solve 6x^2 - 12x + 24 = 0 by completing the square

The dimensions of the poster with the smallest area are as follows: The width is 20 cm, and the height is 16 cm.

To determine these dimensions, we need to consider the area of the printed material on the poster, which is fixed at 388 square centimeters. Let's assume the width of the printed material is x cm.

Since the side margins are each 2 cm, the total width of the poster (including the margins) becomes x + 2 cm + 2 cm = x + 4 cm.

Similarly, the total height of the poster is x + 4 cm as well because the top and bottom margins are both 4 cm.

To calculate the area of the entire poster, we multiply the width by the height: (x + 4 cm) * (x + 4 cm) = (x + 4)^2 cm^2.

According to the problem, the area of the printed material is 388 square centimeters. Therefore, we have the equation (x + 4)^2 cm^2 = 388 cm^2.

Solving this equation, we find x + 4 = 19 cm, which means x = 15 cm.

Hence, the dimensions of the poster, width is 15 cm + 4 cm = 19 cm, and the height is also 15 cm + 4 cm = 19 cm.

To know more about dimensions, visit:

https://brainly.com/question/31106945

#SPJ11

Therefore, the probability that it will be raining at the end of time is 37.5%.

A) To describe the transition matrix, we can use the following notation: R = It will rain N = It will not rain

Since it is given that if it rained yesterday, then there is a 60% chance of rain today, and if it did not rain yesterday there is an 85% chance of no rain today.

Thus, the transition matrix would be as follows:| P(R/R)  P(N/R)| P(R/N)  P(N/N)| = |0.6  0.4| |0.15  0.85|

B) If it rained Monday, then we need to find the probability that it will rain Wednesday.

We can find this by multiplying the probability of rain on Wednesday given that it rained on Monday and the probability that it rained on Monday.

Thus, the probability of rain on Wednesday, given that it rained on Monday would be:0.6 x 0.6 = 0.36So, there is a 36% chance that it will rain on Wednesday given that it rained on Monday.

C) If it did not rain Friday, then we need to find the probability of rain on Monday. Using Bayes' theorem, we can write: P(R/M) = P(M/R)P(R)/[P(M/R)P(R) + P(M/N)P(N)]where, M = It did not rain Friday= 0.15 (from the transition matrix)P(R) = Probability of rain = 0.6 (given in the problem)P(N) = Probability of no rain = 0.4 (calculated from 1 - P(R))P(M/R) = Probability of it not raining on Friday given that it rained on Thursday = 0.4P(M/N) = Probability of it not raining on Friday given that it did not rain on Thursday = 0.85Substituting these values, we get: P(R/M) = 0.4 x 0.6/[0.4 x 0.6 + 0.85 x 0.4] = 0.31 So, there is a 31% chance of rain on Monday given that it did not rain on Friday.

D) The steady-state vector is the vector that describes the probabilities of being in each of the states in the long run. To find the steady-state vector, we need to solve the following equation: πP = πwhere,π = steady-state vector P = transition matrix Substituting the values from the transition matrix, we get:| π(R)  π(N)| |0.6  0.4| = | π(R)  π(N)| | π(R)  π(N)| |0.15  0.85| | π(R)  π(N)|

Simplifying this, we get the following two equations:π(R) x 0.6 + π(N) x 0.15 = π(R)π(R) x 0.4 + π(N) x 0.85 = π(N) Solving these equations, we get: π(R) = 0.375π(N) = 0.625So, the steady-state vector is:| π(R)  π(N)| = |0.375  0.625|This means that in the long run, there is a 37.5% chance of rain and a 62.5% chance of no rain.

To Know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Some information that someone might use to solve problems related to a circle design is the Tangent Arc theorem.

The tangent arc theorem states that if an angle is formed by two secants, one secant, one tangent, or two tangents, and also intersects in a space outside of the circle, then the value obtained will be equal to the difference of the values of the intercepted arcs divided by one and a half.

