What is the vertex form of a line
Answers
The vertex form of line f(x) = ax² + bx + c is y = a(x - h)² + k where the vertex is (h, k).
What is the vertex form of a line and what is its formula?The vertex form of a line is one of the representations of the line in an equation format. Here the line focused on the coordinates of the vertex.
For a line, f(x) = ax² + bx + c, the vertex form is y = a(x - h)² + k; vertex at (h, k).
To convert the general form to the vertex form, the general equation is simplified as below:
y = ax² + bx + c
= ax² + bx + c + b²/4a - b²/4a
= a(x² + b²/4a² + b/a) + (c - b²/4a)
= a(x² + (b/2a)² + 2b/2a) + (c - b²/4a)
= a(x + b/2a)² + (c - b²/4a)
⇒ y = a(x - (-b/2a))² + (c - b²/4a)
Consider -b/2a = h and (c - b²/4a) = k, then we get
y = a(x -h)² + k; vertex form of the given line.
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Related Questions
4/15 + 1/2 what is a reasonable estimate.
Answers
Answer:
23/30
Step-by-step explanation:
add them together
Answer:
4.5
Step-by-step explanation:
because 4/15 is estimated 4 and add half so
THE ESTIMATED ANSWER IS 4.5! pls mark as brainliest!
the series 7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... can be rewritten as[infinity]\sum(-1)^(n-1) 7/??n=1
Answers
The series 7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... is an alternating series, meaning that the signs of the terms alternate between positive and negative. To rewrite this series as a summation notation with an infinity symbol, we need to first determine the pattern of the denominator.
The denominators of the terms in the series are 8, 10, 12, 14, 16, .... We can see that the denominator of the nth term is 8 + 2(n-1), or 2n + 6.
Using this pattern, we can rewrite the series as:
7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... = ∑(-1)^(n-1) 7/(2n + 6) from n = 1 to infinity.
Therefore, the answer to your question is:
The series 7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... can be rewritten as ∑(-1)^(n-1) 7/(2n + 6) from n = 1 to infinity.
Rewriting the given series using summation notation. The series you provided is:
7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ...
This series can be rewritten using the summation notation as:
∑((-1)^(n-1) * 7/(6+2n)) from n=1 to infinity.
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Janice deposited $750 in a savings account that earns 3.5% simple interest. How much interest has Janice earned by the end of the first year? (1 point)
Answers
Answer:
$26.25
Step-by-step explanation:
We know that I = Prt where I = Interest, P = Principal, r = rate (as a decimal) and t = time (in years). Therefore:
I = 750 * 0.035 * 1 = $26.25
A line has a slope of -3 and includes the points (-3, j) and (-8,6). What is the value of j?
Answers
Answer:
-9
Step-by-step Explanation
Zoey read a novel in 30 days she made it a habit to read 13 pages everyday for the first 20 days. if in the last 10 days she reads 6 pages everyday how many pages are in the book?
Answers
Explanation:
20 days times 13 pages= 260pages
10 days times 6 pages = 60pages
Total for the 30 days:
260+60= 320 pages total
Answer:
320 pages.
Step-by-step explanation:
We can simply multiply and add to find how many pages are in the book.
So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.
Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:
\(\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320\)
2, (5 marks) Consider 1-in-k systematic sampling in Chapter 7. Construct a popula- tion such that V(īsy) = 0, where Tsy is the 1-in-k systematic sample mean, and o2 is the population variance.
Answers
By arranging the population in a systematic pattern where every kth element has the same value, we ensure that the variance of the 1-in-k systematic sample mean is 0.
To construct a population such that V(īsy) = 0 for 1-in-k systematic sampling, we need to ensure that the population variance is evenly distributed throughout the sample. This can be achieved by selecting a population where the variability within each kth interval is the same.
