at 12 and maximum at 60

The difference is = 60 - 12 = 48

So, The amplitude = 48/2 = 24

Part B:

Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.

We can deduce that the function completes one cycle within 24 months

So, the period = 24

Part C:

Vertical shift is obtained at m = 0

So, f(m) = 36

36 = A sin (0) + C

C = 36 ⇒ Vertical shift

So, The amplitude = 24

The period = 24

Vertical shift = 36

8 0

3 years ago

Rewrite the function f(x) = -2(x+3)^2 – 8 in the form f (x) = ax²+bx+c.

OverLord2011 [107]

Answer:

-2x^{2}-12x-26

Step-by-step explanation:

(x+3)^2 = x^2+6x+9

-2(x^2+6x+9)-8

-2x^2-12x-18-8

-2x^2-12x-26

8 0

3 years ago