Answers
A graph of the given quadratic equation is shown below.
The axis of symmetry is equal to 3.
The vertex is equal to (3, -1).
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function y = x² - 6x + 8 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -1.
In conclusion, the axis of symmetry is 3 while the vertex is given by the ordered pair (3, -1).
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Related Questions
What value will make the equation true?
Answers
Answer: C (-0.6)
Step-by-step explanation:
-2.1--0.6=-1.5
-1.5 as fraction = -1 1/2
Match each pair of points, to the slope of the line between them. (1,3) and (5,6) (1,7) and (5,4) (5,5) and (2,1)
answers 4/3,-4/3,3/4,-3/4
Answers
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ 3 }{ 4 } \implies \cfrac{3}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -4 }{ -3 } \implies \cfrac{4}{3}[/tex]
let u d 2 4 5 6 7 3 5 , and let w be the set of all x in r 3 such that u ? x d 0. what theorem in chapter 4 can be used to show that w is a subspace of r 3 ? describe w in geometric language.
Answers
Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.
How to solve
To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.
A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:
For any vectors a, b ∈ S, their addition a + b ∈ S.
For any vector a ∈ S and any scalar k, the product ka ∈ S.
Now, let's define a vector m = v - e.
Observe that for any y in S, we have:
m • y = (v - e) • y = (v • y) - (e • y) = 0.
This implies that y is orthogonal to the vector m.
Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.
As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.
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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).
What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.
I might need some help with this question lol
Answers
The volume of the box is 72 cubic feet.
We have,
To find the volume of the box, we need to multiply its length, width, and height.
Given:
Length = 4 ft
Breadth = 6 ft
Height = 3 ft
The volume of the box is:
Volume = Length x Breadth x Height
Volume = 4 ft x 6 ft x 3 ft
Volume = 72 cubic feet
Therefore,
The volume of the box is 72 cubic feet.
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PLEASE HELP IM GOING T0O FAIL THIS :(
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Answers
The measure of variability that the Charity should use is B. The IQR of 13 is the most accurate to use, since the data is skewed.
Why is the IQR best ?Adopting the IQR gives a better picture of the standard donations, since it is less responsive to outliers and unbalanced data than the range. The charity must take advantage of the Interquartile Range (IQR) for an exact depiction of the data, as it is less impressionable to outliers and skewed data.
The IQR would be:
= Q3 - Q1
Q1 from the data is:
= (6 + 8) / 2 = 7
Q3 is :
(20 + 20) / 2 = 20
The IQR is:
= 20 - 7
= 13
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Yoshi has 22$ in his wallet and makes 5$ per hour
Answers
Answer:
Number of Hours | Money
0 hrs — 22$ (+0$)
1 hrs — 27$ (+5$)
2 hrs — 32$ (+5$)
3 hrs — 37$ (+5$)
(he would gain 15$ after 3 hours of baby sitting)
Step-by-step explanation:
Y = 5x + 22
5x is the amount being added each time, 22 is the y-intercept of the slope; the slope is going at a linear rate of 5 per hour.
In a survey about shopping behaviors, 300 300 randomly selected sophomores are asked about their shopping preferences. It is found that 12.5% 12.5 % of the sophomores shop online at least once per month. The margin of error is ±1% ± 1 % . There are approximately 12,000 12,000 sophomores in the state. Using the data from the sample survey, what is the estimated number of sophomores who shop online, at least once per month? Between 1,380 1,380 and 1,500 1,500 Between 1,500 1,500 and 1,620 1,620 Between 1,380 1,380 and 1,620 1,620 Between 1,350 1,350 and 1,620 1,620
Answers
The estimated number of sophomores is between 1,380 and 1,620. Then the correct option is C.
Given that:
The sample proportion is 12.5% or 0.125, and the population size is 12,000.
We can use the following formula to calculate the estimated number of sophomores who shop online at least once per month:
Estimated number = sample proportion x population size
The estimated number using this lower bound (i.e., 12.5% - 1%):
Estimated number = 0.115 x 12,000 = 1,380
Similarly, the estimated number using this upper bound (i.e., 12.5% + 1%):
Estimated number = 0.135 x 12,000 = 1,620
Therefore, the estimated number of sophomores who shop online, at least once per month, is between 1,380 and 1,620, which means that the answer is "Between 1,380 and 1,620".
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pls answer
worth 20 points!!!!
Answers
Step-by-step explanation:
Circumference of a circle is found by:
Circ = pi * d
= pi * 9.7 cm = 30.5 cm
a 5lb force acting in the direction of (5,-3) moves an object just over 12 ft from point (0,6) to (7,-4). find the work done to move the object to the nearest foot-lb.
a. 11ft lb
b. 34ft lb
c. 56ft lb
d. 61ft lb
Answers
ventajas y desventajas del modelo atómico de rutherford
Answers
The Rutherford model of the atom is known to be a term that is also seen as planetary model. It was said to have been proposed by Ernest Rutherford in 1911. It was a vital improvement over previous models, but it had some few limitations.
What is Rutherford model of the atom?Below are some advantages and disadvantages of the Rutherford model:
In terms of Advantages:
The Rutherford model was said to be one that was first model that introduced the concept of the nucleus.The Rutherford model aids man to explain the reason most of the alpha particles passed straight through the gold foil, while a few were deflected.In terms of Disadvantages:
The Rutherford model was unable to tell the ways of electrons.The Rutherford model was said to have assumed that the positive charge in the nucleus was one that is uniformly distributed and this was notLearn more about Rutherford model from
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See text below
advantages and disadvantages of the rutherford model of the atom
1. explain what is meant by decision variables, objective function and constraints in linear programming.
Answers
Decision variables are the unknown quantities that need to be determined in a linear programming problem.
The objective function is a mathematical expression that needs to be maximized or minimized. It represents the goal or objective of the problem. Constraints are the restrictions or limitations that need to be satisfied in a linear programming problem. These constraints limit the feasible region of the problem and provide boundaries for the decision variables. Linear programming involves finding the optimal solution by maximizing or minimizing the objective function, subject to the constraints. The solution must satisfy all the constraints and provide the best possible value for the objective function.
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which type of error occurs when certain sample elements are excluded or when the entire population is not accurately represented in the sampling frame? a. type i error b. sampling frame error c. statistical error d. list error
Answers
The type of error occurs when certain sample elements are excluded is sample frame error. Then the required answer for the given question is Option B.
The type of error that takes place when a particular sample elements are eliminated or when the whole population is not accurately projected in the sampling frame is called sample frame error.
There are 4 types of sampling error
When only those participants who are interested respond is known as self-selected.
It takes place only when researchers places a target on the sub-population wrongly when selecting samples.
Non-response error happens when respondents deny to participate in a survey.
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a card is drawn at random from a pack of 52 playing cards. what is the probability that it is a red king or the 4 of diamonds?
Answers
If a card is drawn from a pack of playing cards, then the probability that card is "red-king" or "4-of-diamonds" is 3/52.
There are 2 card of "red-kings" and 1 card of "4-of-diamonds" in a deck of cards. There are 52 cards in total.
So, probability of drawing a "red-king" is "2/52", because there are two "red-kings" out of 52 cards, and
The probability of drawing 1-card of "4-of-diamonds" is "1/52", because there is only 1 "4-of-diamonds" out of 52 cards,
To find probability of drawing a "red-king" or "4-of-diamonds", we add the probabilities of these two events and subtract the probability of drawing both of them, because they are not mutually exclusive,
⇒ P(red-king or 4-of-diamonds) = P(red king) + P(4 of diamonds) - P(red king and 4 of diamonds),
⇒ P(red-king or 4-of-diamonds) = 2/52 + 1/52 - 0,
⇒ P(red-king or 4-of-diamonds) = 3/52,
Therefore, the required probability is 3/52.
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helppp with this geometry problem pleasee
Answers
48 is the section you r trying to find
so 360/48=7.5 gives the ratio
and area of circle=pi*r^2
r=9
whole circle area = 81pi
and 81pi/7.5=33.929
Consider the steps to solve the equation.
(y + 20 ) - = (2y − 1)
Distribute: +8-04-20
10
What is the next step after using the distributive
property?
O Use the multiplication property of equality to isolate
the variable term on one side of the equation.
O Use the multiplication property of equality to isolate
the constant on one side of the equation.
O Combine the like terms on the right side of the
equation.
O Combine the like terms on the left side of the
equation.
Answers
Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.
Given information:
[tex]\dfrac{2}{5} \left ( \dfrac{1}{2} y + 20 \right) - \dfrac{4}{5} = \dfrac{9}{20} \left ( 2y-1 \right)[/tex]
The distributive property is often expressed as:
a(b + c) = ab + ac
a(b - c) = ab - ac
Where "a" is a coefficient (or factor) and "b" and "c" are terms.
