Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y=a( x− ℎ)^2+k and how they can be identified from the equation.
Please help

Answer:

1.6 liters

Explanation:

400x4=1600

1000ml=1l

1600/1000=1.6

Answer:

1 1/3

Step-by-step explanation:

9*6=54

So 6x=8

x=1 1/3

It will take about 9.1 years for $36000 to grow with interest to $51806.67 after continuous compounding .

What is continuous compounding?

The process of continuously compounding involves calculating interest and reinvested it into the balance of an account over an infinite number of periods. When they specifically state that the amount is "compounded continuously" in a problem, they should use the continuous compounding formula. The mathematical constant "e" is used in this formula, and its value is roughly equal to 2.7182818. Here is the formula for continuous compounding.

Here the Principal P = $36000 , Total amount A= $39786.15 and

Time t=2.5 yrs.

Now using continuous compounding formula,

=> A = P[tex]e^(rt)[/tex]

=> 39786.15 = 36000*[tex]e^(r*5/2)[/tex]

=> r = 0.04 = 4%

Now A=51806.67 and Again using continuous compounding formula ,

=>  A = P[tex]e^(rt)[/tex]

=> 51806.67 = 36000*[tex]e^(0.04*t)[/tex]

=> t =9.1 years.

Therefore it will take about 9.1 years for $36000 to grow to $51806.67 .

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The values of x = 2 & y = 3.

A cyclist cycles for x hours at 12 km/hour and y hours at 18km/hour.

To find x and y:

Given kilometers = 78km

Time = 5 hours

So, we know that the

Distance Equation is 12x + 18y = 78 km

Time Equation is x + y = 5 hours

Multiply the equation through the Time Equation by 12:

12x + 18y = 78

12x + 12y = 60

Subtract and solve for "y":

6y = 18

y = 3

So now we have to Solve for "x" using x + y = 5

x + 3 = 5

x = 2

Hence the answer is the values of x = 2 & y = 3.

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Answer: question

Step-by-step explanation: answer

Answer: 2.5 miles

We are given that

Total length of path=10 mile

Han runs at a pace=12 minutes per mile

Tyler runs at a pace=15 minutes per mile

We have to find the distance run by Han after a half hour.

Half hour=30 minutes

Using unitary method

Han runs distance in 12 minutes=1 mile

Han runs distance in 1 minute= mile

Han runs distance in 30 minutes= miles

Hence, Han runs 2.5 miles after half hour.

Step-by-step explanation:

a. The part of the expression that represents the discounted price before tax is (x − 35).

b. The of the expression represent the amount of sales tax, is 0.12x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, the expression 0.12x + (x − 35) models the final price of a scooter.

It should be noted that 0.12x represented the sale tax. In this case, the sales tax is 12% which was depicted as 0.12.

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Answer:

y-2=0

Step-by-step explanation:

Add the 2 to the other side and it would be y=2

Answer:

4x^2 + 16x - 48

Step-by-step explanation:

A quadratic equation with roots 2 and -6 has to have factors of (x - 2) and (x + 6) since both equal 0 when either 2 or 6 are plugged in. To get a leading coefficient of 4, multiply the product of the two factors by 4. When the 4 is distributed it becomes the leading coefficient:

4(x - 2)(x + 6)

4(x^2 + 4x - 12)

4x^2 + 16x - 48

Number of ticket sold for adult = 70

Number of ticket sold for child = 30

Given that,

The number of tickets sold = 100

Cost of ticket for adult = £5.50

Cost of ticket for child =  £1.50

Total sold amount = £430.

Let number of ticket for adult = x

And number of tickets for child = y

We know that,

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Therefore,

Forming the equation according to the given information,

We get two equation as,

5.50x + 1.50y = 430  ...(i)

              x + y = 100    ...(ii)

Now, Subtract equation (ii) with multiplication 1.50 from (i)

4x = 280

 x = 70

Now put the values of x in equation (ii)

y  = 30

Hence number of ticket for child is 30 and for adult is 70.

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The regular selling price per unit for the laptop is $298.6.

Let the regular price per unit be x.

The expense is 19% of the selling price and profit is 25% of the selling price. This will be illustrated as:

x + (19% × x) + (25% × x) = 430

x + 0.19x + 0.25x = 440

1.44x = 430

Divide

x = 430 / 1.44

x = 298.6

The price is $298.6

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1. When you travel 3 miles in New York City, the cost of The Red Cabs and The Green Cabs would be the same.

2. The difference in cost between the two companies if you need to travel 8 miles is $5.

3. It is cheaper to travel with Red Cabs than Green Cabs if the total distance is more than 3 miles.

First, for the costs of both companies to be equal, we set the two cost equations to be equal to each other and solve for the unknown variable (miles).

Based on the equations for the two companies, we can determine the total costs of using any option.

The difference between the total costs is obtained by subtracting.

