The equation that represents the relationship between x and y in the graph is y = -1/4x² + 5/2x + 2.
Describe Quadratic Equation?A quadratic equation is a second-degree polynomial equation of a single variable, often written in the standard form:
ax² + bx + c = 0
where x represents the variable, and a, b, and c are constants with a not equal to 0. The highest degree of the equation is 2, which means that the equation represents a parabolic curve when graphed. The quadratic equation has two solutions or roots, which can be found using the quadratic formula:
x = (-b ± √b² - 4ac)) / 2a
where sqrt() represents the square root function. The discriminant (b² - 4ac) determines the nature of the roots. If the discriminant is greater than zero, the roots are real and distinct; if it is equal to zero, the roots are real and equal; and if it is less than zero, the roots are complex conjugates. Quadratic equations are used in various fields, including physics, engineering, finance, and statistics.
Since the graph shows a curved relationship, it suggests that the equation is quadratic.
We can use the method of finite differences to determine the degree of the equation.
First, we find the differences between successive y-values:
4, 2, 4, 2, 2
Then we find the differences between those differences:
-2, 2, -2, 0
Since the second differences are not constant, the equation cannot be linear. However, they are not all zero either, so it is not a cubic equation. This suggests that the equation is quadratic.
To find the equation, we can use the fact that a quadratic equation can be written in the form y = ax² + bx + c.
Substituting the coordinates into the equation, we get a system of three equations:
64a + 8b + c = 0
36a + 6b + c = 4
25a + 5b + c = 6
Solving this system of equations, we get:
a = -1/4, b = 5/2, c = 2
Therefore, the equation that represents the relationship between x and y in the graph is:
y = -1/4x² + 5/2x + 2
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Please help!!
Determine whether the inverse of F(x) is a function.
Answer:
Two crates, A and B, are connected with a rope of negligible mass over a frictionless pulley as represented in the diagram shown on the left. The crates are at rest.
Crate A has an unknown mass and hangs vertically to the right of the slope and crate B, with mass 14 kg, hangs on the slope to the left. The slope makes and angle of 68° with the horizontal.
The coefficient of static friction between crate B and the surface of the slope is 0.3. The direction of the frictional force is up the slope. Calculate the mass of crate A.
if a runner starts at rest and reaches a speed of 20 m/s in 2 second. what is the acceleration?
Answer:
initial speed (u)= 0m/s (at rest)
final speed (v)= 20m/s
time taken (t)= 2seconds
we have,
acceleration;a= (v-u)/t
=(20-0)/2
=10m/s²
Answer:
\(10\frac{m}{s^{2}}\)
Step-by-step explanation:
Let u = Initial speed \((\frac{m}{s})\)
v = Final speed \((\frac{m}{s})\)
t = time (seconds)
a = Acceleration
According to this question:
\(u= 0 \frac{m}{s}\) (i.e starts at rest)
\(v = 20 \frac{m}{s}\)
\(t = 20s\)
a = ?
\(a = \frac{v - u}{t}\)
= \(\frac{20 \frac{m}{s} - 0\frac{m}{s}}{2s}\)
= \(\frac{20\frac{m}{s}}{2s}\)
Acceleration= \(10\frac{m}{s^{2} }\)
1. The nth term of a sequence is n3 - 5
Write down the first three terms of this sequence
nedzs
Answer:
- 4, 3, 22
Step-by-step explanation:
To obtain the first three terms, substitute n = 1, 2, 3 into the n th term rule
n = 1 → 1³ - 5 = 1 - 5 = - 4
n = 2 → 2³ - 5 = 8 - 5 = 3
n = 3 → 3³ - 5 = 27 - 5 = 22
The first 3 terms are - 4, 3, 22
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). What are the coordinates of the other endpoint?
Answer:
(-1,-6)
Step-by-step explanation:
Answer:
The answer would be (-1,-6)
Step-by-step explanation:
(13 + x)/2 = 6
13+x= 12
x = -1
~~~~~~~~~~~~~~~
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
plSSSSSssssssssssssSsSsS
Answer:
78.54
Step-by-step explanation:
The formula is \(A = \pi r^2\\\). So, substitute the values into the equasion and get the answer.
According to the order of operations, we square the radius first, then multiply by pi. 5^2 = 25. 25 * pi = 78.5398163397. I just rounded it to the nearest hundereth.
For which of the following displays of data is it not possible to find the mean histogram frequency, table, stem, and leaf plot doc plot
The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.
A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.
A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.
A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.
A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.
In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
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What is the expected value of the spinner? And is the game fair? Correct answer gets brainiest!
Answer:
This game is not fair
Step-by-step explanation:
This game is not fair because there is a 25 percent chance of 8 and about 37 percent chance for 24 and 6
laura spends 4 hours reading a book that is 76 pages long. what is the average number of pages she read per hour?
The average number of pages she reads per hour is 19 pages per hour
How to determine the average number of pages she read per hour?The given parameters are:
Number of pages = 76 pages
Number of hours = 4 hours
The average number of pages she reads per hour is calculated using the following formula
Average = Number of pages/Number of hours
Substitute the known values in the above equation
Average = 76 pages/4 hours
Evaluate the quotient
Average = 19 pages per hours
Hence, the average number of pages she reads per hour is 19 pages per hours
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Which is the best way to describe |-2|?
Answer:
The distance between A and D
Step-by-step explanation:
sorry if incorrect
Answer:
\(91 + 1 |yx {?}^{2} | \)
Stephanie played soccer for 2.25 hours before lunch. She played again in the afternoon for 1.5 hours how long did Stephanie play soccer
Answer:
3.75 hours.
Step-by-step explanation:
Just add both of the decimals in the question to get the sum, which is 3.75.
Answer:
3.75 she worked 3 and 3 quarters of an hour
Step-by-step explanation:
Which point would NOT be a solution to the system of linear inequalities shown below?
It's asking would not be a solution soo
(-10, -9) as you can see
You're welcome thank me later
A total of 5000 tickets were sold for a raffle. the prizes are $1000, $500, $200, and $100. what price should be charged so there is a 60% profit per ticket?
Answer: $0.576
Step-by-step explanation:
The total amount in prizes is $1800.
For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).
Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)
13 more cookies in the first batch
Answer:
I dont understand what im answering?
Step-by-step explanation:
Answer:
Okie doki x< x+13
Step-by-step explanation:
the number of ways to pick a digit, a lowercase letter, an uppercase letter, or one of eight allowable punctuation marks
The number of ways to pick a digit, a lowercase letter, an uppercase letter, or one of eight allowable punctuation marks is 70.
The total number of digits (0-9) = 10.
Thus, the number of ways to pick a digit = 10.
The total number of lowercase letters (a - z) = 26
Thus, the number of ways to pick a lowercase letter = 26.
The total number of uppercase letters (A - Z) = 26
Thus, the number of ways to pick an uppercase letter = 26.
The total number of allowable punctuation marks = 8
Thus, the number of ways to pick a punctuation = 8.
Hence, the total number of ways to pick a digit, a lowercase letter, an uppercase letter, or one of eight allowable punctuation marks is -
10 + 26 + 26 + 8 = 70.
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-w/20=-2.5 help please its due today
Answer:
w = 50
Step-by-step explanation:
−w /20 = −2.5
Step 1: Simplify both sides of the equation.
−1 /20 w = −2.5
Step 2: Multiply both sides by 20/(-1).
( 20/ −1 ) * ( −1/ 20 w) = ( 20 /-1 ) * (−2.5)
w = 50
given sine of theta equals 8 over 17 and cosine of theta equals 15 over 17 comma which of the following can be proven using a pythagorean identity? 1 plus the quantity 8 over 17 end quantity squared equals the quantity 15 over 17 end quantity squared 1 plus the quantity 15 over 17 end quantity squared equals the quantity 8 over 17 end quantity squared the quantity 8 over 17 end quantity squared plus the quantity 15 over 17 end quantity squared equals 1
The correct answer is: the quantity 8 over 17 end quantity squared plus the quantity 15 over 17 end quantity squared equals 1
What is a Pythagorean identity?
The Pythagorean identity for sine and cosine states that for any angle θ,
sin²θ + cos²θ = 1
We can use the given values of sine and cosine to find the missing trigonometric function:
tan(θ) = sin(θ) / cos(θ) = (8/17) / (15/17) = 8/15
Now, we can use the Pythagorean identity to determine which of the given statements is true:
1 + (8/17)² = 1 + 64/289 = 353/289 ≠ (15/17)²
1 + (15/17)² = 1 + 225/289 = 514/289 ≠ (8/17)²
(8/17)² + (15/17)² = 64/289 + 225/289 = 1
Therefore, the statement that can be proven using the Pythagorean identity is:
(8/17)² + (15/17)² = 1
Hence, the correct answer is: the quantity 8 over 17 end quantity squared plus the quantity 15 over 17 end quantity squared equals 1
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Find the least common denominator (LCD) 8/9 and 4/5
Answer:
45
Step-by-step explanation:
First we write the first 10 multiples of 9 (the first denominator) :
9,18,27,36,45,54,63,72,81,90
Now we write the first 10 multiples of 5 (the second denominator) :
5,10,15,20,25,30,35,40,45,50
As we can see 45 is the lowest number that appears in both list.
Therefore 45 is the LCD of 8/9 and 4/5
Answer:
45
Step-by-step explanation:
So since we are finding the LCD, we only look at the denominators, 9 and 5.
We can count until we find the denominator:
\(9,18,27,36,45\\5,10,15,20,25,30,35,40,45\)
So the LCD would be 45.
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10 degrees to the horizontal. Calculate the length of the zip wire.
∘
to the horizontal. Calculate the length of the zip wire
The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.
To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.
Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).
The formula for sine is:
sin(angle) = opposite / hypotenuse
Rearranging the formula, we have:
hypotenuse = opposite / sin(angle)
In this case, the opposite side is the vertical distance, which is h.
So, the formula becomes:
hypotenuse = h / sin(angle)
To find h, we can use the formula for the length of the zip wire:
h = 25 * tan(angle)
Substituting this into the previous formula, we get:
hypotenuse = (25 * tan(angle)) / sin(angle)
Calculating the value, we have:
hypotenuse = (25 * tan(10°)) / sin(10°)
Using a calculator, we find:
tan(10°) ≈ 0.1763
sin(10°) ≈ 0.1736
Substituting these values, we can calculate the length of the zip wire:
hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters
Therefore, the length of the zip wire is approximately 25.35 meters.
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To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 9%. The first credit card compounds interest quarterly, while the second credit card compounds monthly. The homeowner plans to pay off the loan in 10 years.
Part A: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)
Part B: Determine the total value of the loan with the monthly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)
Part C: What is the difference between the total interest accrued on each loan? Explain your answer in complete sentences. (2 points)
Please only responded if you know how to do it, will give the brainiest to however answers it correctly
The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.
Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A is the total value of the loan,
P is the principal amount (initial loan amount),
r is the interest rate (in decimal form),
n is the number of times interest is compounded per year,
and t is the number of years.
Given:
P = $20,000,
r = 9% or 0.09,
n = 4 (quarterly compounding),
t = 10 years.
Substituting the values into the formula, we have:
A = 20000(1 + 0.09/4)^(4*10).
Calculating this value, we find:
A ≈ $45,288.38.
Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.
Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:
n = 12 (monthly compounding).
Substituting the values into the formula, we have:
A = 20000(1 + 0.09/12)^(12*10).
Calculating this value, we find:
A ≈ $45,634.84.
Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.
Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.
For the loan with quarterly compounding:
Total interest = Total value - Principal
Total interest = $45,288.38 - $20,000
Total interest ≈ $25,288.38.
For the loan with monthly compounding:
Total interest = Total value - Principal
Total interest = $45,634.84 - $20,000
Total interest ≈ $25,634.84.
The difference between the total interest accrued on each loan is approximately $346.46.
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a) 8801
+2031
_______
Answer:
the answer is 10832
Step-by-step explanation:
you can use a calculator
Answer:
10832
Step-by-step explanation:
Add one digit at the time (from right to left):
1 + 1 = 2
0 + 3 = 3
8 + 0 = 8
8 + 2 = 10
Now we get 10832
The function .... is symmetric with respect to what ?
Answer:
Reflection symmetry, lines of symmetry, mirror symmetry, mirror-image symmetry, are symmetry with respect to reflection. That is, a figure that does not change after undergoing reflection has re-symmetry
1 point
Francis heard that a car stereo system was on sale for 30% off. If the sale price was $57.75, what was the original price of the stereo?
Answer:
The original price of the sterio was $82.50
For the function f(x)=x+4−−−−−√
, the average rate of change to the nearest hundredth over the interval 2 ≤ x ≤ 6 is
The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.
To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.
The change in the function between x = 2 and x = 6 is:
f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6
The change in the input variable between x = 2 and x = 6 is:
6 - 2 = 4
So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:
(√10 - √6) / 4
To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:
(√10 - √6) / 4 ≈ 0.29
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No scams. Show your work. write answer as a percent and round the nearest whole number if needed.
Answer:
Step-by-step explanation:
we will find the area of the inner circle and then the area of the outer circle and see what the ratio is between those 2
area of a circle = \(\pi\)\(r^{2}\) (where r is the radius, NOT the diameter, easy to confuse)
the radius of the inner circle is 2.5. which is half of the diameter of 5
inner circle = \(\pi\)*(2.5)^2
inner circle = 19.6349...
outer circle = \(\pi\)*(10^2)
outer circle = 314.1592...
the ratio is 19.6349... / 314.1592... = 0.0625
0.0625 = 6.25%
= 6% ( rounded to nearest whole number )
Provide the missing statement and reasons for the following proof:
Answer:
I need more points
the picture is very blurry
The functions f(x) = −(x − 1^)2 + 5 and g(x) = (x + 2)^2 − 3 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.
If we write a quadratic in vertex form:
\(y=a(x-h)^2+k\)
Then:
\(\bold{a}\) \(\longrightarrow\) is the coefficient of \(x^2\)
\(\bold{h}\) \(\longrightarrow\) is the axis of symmetry.
\(\bold{k}\) \(\longrightarrow\) is the max/min value of the function.
Also:
If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.
\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.
For the given functions:
\(a < 0\)
\(f(x)=-(x-1)^2+5\) this has a maximum value of \(\bold{5}\)
\(a > 0\)
\(f(x)=(x+2)^2-3\) this has a minimum value of \(\bold{-3}\)
the difference of 4 , and 5 times h
Answer:
Step-by-step explanation:
4 - 5*h
The question is not totally clear. It could be the other way around.
5h - 4
Given the grammar, I'll stick with the first answer.
Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options.
•6 (5/6x + 2/3) = -9
•6 (5/6x + 2/3) = 9(6)
•5x + 4 = -54
•5x + 4 = -9
•5x = -13
•5x = -58
ANSWER: B,C,F
Answer:
B, C, F C:
Step-by-step explanation:
Sketch and label a net of the right triangular prism. Each square on the grid represents
1 square centimeter. Calculate the surface area of the prism by using its net.
The total surface area of the prism is determined as 216 cm².
What is the surface area of the prism?The surface area of the prism is calculated by applying the following formula.
The area of the two triangular faces is calculated as follows;
Area of the two triangles = 2 (¹/₂ x base x height )
Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )
Area of the two triangles = 24 cm²
The area of rectangular faces is calculated as follows;
A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )
A = 192 cm²
The total surface area of the prism is calculated as follows;
Area = 24 cm² + 192 cm²
Area = 216 cm²
The sketch of the triangular prism is in the image attached.
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What is the function?
Answer:
an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)