For example, if we have a population of 1000 individuals, we can divide it into intervals of 10. Within each interval, we can ensure that the variance is the same by selecting individuals with similar characteristics or attributes. This ensures that when we take a 1-in-k systematic sample, the variance within each interval remains the same, resulting in V(īsy) = 0.
It is important to note that systematic sampling is a type of probability sampling where every kth individual is selected from the population. This method is often used when the population is large and spread out, and random sampling is not feasible. However, it is important to ensure that the systematic sampling is truly random and not biased towards any particular group within the population.
To construct a population where the variance of the 1-in-k systematic sample mean (V(īsy)) equals 0, we need to make sure that the sample means are the same for all possible systematic samples.
Step 1: Choose a population size, N, and a sampling interval, k. For simplicity, let's select N=12 and k=3.
Step 2: Arrange the population elements in a systematic pattern. Since we want the variance of the systematic sample mean to be 0, we'll arrange the elements such that every kth element has the same value. For example:
Population: 5, 2, 7, 5, 2, 7, 5, 2, 7, 5, 2, 7
Step 3: Perform 1-in-k systematic sampling. With k=3, we'll take every 3rd element starting from the first element:
Sample 1: 5, 5, 5, 5 (Mean: 5)
Sample 2: 2, 2, 2, 2 (Mean: 2)
Sample 3: 7, 7, 7, 7 (Mean: 7)
Step 4: Verify that V(īsy) = 0. The variance of the sample means is 0, as they are all equal for each possible systematic sample. Therefore, V(īsy) = 0 for this population.
In summary, by arranging the population in a systematic pattern where every kth element has the same value, we ensure that the variance of the 1-in-k systematic sample mean is 0.
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Please help due in 10 minutes
Answers
Answer:
One solution
Step-by-step explanation:
maybe
Answer:
There is only one solution to the equation.
x = 0
Step-by-step explanation:
Let rewrite the following equation so that x will be separated from the other numbers. So we do the following......
\(\frac{x+4}{4} = \frac{x +3}{3}\)
\(12(\frac{x+4}{4}) = 12(\frac{x +3}{3})\)
\(3(x +4) = 4(x+3)\)
\(3x +12 = 4x +12\)
\(12 = 4x - 3x +12\)
\(0 = x\)
There are 10 workers in a factory making widgets. They work 8-hour days and must complete their orders by the end of the day. The foreman walks in on Monday and tells the workers that they have an order for 100 widgets, which is promptly finished before lunchtime. On Tuesday, the foreman gives them an order for 200 widgets and they tinish some time after lunch. On Wednesday, the workers get an order for 275 widgets. They work harder and finish right at the end of the day. Then on Thursday, there is an order for 325 widgets and again, they get the job
done on time.
How do you think the workers will fair if on Friday, they get an order for 350 widgets? 400? or 450?
Answers
Based on the workers performance of consistently meeting orders for 100, 200, 275, and 325 widgets within the workday, it is likely that they will successfully complete the order for 350 widgets on Friday. However, fulfilling orders for 400 or 450 widgets may present a challenge and require additional resources or extended work hours.
Based on the information, it seems that the workers have been consistently meeting their production targets within the allocated time. They have successfully completed orders for 100, 200, 275, and 325 widgets within the workday.
Based on their previous performance, it is likely that the workers will continue to work diligently and efficiently to meet the order for 350 widgets on Friday.
However, meeting an order for 400 or 450 widgets may pose a challenge as it exceeds the previous order quantities.
The workers may need to work extra hours, increase their pace, or employ additional resources to complete these larger orders within the same time frame. It is important to consider the capacity and capabilities of the workers and the factory to determine if such larger orders can be fulfilled successfully.
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Suppose the water depth during low tide at a certain bay is about 3.0 m, and at high tide it is about 9.0 m. The natural period of oscillation is about 12 hours, and on a particular day, high tide occurred at 6:45 a.m. Find the amplitude (in meters) of the model. Xm
Answers
The amplitude of the model is 3.0 meters.
The amplitude of a harmonic oscillator represents the maximum displacement from the equilibrium position. In the case of tidal oscillations, the equilibrium position is the average water level.
The amplitude of the model can be determined by considering the difference between the high and low tide water depths, which represents the maximum displacement of the water from the average level. Dividing this difference by two gives us the amplitude of the model.
The amplitude of the model can be found using the formula:
Xm = (H - L)/2
where H is the high tide water depth, L is the low tide water depth, and Xm is the amplitude of the model.
Substituting the given values, we get:
Xm = (9.0 - 3.0)/2
Xm = 3.0 meters
Therefore, the amplitude of the model is 3.0 meters.
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simplify expression
Answers
Answer:
-31
Step-by-step explanation:
Answer:
-2 x 4^2 + 1 = -31
Calculate exponents 4^2 : 16
= 2 x 16 + 1
Multiply and divide (left to right) -2 x 16: -32
= -32 + 1
Add and subtract (left to right) -32 +1: -31
= -31
Your bicycle has a 4-digit combination lock. you forgot your combination but you do know that your lock uses 4 different numbers. if each digit on your lock has a number from 0 to 9, how many lock codes are possible?
Answers
Answer:
There are 10,000 possible lock codes.
Each digit on the lock can be any number from 0 to 9. Since the lock uses 4 different numbers, there are 10 choices for each digit. This gives us 10 x 10 x 10 x 10 = 10,000 possible combinations.
For example, some possible combinations are 0123, 4567, 8901, and 9876.
Note that the order of the digits matters. So, 1234 is a different combination from 4321.
Step-by-step explanation:
Add the rational expressions and type your answer in simplest form, multiplying any factors you may have in the numerator or denominator. When typing your answers, type your terms with variables in descending power and in alphabetical order without any spaces between your characters. If needed use the carrot key ^ (press shift and 6) to indicate an exponent. \frac{4}{a+1} + \frac{5}{a-3}
Answers
Given:
The expression is,
\(\frac{4}{a+1}+\frac{5}{a-3}\)Simpify the expression,
\(\begin{gathered} \frac{4}{a+1}+\frac{5}{a-3} \\ \text{Adjust fractions based on least common multiple,} \\ =\frac{4\left(a-3\right)}{\left(a+1\right)\left(a-3\right)}+\frac{5\left(a+1\right)}{\left(a+1\right)\left(a-3\right)} \\ =\frac{4(a-3)+5\mleft(a+1\mright)}{(a+1)(a-3)} \\ =\frac{4a-12+5a+5}{(a+1)(a-3)} \\ =\frac{9a-7}{(a+1)(a-3)} \end{gathered}\)Answer:
\(\begin{gathered} \text{Numerator}=\text{ 9a-7} \\ \text{Denominator}=\text{ (a+1)(a-3)} \end{gathered}\)Express
as a unit rate.
Betty drives her car 150 km in 2 h. Explain
Answers
Answer:
75 km per hourStep-by-step explanation:
\(\frac{150km}{2hr}\) divided by two is \(\frac{75km}{1hr}\).
How many triangles can I make out of this shape?
Answers
Answer:I think it is 84
Step-by-step explanation: 9.3 x 9
Answer:
1,302 triangles
Step-by-step explanation:
All triangles are formed by the intersection of three diagonals at three different points. There are five arrangements of three diagonals to consider. We classify them based on the number of distinct diagonal endpoints. We will directly count the number of triangles with 3, 4, and 5 endpoints. We will then count the number of potential triangles with 6 endpoints, then correct for the false triangles.
You can make 84 triangles with 3 diagonal endpoints, 504 triangles with 4 diagonal endpoints, 630 triangles with 5 diagonal endpoints, and 84 triangles with 6 diagonal endpoints. This adds up to be 1,302 triangles altogether.
7. A stereo speaker in the shape of a triangular pyramid
has a height of 12 inches. The area of the base of the
speaker is 22 square inches.
What is the volume of the speaker in cubic inches?
Answers
Answer:
88
Step-by-step explanation:
memorize this formula:
V = 1/3AH
a is base area
h is height
so V = 1/3 *22*12= 88
luigi uses 39 mozzarella pearls for every 6 pizzas they make i need help
Answers
Answer:
what is the problem in this question
Answer:
Step-by-step explanation:
6 pizzas = 39 cups of flour
1 pizza = 39/6 cups of flour
4 pizzas = 39*4/6 cups of flour = 39*2/3 = 26 cups of flour
26 cups of flour = 4 pizzas
13 cups of flour = 4/2 = 2 pizza
simplify -8/2 ÷ 6/-3
Answers
Answer: the answer is 2 or C
-8/2 x -3/6
*Always do the recipical*
(-8 x -3) / (2 x 6)
-8 x -3= +24
2 x 6= 12
24/12= 2
The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Given that the expression is,
-8/2 x -3/6
The expression will be solved as below,
E = (-8 x -3) / (2 x 6)
The numerator will get reciprocal and multiplied to the denominator,
E = 24 / 12
Divide the number 24 by 12 and get the solution,
E = 2
Therefore, the solution of the expression will be 2. The correct option is B.
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For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.Immersive Reader
(1.5 Points)
A )D: {1, -3, -4,}-R: {0, 1, 2, -4}
B) D:{0, 1, 2, 3, 4}- R:{1, -3, -4}
C) D:{0, 1, 2, -4}- R:{1, -3, -4}
D) None of the above
Answers
Answer:
C. D:{0, 1, 2, -4}- R:{1, -3, -4}
Step-by-step explanation:
A retailer incurs a fixed cost of N$ 500 when purchasing sugar for his stock. He pays N$ 10.00 per packet which he resells at N$ 15.00 per packet. How many packets should he purchase and sell in order to break even?
Answers
Answer:
100 packets
Step-by-step explanation:
Given :
Cost = fixed cost + variable cost
Fixed cost = $500
Variable cost = $10
Sales price = $15
Let :
Number of packets = x
To break even :
fixed cost + variable cost = sales made
500 + 10x = 15x
500 = 15x - 10x
500 = 5x
x = 500 / 5
x = 100
100 packets
Pleaseeee someone help me with this answerrrrr
Answers
deter mainAnswer:
Don't answer this.
Step-by-step explanation:
Iowa assesments are supposed to be done by the person taking them to where they are at in school. They are meant to challange the person. They also don't effect your grade in anyway, so do your best. If you don't know the answer and it is multiple choice, pick B or C and move on.
The price of a laptop is decreased by 10% to $360. What is its original price?
Answers
Answer:
$400
Step-by-step explanation:
Given the following question:
\(t=360\)
s = -10%
In order to find the original price of the laptop we have to find 10% of a given price and then subtract that number to see if it gives us the total price.
\(\frac{10\times400}{100} =10\times400=400\div100=40\)
\(400-40=360\)
10% of 400 is 40
\(400-40=360\)
\(op=400\)
Hope this helps.
There are 44,000 adults living in Oak city in examining attitudes according to the news of research group as random sample of Oak city adults what is your main source of news the results are shown below based on the sample predict the number of adults in Oak city whose main source of the news is television on your answer to the nearest whole number do not run by any intermittent calculations
Answers
The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85
To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".
According to the sample data
Number of adults who answered "Newspapers": 64
Number of adults who answered "Radio": 21
Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition
64 + 21 = 85
Rounding this answer to the nearest whole number, we get
85 ≈ 85
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The given question is incomplete, the complete question is:
There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.
Jodie has c pieces of candy. She gives away 11 of the pieces. Write an expression that shows the number of pieces of candy Jodie has left
Answers
The expression which represents the number of pieces of candy left with Jodie is given by c - 11 .
Original number of pieces of candy with Jodie is equal to 'c'.
Number of pieces of candy Jodie gives away is equal to 11.
Expression used to represents the number of pieces of candy left with Jodie is written as,
Subtract 11 from the original number of candy
= ( c - 11 )
Therefore, the representation of the expression for number of pieces of candy left with Jodie after she gives away 11 candy is equal to ( c - 11 ).
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classify the following random variables as Discrete or Continuous
1Shoe size
2foot length
3Students in a class
4distance travelled to school
5children per family
6the height of a horse
7the number of TV sets in a home
8time to complete a task
9the outdoor temperature at noon
10the speed of a car on route 3
Answers
1 discrete
2 continuous
3 discrete
4 continuous
5 discrete
6 continuous
7 discrete
8 continuous
9 continuous
10 continuous
Help DUE IN 30 MINUTES
Answers
Hope it helps :)
Please help thank you!!
Answers
Answer:
awnser would be d x is multiplied by 1/3 so horizontal stretch
reflect in the line with equation y = x
Answers
The coordinates of the quadrilateral after a reflection over the line with equation y = x are:
Ordered pair (1, -3).
Ordered pair (2, -4).
Ordered pair (5, -5).
Ordered pair (5, -3).
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.
Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is given by this transformation rule:
(x, y) → (y, x)
Ordered pair (-3, 1) → Ordered pair (1, -3).
Ordered pair (-4, 2) → Ordered pair (2, -4).
Ordered pair (-5, 5) → Ordered pair (5, -5).
Ordered pair (-3, 5) → Ordered pair (5, -3).
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6⋅10 ^ −2 is how many times as large as 2.10^-8
Answers
Answer:
4 5/6
Step-by-step explanation:
In the year 2000, the state of Florida named an existing town after their greate
and brightest (not to mention best looking) resident. The town of Spoonerville
was founded in 2000 but unfortunately the population decreased by 150 people
per year. In 2007 the population was 75,450 people. Write a linear equation that compares the population (y) of Spoonerville as it
relates to the number of years since 2000 (x).
Answers
The linear equation that compares the population y of spoonerville as it relates to the number of years since 2000 be,
y - 150x
Given, In the year 2000, the state of Florida named an existing town after their great and brightest resident.
The town of Spoonerville was founded in 2000 but unfortunately the population decreased by 150 people per year. In 2007 the population was 75,450 people.
Let the population of Spoonerville be y,
and the number of years since 2000 be x
So, the equation be
Population = y - 150x
Hence, the linear equation that compares the population y of spoonerville as it relates to the number of years since 2000 be,
y - 150x
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Tiffany and Dion are having a walking race. The equation and graph show the distance each person is from the starting line,
Tiffany's Distance
d = 2.5t, where d is the distance, in yards that Tiffany is from the starting line after t seconds
PLEASE ANSWER A., B. And C.
Answers
Answer:
Step-by-step explanation:
Tiffany's distance is defined by the equation,
d = 2.5t
Here, d = distance of Tiffany from the starting line
t = time
a). d = 2.5t
\(\frac{d}{t}=2.5\)
Tiffany's rate = 2.5 yards per second
b). Since, slope of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,
Slope = \(\frac{y_2-y_1}{x_2-x_1}\)
Therefore, slope of the line passing through two points (0, 10) and (10, 35)
= \(\frac{35-10}{10-0}\)
= 2.5 yards per second
Dion's walking rate = 2.5 yards per second
Equation that defines the distance of Dione,
d = mt + b
Here, m = rate of the walking by Dione
b = y-intercept
Hence, equation will be,
d = 2.5t + 10
c). If d = 60 yards
For Tiffany,
d = 2.5t
60 = 2.5t
t = 24 seconds
For Dion,
d = 2.5t + 10
60 = 2.5t + 10
2.5t = 50
t = 20 seconds
Therefore, Dion will take less time and finish first.