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Gemiola [76]
3 years ago
9

Identify the equation that translates Y = In(x) five units down

Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
8 0

Answer:

y = In(x) - 5

Step-by-step explanation:

The translation is a geometrical transformation, that changes the location of a figure. In a function, the independent term exerts a role in the translation of the graph.

Algebraically, to translate the function by shifting down 5 units. We have to insert in the domain a value that will return to zero and add negative 5 units.

To satisfy this condition, all that's left is the first and the last option.

Let's test.

y = In(x-5)

y=log_{e} (x-5)\\ y=ln (1-5)\\ y=ln(-4)\\ y=

There is no logarithm < 0

y = In(x) - 5

lnx=log_{e} x\\ y=log_{e}(x)-5\\ y=log_{e}(1)-5\\ y=0-5\\ y=-5

So (1,-5) this is the first point after the curve leaves the y axis

Geometrically, Check the graph below.

slamgirl [31]3 years ago
7 0
Y=ln(x)-5 because when shifting down you look at the number outside parenthesis
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PLZ HELP QUICK--------------&gt;
sveticcg [70]
<h2>>>> Answer <<<</h2>

Let's check which polynomial is divisible by ( x - 1 ) using hit , trial and error method .

A ( x ) = 3x³ + 2x² - x

The word " divisible " itself says that " it is a factor "

Using factor theorem ;

Let;

=> x - 1 = 0

=> x = 1

Substitute the value of x in p ( x )

p ( 1 ) =

3 ( 1 )³ + 2 ( 1 )² - 1

3 ( 1 ) + 2 ( 1 ) - 1

3 + 2 - 1

5 - 1

4

This implies ;

A ( x ) is not divisible by ( x - 1 )

Similarly,

B ( x ) = 5x³ - 4x² - x

B ( 1 ) =

5 ( 1 )³ - 4 ( 1 )² - 1

5 ( 1 ) - 4 ( 1 ) - 1

5 - 4 - 1

5 - 5

0

This implies ;

B ( x ) is divisible by ( x - 1 )

Similarly,

C ( x ) = 2x³ - 3x² + 2x - 1

C ( 1 ) =

2 ( 1 )³ - 3 ( 1 )² + 2 ( 1 ) - 1

2 ( 1 ) - 3 ( 1 ) + 2 - 1

2 - 3 + 2 - 1

4 - 4

0

This implies ;

C ( x ) is divisible by ( x - 1 )

Similarly,

D ( x ) = x³ + 2x² + 3x + 2

D ( 1 ) =

( 1 )³ + 2 ( 1 )² + 3 ( 1 ) + 2

1 + 2 + 3 + 2

8

This implies ;

D ( x ) is not divisible by ( x - 1 )

<h2>Therefore ; </h2>

<h3>B ( x ) & C ( x ) are divisible by ( x - 1 ) </h3>
6 0
3 years ago
Which line plot displays a data set with an outlier?<br><br> Plz answer quickly!
iren2701 [21]
The answer is the first data set because remember, an outlier is a number in a data set that is extremely far away from all of the other numbers.

You can easily tell which one is the outlier, the first data set's outlier is 13, because it is was placed so far away from the other data points.

We know that the first data set is correct because all of the other data sets have numbers that are clustered together.

~Hope I helped!~
7 0
3 years ago
Please help, any help would be appreciated.
k0ka [10]

Answer:

160,170 and 240,250

Step-by-step explanation:

sorry if wrong

3 0
2 years ago
The table shows the height of a plant as it grows. Which equation in point ­slope form gives the plant’s height at any time
vodka [1.7K]

Answer:

Option A is correct.

y-16=8(x-2) is the equation represent the point slope form gives the plant's height at any time.

Step-by-step explanation:

Point slope intercept form: For any two points (x_1, y_1) and  (x_2, y_2) then,

the general form

y-y_1=m(x-x_1) for linear equations;  where m is the slope given by:

m =\frac{y_2-y_1}{x_2-x_1}

Consider any two points from the table;

let A= (2 , 16) and B =(4, 32)

First calculate the slope of the line AB:

m =\frac{y_2-y_1}{x_2-x_1}=\frac{32-16}{4-2}=\frac{16}{2} = 8

Therefore, slope of the line m = 8

Then,

the equation of line is:

y-y_1=m(x-x_1)

Substitute the value of m=8 and (2, 16) above we get;

y-16=8(x-2)

Therefore, the equation in point slope form which gives the plant's height at any time is; y-16=8(x-2) , where x is the time(months) and y is the plant height (cm)


5 0
3 years ago
Read 2 more answers
Brainliest to most helpful! Answer asap!
kap26 [50]

ΔAOB is a right angled triangle. Therefore the Pythagorean Theorem applies in this situation.
θ is the angle from a standard position of the line OA

The length of the y component is √(1-0)2 +(-3-(-3))2] =√(12+ 02) = 1 A(-3,1) to B(-3,0) which is opposite

Then the length of the x-component is √[(-3-0)2 +(0-0)2] = √(9+0)= 3 B(-3,0) to O(0,0) which is adjacent

The length of vector OA is √[(-3-0)2 + (1-0)2] = √(9+1) = √(10) A(-3,1) to O(0,0) which is the hypotenuse of the triangle

θ = 180 - α
sinθ = sin(180-α) = opposite/hypotenuse = 1/√10
cosθ = adjacent/hypotenuse = -3/√10
tanθ = opposite/adjacent = 1/-3 = -1/3

α= arcsin(1/√10) ≈ 18
θ =180 -18 ≈162
8 0
3 years ago
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