Also, note that angles outside a circle are those whose vertex or arc is pointed outwards and their sides are either secants or tangents. With this information, it will be possible to solve problems related to tangent lines and arc measures.

Learn more about the tangent arc theorem here:

https://brainly.com/question/29239907

#SPJ1

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

For similar question on maximum number.

https://brainly.com/question/28066919  

#SPJ8

The answer to 3 644 mod 645 is 3.

To solve this problem, we need to find the remainder when 3644 is divided by 645.

Learn more related to the topic:

brainly.com/question/31391032

#SPJ11

The answer to 3 644 mod 645 is 3.

To solve this problem, we need to find the remainder when 3644 is divided by 645.

Learn more related to the topic:

brainly.com/question/31391032

#SPJ11

Answer:

\(\sqrt[15]{x^7}\)

Step-by-step explanation:

If we have the expression

\(\frac{x^{\frac{4}{5}}}{x^{\frac{1}{3}}}\), we have to think about exponent rules.

If we have \(a^b \div a^c\), then the value will be equal to \(a^{b-c}\).

So \(\frac{x^{\frac{4}{5}}}{x^{\frac{1}{3}}}\) simplified will be \(x^{\frac{4}{5} - \frac{1}{3}}\)

Converting \(\frac{4}{5}\) and \(\frac{1}{3}\) into fifteenths (lcm) gets us \(\frac{12}{15} - \frac{5}{15} = \frac{7}{15}\).

We can convert \(x^{\frac{7}{15}}\) into a radical by taking the denominator root of x to the numerator.

\(\sqrt[15]{x^7}\).

Hope this helped!

The hotel owner needs approximately 2,248 square feet of fabric to make a pool covering for the winter for their regular hexagonal pool with a side-to-side length of 30 feet.

To calculate the area of the pool, we first need to find the apothem (the distance from the center of the hexagon to the midpoint of any side). For a regular hexagon, the apothem is equal to the side length times the square root of 3 divided by 2. So, the apothem of this hexagonal pool is:

apothem = 30 × √3/2 = 25.980762

The area of a regular hexagon is given by the formula:

area = 3 × √3/2 × apothem^2

Substituting the value of the apothem, we get:

area = 3 × √3/2 × 25.980762^2 = 2247.72

Rounding this to the nearest square foot, the hotel owner will need approximately 2,248 square feet of fabric to construct the cover for the pool.

To know more about hexagon pool:

https://brainly.com/question/23568234

#SPJ4

Based on the equation, in 10 years, the amount owed would be $37,226.90

The equation to represent the amount owed after x years is:

A = P(1 + r/n)^nt

where:

A is the amount owed after x years

P is the principal amount (initial loan amount)

r is the annual interest rate

n is the number of times per year that interest is compounded

t is the number of years

In this case, we have:

P = $10,000

r = 15% = 0.15

n = 12 (monthly compounding)

So, the equation becomes:

A = $10,000(1 + 0.15/12)^12t

The rate charged each month is:

r/n = 0.15/12 = 0.0125

In 10 years, the amount owed would be:

A = $10,000(1 + 0.0125)^120

= $37,226.90

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

Answer:

Please check the explanation below.

Step-by-step explanation:

Note: As you forgot to mention the graphs of a linear function. But, let me clear your concept with an example of a linear function.

We know that linear function is of the form

y = mx+b

where

We know that the graph of a linear function is a straight line because the highest power of the exponent of the x variable is 1.

Thus, y = mx+b represents a straight line.

For example,

Let the linear function

y = 2x+3

comparing with the linear function of the form y = mx+b

As the highest power of the exponent of a variable is 1, therefore y = 2x+3 represents a straight line.

The graph of the linear function y = 2x+3 is also attached below.

Answer:

3.8

Step-by-step explanation:

By using the fundamental theorem of calculus, the derivative of the given function g(x) = ∫1-x cos \(\sqrt(t)\) dt is obtained as  -cos(\(\sqrt{(1-x)}\)) .

