How would you graph this parabola? it's just confusing because of the fractions ...
Answers
To graph the parabola [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], plot the vertex at (2, -4), note the axis of symmetry at x = 2, and create a downward-opening parabolic shape on a coordinate plane.
To graph the parabola given by the function [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], follow these steps:
1. Identify the vertex: The vertex of a parabola in the form of [tex]y = ax^2 + bx + c[/tex] is given by (-b/2a, f(-b/2a)). In this case, a = -1/3 and b = 4/3. Calculate the x-coordinate of the vertex using -b/2a:
x-coordinate of the vertex = -b / (2a) = -(4/3) / (2 * (-1/3)) = 2.
Now, find the corresponding y-coordinate by plugging the x-coordinate back into the function:
[tex]f(2) = (-1/3)(2)^2 + (4/3)(2) - 16/3 = (-4/3) + (8/3) - 16/3 = -12/3 = -4.[/tex]
So, the vertex is at (2, -4).
2. Find the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. In this case, it's the vertical line x = 2.
3. Calculate additional points: To create a more accurate graph, you can choose additional x-values and calculate their corresponding y-values. For instance, you can select x-values to the left and right of the vertex.
- For x = 0:
[tex]f(0) = (-1/3)(0)^2 + (4/3)(0) - 16/3 = -16/3.[/tex]
- For x = 4:
[tex]f(4) = (-1/3)(4)^2 + (4/3)(4) - 16/3 = -64/3 + 16/3 - 16/3 = -64/3.[/tex]
4. Plot the points: Plot the vertex (2, -4) and the additional points you calculated on a coordinate plane.
5. Draw the parabola: Connect the points smoothly to form the parabolic shape. Since the leading coefficient (-1/3) is negative, the parabola opens downward.
6. Label the axis of symmetry: Label the vertical line x = 2 as the axis of symmetry.
Your graph of the parabola f(x) = -1/3x^2 + 4/3x - 16/3 should resemble a downward-opening parabola with the vertex at (2, -4) and the axis of symmetry at x = 2.
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Related Questions
How do i do this problem?
(13z^9+6v)-11z^9
Answers
13z^9 + 6v-11z^9 =
2z^9 + 6v
Given ONL=MLN, O and M are right angles prove LM=NO
Answers
Using the properties of Isosceles triangles and right-angled triangles, it can be deduced that LM = NO given that angles ONL = MLN and O and M are right angles.
Explanation:The given question is about proving equivalency of lines in a geometric figure. Given the figure has the angles ONL and MLN that are equal and O and M are right angles. Given these conditions, using the properties of triangles especially the Isosceles Triangle (where two sides are equal), we can conclude that LM = NO.
To prove this assumption, we incorporate the following facts: In an isosceles triangle, the angles opposite to equal sides are equal. Hence, if ONL = MLN, it implies that NO = LM. Additionally, if angles O and M are right angles, it signifies that the triangles formed are right angled triangles. Therefore, using the property of isosceles right angled triangles, the sides opposite to equal angles are equal.
Based on these facts and the properties of geometric concepts [Isosceles Triangle, Pythagorean theorem and right angled triangles], we can confidently conclude that LM = NO. This proves that given the conditions in the problem, the lines LM and NO are equal in length.
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Given that ONL=MLN and O and M are right angles, we can say that triangles ONL and MLN are congruent right-angled triangles. Therefore, according to the property of congruent triangles, the sides opposite the equal angles in these triangles (i.e., LM and NO) should also be equal to each other.
Explanation:The question involves proving the equivalence of two lines in a geometric configuration, LM and NO, where two angles, ONL and MLN, are given as equal and O and M are right angles. This is quite a typical problem in Geometric Proof, an important topic in High School Mathematics.
To solve this, we need to apply the properties of triangles and the concept of congruent triangles. Since ONL and MLN are given as equal angles and O and M are right angles, we know that triangle ONL and MLN are right-angled triangles. In a right-angled triangle, if one angle is equal, then the other angles will be equal because the summing of angles in a triangle is 180 degrees.
Because we have now two right-angled triangles with their respective angles equal (ONL = MLN and NOM = LNM), they must be congruent triangles by the Angle-Angle (AA) criterion for congruency. This implies that the sides opposite the equal angles in these two triangles should also be equal. So, LM = NO in these triangles.
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What is the capacity of the cube in liters? Cube with length, width, and height labeled as 9 centimeters. 0.81 L 0.729 L 81 L 729 L
Answers
=> Conversión factor: 1 dm / 10 cm
=> 9 cm * 1 dm / 10 cm = 0.90 dm
Volume of cube with legth, width and height 0,9 dm = (0.90 dm)^3 = 0.729 dm^3 = 0.729 liter.