Let cost of Green Cab = 2 + 2m

Let cost of Red Cab = 5 + m

For the two companies costs to be equal, 2 + 2m = 5 + m

= 2m - m = 5 - 2

m = 3

Green Cab = 2 + 2m

= 2 + 2(8)

= 18

= $18

Red Cab = 5 + m

= 5 + 8

= 13

= $13

The difference in cost = $5 ($18 - $13)

Thus, based on the solution to the cost equations, cost-conscious travelers should prefer Red Cabs to Green Cabs when they travel in New York City for a distance exceeding 3 miles.

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The equation of the quadratic model is f(x) = -16x^2+99x+6.

From the given table:

A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 90, 140, 160, 150.

we know that:

regression equation = ax^2 + bx + c.

a∑x^4+b∑x^3+c∑x^3 = ∑x^2y

a∑x^3+b∑x^2+c∑x = ∑xy

a∑x^2+b∑x+cn = ∑y

After substituting and solving these three equations we get:

a = -15.714

b = 98.857

c = 5.571

Approximate values

a = -16

b = 99

c = 6

substitute these values

f(x) = -16x^2+99x+6.

Therefore the equation of the quadratic model is f(x) = -16x^2+99x+6.

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Answer:

Step-by-step explanation:

To find the value of g(x), find the point x on the horizontal axis, then find the intersection of the vertical segment from that point to the graph, then trace the corresponding value of intersection on the vertical axis. This is the value of the function at the point x.

This is all done on the attached.

The value of g(- 3) is 3.5.

Answer:

i think the denominator of 5,12,3,8, is 24

Step-by-step explanation:

The probability of getting prime numbers is =3/6=1/2. So, in 3 throws the probability of getting prime numbers is (1/2)^3=1/8=0.125

a) The ball was struck from a height of one foot.
b) It took the object one second to reach its highest point.

c) The baseball may fly up to a height of 17 feet.

Given the function that represents the height of an object in air expressed as;

h(t)=-16t^2+ 32t+ 1

a) The ball is hit at the point where the time is zero. Equating the function to zero.

h(0) = -16t^2+ 32t+ 1

h(0) = -16(0) + 32(0) + 1

h(0) = 1 feet

Hence the ball was hit at the height of 1 feet

b) At maximum height, the velocity of the object is zero. Hence;

v(t) = -32t + 32

v(t) = 0 = -32t + 32

32t = 32

t = 32/32

t = 1sec

Hence the object reach its maximum height after 1 seconds.

c) Substitute t = 1 into the function to have:

h(1)=-16(1)^2+ 32(1)+ 1

h(1) = -16 + 33

h(1) = 17 feet

The maximum height reached by the baseball is 17 feet.

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The portion that were taking summer classes in 2016 is 31.4%.

From the information, the portion of students taking summer classes decreased 6.3% from 2015 to 2016 and it was stated that 38% of students took summer classes in 2015.

In this case, the portion of the people taking dinner classes will be:

= Original percentage - Reduction in percentage

= 38% - 3.6%

= 31.4%

The percentage is 31.4%

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No- The probability of obtaining this data is high enough to have been a chance occurrence.

It is a branch of mathematics that deals with the occurrence of a random event.

Test statistic (z) = (sample mean - population mean) ÷ (population sd/√n)

sample mean = 3 years

population mean = 3.2 years

population sd = 0.6 year

n = 28

z = (3 - 3.2) ÷ (0.6/√28) = -0.2 ÷ 0.1134 = -1.764

The cumulative area of the test statistic is subtracted from 1 to obtain the probability that 28 randomly selected laptops would have a mean replacement time of 3 years or less

The cumulative area is 0.9982.

Therefore, the probability is (1 - 0.9982 = 0.0018)

Hence No- The probability of obtaining this data is high enough to have been a chance occurrence.

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Yes, they justified giving us a ticket, even though we were not caught speeding, because we drove at a speed higher than the posted speed limit.

It is given that we are driving down a straight country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road, tracking vehicle speeds, and are in contact with each other. At the first officer’s position, we drive by going 39 miles per hour. At the second officer’s position, 63 seconds later, we drive by, going 38 miles per hour.

The second officer pulls us over and gives us a ticket. We will use the mean value theorem to check whether getting a ticket was justified or not. Let the maximum speed be "v" that we reach between the officers at time "c". Let the function f(t) denote the distance at time "t".

f'(c) = [f(b) - f(a)]/(b - a)

v = (1 - 0)/(63 - 0)

v = 1/63 miles per second

We need to convert the speed into miles per hour.

v = 3600/63 = 57.143 miles per hour

The speed is higher than the posted speed limit. Hence, they justified giving us a ticket, even though we were not caught speeding.

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The area of triangle DEF, in square units, is given as follows:

4.08 units squared.

The area of a triangle is given by half the multiplication of it's base by it's height, as follows:

Area = 0.5 x base x height.

