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Rainbow [258]
2 years ago
8

Which steps transform the graph of y=x^2 to y=-(x-3)^2+2

Mathematics
1 answer:
damaskus [11]2 years ago
8 0

Answer:

reflection over the x-axis

shifted 3 right

shifted 2 up

Step-by-step explanation:

This function is quadratic. Quadratic graphs are written as y=a(x-h)^2+k. Where a is a non-zero number that affects the vertical appearance of the graph, h is the horizontal placement, and k is the vertical placement.

When a is negative then, the graph has been reflected over the x-axis. This makes it look like it has been turned upside down. The variable h affects how the x-values are shifted. In this equation, h looks negative but it is actually positive because if you look at the formula, h is being subtracted. Positive h values move the graph right. So, the graph is shifted 3 units to the right. Finally, k does the same thing as h but on the vertical (y) axis. So, +2 makes the graph shift 2 units up.

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Factor completely x2 − 36. (1 point)
puteri [66]

Answer:

Solution given:

x²-36

x²-6²

(x+6)(x-6)

is your answer

6 0
3 years ago
Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is 13.4 years with a s
Aliun [14]

Answer : 0.0129

Step-by-step explanation:

Given : Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is \mu=13.4 years and standard deviation is \sigma=1.7 years.

Sample size : n=40

Let X be the random variable that represents the age of fleets.

We assume that the ages of the fleets of the 10 largest U.S. commercial passenger carriers are normally distributed.

For z-score,

z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

For x=14

z=\dfrac{14-13.4}{\dfrac{1.7}{\sqrt{40}}}\approx2.23

By using the standard normal distribution table , the probability that the average age of these 40 airplanes is at least 14 years old will be :-

P(x\geq 14)=P(z\geq2.23)\\\\=1-P(z

Hence, the required probability = 0.0129

6 0
3 years ago
1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING
iogann1982 [59]

If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

then

y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}

We can solve the recurrence exactly by substitution:

a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0

\implies a_n=\dfrac{(-2)^n}{n!}a_0

So the ODE has solution

y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

which you may recognize as the power series of the exponential function. Then

\boxed{y(x)=a_0e^{-2x}}

7 0
3 years ago
Jenny's father works at the local grocery store. He just finished setting up a display of soup cans in the shape of a triangle.
Anit [1.1K]
If i’m correct, the answer is simply 48!!
7 0
1 year ago
What percent of 8 is 14
seraphim [82]

Answer:

57.14

Step-by-step explanation:

8/14 =x/100

cross multiply

800= 14x

x=57.1428

7 0
3 years ago
Read 2 more answers
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