Determine the vertex of the function f(x) = 3x2 – 6x + 13.

1. Identify the values of a and b.

a =
and b =

2. Find the x-coordinate of the vertex.

negative StartFraction b Over 2 a EndFraction =

3. Find the y-coordinate by evaluating the function at the x-value found in the previous step.

The vertex is

.

Answer:

Exponential decay is the decrease in a quantity according to the law. (1) for a parameter and constant (known as the decay constant), where is the exponential function and is the initial value.

Answer:

When a population or group of something is declining, and the amount that decreases is proportional to the size of the population, it's called exponential decay. In exponential decay, the total value decreases but the proportion that leaves remains constant over time.

Step-by-step explanation:

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)  

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2  

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4  

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16    

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17  

The required answer is 17.  

The value of m+n in which m and n are relatively prime positive integers is 17.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the base rule of logarithmic function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the Power rule of logarithmic function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The number x can be written as

[tex]\dfrac{m}{n}[/tex]

Here, m and n are relatively prime positive integers. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of m+n in which m and n are relatively prime positive integers is 17.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

Answer:

x ≈ 1.893 ( to 3 dec. places )

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] = n logx

Given

[tex]3^{x}[/tex] = 8 ( take the log of both sides )

log[tex]3^{x}[/tex] = log8, that is

xlog3 = log8 ( divide both sides by log3 )

x = [tex]\frac{log8}{log3}[/tex] ≈ 1.893

Answer:

See explanation below.

Step-by-step explanation:

First, read this explanation of how to understand probability numbers.

A probability number is a number from 0 to 1. It can be written as a decimal, a fraction, or a percent, but it must be from 0 to 1. The numbers 0, 25%, 1/3, 0.75 are all examples of probabilities since they are all from 0 to 1. 25% is the same as 0.25; 1/3 is the same as 0.333... All probabilities are expressed as 0, 1, or a number in between 0 and 1.

A probability of 0 means the event will not happen. It is an impossibility.

A probability of 1 or 100% is a sure thing it will happen. It is certain it will happen.

A probability of 50% or 0.5 or 1/2 means it is as likely to happen as it is not to happen.

A probability of between 0 and 0.5 is more likely not to happen than to happen.

A probability of between 0.5 and 1 is more likely to happen than to not happen.

Now let's look at each one of the probabilities in your problem.

1. 1/4

1/4 is the same as 0.25 which is between 0 and 0.5. It is more likely to not happen.

1. b. Unlikely

2. 0.0

0.0 will definitely not happen.

2. e. Impossible

3. 0.50

0.50 can just as easily happen or not happen.

3. d. Equally Likely

4. 100%

100% is the same as 1. A probability of 1 means an event that is certain to happen.

4. a. Certain

5. 75/100

75/100 is the same as 3/4 and 0.75; 0.75 is between 0.5 and 1, so it is more likely to happen than to not happen.

5. c. Likely

Answer:

what are you asking the total or what

Answer:

1/6

Step-by-step explanation:

If you're asking for the probability that the coin is heads and the die is even. Hope this helps :)

1/3*1/2= 1/6

Answer:

The answer is 1/6

Step-by-step explanation:

This is because the dice has 6 sides so the possibility of getting a even is 1/6

Answer:

C. Estimate the probability using your simulation.

Step-by-step explanation:

Answer:

Perimeter =63 inches

Area = 243in²

Step-by-step explanation:

Given data

Length of computer = 18in

Width of computer = 13.5in

From the given data the computer has a rectangular shape

Perimeter of the computer = L+L+W+W= 2L+2W

Perimeter = 2(18)+ 2(13.5)

Perimeter = 36+27=63 inches

Area of rectangular shape = L*W

Area = 18 x 13.5= 243in²

Answer:

Perimeter: 63 inches

Area : 243 square inches  

Step-by-step explanation:

Hi, to answer this question w eave to apply the next formulas:

Perimeter of a rectangle: (2 x width) + (2 x length )

Area of a rectangle: width x length

Replacing with the values given:

Perimeter: 2(18) +2(13.5) = 36+27 = 63 inches

Area = 18 x 13.5 = 243 square inches  

Feel free to ask for more if needed or if you did not understand something.

Answer:

-15

Step-by-step explanation:

3(2 - 7)​

PEMDAS says parentheses first

Subtract

3 (-5)

Multiply

-15

Answer: 20x + 20

Step-by-step explanation: In this problem, the 5 "distributes" through the parentheses, multiplying by each of the terms inside.

So we have 5(4x) + 5(4) which simplifies to 20x + 20.

Answer:

The correct answer is 11 ft.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.

Subtract x from each side:

x+4-x=2x-7-x

4=x-7.

Add 7 to both sides:

4+7=x-7+7

11=x

Answer:

11

Step-by-step explanation:

On edge

Answer:

x = -9

Step-by-step explanation:

-4x = -1/2(10x + 18)

Distribute

-4x= - 5x -9

Add 5x to each side

-4x+5x = -5x+5x -9

x = -9

Answer:

(0,-41)

Step-by-step explanation:

You can see that for each 9 units that x goes up, y goes up by 19. If we continue this pattern, it will take 2 more jumps of 9 units for the x value to be 0 or to reach the y intercept. Adding 19 twice to -79 gives -41. Hope this helps!

Answer:

Move all terms not containing k to the right side of the equation.

Exact Form:

k = 43/4

Decimal Form: k = 10.75

Mixed Number Form:

k = 10 3/4

Answer:

Find the area of the shape

First the two triangles

3 x 4 = 12 so the area of both triangles is twelve

Now it is only 1 big rectangle left

The side lengths can be added 3 + 4 + 5 = 12

12 x 11 = 132

132+12=144

144 is the surface area/area

If you have any questions please ask

Step-by-step explanation:

Answer:

7*3=21

8-5=3

21+3-24

Step-by-step explanation:

Answer: x = 2

Step-by-step explanation:

[tex]10x - 15x + 5= -45 + 40[/tex]

subtract 5

[tex]10x - 15x= -45 + 40-5[/tex]

Combine like terms;

[tex]-5x=-10[/tex]

Divide by -5

[tex]x=\frac{-10}{-5}\\ x=2[/tex]

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]

Answer:

3 cones

Step-by-step explanation:

This is why the formula for the volume of a cone is 1/3 (π×r^2)× h, while the volume for a cylinder is (π× r^2)× h, respectively.

Answer:

C) 3 Cones.

Explanation:

Hope this helps! :)

Answer:

D

Step-by-step explanation:

The formula for the surface area of a square pyramid is [tex]a^2+2a\sqrt{\dfrac{a^2}{4}+h^2}[/tex], where a is the length of one of the base side lengths and h is the height. Plugging in the given values into this equation, you get:

[tex]75^2+2(75)\sqrt{\dfrac{75^2}{4}+90^2}=[/tex]

[tex]5625+150\cdot \sqrt{9506.25}=[/tex]

[tex]5625+14625=[/tex]

[tex]20,250[/tex]  square yards, or answer choice D.

Hope this helps!

Answer:

Step-by-step explanation:

−189=4x−3(−4x+15)

−189=16x−45

16x−45=−189

16x−45+45=−189+45

16x=−144

16x /16

= −144 /16

x=−9

Good luck honey !!

Answer:

x=-9

Step-by-step explanation:

-3×-4= 12x -3×15=-45

4x+12x-45=-189

4x+12x=16x

16x-45=-189

16x=-144

x=-9

Answer:

Therefore the largest number that these fractions can be divided by to give them a whole number is

a) 8/15 = The largest number is 8/15

b) 18/35 = The largest number is 18/35

Step-by-step explanation:

A quotient is the result obtained by dividing two numbers.

So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.

Let's assume the whole number is 1

a. 8/15

8/15 ÷ x = 1

8/15 × 1/x = 1

8/15x = 1

We would cross multiply

8 = 15x

We would divide both sides by 15

8/ 15 = x

Hence the largest number that would divide 8/15 and give it a whole number = 8/15

b) 18/35

18/35÷ x = 1

18/35 × 1/x = 1

18/35x = 1

We would cross multiply

18 = 35x

We would divide both sides by 35

18/ 315 = x

Hence the largest number that would divide 18/35 and give it a whole number = 18/35

Answer:

The answer is 2/105

Step-by-step explanation:

first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.

Now, put the GCF you found over the LCM.

ANSWER: 2/105

This fraction is the largest number you can divide both numbers by to get a whole number.

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

Answer: 8.54701% difference

Step-by-step explanation: (61-56)/[(61+56)/2] x 100= 8.55%

Answer:

Side AB has a length of 4, and side BC has a length of 11.7

Answer:

[tex]6x + 42[/tex]

Step-by-step explanation:

Apply the distributive property:

[tex]6x + 6 \times 7[/tex]

Multiply 6 by 7

[tex]6x + 42[/tex]

Answer:

EASY-ACCESS CREDIT:

1. title loan with collateral

2. two-week payday loan

OPEN-END CREDIT:

1. Credit card

2. $2000 monthly line of credit

CLOSE-END CREDIT:

1. home loan

2. car loan

The division of category on the basis of type of credit would be as follows:

Easy-Access Credit

1. Title loan with collateral

2. Two-week payday loan

OPEN-END CREDIT:

1. Credit card

2. $2000 monthly line of credit

CLOSE-END CREDIT:

1. Home loan

2. Car loan

Credit is described as the amount that has been added to a specific account.

Easy-access credit is defined as the credit that is granted for an extremely short period of time and for such loans, the interests are extremely high.

While the open credit keeps the amount lent on repeat which is set at a particular limit(maximum).

Close-end credit in which the amount remains specified initially while it is being lent.

Learn more about "Credit" here:

brainly.com/question/1995705

Answer:

x >-2

Step-by-step explanation:

-3 (x -3) > 5 - 5x

Distribute

-3x +9 > 5-5x

Add 5x to each side

-3x +9+5x > 5-5x+5x

2x +9> 5

Subtract 9 from each side

2x+9-9>5-9

2x > -4

Divide each side by 2

2x/2 >-4/2

x >-2

Answer:

A. x > -2.

Step-by-step explanation:

-3 (x -3) > 5 - 5x

-3x + 9 > 5 - 5x Subtract 9 from both sides and add 5x to both sides:

-3x + 5x = 5 - 9

2x > -4

x > -2.