According to Fundamental Theorem of Calculus, if we have a function defined as the integral of another function with respect to a variable, then the derivative of that integral is given by evaluating the integrand at the upper limit of integration and multiplying it by the derivative of the upper limit minus evaluating the integrand at the lower limit of integration multiplied by the derivative of the lower limit.

To find the derivative of the function g(x) = ∫(1-x) cos(\(\sqrt(t)\)) dt using part 1 of the Fundamental Theorem of Calculus, we first need to rewrite the function in terms of x.

Let's denote the variable of integration as u. Then we have:

g(x) = ∫(1-x) cos(\(\sqrt(u)\)) du.

Now, according to part 1 of the Fundamental Theorem of Calculus, if we have a function F(x) defined as:

F(x) = ∫[a(x), b(x)] f(t) dt,

where a(x) and b(x) are functions of x, then the derivative of F(x) with respect to x is given by:

F'(x) = f(b(x)) × b'(x) - f(a(x)) × a'(x).

In the given case, the function g(x) can be expressed as:

g(x) = ∫[0, 1-x] cos(\(\sqrt(u)\)) du.

To find g'(x), we need to evaluate the integrand at the upper limit (which is 1-x) and multiply it by the derivative of the upper limit. We also need to evaluate the integrand at the lower limit (which is 0) and multiply it by the derivative of the lower limit.

Applying the formula, we have:

g'(x) = cos(\(\sqrt{(1-x)}\)) × (1-x)' - cos(\(\sqrt(0)\))× (0)'.

Since (0)' is 0, we can simplify it further:

g'(x) = -cos(\(\sqrt{(1-x)}\)).

Therefore, the derivative of g(x) is -cos(\(\sqrt{(1-x)}\)).

Learn more about Fundamental Theorem of Calculus here:

brainly.com/question/30761130

#SPJ11

The solution to the inequality over the interval g(3x² - 2x) ≥ g(3x - 2) is   x < 2/3 or 2/3 < x < 1

Since g is decreasing over its domain, we have:

if a < b, then g(b) ≤ g(a)

Using this property, we can write:

3x² - 2x < 3x - 2

Simplifying, we get:

3x² - 5x + 2 < 0

Factoring, we get:

(3x - 2)(x - 1) < 0

The critical points are x = 2/3 and x = 1. These divide the number line into three intervals:

(-∞, 2/3), (2/3, 1), and (1, ∞).

We can choose a test point from each interval to determine the sign of the inequality:

For x < 2/3, let x = 0: (3x - 2) < 0 and (3x² - 2x) > 0, so g(3x - 2) > g(3x² - 2x).

For 2/3 < x < 1, let x = 3/4: (3x - 2) < 0 and (3x² - 2x) < 0, so g(3x - 2) > g(3x² - 2x).

For x > 1, let x = 2: (3x - 2) > 0 and (3x² - 2x) > 0, so g(3x - 2) < g(3x² - 2x).

Therefore, the solution to the inequality g(3x² - 2x) ≥ g(3x - 2) is:

x < 2/3 or 2/3 < x < 1

Note that we have excluded the endpoint x = 1 because the inequality is strict.

Learn more on inequality here;

https://brainly.com/question/24372553

#SPJ1

Answer:

2 - 7i

Step-by-step explanation:

v + w = -3i + 2 - 4i = 2 - 7i

Answer:

Step-by-step explanation:

Given that v = -3i and w = 2-4i

Substituting them and simplifying,we obtain

Collecting like terms,

For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

A solution is a process of giving the unknown variables values that make the equation's equality true. A value or group of values (one for each unknown) that, when substituted for the unknowns, cause the equation to produce an equality is known as a solution.

In order to build an equation, the equal sign is placed between two numerical or variable expressions, as in 3x+5=11. The solution to an equation is a number that may be used as the variable to generate a true number statement. 6+5=11 is true, as stated by the formula 3(2)+5=11. The solution is consequently 2,

6+(x/2)=1/4(x-4)-1

(12+x)/2=(x-4-4)/4

24+2x=x-8

x= -32

Therefore, option D is correct.

For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

To know more about solutions, visit:

https://brainly.com/question/24816340

#SPJ1

Answer:

110°

Step-by-step explanation:

Answer:

110 degrees

Step-by-step explanation:

The dependent variable in this hypothesis is test performance.

What is a dependent variable?

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, one‘s values are examined under the assumption as well as demand that they are dependent on the value of another variable due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not thought to be depending on other variables. Time, space, specific gravity, mass, fluid flow rate and previous values of certain observed value of interest (such as the size of the human population) are examples of common independent variables that can be used to forecast future value systems (the dependent variable).

The outcome of this hypothesis is the dependent variable.

Hence, the dependent variable in this hypothesis is test performance.

To learn more about the dependent variable

https://brainly.com/question/13172624

#SPJ4

Answer:

Step-by-step explanation:

1.25=0.75+r

1.25-0.75=r

r=0.50

r=0.5

hope it helps you

There are 7,560 ways to split the 12 people into 3 groups consisting of 3, 4, and 5 people, respectively, with each group having one tech lead.

To calculate the number of ways to split the 12 people into 3 groups with specific sizes and one tech lead in each group, we can use the concept of combinations.

First, we need to select one tech lead for each group. Since there are 3 tech leads in total, we have 3 choices for the tech lead in the first group, 2 choices for the tech lead in the second group (after one tech lead has already been assigned to the first group), and 1 choice for the tech lead in the third group (after two tech leads have already been assigned to the previous groups). Therefore, the number of ways to select the tech leads for the groups is 3! = 3 × 2 × 1 = 6.

After assigning the tech leads, we are left with 9 people to distribute among the groups. We can select 3 people from the remaining 9 to form the first group, then 4 people from the remaining 6 for the second group, and the remaining 5 people will automatically form the third group.

The number of ways to select 3 people from 9 is given by the combination formula: C(9, 3) = 9! / (3! × (9-3)!) = 84.

Similarly, the number of ways to select 4 people from 6 is C(6, 4) = 6! / (4! × (6-4)!) = 15.

Finally, since the remaining 5 people automatically form the third group, there is only one way to arrange them.

To obtain the total number of ways to split the 12 people into 3 groups with the specified sizes and one tech lead in each group, we multiply the choices together: 6 × 84 × 15 × 1 = 7,560.

Therefore, there are 7,560 ways to split the 12 people into 3 groups consisting of 3, 4, and 5 people, respectively, with each group having one tech lead.

Learn more about combinations here:

https://brainly.com/question/29594894

#SPJ11

Answer:

-2,-1,0,1,2

Step-by-step explanation:

Answer:

-2.0

0,0

Step-by-step explanation:

i just did the test

Answer:

1/4

Step-by-step explanation:

We can use the slope formula to find the slope

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

    = (2-0)/(4 - -4)

    = (2-0)/( 4+4)

    = ( 2/8)

    = 1/4

According to the equation model V=P(1-r)^t, the approximate value of Doug's car after 4¹/₂ years is $9,200.

The equation is a mathematical statement or model that shows that two mathematical expressions are equal.

In this situation, the mathematical expressions equal to each other are V, the car's depreciated value, and P(1-r)^t, which combines variables.

Cost of the new car = $25,000

Depreciation rate per annum = 20%

Value of the car = V

The price paid initially = P = $25,000

The annual rate of depreciation = r

Depreciation period = 4¹/₂ years

Equation model: V=P(1-r)^t

Depreciated value after 4 1/2 years, V = $25,000 (1 - 0.2)^4¹/₂

= $9,158.93

= $9,200

Thus, using the equation model, after 4¹/₂ years, the value of Doug's car has depreciated to $9,200.

