Simplify
a(2a - 3) + 6(a - 0.5) - (2a^2 - 5)

Answer:

min = (4, -136) ; max = (-2,80)

Step-by-step explanation:

The option is B

The (-2, 80) is a relative minimum, (4, -136) relative maximum option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The cubic function:

f(x) = 2x³ - 6x² - 48x + 24

Find f'(x):

f'(x) = 6x² - 12x - 48

Equate f'(x) to zero:

6x² - 12x - 48 = 0

Find the roots of the quadratic equation:

x = -2

x = 4

Find f''(x):

f''(x) = 12x - 12

Plug x = -2

f''(-2) = -24 - 12 = -36 < 0

At x = -2 f(x) is minimum

f(-2) = 80

Plug x = 4

f''(4) = 48 - 12 = 36 > 0

At x = 4 f(x) is maximum

f(4) = -136

Thus, the (-2, 80) is a relative minimum, and (4, -136) relative maximum option (C) is correct.

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Answer:

792, 784, 775, 675, 645, 434, 432, 415, 342, 324.

Answer:

La lancha y el bote se encontrarán a 70 metros de distancia del puente.

Step-by-step explanation:

Sea el punto debajo del puente el punto de referencia y que ambas lanchas se desplazan a velocidad a continuación, las ecuaciones cinemáticas para cada embarcación son presentadas a continuación:

Bote a 7 metros por segundo

[tex]x_{A} = x_{o}+v_{A}\cdot t[/tex] (Ec. 1)

Lancha a 10 metros por segundo

[tex]x_{B} = x_{o}+v_{B}\cdot (t-3\,s)[/tex] (Ec. 2)

Donde:

[tex]x_{o}[/tex] - Posición debajo del puente, medido en metros.

[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Posición final de cada embarcación, medido en metros.

[tex]v_{A}[/tex], [tex]v_{B}[/tex] - Velocidad de cada embarcación, medida en metros por segundo.

[tex]t[/tex] - Tiempo, medido en segundos.

Para determinar la posición en la que ambas embarcaciones se encuentran, se debe determinar el instante en que ocurre a partir de la siguiente condición: [tex]x_{A} = x_{B}[/tex]

Igualando (Ec. 1) y (Ec. 2) se tiene que:

[tex]v_{A}\cdot t = v_{B}\cdot (t-3\,s)[/tex]

Ahora despejamos el tiempo:

[tex]3\cdot v_{B} = (v_{B}-v_{A})\cdot t[/tex]

[tex]t = \frac{3\cdot v_{B}}{v_{B}-v_{A}}[/tex]

Si sabemos que [tex]v_{B} = 10\,\frac{m}{s}[/tex] y [tex]v_{A} = 7\,\frac{m}{s}[/tex], entonces:

[tex]t = \frac{3\cdot \left(10\,\frac{m}{s} \right)}{10\,\frac{m}{s}-7\,\frac{m}{s}}[/tex]

[tex]t = 10\,s[/tex]

Ahora, la posición de encuentro es: ([tex]x_{o} = 0\,m[/tex], [tex]v_{A} = 7\,\frac{m}{s}[/tex] y [tex]t = 10\,s[/tex])

[tex]x_{A} = 0\,m + \left(7\,\frac{m}{s} \right)\cdot (10\,s)[/tex]

[tex]x_{A} = 70\,m[/tex]

La lancha y el bote se encontrarán a 70 metros de distancia del puente.

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

[tex]6x+3=38-x[/tex]

Subtract 3 from both sides:

[tex]6x+3-3=38-x-3[/tex]

[tex]6x=-x+35[/tex]

Add x to both sides:

[tex]6x+x=-x+35+x[/tex]

[tex]7x=35[/tex]

Divide 7 on both sides:

[tex]\frac{7x}{7}=\frac{35}{7}[/tex]

[tex]x=5[/tex]

Answer:

x=16

Step-by-step explanation:

I hope this helps you

Dear student,

I request you to make you question more clear.

thank you,

________ ___________________________________

Answer:

-22

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter = Circumference

Step 1. Know and recognize what you have

C = pi*d

pi = 3.142

d = 10

Step 2. Solve for the circumference of whole circle

C = 3.142*10

C = 31.42

Step 3. Solve for the questions answer

C of semicircle = 31.42/2

Hope this helped,

Kavitha

Answer:

7

Step-by-step explanation:

3x – one-ninthy = 18, when y = 27?

one-ninthy 27 = 3

3x - 3 = 18

3 x 7 = 21

21 - 3 = 18

hope this helps

Answer:

7

Step-by-step explanation:

answered on edge

Answer:

The arrow has the rotational symmetry after a 180 degree rotation

Step-by-step explanation:

It looks the same after tuning it by that degree, also i took the test :)

The terminal point on the unit circle determined by π radians is (-1, 0).

