What is f x )= x 2 called?

Answer:

[tex]f"'(x) = 2(x-4)^2 - 1[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2[/tex] --- the quadratic function

Vertically stretched by 2

Translation: [tex]4\ units[/tex] left and [tex]1\ unit[/tex] down

Required

Determine the new function

[tex]f(x) = x^2[/tex]

The rule for vertical stretch is:

[tex](x,y) \to (x,ay)[/tex]

In this case:

[tex]a = 2[/tex]

So, we have:

[tex]f(x) = x^2[/tex]

[tex]f'(x) = a * f(x)[/tex]

[tex]f'(x) = a * x^2[/tex]

Substitute: [tex]a = 2[/tex]

[tex]f'(x) = 2 * x^2[/tex]

[tex]f'(x) =2x^2[/tex]

Translation: 4 units left

The rule is:

[tex](x,y) \to (x - c,y)[/tex]

In this case: [tex]c =4[/tex]

So, we have:

[tex]f"(x) = 2(x - 4)^2[/tex]

Translation: 1 unit down

The rule is:

[tex](x,y) \to (x,y-d)[/tex]

In this case, [tex]d=1[/tex]

So, we have:

[tex]f"'(x) = f"(x) - 1[/tex]

[tex]f"'(x) = 2(x-4)^2 - 1[/tex]

Answer:

Answer with steps........

Answer:

Step-by-step explanation:

8.13<8.4

.004<.05

.4 repeating>.4

Answer:

The value of the angle is 60 degrees

Step-by-step explanation:

Here, we want to find the value of the angle marked 2

From the question, we can see that we have three marked interior angles

These are the angles 1, 2 and 3

Mathematically, the interior angles of an equilateral triangle are equal

This means that each of the interior angle of an equilateral triangle measures 60 degrees

Hence, this means that the value of the angle marked 2 is 60 degrees

Answer:

the answer should be 38.75

Answer:

preferred

ability

extraordinary

parading

playing

squeaky clean

occasion

immediately

Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3 ?

Let the given points be A(-1,7) and B(4,-3)

Now,

Let the point be P(x, y) which divides AB in the ratio 2:3

Here,

Where,

[tex] m_1 [/tex] = 2 , [tex] m_2 [/tex] = 3

[tex] x_1 [/tex] = -1 , [tex] x_2 [/tex] = 4

[tex] \therefore [/tex] Putting values we get,

x = [tex] \frac{2 \: × \: 4 \: + \: 3 \: × \: -1}{2 \: + \: 3} [/tex]

x = [tex] \frac{8 \: - \: 3}{5} [/tex]

x = [tex] \frac{5}{5} [/tex]

x = 1

Now,

Finding y

Where,

[tex] m_1 [/tex] = 2 , [tex] m_2 [/tex] = 3

[tex] x_1 [/tex] = 7 , [tex] x_2 [/tex] = -3

[tex] \therefore [/tex] Putting values we get,

y = [tex] \frac{2 \: × \: -3 \: + \: 3 \: × \: 7}{2 \: + \: 3} [/tex]

y = [tex] \frac{-6 \: + \: 21}{5} [/tex]

y = [tex] \frac{15}{5} [/tex]

y = 3

Hence x = 1, y = 3

So, the required point is P(x, y)

= P(1, 3)

_______________________________________

Note:- Refer the attachment.

_______________________________________

Answer:

ruffles classic + those two bite cupcakes literally best thing to exist

Step-by-step explanation:

Answer:

Honestly, twinkies with twinkies

Step-by-step explanation:

#WhyNot

Answer:

The equation of the the line that is perpendicular to 4·x + 6·y = 1 and that has a greater intercept to the line 2·x + 3·y = 18 can be 2·y - 3·x = 14

Step-by-step explanation:

The line which is perpendicular to the required line = 4·x + 6·y = 1

The line with which the required line has a greater intercept = 2·x + 3·y = 18

Solution;

The relationship between the slope, m₁, of a straight line, y = m₁·x + c₁ perpendicular to another straight line, y = m₂·x + c₂, with slope m₂ is given as follows;

m₁ = -1/m₂

Rewriting the equation of the given line in slope and intercept form gives;

4·x + 6·y = 1

6·y = 1 - 4·x

y = 1/6 - 4·x/6 = 1/6 - 2·x/3 =  1/6 - (2/3)·x

∴ y = 1/6 - (2/3)·x

Therefore, the slope, 'm₁', of the line y = 1/6 - (2/3)·x, is m₁ = -(2/3)

The slope of the perpendicular line, is therefore, m₁ = -1/m₂

∴ m₂ = -1/m₁

m₂ = -1/(-(2/3)) = 3/2

The intercept of a straight line of the form y = m·x + c is 'c'

The intercept of the line 2·x + 3·y = 18 is obtained by rewriting the equation of the line in slope and intercept form as follows;

2·x + 3·y = 18

y = 18/3 - (2/3)·x = 6 - (2/3)·x

y = 6 - (2/3)·x = -(2/3)·x + 6

y = -(2/3)·x + 6

By comparing the above equation to the equation, y = m·x + c, we have;

c = 6

The intercept of the line y = -(2/3)·x + 6, which is the same line as 2·x + 3·y = 18 is 6

∴ The intercept of the required line, c₂ > 6

The equation of the required  line in slope and intercept form, y = m·x + c, can therefore be;

y = (3/2)·x + 7

By multiplying by 2, we get;

2·y = 3·x + 14

∴ The equation of the line can be 2·y - 3·x = 14.

Respuesta: 3/2= 1 1/2

Answer:

1 1/2 or 1.5

Step-by-step explanation:

To divide a fraction, use the phrase, "keep, change, flip"

We keep the first fraction as it is, change the sign to multiplication, and flip the second fraction to its multiplicative inverse.

So 3/4 divided by 1/2 becomes:

3/4 x 2/1

= 6/4 = 1 1/2

Answer:

No, Estelle made a mistake in step 2

Step-by-step explanation:

Answer:

-11/42, -10/42, 10/42, 11/42, 12/42

Step-by-step explanation:

First of let's find the LCM of the denominators.

LCM of 6 and 7 is 42

Thus, -2/7 can also be expressed in terms of 42 as denominator as; -12/42

Similarly, 5/6 can also be expressed in terms of 42 as denominator as; 35/42

Thus, any five rational numbers could come in the form of the numerator being between -12 to 35 with the denominator being 42.

Thus, five rational numbers between -2/7 and 5/6 are;

-11/42, -10/42, 10/42, 11/42, 12/42

Answer:

Hieight is 65m

volume is 35

Step-by-step explanation:

Answer:

18cm

Step-by-step explanation:

Answer:

me ig

Step-by-step explanation:

X-intercept (5,0),(1,0)

Y-intercept (0,5)

Vertex (3,-4)

Axis of Symmetry x=3

Answer:

blank 1- 2304

blank 2-  2736

Step-by-step explanation:

hope it helps

Answer:

x = 15

Step-by-step explanation:

x² = 12² + 9²

x² = 144 + 81

x² = 225

x = √225

x = 15

Answer:

Step-by-step explanation:

Divide the US population by the world population:

328,200,000/7,674,000,000 = 0.0428

Multiply 0.0428 with 100:

0.0428 x 100 = 4.28

Approximately 4 out of 100 people in the world would live in the USA.

Answer:6

Step-by-step explanation: for mean you add up the heights and divide it by the amount of numbers there are

Answer:

Probability: 131/195

Step-by-step explanation:

Total cookies:

7 + 6 + 2  = 15

Total candies:

14 + 12 = 26

Probability of raisin:

2/15

Probability of peppermint:

14/26 = 7/13

Probability of both:

2/15 + 7/13

131/195

Answer:

2/3 x 12=8

1/4 x 12= 3

3/4 x 12 =9

1/2 x 12 = 6

Answer:

65.38degrees

Step-by-step explanation:

Given the following

Length of ladder = 12foot = hypotenuse

Distance of the ladder from the wall = 5ft = adjacent

Required

Angle between the ground and the ladder theta

Using the SOH CAH TOA identity

Cos theta = adj/hyp

Cos theta = 5/12

Cos theta = 0.41667

theta = arccos(0.41667)

theta = 65.38 degrees

Hence the angle between the ground and the floor is 65.38degrees

Answer:

The answer of this question is False

Answer:

19.550

Step-by-step explanation:

Sorry if I am wrong.....

Answer:

p(x - 4) = x³ - 12x² + 48x - 69

Step-by-step explanation:

To evaluate p(x - 4), substitute a = x - 4 into p(a), that is

p(x - 4) = (x - 4)³ - 5

            = (x - 4)(x - 4)(x - 4) - 5 ← expand 2nd/ 3rd factors using FOIL

            = (x - 4)(x² - 8x + 16) - 5 ← distribute parenthesis

            = x³ - 8x² + 16x - 4x² + 32x - 64 - 5 ← collect like terms

           = x³ - 12x² + 48x - 69

Answer:

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

Step-by-step explanation:

Answer:

hight is 158

Step-by-step explanation: