For which interval is the average rate of change of f(x) negative?

Answer:

x = 1, x = 2

Step-by-step explanation:

Given

3x(x - 2) = x² - 4 ← distribute parenthesis on left side

3x² - 6x = x² - 4 ( subtract x² - 4 from both sides )

2x² - 6x + 4 = 0 ( divide through by 2

x² - 3x + 2 = 0 ← in standard form

Consider the factors of the constant term (+ 2) which sum to give the coefficient of the x- term (- 3)

The factors are - 1 and - 2 , since

- 1 × - 2 = + 2 and - 1 - 2 = - 3 , then

(x - 1)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.

I've added the image of the ticket as an attachment.

(a) The missing side length

From the attachment, the 4 unknown side lengths are equal. Represent this side length with L.

So, we have:

[tex]Perimeter =2\times 11 + 4 \times L[/tex]

This gives

[tex]2\times11 + 4 \times L = 42[/tex]

[tex]22 + 4 \times L = 42[/tex]

Collect like terms

[tex]4 \times L = 42-22[/tex]

[tex]4 \times L = 20[/tex]

Divide both sides by 4

[tex]L =5cm[/tex]

(b) The length of the gold lines

There are 4 slant lines and the length of one of the slant lines is 5 cm (as calculated above).

So, the length of the gold line is:

[tex]Gold = 4 \times L[/tex]

[tex]Gold = 4 \times 5cm[/tex]

[tex]Gold = 20cm[/tex]

(c) The number of gold ink bottles.

[tex]n = 200[/tex] --- number of tickets

The length of all gold line in the 200 tickets is:

[tex]Length = 200 \times Gold[/tex]

[tex]Length = 200 \times 20cm[/tex]

[tex]Length = 4000 cm[/tex]

[tex]Length = 4000 \times 0.01m[/tex] ---- convert to meters

[tex]Length = 40m[/tex]

Given that:

[tex]Bottle = 20m[/tex] --- 1 bottle for 20 m

The number of bottles (n) is:

[tex]n = \frac{Length}{Bottles}[/tex]

[tex]n = \frac{40m}{20m}[/tex]

[tex]n = 2[/tex]

Hence, 2 bottles of gold ink are enough.

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Answer:

HCF is 4

LCM is 336

Step-by-step explanation:

2/28 , 48

2/14 , 24

2/7 , 12

2/7 , 6

3/7 , 3

7/7 , 1

1 , 1

HCF is 2 × 2 =4

LCM is 2 × 2 × 2 × 2 × 3 × 7 = 336

Answer:

x = 100

Step-by-step explanation:

(100-40)/2

= 60/2

= 30

So it's 100

Answered by GAUTHMATH

Answer:

4x² - 5x - 8 = 0

Step-by-step explanation:

Standard form of a quadratic: ax² + bx + c

Move all terms to one side and sort them based on the level of degree:

[tex]4x^2-9x-8=-4x\\4x^2-9x+4x-8=0\\4x^2-5x-8=0[/tex]

Answer:

4x^2 -5x-8 =0

Step-by-step explanation:

ax^2 + bx + c = 0 is the standard form

4x^2 -9x-8 =-4x

Add 4x to each side

4x^2 -9x+4x-8 =-4x+4x

4x^2 -5x-8 =0

Answer:

3

Step-by-step explanation:

Answer:

V = 180 ft^3

Step-by-step explanation:

The volume of a cone is found by

V = 1/3 pi r^2 h  where r is the radius and h is the height

The diameter is 12 so the radius is 1/2 the diameter or 1/2(12) = 6

The height is 5 and we are using 3 for pi

V = 1/3 (3) *6^2 *5

V = 180 ft^3

Answer:

The p is 4

Step-by-step explanation:

Answer:

y = 2x+4

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

    = ( 12-6)/(4-1)

   = 6/3

    = 2

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 2x+b

Using a point from the table

10 = 2(3)+b

10 = 6+b

10-6 = b

4=b

y = 2x+4

Answer:

-5x = 26 is 5.2

x/2 = 4 is -8

3/2x=6 is 4

x/-7.2=4 is 28.8

Answer:

17 and 19

Step-by-step explanation:

Let n denote the first odd integer.

If the two integers are consecutive and odd, then the second number is n+2.

Hence, n+n+2=36

=2n=34

Divide both sides by 2

=n=17

Therefore, the numbers are 17 and 19.

Answer:

72

The result is rational because it can be written as the ratio of two integers and its decimal expansion can terminate or repeat.

Answered by GAUTHMATH

Answer:

m = - 31

Step-by-step explanation:

Given

[tex]\frac{m-1}{2}[/tex] - [tex]\frac{m-2}{3}[/tex] = [tex]\frac{m-4}{7}[/tex]

Multiply through by 42 , the LCM of 2, 3 and 7 , to clear the fractions

21(m - 1) - 14(m - 2) = 6(m - 4) ← distribute parenthesis

21m - 21 - 14m + 28 = 6m - 24

7m + 7 = 6m - 24 ( subtract 6m from both sides )

m + 7 = - 24 ( subtract 7 from both sides )

m = - 31

Answer:

[tex]x=32[/tex]°

Step-by-step explanation:

The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:

[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]

Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).

Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.

[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}[/tex]

One can shorten the equation so it only holds the parts that will play a role in solving this equation,

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]

Now take the cross product in this equation to simplify it further,

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]

[tex]17(sin(x))=10(sin(116))[/tex]

Inverse operations, solve this equation for (x),

[tex]17(sin(x))=10(sin(116))[/tex]

[tex]sin(x)=\frac{10(sin(116))}{17}[/tex]

[tex]x=sin^-^1(\frac{10(sin(116))}{17})[/tex]

[tex]x=31.91782...[/tex]

[tex]x\approx32[/tex]

Answer:

hello,

Step-by-step explanation:

the triangle is isocele,

x+x+116=180

x=(180-116)/2

x= 32° (thirty-two , trente-deux in french)

Answer:

B) Multiply by 3/2 on both sides of the equation by the multiplication property of equality

Answer:

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.

Step-by-step explanation:

La probabilidad condicional :

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

En el cual:

P(B|A) es la probabilidad de que ocurra el evento B, dado que A sucedió.  

[tex]P(A \cap B)[/tex] es la probabilidad de que ocurran tanto A como B.  

P(A) es la probabilidad de que ocurra A.

En esta pregunta :

Evento A: Estudiante A aprueba.

Evento B: Estudiante B aprueba.

La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6

Entonces [tex]P(A) = 0.6[/tex]

La probabilidad de que ambos estudiantes aprueben es 0.3

Entonces [tex]P(A \cap B) = 0.3[/tex]

¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.6} = 0.5[/tex]

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.

Answer:

75 degrees

Step-by-step explanation:

From the first part of the diagram,

vertically opposite angles are equal,

hence we have

125° + (4x-5)° + 125° + (4x-5)° = 360°

(Angles about a point equals 360°)

4x – 5 + 4x – 5 + 125 + 125 = 360

8x + 250 – 10 = 360

8x = 360–250 + 10

8x = 120

x = 15°

Now we have (5x)° in the second part.

5x = 5 × 15 = 75°

1 is vertically opposite to angle 75°

hence it is equal to 75 degrees.

Answer:75

Step-by-step explanation:

Answer:

The Polynominal is not shown. So how can i answer???

Step-by-step explanation:

Thank You! Hope it helps! Please Mark me brainliest!

Answer:

y>17

Step-by-step explanation:

[tex]x + y = 30 \\ 13 + y = 30 \\ y = 17 \\ for \: x < 13 \\ y > 17[/tex]

Answer:

y>17

Step-by-step explanation:

x+y=30

x<13

What + 13 is 30?

17. So if x+y=30. Because x will be less than 13, y must make up the differnce by being greater than 17.

Ex: x=12

y+12=30

y=18

18 is greater than 17.

This is a great way to check because if your not sure, it elimates the other options!

Hope this helps!

Answer:

Let the number be x

Given that

⇒(x+

3

2

)×2=

3

16

⇒x+

3

2

=

3

8

⇒x=

3

8

−

3

2

⇒x=

3

6

⇒x=2

Thus the number is 2

Answer:

554,000

Step-by-step explanation:

that is the answer

Emma earns $554,064.80  in total in the first 11 years of her career

We are to determine the future value of $39,000 each year for 11 years given the growth rate of 5%

The formula for calculating future value:

FV = P (1 + r)^n

Where :

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

First year =  $39,000

Second year = 39,000 x (1.05) = $40,950

Third year = 39,000 x (1.05)^2 = $42,997.50

Fourth year = 39,000 x (1.05)^3 = $45,147.38

Fifth year = 39,000 x (1.05)^4 = $47,404.75

Sixth year = 39,000 x (1.05)^5 = $49,774.99

seventh year = 39,000 x (1.05)^6 = $52,263.74

eighth year = 39,000 x (1.05)^7 = $54,876.93

ninth year = 39,000 x (1.05)^8 = $57,620.78

tenth year = 39,000 x (1.05)^9 = $60,501.82

eleventh year = 39,000 x (1.05)^10 = $63,526.91

Sum of the earnings for the first eleven years = $554,064.80

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{4[30-(10-2)\times3]}}[/tex]

[tex]\huge\boxed{\rightarrow\mathsf{4[30 - (\bold{8}}) \times3]}[/tex]

[tex]\huge\boxed{\rightarrow \mathsf{4[30 - \bf 24]}}[/tex]

[tex]\huge\boxed{\rightarrow \mathsf{4(30) + 4(-24)}}[/tex]

[tex]\huge\boxed{\rightarrow \mathsf{\bf 120 - 96}}}[/tex]

[tex]\huge\boxed{\rightarrow\mathsf{\bf 24}}[/tex]

[tex]\huge\boxed{\rm{Answer: \mathsf{24}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

340 x 0.03 = 10.2 (in state)

84 x 0.11 = 9.24 (out of state)

10.2 + 9.24 + 11.25

= $30.69 monthly charge

hope it helps :)

The total monthly charge for a customer is given as $30.69.

Simplifying allows us to test each process and strategy to determine which is the most efficient and best suited for its specific goal.

here,

A phone provider costs each customer $11.25 per month. Furthermore, it charges $0.03 per minute for in-state calls and $0.11 for out-of-state calls.

Charge within the boundary  of state for 340 minutes = 340 x 0.03 = 10.2

Charge beyond the boundary  of state for 84 minutes  = 84 x 0.11 = 9.24

Total monthly charge = 10.2 + 9.24 + 11.25

                                = $30.69 monthly charge

Thus, A customer's total monthly price is shown as $30.69.

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Answer:

Step-by-step explanation:

F(x)=2^x

[tex]F(-2)=2^{-2} =\frac{1}{2^2} =\frac{1}{4}[/tex]

except for letter a. LIZM

Answer:

2^0

Step-by-step explanation:

When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.

There are two ways to go about this problem.

The first way, the generic way, is to know that,

[tex]\frac{a^n}{a^m}=a^{n-m},a\neq0[/tex].

So,

[tex]\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}[/tex].

The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,

[tex]\frac{a}{a}=1, a\neq0[/tex]

And 1 equals to any number raised to the power of zero,

[tex]a^0=1,a\neq0[/tex]

So we just have to say that the 1 we got is rewritten as some base to the power of zero.

Since our base needs to be 2, we just simply say,

[tex]2^0[/tex].

Et Viola.

Hope this helps.

Answer:

vertex of 4 is 2

Step-by-step explanation:

cuh cuh uchuch uch uch uch

u need to finish 4 assignments in 1 hour

Answer:

Step-by-step explanation:

The answer is D. Use the Stat and then Edit button on your TI calculator to edit the values in L1 and L2 tables. In L1 enter 0, 1, 2, 3, 4, 5 and then arrow over and enter the y values into L2 the same way. Enter the number 12, then hit enter; enter the number 14, hit enter; enter the number 15 and then hit enter, etc. Do the same for the values that are going into L1.

When that is done, hit the Stat button again and arrow down to QuadReg and hit enter. Depending upon your calculator, you may have to arrow down to "calculate" or the calculator may display the equation immediately after hitting QuadReg. Again, it all depends upon your calculator.

The required correct quadratic regression equation that fits the given data is y = -0.89x² + 3.24x+11.93. Option D is correct.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
To find the quadratic regression equation, we need to use a calculator or software that can perform a quadratic regression analysis. Using such a tool, we obtain the following equation:

y = -0.89x² + 3.24x+11.93

This equation fits the data points (0, 12), (1, 14), (2, 15), (3, 14), (4, 10), and (5, 6) with a high degree of accuracy.

The equation is in the form of a quadratic function, which has a parabolic shape when graphed. The coefficient of the x² term (-0.89) indicates that the parabola is downward-facing, while the other coefficients determine the exact shape and position of the parabola.

Option A is incorrect because its equation does not fit the data points accurately. Option B is also incorrect because it is not a quadratic equation, and option C is incorrect because its equation also does not fit the data points accurately.

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