To find the terminal point on the unit circle determined by π radians, we can use the properties of the unit circle.

The unit circle is a circle with a radius of 1 unit centered at the origin (0, 0) in a coordinate plane. The point on the unit circle determined by an angle θ is given by (cosθ, sinθ).

Since we want to find the terminal point determined by π radians, we can substitute π into the formulas for cosine and sine:

x = cos(π) = -1

y = sin(π) = 0

The terminal point on the unit circle determined by π radians is (-1, 0).

It's important to note that on the unit circle, π radians corresponds to half of the circumference of the circle. In other words, it represents a point on the circle that is diametrically opposite to the point (1, 0) which corresponds to 0 radians.

By understanding the relationship between angles and their corresponding points on the unit circle, we can easily determine the coordinates of terminal points for various angles.

For more such questions on terminal point on the unit circle

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Answer:

$98

Step-by-step explanation:

56/8= 7

7x14=98

Hope this helps.

Answer:

It is 12.9, 13.1, 13.2 C.

Step-by-step explanation:

List C shows the times in order from least to greatest i.e. 12.9, 13.1, 13.2.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that, three sixth-grade students competed in the 100-meter dash time taken by Tiana, James and Dakota will be 13.1, 13.2 and 12.9

The numbers are written in an ordered list according to their values when they are arranged from least to greatest.

The smallest number should be written on the left, followed immediately by the next smallest number. Numbers should be ordered from lowest (first) to highest (last). It is known as "Ascending Order."

The numbers are arranged as 12.9< 13.1 < 13.2

Thus, list C shows the times in order from least to greatest i.e. 12.9, 13.1, 13.2.

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Answer:c

Step-by-step explanation:

Answer:

[tex]\sqrt{136}[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem!

Steps to solve:

10/r - 7 - 6b when r = 5 and b = -6

~Substitute

10/5 - 7 - 6(6)

~Simplify

5 - 7 + 36

~Subtract

-2 + 36

~Add

34

Best of Luck!

Answer:

The box plot

Step-by-step explanation:

Answer:

- 14

Step-by-step explanation:

[tex]f(x) = - 5 {x}^{2} - 4x + 19 \\ plug \: x = - 3 \\ f( - 3) = - 5 {( - 3)}^{2} - 4( - 3) + 19 \\ f( - 3) = - 5 \times 9 + 12 + 19 \\ f( - 3) = - 45 + 31 \\ f( - 3) = -14[/tex]

Answer:

34

Step-by-step explanation:

1. if to guess the Caleb's age is 'x' years and Linda's age is 'y' years now, then

2. according to the 'sum of the ages of Caleb and Linda is 55 years' it may be written: x+y=55 - the first equation of the system;

3. according  to the condition '8 years ago, Caleb's age was 2 times Linda's age' it may be written: (x-8)(y-8)=2 - the second equation of the system;

4. if to make up the system of two equation and calculate the values of 'x' and 'y':

5. if x=34, then Caleb is 34 old now.

Answer:

C≈31.42

r Radius 5

Answer:

Step-by-step explanation:

the answer is .25 because i got it right and it makes alot of sense

Answer:

Step-by-step

i) a² - 2ab + b² = (a + b)²

a² = p² ;     a  = p

b² = 16 = 4²  ;        b = 4

2ab = 2*p*4 = 8p

p² - 8p + 16 = (p - 4)²

ii) a² + 2ab + b² = (a +b)²

a² = 121x² = (11x)²                 ;  b² = 4y² = (2y)²

2ab = 2 * 11x * 2y = 44xy

121x² + 44xy + 4y² = (11x + 2y)²

Answer:

If B is the midpoint, it means

AC=2AB

8= 2(3x-1)

8= 6x-2

8+2= 6x

10= 6x

x= 10/6

x= 1.67

Hope it helps :-)

Answer:

1) mass divided by volume

Step-by-step explanation:

Answer:

1. Mass Divided By Volume

Step-by-step explanation:

D = M / V

Density is equal to mass. (In any form such as: grams, pounds or another unit)

Answer:

first term (a) = 54

Second term (b) = 18

common ratio = b/a = 18/54 = 1/3

Answer:

The numeric value is a statistic because the data set of salaries of 50 employees is a sample

Step-by-step explanation:

50 of a company's 800 employees is $54,000.

800 is the population, of all the employees of the company

$54,000 is the value of 50 employees which sample or subset is of 800 employees

23.67 X 2.03 = 48.0501

Hope this helps! :)

Answer:

48.0501

Step-by-step explanation: