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Arlecino [84]
3 years ago
6

How to change numbers into decimals using common core standards?

Mathematics
1 answer:
VLD [36.1K]3 years ago
4 0
Assuming you are talking about converting fractions to decimals, divide the numerator (top number) by the denominator (bottom number). If it isn't one you can solve in your head, use long division.
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In the year 1995, there were 1200 students at pine elementary school. In the year 2010 there were 1500 students. Find the rate o
AnnZ [28]

The rate of change from 1995 to 2010 is 20 students per year and the linear function that models the data will be: y=20x-38700

<em><u>Explanation</u></em>

In the year 1995, there were 1200 students and in the year 2010, there were 1500 students.

If x represents the year and y represents the number of students, then two points in form of (x,y) will be: (1995, 1200) and (2010, 1500)

So, the rate of change or slope = (change in value of y / change in value of x) =\frac{1500-1200}{2010-1995}= \frac{300}{15}=20

Now, plugging  slope(m) = 20 and first point (x_{1}, y_{1}) =(1995,1200)  into <u>point slope form of linear equation</u> y-y_{1} =m(x-x_{1}) , we will get.....

y-1200=20(x-1995)\\ \\ y-1200=20x-39900\\ \\ y= 20x-39900+1200\\ \\ y= 20x-38700



4 0
3 years ago
By driving 8 mph faster than Bob, John can make a 230 mile trip in one half hour less. How fast does Bob drive on the trip? Roun
____ [38]

Answer: The speed of Bob is 56.8 km/hr.

Step-by-step explanation:

Let the speed of Bob be 'x'.

Let the speed of John be 'x-8'.

Distance covered = 230 miles

time = 1\dfrac{1}{2}=\dfrac{3}{2}\ hr

According to question, we get that

\dfrac{230}{x}-\dfrac{230}{x+8}=\dfrac{3}{2}\\\\230\dfrac{x+8-x}{x(x+8)}=\dfrac{3}{2}\\\\\dfrac{230\times 8}{x^2+8x}=\dfrac{3}{2}\\\\\dfrac{1840}{x^2+8x}=\dfrac{3}{2}\\\\1840\times 2=3x^2+24x\\\\3680=3x^2+24x\\\\3x^2+24x-3680=0\\\\x\approx 56.8\ km/hr

Hence, the speed of Bob is 56.8 km/hr.

6 0
3 years ago
The answer and I will mark Brainalist
Oliga [24]

Answer: G would be your answer, or c = 8k + 24

Step-by-step explanation:

6 0
2 years ago
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FinnZ [79.3K]
A. 8/$12=21/$x then cross multiply.
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3 0
3 years ago
HELP PLS Given a polynomial function f(x), describe the effects on the Y-intercept, regions where the graph is increasing and de
Mashcka [7]
1. Remarks:

f(x) to f(x)-3 is the whole graph of f(x), shifted 3 units down. 

f(x) to -2f(x): 

The effect of "multiplication by -" is that the whole graph is reflected with respect to the x axis, so it is turned upside down.
 
The effect of "multiplication by 2" is that every point is "stretched vertically by a factor of 2" . So for example the point (-1, -4) in the original function, becomes (-1, -8) in the second one. Or (2, 5) would become (2, 10). 

The only points that do not change (are not streched vertically) are the roots. For example if (4,0) is an x-intercept (a root) in the original function, (4,0) is still a root in the second one because  2 times 0 is still 0.


2. Consider the polynomial function of degree n: 

f(x)= a_{n} x^{n} +a_{n-1} x^{n-1}+....+a_{2} x^{2}+a_{1} x^{1}+a_{0}

a. Y-intercept

The y - intercept is the value of the polynomial function at x=0. 
So it is f(0)=a_{0}, that is, the constant term of f(x)

in f(x)-3 the y intercept is shifted 3 units down as any other point, so it becomes  a_{0}-3

In -2f(x), the y-intercept a_{0} becomes -2a_{0}

b. Regions of f decreasing or increasing

f(x)-3 is f(x) just shifted down 3 units, so they are both increasing and decreasing in the same intervals of x

-2f(x) is f(x) turned upside down, so -2f(x) is increasing in all intervals f(x) is decreasing and it is decreasing in all intervals f(x) is increasing.

c. End behaviors

By now it is clear that end behaviors of f(x) and f(x)-3 are same, and f(x) with -2f(x) are opposite

d. Evenness, oddness

If f(x) is even, then f(x)=f(-x)

Let g(x)=f(x)-3

g(x)=f(x)-3=f(-x)-3=g(-3), so in this case f(x)-3 is even

If f(x) is odd, then f(-x)=-f(x)

g(x)=f(x)-3=-f(-x)-3,

so -g(x)=f(-x)+3

g(-x)=f(-x)-3,  

so g(-x) is not equal to -g(x). Which means f(x)-3 is not odd if f(x) is


Consider f(x)=-2f(x)

If f(x) is even, f(x)=f(-x)

g(x)=-2f(x)=-2f(-x)
g(-x)=-2f(-x)

So g(x)=g(-x), which means -2f(x) is even if f(x) is even

If f(x) is odd, f(x)=-f(-x)

let g(x)=-2f(x)=-2(-f(-x))=2f(-x)

g(-x)=-2f(-x)=-2(-f(x))=2f(x)

so g(-x) is not equal to -g(x), thus -2f(x) is not odd if f(x) is odd.

The conclusions about oddness and evenness can be also derived from the discussions about the graphs.
 

6 0
3 years ago
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