When a quadratic equation is given in the form y = a( x− ℎ )^2 + k the easily seen features are
coordinates of the vertex = v(h, k) the axis of the parabola - y axisthe opening of the curve in the axis - open upwardWhat is equation of a parabola?Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation
The quadratic equation in the factored form is written as
y = a ( x − ℎ )^2 + k
This equation shows the coordinates of the vertex which is v(h, k)
The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis
"a" helps to determine if the curve opens upwards or downwards. when a is:
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William sold 100 tickets for his show.
An adult ticket costs £5.50 and a child ticket costs £1.50.
William's ticket sales totalled £430.
a) How many adult tickets did he sell?
b) How many child tickets did he sell?
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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Find the coordinates of point P along the directed line segment AB, from A(1,6) to B(-2,-3), so that the
ratio of AP to PB is 5 to 1.
The coordinates are P().
Answer: question
Step-by-step explanation: answer
You are driving (too fast) 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, you drive by going 39 miles per hour. At the second officer’s position 63 seconds later, you drive by going 38 miles per hour. The second officer pulls you over and gives you a ticket. Were they justified in giving you a ticket, even though you were not caught speeding?
Hint: refer to the Mean Value Theorem to assist with your justification and reasoning.
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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Make d the subject of this formula:
d+x=V
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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What is the greatest Comon factor of 30,72,54?
The greatest common factor of 30, 72, and 54 would be 6.
Last year, Lisa opened an investment account with $6600. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of last year?
Increase in amount:
Year-end amount:
Answer: $429
Step-by-step explanation:
$6600 + 6.5% = $7029
$7029 - $6600 =$ 429
Show Me How
Question Content Area
Cost Flow Methods
The following three identical units of Item K113 are purchased during April:
Item Beta Units Cost
April 2 Purchase 1 $165
April 15 Purchase 1 169
April 20 Purchase 1 173
Total 3 $507
Average cost per unit $169 ($507 ÷ 3 units)
Assume that one unit is sold on April 27 for $210. Determine the gross profit for April and ending inventory on April 30 using the (a) first-in, first-out (FIFO); (b) last-in, first-out (LIFO); and (c) weighted average cost method.
Gross Profit Ending Inventory
a. First-in, first-out (FIFO) $fill in the blank 1
$fill in the blank 2
b. Last-in, first-out (LIFO) $fill in the blank 3
$fill in the blank 4
c. Weighted average cost $fill in the blank 5
$fill in the blank 6
Feedback Area
Feedback
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
What is the gross profit?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.
What is the ending inventory?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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A baseball is hit into the air, and its height h in feet after t seconds is given by h(t)=-16t^2+ 32t+ 1
a What is the height of the baseball when it is hit?
(b) After how many seconds does the baseball reach its maximum height?
(c) Determine the maximum height of the baseball.
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.
Determining the maximum height of an object using functions.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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what is the common denominator of 5, 12, 3 , 8
Answer:
i think the denominator of 5,12,3,8, is 24
Triangle DEF, with vertices D(3,-5), E(8,-6), and F(4,-2), is drawn inside a rectangle, as shown below.
The area of triangle DEF, in square units, is given as follows:
4.08 units squared.
What is the area of a triangle?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.
Missing InformationThe problem asks for the area of the triangle, as shown in the image given at the end of the answer.
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What is the general form of the equation of the line shown?
Answer:
y-2=0
Step-by-step explanation:
Add the 2 to the other side and it would be y=2
The expression 0.12x + (x − 35) models the final price of a scooter with an instant rebate in a state that charges sales tax.
a) Which part of the expression represents the discounted price before tax?
b) Which part of the expression represent the amount of sales tax, in dollars (not the tax rate, the amount of sales tax paid)?
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.
What is an expression?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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suppose that $36,000 is deposited in an account and the balance increases to $39,786.15 after 2.5 years. how long will it take for the account to grow to $51,806.67? Assume continous compounding
It will take about _ years for $36,000 to grow to $51,806.67
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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Question 10
An electronics retailer purchases a laptop for $430 per unit. Per unit, the expense is 19% of the selling price
and profit is 25% of the selling price. What is the regular selling price per unit?
