What are the vertices of triangle ABC'if triangle ABC is dilated by a scale factor of 3?

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:

[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:

me ig

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:

Complex numbers often use the letter i (that is, they often have imaginary elements) while real numbers don't have any imaginary elements. Below are some examples:

Step-by-step explanation:

1+2i is an example of a complex number.

3a - 4b is an example of a real number.

Answer:

18cm

Step-by-step explanation:

Answer:6

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

Answer:

The answer of this question is False

Answer:

50.27in

Step-by-step explanation:

Given data

Diameter of small tire= 13in

Radius= 13/2= 6.5in

Circumference= 2πr

C= 2*3.142*6.5

C= 40.85 in

Diameter of Big tire= 29in

Radius= 29/2= 14.5in

Circumference= 2πr

C= 2*3.142*14.5

C= 91.118in

Hence the difference in distance between the two tires after on revolution is

=91.118-40.85

=50.27in

Answer:

19.550

Step-by-step explanation:

Sorry if I am wrong.....

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:

A

Step-by-step explanation:

A because it is the only one the recipe calls for 1 cup of sugar and 1/2 cup of flour, the point is in the middle but also on one.

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:

Step-by-step explanation:

8.13<8.4

.004<.05

.4 repeating>.4

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.

Answer:

(5,3) and (0,-1)

Gradient,m =3-(-1)/5-0

m=4/5

y=mx+C

y-3=4/5 (x-5)

y=4x/5-4+3

y=4x/5 -1

B. Michelle weighed 75 pounds two years ago

Answer:

x = 15

Step-by-step explanation:

x² = 12² + 9²

x² = 144 + 81

x² = 225

x = √225

x = 15

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:

No, Estelle made a mistake in step 2

Step-by-step explanation:

Answer:

5x-3=3x+5

5x-3x=5+3

2x=8

x=8/2

x=4

Therefore,

Value of 2x-8

Substitute the value of x

2(4)-8

8-8=0

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Answer:

Answer with steps........

Answer:

preferred

ability

extraordinary

parading

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squeaky clean

occasion

immediately

Answer:

5

Step-by-step explanation:

like my answer please...

Answer:

30.67

Step-by-step explanation:

Given the following

Opposite side = x

Adjacent = 17

Angle = 61degrees

Using the SOH  CAH TOA identity

tan theta = opp/adj

tan 61 = x/17

x = 17tan61

x = 17(1.8040)

x = 30.67

Hence the value of x is 30.67

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

Y-intercept (0,5)

Vertex (3,-4)

Axis of Symmetry x=3