We consider the base as the segment DE, hence it's length is given by the distance between these two points, obtained as follows:

[tex]b = \sqrt{(8 - 3)^2 + (-6 - (-5))^2}[/tex]

[tex]b = \sqrt{26}[/tex]

b = 5.1 units.

The midpoint of the base is given as follows:

(5.5, -5.5).

As it is obtained with the mean of the coordinates.

The height is the distance between the midpoint of the base and the other vertex, hence:

[tex]h = \sqrt{(5.5 - 4)^2 + (-5.5 - (-5))^2}[/tex]

h = 1.6 units.

Hence the area of the triangle is obtained as follows:

Area = 0.5 x 5.1 x 1.6 = 4.08 units squared.

The problem asks for the area of the triangle, as shown in the image given at the end of the answer.

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The greatest common factor of 30, 72, and 54 would be 6.

Answer: i believe its B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

because ×=82822929929283838399388

The rectangular design should be 2.5 m tall.

What is area of rectangle?

 A flat surface of a specific shape can be thought of as the area it occupies in space. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle is known as the area of a rectangle. The flat surfaces of laptop monitors, chalkboards, canvases, and other objects are a few instances of rectangular shapes. To determine the area that these items occupy, use the formula for a rectangle's area.

Here area of rectangle = 2[tex]m^2[/tex]

And width of the rectangle w= 4/5 m .

Using area of rectangle formula ,

=> A = h*w

=> 2= h*4/5

=> h = 10/4 = 2.5 m.

Therefore the rectangular design would be 2.5 m tall.

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The answer to the arithmetic 15 x 2 - 8 x 40 + 896 x 2 is 1502

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them

Using the PEDMAS rule which  states that mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.

15 x 2 - 8 x 40 + 896 x 2  can be solved thus:

Solving the multiplication first;

(15 x 2) - (8 x 40) + (896 x 2)

solving the addition and subtraction

30 - 320 + 1792

1502

Using PEDMAS, the answer to the arithmetic is 1502

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Answer:

d = V- x

Step-by-step explanation:

To make 'd' as the subject, isolate 'd'.

To isolate d, subtract 'x' from both sides,

              d +x = V

        d + x - x = V - x

                  d = V - x

The formula using d as the subject is d = V-x.

The formula is d+x = V

The subject of the formula is nothing but a variable that is being worked out. Here, we have to convert the given formula to describe d as the subject.

According to the property of equality, the two sides of the equation should be balanced. To solve the given expression, we use the subtraction property of equality.

The subtraction property of equality refers to balancing an equation by using the subtraction operation on both sides of the equation.

Therefore, subtract x on both sides of the given formula,

[tex]\begin{aligned}d+x&=V\\d+x-x&=V-x\\d&=V-x\end{aligned}[/tex]

Therefore, the final answer is d=V-x.

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The parabola have a vertex of (-1, -64), it's x-intercept is (3, 0), (-5, 0), it's y-intercept is (0, -60) and it's axis of symmetry is x = -1

This is a curve formed by the intersection of a cone with a plane parallel to a straight line in its surface. It can also be defined as a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. In mathematics, it is a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

f(x) = 4x² + 8x - 60

The vertex = (-1, -64)

The x-intercept = (3, 0), (-5, 0)

The y-intercept = (0, -60)

The axis of symmetry = x = -1

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Answer: $429

Step-by-step explanation:
$6600 + 6.5% = $7029
$7029 - $6600 =$ 429

The determination of the gross profit for April and the ending inventory on April 30, using the FIFO, LIFO, and weighted average cost methods, is as follows:

                                 Gross Profit    Ending Inventory

FIFO                                 $45                  $342

LIFO                                 $37                  $334

Weighted Average         $41                   $338

The gross profit is the difference between the net sales revenue and the cost of goods sold.

It is the first profit point in the income statement which measures the financial performance of an entity during a period.

The ending inventory is the difference between the cost of goods available for sale and the cost of goods sold, depending on the inventory method in use.

Some of the inventory methods include FIFO, LIFO, Weighted Average, and Specific Identification.

Item       Beta          Units    Cost

April 2   Purchase      1       $165

April 15  Purchase      1        169

April 20 Purchase      1        173

April 27 Sales          1                  $210

Total                           3    $507

Average cost per unit $169 ($507 ÷ 3 units)

Cost of goods available for sale = $507

a) First-in, First-out (FIFO):

Ending inventory = $342 ($169 + $173)

Cost of goods sold = $165 ($507 - $342)

Gross profit = $45 ($210 - $165)

b) Last-in, First-out (LIFO):

Ending inventory = $334 ($165 + $169)

Cost of goods sold = $173 ($507 - $334)

Gross profit = $37 ($210 - $173)

c) Weighted average cost method:

Ending inventory = $338 (2 x $169)

Cost of goods sold = $169 (1 x $169)

Gross profit = $41 ($210 - $169)

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