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Alenkasestr [34]
2 years ago
6

The line 3x - 2y = 12 has:

Mathematics
1 answer:
faltersainse [42]2 years ago
4 0

Answer: a slope of 3/2 and a y-intercept of -6

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Identify the vertex and zeros of the function.
kirza4 [7]

Answer:

zeros: x=-6, x=2

Vertex: (-2,-16)

Step-by-step explanation:

try using math-way

5 0
3 years ago
Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i
jenyasd209 [6]

Answer:

If the limit that you want to find is \lim_{x\to \infty}\dfrac{P(x)}{Q(x)} then you can use the following proof.

Step-by-step explanation:

Let P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0} and Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0} be the given polinomials. Then

\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}

Observe that

\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}

and

\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}

Then

\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}

3 0
3 years ago
The weights (in pounds) of 18 preschool children are
ivanzaharov [21]

Answer:

22.8 and 37.5

Step-by-step explanation:

Given the

The weights (in pounds) of 18 preschool children are

32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29

To find its 20th percentile and 75th percentile.

In ascending order we get like this

Position  X (Asc. Order)

1  20

2  21

3  22

4  23

5  24

6  25

7  27

8  29

9  30

10  31

11  32

12  33

13  34

14  37

15  39

16  41

17  44

18  45

Percentile position = (no of entries +1)20/100 = 19/5 = 3.8

Since posiiton is not integer we use interpolation method.

The value of 3.8 - 3 = 0.8 corresponds to the proportion of the distance between 22 and 23 where the percentile we are looking for is located at.

Hence 20th percentile = 22+0.8(23-22)=22.8

So answer is 22.8

----------------------

75th percentile

Percentile posiiton = 19(75)/100 = 14.25

75th percentile= 37+0.25(39-37)=37.5

6 0
3 years ago
How many solutions will this system of equations have?
elena55 [62]
This system will have 1 solution, or C. That's because since the equations are different, meaning that there is 1 solution. 
7 0
3 years ago
Last month 4,861 books were checked out from the Library.this month 3,278 books were checked out.how many more books were checke
ludmilkaskok [199]

Answer:

1,583

Step-by-step explanation:

4,861 - 3278 = 1,583. All you have to do is subtract each amount of books from both months.

6 0
2 years ago
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