Answer: 0.729 L
According to a survey, 75% of adults in the united states think the u. s. government system is broken. of these 75%, about 7 out of 10 think that the government can be fixed.
a.find the probability that a randomly selected adult thinks the u. s. government system is broken and thinks the government can be fixed.
b.given that a randomly selected adult thinks the u. s. government system is broken, find the probability that he or she thinks the government cannot be fixed.
Answers
1. Probability that a randomly selected adult thinks the U.S. government system is broken and can be fixed:
P (A and B) = P (A) * P (B|A) = .75 * .7 = 0.525
2. Probability that given that a randomly selected adult thinks the U.S. government system, he or she thinks the government cannot be fixed.
P (B|A) = (1 – P (B|A) = 3/10 = 0.3
To calculate the probability that an adult thinks the U.S. government is broken and can be fixed, multiply 75% by 70%, resulting in 52.5%. The probability that an adult thinks the government is broken but can't be fixed is found by subtracting 70% from 100%, yielding 30%.
The subject in question pertains to probability and statistics, which involves calculating the likelihood of certain outcomes based on given data and constructing confidence intervals to understand the population parameters.
Part A:
To find the probability that a randomly selected adult thinks the U.S. government system is broken and thinks the government can be fixed, we multiply the two given probabilities: 75% of adults think the system is broken and, of these, 70% think it can be fixed. Therefore:
0.75 (probability of thinking the system is broken) × 0.70 (probability of thinking it can be fixed given the system is broken) = 0.525 or 52.5%.
Part B:
Given that an adult thinks the government system is broken, to find the probability that they think it cannot be fixed, we subtract the probability that they think it can be fixed from 1:
1 - 0.70 = 0.30 or 30%.
In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?
b/a⋅c/d=−1
b/a=c/d
b/a=d/c
b/a⋅d/c=−1
Answers
Three friends have some ribbon.carol has 42 inches of ribbon,tino has 2.5 feet of ribbon,and baxter has 1.5 yards of ribbon.express the total length of ribbon the three friends have in inches,feet and yards
Answers
1.5 yd = 54 in.
42 + 30 = 72 in.
72 + 54 = 126 in.
So, they have one hundred twenty-six inches of ribbon.
Part B: 126 in. = 10.5 ft
In other words, they have ten and a half feet of ribbon.
Part C: 126 in. = 3.5 yd.
In other, OTHER, words, they have three and a half yards of ribbon.
The hypotenuse of a right triangle is 6 inches and one of the legs is √ 6 inches, the exact value of the other leg is _______ inches.
A. 30
B. √ 15
C. 15
D. √ 30
Answers
What is the probability of finishing a project on or before 22 weeks if the mean (expected) total duration is 18 weeks and the variance is 4 weeks?
Answers
How do you simplify -3.3+5.5
Answers
C write function distance that calculates the distance between two points (x1, y1) and (x2, y2). all numbers and return values should be of type double.
Answers
Given (0, 5) and (5, 0), find the distance between the two points.
Let (0, 5) and (5, 0) be the two points.
Let d = distance
d = sqrt{(5 - 0)^2 + (0 - 5)^2}
d = sqrt{(5)^2 + (-5)^2}
d = sqrt{25 + 25}
d = sqrt{50}
d = sqrt{25}•sqrt{2}
d = 5•sqrt{2}
The number 0.4 can written as 4/10, so it is a rational number
Answers
An easy way to tell if a number is irrational if you cannot count it, or convert it into a decimal/fraction.
Such as pie, square root of 11, etc.
0.4=4/10
Your answer is yes it is a rational number.
CAN SOMEONE HELP ASAP!! Please!
Answers
The product of two prime numbers is one less than 12 squared. What are they two prime numbers?
Answers
144-1=143
143/11=13
So the answer would be 11 and 13.
Hope this helps!
he equation for the line of best fit is y = 0.39x + 15.89. Which of the following statements is true for the above graph?
Answers
y = mx + b
where: y = y coordinate
x = x coordinate
m = slope
b = y-intercept
In the equation, y = 0.39x + 15.89. The y-intercept is 15.89 or approximately 16. Meaning at x = 0, there's already approximately 16 dogs visiting at the park.
Therefore, the answer is the last statement.
ANSWER: The y-intercept of the line is 15.89, meaning that on the day the dog park opened, there were about 16 dogs visiting the park.
PLEASE HELP!!!!!!!!
Whats the value of m?
0.61m-1.51m=9
m=
Answers
m= -10. I hope that helps.
-0.9m = 9
/-0.9 /-0.9
m = -10
BRAINLIEST TO BEST ANSWER!!!!
The table shows a linear function. Write an equation that represents the function using function notation.
Answers
A quiz consist of 2 true-or-false questions 3 are multiple choice questions. The multiple choice questions have 3 options each. How many ways can a student complete the quiz?
a.36
b.162
c.108
d.18
A secrete code consist of 2 digits, followed by 2 letters, followed by 1 of the following symbols @,#,%, and &. Digits and letters cannot repeat.
a.243,360
b.260,000
c.234,000
d.270,400
How many distinct arrangements can you make using the letters in the word EXPERIMENT?
a.1,209,600
b.3,628,800
c.725,760
d.604,800
How many ways can a dance instructor send 4 of her 11 students to a summer dance program?
a.330
b.720
c.7920
d.1980
There are 5 keys on a key chain. 1 of the keys start a car. A random key is chosen. What is the probability that it starts the car?
a.25%
b.5%
c.20%
d.15%
The probability of choosing a winning card from a stack of cards is 2.9%. What is the probability of choosing the losing card
a.87.1%
b.92.9%
c.99.71%
d.97.1%
Answers
n = 2 x 2 x 3 x 3 x 3
n = 108
Answer: C. 108
B. From 0 to 9, there are 10 digits. There are also 26 and as per given, there are 4 symbols. The number of ways that the code can be made is,
n = 10 x 9 x 26 x 25 x 4
n = 234,000
Answer: C. 234,000
C. In the word, EXPERIMENT, there are 10 letters. Three of which are letter Es. The number of ways that the letters can be arranged is,
n = 10!/3!
n = 604,800
Answer: D. 604,800
D. If the arrangement is not important and that only the combination is important, the number of ways that the instructor can send 4 out of the 11 is,
n = 11C4 = 330
Answer: A. 330
E. If only one of the five keys can start the car then, the probability that the chosen key can start the car is equal to the ratio of the number of key to the total number of keys.
n = (1/5)(100%) = 20%
Answer: C. 20%
F. The events of picking the winning card and picking or choosing the losing card are complementary events such that the sum of their probabilities should be equal to 1 or 100%.
P = 100 - (2.9%)
P = 97.1%
Answer: D. 97.1%
Final answer:
Calculating possibilities ranges from completing a quiz to creating secret codes, with correct answers including 108 ways to complete a quiz and 234,000 combinations for a secret code. The arrangement of the word EXPERIMENT yields 1,209,600 unique arrangements, and other questions involve calculating probabilities and combinations in different scenarios.
Explanation:
Calculating Various Probabilities and Combinations
Let's break down each part of the question to provide clear and step-by-step solutions.
1. Completing a Quiz
For the quiz with 2 true-or-false questions and 3 multiple-choice questions (each with 3 options), the number of ways to complete the quiz can be calculated as 22 * 33, which equals 4 * 27 = 108. So, the correct answer is 108 ways.
2. Creating a Secret Code
For a secret code consisting of 2 digits (10 options each, but cannot repeat, so 10*9), 2 letters (26 options each, but cannot repeat, so 26*25), followed by 1 symbol from 4 options, the total number of combinations is 10*9*26*25*4 = 234,000. Thus, the correct choice is 234,000 combinations.
3. Arrangements of the Word EXPERIMENT
To find the number of distinct arrangements of the letters in EXPERIMENT, considering the repeated letters, the formula is the total factorial divided by the product of factorials of each repeated letter: 10!/ (2! * 3!), which calculates to 1,209,600. Therefore, option a is correct.
4. Sending Students to a Summer Dance Program
To determine how many ways a dance instructor can send 4 of her 11 students to a summer dance program, we use combinations: 11C4 = 330. So, the answer is 330 ways, option a.
5. Probability of Starting a Car
With 5 keys, the probability that a randomly chosen key starts the car is 1/5, which translates to 20%, option c.
6. Probability of Choosing a Losing Card
If the winning probability is 2.9%, the losing probability is 100% - 2.9% = 97.1%, thus the correct answer is option d.
You want to buy a new TV. The diagonal measure of the screen is 42 inches, and the screen width is 36.6 inches. What is the screen height? Round your answer to the nearest hundredth.
Answers
What is the point-slope form of the equation of a line that passes through the point (6, −8) and has a slope of −2? y+8=2(x-6) openstudy?
Answers
Passes through (6, -8) ; Slope is -2
Simply plug everything in :)
y - (-8) = -2(x - 6)
Simplify.
y + 8 = -2x + 12 → Answer
The answer from Openstudy is incorrect, because our slope is negative, not positive.
~Hope I helped!~
Use the given property to complete the statement. Transitive Property of Congruence If Angle X Y Z is congruent to angle A O B and Angle A O B is congruent to angle W Y T, then A. Angle W Y T is congruent to angle A O B B. Angle A O B is congruent to angle A O B C. Angle X Y Z is congruent to angle W Y T D. Angle A O B is congruent to angle X Y Z
Answers
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The correct option is C, ∠XYZ ≅ ∠WYT.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
Given that Angle XYZ is congruent to angle AOB, therefore, we can write,
∠XYZ ≅ ∠AOB
Also, it is mentioned that Angle AOB is congruent to angle WYT, Therefore, we can write,
∠AOB ≅ ∠WYT
Now, we can write the two congruency together as,
∠XYZ ≅ ∠AOB ≅ ∠WYT
∠XYZ ≅ ∠WYT
Hence, the correct option is C, ∠XYZ ≅ ∠WYT.
