Diagram 2 shows the graph of a quadratic function f(x) =3+p (x-r)²Finda) value of p,q and rb) if the graph is reflected about to y-axis, write the equation of the curve
Answers
Given the graph of the function:
\(f(x)=3+p(x-r)^2\)From the graph of the function:
Vertix = (2, q)
The y-intercept = (0, 23)
We will find the values of p, q, and r
From the point of the vertex of the graph: r = 2, q = 3
And from the point of the y-intercept
When x = 0, f(x) = 23 and substitute with r
so,
\(23=3+p(0-2)^2\)Solve the equation to find p
\(\begin{gathered} 23-3=4p \\ 20=4p \\ p=\frac{20}{4}=5 \end{gathered}\)so, the answer of part A:
\(\begin{gathered} p=5 \\ q=3 \\ r=2 \end{gathered}\)b) if the graph is reflected about to y-axis, write the equation of the curve
So, the equation of the function will be:
\(f(x)=-(3+5(x-2))\)simplifying the equation
So,
\(f(x)=-3-5(x-2)\)Related Questions
10 Ten Atlas batteries were tested to find their average life. The times, in hours, that the batteries lasted were as follows: 10.8, 10.6, 11.4, 8.9, 10.1, 10.6, 9.9, 12.6, 10.5, 11.9. a Find, to the nearest tenth of an hour, the average life of the ten batteries. b Which of the following advertisements is more accurate? i Atlas batteries are guaranteed to last 10 hours. ii Atlas batteries have an average life of over 10 hours.
Answers
a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2
Number of values = 10
Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63
Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.
b) Comparing the two advertisements:
i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum
ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.
Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.
In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.
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1,320 feet is what fraction of a mile?
Answers
Answer:
1/4
Step-by-step explanation:
divide the value in feet by 5280 because 1 mile equals 5280 feet.
Answer:There are 5280 feet in one mile; thus
1320/5280 = 1/4
Step-by-step explanation:
sorry if its not correct }:
how do i convert (-∞,∞) to inequality notation. I am being told -∞
Answers
Answer:
-inf<x<inf
Step-by-step explanation:
Find the volume of this.
Show work.
Answers
Answer: 471.24 (with 3.14 as pi)
Step-by-step explanation:
Volume of cylinder = pi*r^2*height
Radius = 10/2 = 5
Pi*25^2*6 = 471.24
The graph represents the distance, in kilometers, that a car traveled. How far had the car traveled in 3/4 of an hour?
Answers
Answer: if you dont show the picture i cant answer!
Step-by-step explanation:
I need help with this problem please.
Answers
Answer:
15 adults were questioned.
33.3% had 2 children.
Step-by-step explanation:
To find the number of adults add all the number of adults for each number of children. For example 2 adults had 0 children.
To find the percentage
100/15= 6.66
6.66× 5= 33.3
Answer:
15 adults were questioned. (2+4+5+1+1+2) (y-axis)
5 of the 15 adults had 2 children = 5/15 = 1/3 = 33,3%
Differentiate the following four levels of measurement and give an example of each: nominal, ordinal, interval and ratio.
-Nominal: a level of measurement describing a variable that has attributes that are merely different, as distinguished from ordinal, interval, or ratio measures. Gender is an example.
-Ordinal: a level of measurement describing a variable with attributes we can rank-order along some dimension. An example is socioeconomic status as composed of the attributes high, medium, and low.
-Interval: a level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes. There is however, no "true" zero point. Like the difference in temperature.
-Ratio: a level of measurement describing a variable with attributes that have all the qualities of nominal, ordinal, and interval measures and in addition are based on a "true zero" point. Ex. Number of children you have, makes sense to have a zero
Answers
The process of associating numbers with physical quantities and phenomena. Measurement is used in our day-to-day life
Nominal: A level of measurement describing a variable that has attributes that are merely different, as distinguished from ordinal, interval, or ratio measures.
Gender is an example.
Ordinal: A level of measurement describing a variable with attributes we can rank-order along some dimension.
An example is socioeconomic status as composed of the attributes high, medium, and low.
Interval: A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes. There is however, no "true" zero point. Like the difference in temperature. An example will be the measuring temperature.