The equation is simplified as,
[tex]\dfrac{1}{5} y + 8 - \dfrac{4}{5} = \dfrac{9}{10} y- \dfrac{9}{20}[/tex]
Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.
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Help please, I'm very confused
Answers
We can use the two points (0, 50) and (2, 40) from the table to find the slope of the line:
slope = (change in y) / (change in x) = (40 - 50) / (2 - 0) = -10 / 2 = -5
Therefore, the rate of change of the linear function represented by the table is -5. This means that for every increase of 1 unit in the x-value, the y-value decreases by 5 units.
four identical glasses are shown below. one glass is empty, and the other three glasses are 1/4 full, 1/2 full and 4/5 full of water, respectively. if the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled
Answers
If the water were redistributed equally among the 4 glasses, the fractional part of each glass that would be filled include the following: K. 31/80.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Based on the information provided above, the division can be calculated as follows;
Fraction = (1/4 + 1/2 + 4/5) ÷ 4
Fraction = 31/20 ÷ 4
Next, we would multiply the fraction 31/20 by the reciprocal of 4 as follows;
Fraction = 31/20 × 1/4
Fraction = 31/80
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
An exponential function in the form y=20(b)^x contains the points (0,20) and (1,10). What is the value of b?
Answers
Step-by-step explanation:
When x = 0 y = 20 Plug in:
20 = 20 b^0
20 = 20 true , but we didn't find 'b'
when x = 1 y = 10 Plug in:
10 = 20 * b^1
10 = 20 b
b = 1/2
According to a recent survey of adults, approximately 62% carry cash on a regular basis. The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis. Is carrying cash independent from having children in this sample? No, P(carry cash) = P(carry cash|have children). No, P(carry cash) ≠ P(carry cash|have children). Yes, P(carry cash) = P(carry cash|have children). Yes, P(carry cash) ≠ P(carry cash|have children).
Answers
The correct statement regarding whether the events are independent is given as follows:
No, P(carry cash) ≠ P(carry cash|have children).
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the result of a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.An event B is classified as independent if:
P(B|A) = P(B).
According to a recent survey of adults, approximately 62% carry cash on a regular basis, hence:
P(carry cash) = 0.62.
The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis, hence the conditional probability is given as follows:
P(carry cash|children) = 0.85.
As the probabilities are different, the events are not independent.
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How come math is hard and not all that easy
Answers
Answer: it is only a mind set
Step-by-step explanation: when you are in a good mindset you will do well but when you are in a negative mindset it will be hard.
Answer:
It depends if its like 1st grade then you might have to get that checked out but if its 12th grade probally to make kids question life :)
Step-by-step explanation:
PLS GIVE BRAINLIST
HAVE A GOOOOODY DAY!!!
Which table matches the data in the graph?
Math Test Raw Scores
Points
2288 2288 2 2 2 2
120
110
100
90
80
70
50
40
30
20
10
X
y
X
0 2 4 6 8 10 12 14 16 18 20 22 24
Correct answers
Y
X
y
X
y
(5,30)
(12, 72)
1
2
1
3
5
120
1
6
(20, 120)
(18. 108)
24
4
2
10
12
108
3
18
3
6
3
12
18
72
5
30
4
8
4
13
20
30
7
42
Answers
A table that matches the data in the graph include the following:
Correct answers Points
0 0
5 30
12 72
18 108
20 120
What is a proportional relationship?In Mathematics, a proportional relationship produces equivalent ratios and it can be represented by the following mathematical equation:
y = kx
Where:
k is the constant of proportionality.y represent the points.x represent the correct answers.Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:
Constant of proportionality, k = y/x = t/d
Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20
Constant of proportionality, k = 6.
Therefore, the required equation is given by;
y = kx
y = 6x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
PLEASE HELP ME! I DON'T UNDERSTAND HOW TO SOLVE THIS!!
If the volume is 64π how would i solve this equation for r?
V=4/3πr^3
Answers
Step-by-step explanation:
V = 4/3 pi r^3
64 pi = 4/3 pi r^3 divide both sides of the equation by pi :
64 = 4/3 r^3 multiply both sides by 3/4
3/4 * 64 = r^3 simplify a bit
48 = r^3 take cube root of both sides
r = 3.63 units
Please help!!!
What is 3^2, aka 3*3*3?
Answers
Answer:
Step-by-step explanation:
First of all 3^2 is equal to 3*3 NOT 3*3*3
3^2 means "3 raised to the power of 2," which is equal to 3 multiplied by itself 2 times:
3^2 = 3 x 3 = 9
Therefore, 3^2 is equal to 9.
Your welcome
Brooke is purchasing tile to add a backsplash to her kitchen wall. Each tile covers 25 in sq. If each tile cost $1.75, what is the total amount Brooke will spend on tile?
Answers
Answer:
Step-by-step explanation:
ee
Answer: $92.75
Step-by-step explanation:
I think this is the answer, sorry if incorrect. When finding the total area of the wall you split the shape in 2. You would get 175 + 1150 inches squared. You then get the total of 1,325 inches squared as the total area of the wall. You divide that number by the number of inches of each tile, which would get you 53 tiles that will be on the wall. Times 53 by the price of each tile, $1.75, and get the answer of $92.75. Hope this helps!
Rowan thinks of a number. His number is a factor of both 18 and 30. His number is odd. What is the largest possible number he could be thinking of?
Answers
The largest possible number that he could be thinking of is given as follows:
3.
How to obtain the number?A number a is said to be a factor of another number b when the divisibility of b by a has a remainder of zero, that is, it is an exact division.
The factors of 18 are given as follows:
{1, 2, 3, 6, 9}.
The factors of 30 are given as follows:
{1, 2, 3, 5, 6, 10, 15, 30}
The number is odd, hence the largest possible number is of 3.
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pls help due in an hour if you get it right ill mark you brainiest
Answers
Step-by-step explanation:
B to B'
( 7,-2) to (-2,-7)
(x,y) changed to (y,-x) this is a 90 degree clockwise rotation
Answer:
Step-by-step explanation:
It is a 90 degree clockwise rotation.
A = (2, -5)
A' = (-5, -2)
90° clockwise will reverse the x an y points and change the sign of x.
(x, y) becomes (y, -x)
You only need to use one point to figure the rotation.
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
900
2,000
2,100
4,000
Answers
Answer:We can estimate that 900 people in attendance would prefer mustard on a hot dog.
Step-by-step explanation:What is proportion?
Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.
To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.
The proportion of people in the sample who prefer mustard is:
27/150 = 0.18
To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:
0.18 x 5,000 = 900
Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.
sam wants a wall purple and the mixture says to use 1:3 of blue paint to red paint. if she uses 2 tins of blue paint,how many tins of red paint will she use?
Answers
Answer:
6 tins of red paint
Step-by-step explanation:
blue = 1, red = 3 so:
from 1 to 2 tins of blue, you multiply 1 x 2 = 2 tins. Now we have to multiply by 2 on the other side
So: 3 x 2 = 6 tins of red
In ratios, multiplying or dividing has to be applied to both sides
1 : 3 becomes 2: 6
given that 3 feet equal 1 yard how many yards equal 7 feet
Answers
Answer: 2.333
Step-by-step explanation:
Since 3 feet equal 1 yard, we can divide 7 feet by 3 to get the equivalent distance in yards:
7 feet ÷ 3 feet/yard = 2.333 yards (rounded to 3 decimal places)
Therefore, 7 feet is equivalent to approximately 2.333 yards.
hope this help mark me brainst
Write the equation of the conic satisfying the given conditions.
focus at the pole, e=d
=,directrix rsin0 = -2
Answers
The equation about the conic is r = 6/(4|sinθ| - 3cosθ).
We have,
Since the focus is at the pole, the conic is a polar equation with the form
r = e d / (1 - e cosθ), where d is the distance from the pole to the directrix and e is the eccentricity.
In this case,
e = 3/4 and the directrix is r sinθ = -2.
We can rewrite the equation of the directrix in Cartesian coordinates as
y = -2/sinθ.
Now we can use the formula for the distance from a point (x, y) to a line Ax + By + C = 0, which is:
d = |Ax + By + C| / sqrt(A^2 + B^2)
In our case,
The equation of the directrix is y + 2/sinθ = 0, which we can rewrite as
y = -2/sinθ.
The coefficients of x and y are both 0 and the constant term is 2/sinθ, so
A = 0, B = 1, and C = -2/sinθ.
Substituting into the formula.
d = |-2/sinθ| / √(0² + 1²)
d = 2/|sinθ|
Now we can write the equation of the conic as:
r = e d / (1 - e cosθ) = (3/4) (2/|sinθ|) / (1 - (3/4) cosθ)
Simplifying.
r = 6/(4|sinθ| - 3cosθ)
This is the polar equation of the conic with focus at the pole and directrix r sinθ = -2, and eccentricity e = 3/4.
Thus,
The equation about the conic is r = 6/(4|sinθ| - 3cosθ).
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