(rounded to nearest cent)
The regular selling price per unit for the laptop is $298.6.
How to calculate the price?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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At 10:00 a.m. han and Tyler both start running toward each other from opposite ends of a 10 mile path along the river how han can run at a pace of 12 miles per minute Tyler can run at a pace 15 miles per minute how far does han run after a half an hour
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:
Find the value of x so that the ratios are equivalent.
9:x and 54:8
Answer:
1 1/3
Step-by-step explanation:
9*6=54
So 6x=8
x=1 1/3
Determining the Regression Equation The table below shows the approximate height of a ball thrown up in the air after x seconds. 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. Which quadratic model best represents the data? f(x) = –16x2 + 99x + 6 f(x) = –36x2 + 37x + 5 f(x) = 36x2 + 37x + 5 f(x) = 16x2 + 99x + 6
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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Use the function, to match each key feature listed below.
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
ParabolaThis 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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You are on vacation in New York City, and you need to get around town to different locations. Below are the rates for 2 different cab companies, locally dubbed "The Red Cabs" and "The Green Cabs".
How many miles would you travel for the cost to be the same for both cabs and how much will that cost you?
What is the difference in cost between the two companies if you need to travel 8 miles?
After seeing all your vacation photos on S n a p b o o k, your cousin decided they wanted to visit New York City also. They asked for some general advice on traveling around the city. What advice would you give them about which cab company they should use when they travel around the city?
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.
How is the difference in cost determined?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
The costs of traveling 8 miles: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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algebraically manipulating the formula for finding the simple interest find the principal deposited in a savings account which earned $3500 in interest at a simple interest rate of 8.5% for 10 years
Help pls bro hurry svevd evr
Answer: i believe its B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
because ×=82822929929283838399388
The graph of a function g is shown below. Find the following. g(-3)
Answer:
g(- 3) = 3.5Step-by-step explanation:
GivenGraph of the function g(x)To findThe value of g(-3)SolutionTo 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.
the portion of students taking summer classes decreased 6.3% from 2015 to 2016. if 38% of students took summer classes in 2015, what portion were taking summer classes in 2016
The portion that were taking summer classes in 2016 is 31.4%.
How to calculate the value?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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The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.2 years and a standard deviation of 0.6 years. He then randomly selects records on 28 laptops sold in the past and finds that the mean replacement time is 3 years.
Assuming that the laptop replacement times have a mean of 3.2 years and a standard deviation of 0.6 years, find the probability that 28 randomly selected laptops will have a mean replacement time of 3 years or less.
P(M ≤ 3 years) =
Enter your answer as a number accurate to 4 decimal places.
Based on the result above, does it appear that the computer store has been given laptops of lower-than-average quality? Yes or no question.
Yes- The probability of this data is unlikely to have occurred by chance alone.
No- The probability of obtaining this data is high enough to have been a chance occurrence.
No- The probability of obtaining this data is high enough to have been a chance occurrence.
What is Probability?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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If you have to drink 400 milliliters 4 times a day, how many liters is that for one day?
Answer:
1.6 liters
Explanation:
400x4=1600
1000ml=1l
1600/1000=1.6
How do you do this problem? Show your work
15 x 2 - 8 x 40 + 896 x 2 =
The answer to the arithmetic 15 x 2 - 8 x 40 + 896 x 2 is 1502
What is arithmetic?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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34. A six-sided die is thrown three times. What
is the probability of getting a prime number
on all three rolls?
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
Write the quadratic equation whose roots are 2 and −6, and whose leading coefficient is 4.
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
A cyclist cycles for x hours at 12 km/hour and y hours at 18km/hour.All together she cycles 78km in 5 hours.Find x and y 08106764242
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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Avery is designing a large rectangular sign. They want the sign to have an area of 2 m² and a width of 4/5m.
How tall should the sign be?
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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