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If the number 659983 is rounded to the nearest hundred how many zeros does the rounded number have
Answers
hope this helps
Please help me thank you very much.
Answers
2 is also A
The answer is A.
The one part of the median will always be 2 times bigger than the other when the median is divided by the centroid.
Question 2:
The answer is B.
The obtuse triangle has an orthocenter on the exterior, or the outside.
The orthocenter will be on the INTERIOR for the other triangles.
Have an awesome day! :)
A cold front moved in last weekend. In 8 hours overnight the temperature outside dropped 24 degrees. What was the average temperature change for each hour?
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CAN YOU PLEASE SOLVE THESE PROBLEMS!!! THANKS!!!!!
1) -3/4x=5
2) 0.6x= 0.48
3) -30=1.25x
4) -12 2/3= -1 1/9x
5) 12-3/5x = 27.
6) -17= 6x-5
7) 13= x/3 +4
8) -2/3x -4=10
9) 9x-14=2x
10) 2.5x -15=4x
11) 2x-31=-9x+24
Answers
1. -6 2/3
2. 0.8
3. -24
4. 11 2/5
5. -25
6. -2
7. 27
8. -21
9. 2
10. -10
11. 5
Note: I would've been able to explain to you better how you get these answers had there not been so many questions in one, but I tried my best.
What are the x-intercepts of the graph of the function f(x)=x2-16x+64
Answers
To find the x-intercepts of the function f(x) = x^2 - 16x + 64, we set f(x) to zero and solve for x. The quadratic factors to (x - 8)^2 = 0, revealing that the graph has a single x-intercept at x = 8.
Explanation:To determine the x-intercepts of the graph of the function f(x) = x^2 - 16x + 64, we need to find the values of x for which f(x) equals zero. This involves solving the quadratic equation, x^2 - 16x + 64 = 0.
One approach is to factor this equation if possible. Another approach is to use the quadratic formula.
The given quadratic equation can be factored as (x - 8)^2 = 0.
Therefore, the only solution to this equation is x = 8, which means the graph of the function touches the x-axis at this point and has a vertex at (8, 0), making the x-intercept of the graph equal to 8.
The factored form indicates that the function has a double root at x = 8, which means the parabola touches and then bounces off the x-axis at this point.
Thus, rather than crossing the x-axis at two distinct points, the parabola has a single x-intercept at x = 8. This is often referred to as a repeated or double root because the solution appears twice when the quadratic is factored.
A line has a slope of 2 and passes through the point (4,0)
What are the coordinates of another point that is on the line?
A. (0,2)
B.(2,0)
C.(4,6)
D.(6,4)
Answers
y=2x-8
D. (6,4)
y=2(6)-8
y=12-8
y=4
1250 is deposited in an account that pays 6.5% annual interst compounded continuosly. what is the balance after 8years?
Answers
So, we use the formula y=ab^x.
1250 is what you started out with, so it is your initial value.
We have to change the percentile to a decimal, so we will move the decimal two places to the left, making it 0.065. We see in the problem that the word "compounded" is brought up, implying an increase. Therefore, 0.065 will be added by 1 to get 1.065. You place that value into the parentheses.
The x represents the amount of time, which is 8 years.
So, 1250(1.065)^8 = 2,069 (answer was 2068.74 before being rounded).
Answer:2102.53
Step-by-step explanation:
1250e(0.065)8
Answer+explanation plz and thank you! :) these are quadratic equations.
Answers
3x+2=0
3x=-2
x=-2/3
and
x-5=0
x=5
the solution with a higher value is 5
a baby elephant weighs 250 lb.
What is the elephants weight in TONS AND KILOGRAMS
(1kg=2.2lb)? round to the nearest thousandths place
Answers
2000 lb / 907.185 kg = 250 lb / x kg. 2000x = 907.185(250). x = 113.4 kg
Answer:
250 lb⋅1 ton2000 lb=2502000 tons = 18 ton = 0.125 tons
250 lb⋅1 kg2.2 lb≈2502.2 kg ≈ 113.636 kg
In folding to make a 6-sided snowflake, what shape do you have after completing the first 5 steps?
a.
right triangle
c.
rectangle
b.
square
d.
circle
Answers
Well, let's take a look. Observe carefully at the photo below. We can see that this certainly isn't a circle or a square. It has three equal angles, making it a right triangle.
Answer: Letter A ✅
Hope that helps! ★ If you have further questions about this question or need more help, feel free to comment below or post another question and send the link to me. -UnicornFudge aka Nadia