Learn more about equations at https://brainly.com/question/22688504

#SPJ1

Answer:

the object with no width , lenght or height is s point

Answer:

point

Step-by-step explanation:

a ray has a length

the line also had a length

a point is just a dot

and angle has length and height.

I hope this helps!!!

The area of the flower bed in square yards is 28 Square yards.

The area of the rectangular flower bed in square yards, we need to convert the measurements from feet to yards. There are 3 feet in 1 yard, so:

Length in yards = 21 feet / 3 = 7 yards

Width in yards = 12 feet / 3 = 4 yards

Now we can calculate the area in square yards:

Area = Length × Width

Area = 7 yards × 4 yards

Area = 28 square yards

Therefore, the area of the flower bed in square yards is 28 square yards.

To know more about  Square yards.

https://brainly.com/question/31015948

#SPJ11

Answer:

1. 30

2. 0.83333333

3. 1.2

4. 30

Step-by-step explanation:

H is the only reasinable decimal

The area of the sector formed by the arc of the circle is 14 square feet.

A sector of a circle is a pie-shaped section of a circle formed by the arc and its two radii. A sector is formed when a portion of the circle's circumference (as well known as an arc) and two radii cross paths at both endpoints of a arc. A sector of a circle has the shape of a pizza slice or even a pie.

Now, according to the question;

Length of a sector is estimated by the formula = ∅×r

where ∅ is the angle formed by sector in radians and r is the radius of the circle.

Thus,

∅ = Length of a sector/r

The radius is r = 7 ft

The value of length of a sector = 4 ft

∅ = 4/7

∅ = 0.57 radians

Now, estimate the area of the sector.

area of a sector = (∅/2)×r²

Substituting the values.

area of a sector = (4/7/2)×7²

                          = (4/14)×49

area of a sector = 14 ft²

Therefore, the area of the sector is calculated as 14  ft².

To know more about the sector of the circle, here

https://brainly.com/question/22972014

#SPJ4

The complete question is-

In a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is . The area of the sector formed by the arc is square feet. Assume π = 3.14, and round your answers to the nearest hundredth.

To determine how many pieces of the press must be purchased, we need to consider the production rate, operating hours, efficiency, and scrap rate.

Number of units processed per day = 10,000

Machine efficiency = 95%

Punching operation time = 10 seconds

Number of shifts per day = 2

Number of hours per shift = 8

To calculate the required number of presses, we can use the following formula:

Number of presses = (Number of units processed per day / (Machine efficiency * Number of shifts * Number of hours)) * (Punching operation time / 3600)

Number of presses = (10,000 / (0.95 * 2 * 8)) * (10 / 3600) = 52.08

Therefore, approximately 52 presses would be needed to meet the production requirements.

If the press has a scrap rate of 10%, we need to consider the effect of scrapped units on the required number of presses.

Number of scrapped units per day = 10,000 * 0.10 = 1,000

Number of units that can be reworked = 1,000 * 0.70 = 700

To modify the formula for the new scenario, we subtract the reworked units from the total units processed per day:

Number of units processed per day (after rework) = 10,000 - 700 = 9,300

Number of presses (after considering scrap and rework) = (9,300 / (0.95 * 2 * 8)) * (10 / 3600) = 48.48

Therefore, approximately 48 presses would be needed when considering the scrap rate and rework capability.

The new answer is different from Exercise 11 because the scrap rate reduces the effective production rate, resulting in a lower requirement for punch presses. By accounting for scrap and rework, the company can optimize its resource allocation and production planning to meet the desired output while considering the potential loss due to scrap.

Learn more about accounting here:

https://brainly.com/question/5640110

#SPJ11

Answer:

36 + 72 + 36 = ?

Step-by-step explanation:

Answer:

AB and AC are equal because the triangle is an isosceles triangle

Step-by-step explanation: