What is the equivalent fraction to 2/3

Determine the equation of g(x) that results from translating the function f(x)=x^2+9 upward 10 units.

Rus_ich [418]

The simple/ common sense method:
The typical lay out of a quadratic equation is ax^2+bx+c
'c' represents where the line crosses the 'y' axis.
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change.
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher.
9+10=19,
therefore c=19.
The new equation is: y=x^2+19 

The most complicated/thorough method:
This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x).
Use the -b/2a formula to find the 'x' coordinate of your vertex..
x= -0/2*1, your x coordinate is therefore 0.
substitute your x coordinate into your equation to find your y coordinate..
y= 0^2+0+9
y=9.
Your coordinates of your vertex f(x) are therefore (0,9) 
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x) are therefore:
(0, 19) 
substitute your vertex's y coordinate into f(x)
19=x^2+c
19=0+c
c=19
therefore g(x)=x^2+19

7 0

3 years ago

Read 2 more answers

I can’t figure out how to use the zeros in the polynomial. Please explain

Temka [501]

Answer:

a) $P (x) = (x + 3) (x-1) (x-4)$

b) $P (x) = (2x + 5) (5x - 4) (x-6)$

c) $P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2$

Step-by-step explanation:

For the question a * you need to find a polynomial of degree 3 with zeros in -3, 1 and 4.

This means that the polynomial P(x) must be zero when x = -3, x = 1 and x = 4.

Then write the polynomial in factored form.

$P (x) = (x + 3) (x-1) (x-4)$

Note that this polynomial has degree 3 and is zero at x = -3, x = 1 and x = 4.

For question b, do the same procedure.

Degree: 3

Zeros: -5/2, 4/5, 6.

The factors are

$x = -\frac{5}{2}\\\\x +\frac{5}{2} = 0\\\\(2x +5) = 0$

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

$x =\frac{4}{5}\\\\x-\frac{4}{5} = 0\\\\(5x-4) = 0$

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

$x = 6\\\\(x-6) = 0$

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

$P (x) = (2x + 5) (5x - 4) (x-6)$

Finally for the question c we have

Degree: 5

Zeros: -3, 1, 4, -1

Multiplicity 2 in -1

$x = -3\\\\(x-3) = 0$

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

$x = 1\\\\(x-1) = 0$

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

$x = 4\\\\(x-4) = 0$

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

$x = -1\\\\(x + 1) = 0$

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

$P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2$

8 0

2 years ago

24 candy bars cost $48. How much do 10 candy bars cost?

timofeeve [1]

Answer: $20

$48/24 = $2 for each candy bar

10 candy bars * $2 = $20

8 0

1 year ago

Out of the total respondents, the percentage of respondents from the 46–55 age group who rated the film excellent is %. write yo

Mrrafil [7]

Missing data:

Viewer's Age Group Excellent Good Average Poor Marginal Total

16–25 52 42 12 7 113

26–35 33 50 5 9 97

36–45 58 12 28 34 132

46–55 25 17 22 12 76

56 + 12 5 3 8 28

Marginal Total 180 126 70 70 446

A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.

<h3>How to determine the rating of the film from the 46–55 age group?</h3>

A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.

25/446 = 0.05605

0.05605 $*$ 100% = 5.605%

Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.

To learn more about data refer to:

brainly.com/question/4219149

#SPJ4

3 0

1 year ago

a right triangle has legs of length 3x m and 4x m and hypotenuse of length 75 m. find the lengths of the legs of the triangle

just olya [345]

It is a 3-4-5 right triangle

leg1 := 3x, leg2:=4x, hypotenuse:=5x

given hypotenuse = 75m
=> 5x=75
So, x= 75÷5 = 15
Therefore, leg1 = 3(15) = 45m.
leg2= 4(15) = 60m.

4 0

2 years ago