Ratio: A level of measurement describing a variable with attributes that have all the qualities of nominal, ordinal, and interval measures and in addition are based on a true zero point. An example will be Number of children you have, makes sense to have a zero
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what is a correct name fo the angle shown. R S RTS SRT
Answers
find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
Answers
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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please help ppppppppppppp
Answers
Answer:
112
Step-by-step explanation:
formula = lwh/3 (length x width x height / divided by 3)
Answer:
112in
Step-by-step explanation:
Please mark brainliest.
1. On the set of axes below, graph . State the roots of
Answers
Is this question complete?
need help with this ASAP
!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The fence in dead center is about 399 feet from the third base.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.For the triangle in this problem, we have that:
The sides are d ft and 90 ft.The hypotenuse is of 409 ft.Hence the distance is obtained as follows:
d² + 90² = 409²
\(d = \sqrt{409^2 - 90^2}\)
d = 399 ft.
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The ice cream man just ended his shift for the day. Let 1/2x^2 6/11x + 8 represent the amount of chocolate ice cream bars he sold. Let 5/9x^2 + 2/3 represent the amount of vanilla ice cream bars he sold. Finally let 1/3x^2 + 4x + 4/3 represent the amount of strawberry ice cream bars he sold. Select all the statements that are true
a. The total amount of ice cream bars sold can be represented by the expression 25/18x^2+ 50/11x +10
b. The total amount of ice cream bars sold can be represented by the expression 25/18x^2 + 172/33x +28/3
c. He sold 1/6x^2 + 50/11x + 28/3 more chocolate than strawberry ice cream bars.
d. He sold 1/6x^2 - 38/11x + 20/3 more chocolate than strawberry ice cream bars.
Answers
Answer:
A and D
Step-by-step explanation:
Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.
=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)
=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)
Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]
= (1/6)x2 - (38/11)x +(20/3)
So, the correct options are A and D
Compute the value of the discriminant and give the number of real solutions of the quadratic equation. 2 -25x + 20x -4=0
Answers
If 60 of 200 people in a restaurant have ordered salads, then what % of customers have ordered salad?
Answers
Answer:
30%
Step-by-step explanation:
A number cube is rolled. Event A is rolling an odd number, and event B is rolling a factor of 12. What is P(AU B)?
Answers
Explanation:
A = set of odd numbers = {1,3,5}
B = set of factors of 12 = {1,2,3,4,6}
A U B = union of set A and set B
A U B = {1,3,5} union {1,2,3,4,6}
A U B = {1,3,5, 1,2,3,4,6}
A U B = {1,2,3,4,5,6}
The set union operation combines two sets into one bigger set. Duplicates are tossed out.
There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.
Therefore, the probability event A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.
Side notes:
A U B can be read out as "event A or event B"; so P(A U B) is "the probability event A happens or B happens or both".A intersect B = {1,3} = values that are in both set A and set B at the same time. These are both odd and a factor of 12.50 points
Please show work !!!
Answers
cosx = 4/5 = adjacent side/hypotenuse
5^2 = 4^2 + 3^2
25 = 16 + 9
sin(x/2) = + or - sqr(1-cosx)/2 = + sqr(1-4/5)/2 = - sqr(1/5/2) = sqr(1/10), ignore the negative root as x is in the 1st quadrant, and so is x/2.
sin(x/2) = 1/sqr10 = sqr10/10 = about 3.16/10 = 0.316
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
x = 21
Step-by-step explanation:
Using ratios:
75 : 25 = x : 7
75/25 = x/7
3 = x/7
21 = x
Using Pythagoras' Theorem a² + b² = c², where a and b are the legs and c is the hypotenuse of a right triangle:
\(72^2+x^2=75^2\)
\(\implies x^2=75^2-72^2\)
\(\implies x=\sqrt{75^2-72^2}\)
\(\implies x=21\)
For the graph, find the average rate of change on the intervals given
See attached picture b
Answers
We cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function.
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis. The difference between the change in output values and the change in input values is known as the average rate of change of a function over a period.
Let's assume that the function is denoted by f(x). Then, the average rate of change on the interval (a, b) can be calculated as
average rate of change = (f(b) - f(a)) / (b - a)
Using this formula, we can calculate the average rate of change on the given intervals as follows:
For the interval (-3, -2):
average rate of change = \(\frac{[f(-2) - f(-3)]}{[-2 - (-3)]}\)
For the interval (1, 3):
average rate of change = \(\frac{(f(3) - f(1))}{(3 - 1)}\)
For the interval (-1, 1):
average rate of change = \(\frac{(f(1) - f(-1))}{ (1 - (-1))}\)
Note that we cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function. If you provide the function or the graph, I can help you find the actual values of the average rate of change on these intervals.
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A rectangular eraser is 2^10mm long and 2^5mm wide. Write an expression for the area as a power of 2.
Answers
Answer:
1073741824 mm
Step-by-step explanation:
Hi can someone help me out this is due tomorrow thank you
Answers
To calculate the Mean of Scott's test score,
Mean is calculated by adding all the scores provide and dividing the sum by total counts of the numbers.
Mean = 75 + 52 + 80 + 88 + 100 = 395 = 79
5 5
Mean of the given scores is 79
MedianMedian is the number that appears in the middle when the given scores are arranged in ascending order.
Median = 52, 75, 80, 88, 100. = 80
80 is the number that appears in the middle.
Median = 80.
Mode
Mode is the number that appears most frequently in the given numbers.
In this scenario, all the numbers given appear once. Therefore, Mode is 0
Mode = 0
2. Olivia's test scoresMean = 98+92+88+92+95 = 465 =93
5 5
Mean = 93
Median
Test scores= 88,92,92,95,98
Median = 88, 92, 92, 95, 98
The number that appears in the middle is 92
Median = 92
Mode
Mode is the number that appears most frequently in the given numbers
Test scores = 88,92,98,92,95
92 appears more than once out of the test scores, therefore, 92 is the mode
Mode= 92
3. GemmaMean = 84+92+85+73+86 = 420 =84
5 5
Mean = 84
Median
Test scores= 84,92,85,73,86
Median = 73,84,85,86,92
85 is the number that appears in the middle
So, median= 85
Mode
Test scores= 84,92,85,73,86
Mode is the number that appears most frequently in the given numbers. All the numbers appear once. Therefore, Mode = 0
4. ChrisTest scores= 88,86,93,88,90
Mean
Mean = 88+86+93+88+90 = 445 = 89
5 5
Mean = 89
Median
Test scores= 88,86,93,88,90
Median = 86,88,88,90,93
88 is the number that appears in the middle
Median = 88
Mode
Test scores= 88,86,93,88,90
Mode is the number that appears most frequently in the numbers. 88 appears twice out of the numbers.
Mode = 88
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Sora is also making a salad. Her salad dressing recipe uses 6 teaspoons of vinegar for every 15
teaspoons of olive oil.
2.1 How much vinegar does Sora need for 5 teaspoons of olive oil?
2.2 How much olive oil does Sora need for 8 teaspoons of vinegar?
2.3 If Sora makes 42 teaspoons of salad dressing, how much of each ingredient is in it?
2.4 If Sora makes 14 teaspoons of salad dressing, how much of each ingredient is in it?
Answers
The following answers are given as:
2.1)
2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.
2.2)
8 teaspoons of vinegar are needed for 20 teaspoons of olive oil.
2.3)
There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.
2.4)
There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
6 teaspoons of vinegar = 15 teaspoons of olive oil.
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Now,
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 2 on both sides.
2 teaspoons of vinegar = 5 teaspoons of olive oil.
Now,
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 8 on both sides.
8 teaspoons of vinegar = 20 teaspoons of olive oil.
Now,
Total number of teaspoons = 42
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 12 on both sides.
12 teaspoons of vinegar = 30 teaspoons of olive oil.
12 + 30 = 42 teaspoons
Now,
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 4 on both sides.
4 teaspoons of vinegar = 10 teaspoons of olive oil.
4 + 10 = 14 teaspoons
Thus,
2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.
8 teaspoons of vinegar are needed for 20 teaspoons of olive oil.
There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.
There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.
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Ive been trying to get this question but i still cant seem to understand it please help
Answers
Answer:
D:x=2
Step-by-step explanation:
Rest of the triangle is just a distraction. The distance from B to any point in the bysector is the same as the distance from C to the same point (you can look at BDF and CDF and notice they're congruent by SAS). at this point it's just solving
\(2x + 3 = 4x - 1 \)
which has 2 as a solution
A manager drew this box-and-whisker plot to represent the number of minutes each of his 27 employees took on their break. Each employee took a different amount of time.
How many employees took a break longer than 49 minutes?
Help please!
Note: Put the correct answer! I don't want to get this wrong!
Thank you <3
Answers
Approximately 7 employees took a break longer than 49 minutes.
We have,
In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.
The line within the box represents the median.
The "whiskers" extend to the minimum and maximum values, excluding any outliers.
Given the information provided:
Median = 41
Q1 = 37
Q3 = 49
Largest = 55
Smallest = 35
Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.
Now,
The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:
25% of 27 employees
= (25/100) x 27
= 6.75
Since we cannot have a fractional number of employees, we round up to the nearest whole number.
Therefore,
Approximately 7 employees took a break longer than 49 minutes.
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Simplify the fraction
198/264
as much as possible
Answers
Answer:
What is 198/264 Simplified?
3/4 is the simplified fraction for 198/264.
Step-by-step explanation:
Answer:
3/4.
Step-by-step explanation:
Find the prime factors:
198 = 2 * 99
99 = 3 * 3 * 11
So 198 = 2 * 3 * 3 * 11.
264 = 4 * 66 = 2 *2 * 66
66 = 2 * 3 * 11
So 264 = 2 * 2 * 2 * 3 * 11.
Now we find the Greatest common factor os the 2 numbers:
It is 2 * 3 * 11 = 66.
Therefore we can now simplify the fraction:
198/66 / 264/66
= 3/4.
PLEASE I'M BEGGING YOU, HELP!! IF YOU ANSWER CORRECTLY I WILL GIVE YOU BRAINLIST
Use the information to answer the following question.
Susan has a bank account. For each day that Susan’s bank account balance falls below zero, she is charged by the bank a fee of $5.00 per day. Her current balance in the account is –$2.00.
If Susan does not make any deposits or withdrawals, what will be the new balance in her account after 3 days?
A.
$15.00
B.
-$14.00
C.
-$15.00
D.
-$17.00
Answers
Answer:
-17.00 dollars.
Step-by-step explanation:
Answer:
D
Step-by-step explanation
Keep in mind that her balance is already -$2.00
If she deposit or withdrawal any money for three days, she will be charged $15 (5 x 3 = 15). So the answer would be -$17.00 (D) because you add -$15 and -$2 (her original balance).
Find the partial sum for the sequence.
{2, 3, 5, 8, 13, ...}; S8
S8=
Answers
The partial sum of the sequence {2, 3, 5, 8, 13, ...} for the first 8 terms is 761/2.
The sequence given is a Fibonacci sequence, where each term is the sum of the previous two terms. To find the partial sum for the first 8 terms, we can use the formula for the sum of a finite geometric series:
Sₙ = a(1 - rⁿ)/(1 - r),
where Sₙ is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 2, r = 3/2 (since each term is 1.5 times the previous term), and n = 8. Plugging these values into the formula, we get:
S₈ = 2(1 - (3/2)⁸)/(1 - (3/2))
Simplifying the expression, we get:
S₈ = 761/2
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valuate the summation for the indicated value of the variable. 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!); m = 3
Answers
The answer of the given question based on the expression is , the value of the summation when m = 3 is 137.
What is Expression?In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a set of values. It can be a simple combination of numbers and variables or a more complex combination involving mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic to complex functions and equations.
To evaluate the summation 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!), where m = 3, we substitute m = 3 and simplify:
1(1!)+2(2!) +3(3!) +4(4!) +3(3!)
= 1(1) + 2(2) + 3(6) + 4(24) + 3(6) (since n! = n(n-1)! for all positive integers n)
= 1 + 4 + 18 + 96 + 18
= 137
Therefore, the value of the summation when m = 3 is 137.
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Please help urgent thank you
Answers
If he wants an average of 84, he needs to get at least 93 points.
What score does he need to get in the next test?Remember that the average value between 3 values A, B, and C is:
(A + B + C)/3
Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:
(76 + 83 + x)/3 = 84
159 + x = 252
x = 252 - 159
x = 93
So he needs to get at least 93 points in the next exam.
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Somerville High School raised $740 to buy winter coats for the homeless at $46.25 each. How many coats can they buy?
Answers
Answer: They can buy 16 coats.
Step-by-step explanation:
All you have to do is divide $740 by $46.25 and you will get 16 which will be your final answer.