I need help finding the domain and range of a parabola. The vertex is (-2,1).
Answers
Looking at the parabola, we see that it extends left and right to negative and positive infinity, hence the arrows at at the “tails” of the function.
So, the domain (D) is:
D: (-∞, ∞)
Note: we use ( ) because infinity is not a defined number, so it’s not a starting point nor end point.
The vertex is where the lowest or highest point of the parabola, so this is where the lowest or highest range value is found. Looking at the parabola’s vertex, 1 is the y-coordinate. So, the highest point the parabola reaches is y=1. It extends all the way down to negative infinity, hence the arrows at the “tails” of the function.
So, the range (R) is:
R: [1, -∞)
Note: we use [ for 1 because it is a defined endpoint since it is the y-coordinate of the vertex.
Hope that helps! I like your name btw!
Related Questions
Show how the recursive rule f(0) = a and f(n)=f(n-1)+d for n ≥ 1 generates the explicit rule
f(n)= a + dn for n ≥ 0.
f(0) =
f(1) = f(0)+d=
f(2)=f(1)+d= (a + d) +d=
f(3) =f(2)+d= (a + 2d)+d=
f(4)=f(3)+d= (a +3d)+d=
Generalizing these results gives f(n)=
Answers
On solving the provided question, we can say that - the function value will be [tex]g(x) = -3 + 12x + 15[/tex] and
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
Here,
[tex]y =a(x-x1)(x-x2),[/tex] y equals a(x-5)(x+1)
g(x) = -3(x-5)(x+1)
[tex]g(x) = -3(x-5)(x+1)[/tex]
g(x) = -3 + 12x + 15
y-intercept of g(x) is (0,15)
Therefore , the solution to the given problem of the equation comes out be y-intercept of g(x) is (0,15).
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
Round 543,829 to the nearest 100 1,000 10,000
Answers
Answer:
540,000
Step-by-step explanation:
How do you solve for Y using elimination?
Answers
On solving the given system of equations 3x + 4y = -25 and 2x - 3y = 6 by using the elimination method , we get that the value of x is -3 and value of y is -4 .
The System of equations to be solved by elimination method is given as :
3x + 4y = -25 ....equation(1) and
2x - 3y = 6 ;.....equation(2)
By the method of elimination ;
we multiply the equation(1) by 2 ;
we get ⇒ 6x+8y = -50 ....equation(3) ;
we multiply the equation(2) by 3 ;
we get ⇒ 6x-9y = 18 ....equation(3) ;
Subtracting equation(4) from equation(3) ,
we get ;
⇒ 17y = -68 ;
⇒ y = -4 ,
Substituting y as -4 in the equation "2x - 3y = 6" , we get x = -3 .
The given question is incomplete , the complete question is
How do you solve the system of equations 3x + 4y = -25 and 2x - 3y = 6 , by using the elimination method ?
Learn more about Elimination Method here
https://brainly.com/question/13877817
#SPJ4
Explain briefly the difference between spot heights and trigonometrical stations or points.
Answers
Answer:
Step-by-step explanation:
A spot height shows exact heights by a black dot with a number next to it. The number is the height above sea level in metres. Trig points or Triangulation Pillars are another way of spotting the top of a mountain on a map
avery is throwing a pizza party. she had 7 pounds of cheese available and she needs 3/5 pound of cheese to make each pizza. what is the maximum number of full pizzas she can make?
Answers
The maximum number of full pizzas she can make if Avery had 7 pounds of cheese available, and she needs 3/5 pounds of cheese to make each pizza, is 11.
What is division?When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. For instance, 4 2 = 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.
Given:
Avery had 7 pounds of cheese available, and she needs 3/5 pound of cheese to make each pizza,
Calculate the number of pizzas she can make as shown below,
The number of pizzas = total cheese/cheese required to make one pizza
The number of pizzas = 7 / 3/5
The number of pizzas = 7 × 5 / 3
The number of pizzas = 35 / 3
Thus, the total number of pizzas she can make is 11 and 2 / 3.
To know more about division:
https://brainly.com/question/27566440
#SPJ1
Watch help video
Ruby is designing a new board game, and is trying to figure out all the
possible outcomes. How many different possible outcomes are there if
she flips a coin, rolls a fair die in the shape of a cube that has six sides
labeled 1 to 6, and spins a spinner with three equal-sized sections
labeled Walk, Run, Stop?
Answer:
Submit Answer
attempt 1 out of 2
Answers
The maximum possible outcome for the given situation is 36.
What is Probability?The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.
Given, Ruby is designing a new board game and is trying to figure out all the possible outcomes. she flips a coin, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.
Since there are three things happening simultaneously and favorable moments will be chosen by all three.
Thus Maximum possible outcome = 2 * 6 * 3 = 36
Therefore, For the given situation, 36 outcomes are available in total.
Learn more about the probability here:
https://brainly.com/question/13012411
#SPJ1
HELP PLEASE
HELP ME PLEASE
HELPPPPPPPPPP
10 POINTS
Answers
We can simplify the given expression -6x - 12 + 8y + 16x to get:
10x - 12 + 8y
How to simplify the following expression?Here we want to simplify the expression below:
-6x - 12 + 8y + 16x
To simplify this we need to try to find common factors, the only common factor that we can see on the equation is "x", then we can rewrite the expression:
-6x - 12 + 8y + 16x
-6x + 16x - 12 + 8y
Now we can rewrite the first two terms as:
(-6 + 16)*x - 12 + 8y
10x - 12 + 8y
That is the simplified expression.
Learn more about the simplification of expressions at
https://brainly.com/question/723406
#SPJ1
Discuss the difference between r and p.r represents the p represents theChoose the correct answers below- critical value for the correlation coefficient. -population correlation coefficient. -sample correlation coefficient.
Answers
The difference between r and p. r represents the p represents the
Sample correlation coefficient.
Now, According to the question:
What is sample correlation coefficient?
The sample correlation coefficient (r) is a measure of the closeness of association of the points in a scatter plot to a linear regression line based on those points, as in the example above for accumulated saving over time
The sample correlation coefficient uses the sample covariance between variables and their sample standard deviations. The population correlation coefficient uses the population covariance between variables and their population standard deviations.
Hence, The correct answer is : Sample correlation coefficient.
Learn more about Sample correlation coefficient at:
https://brainly.com/question/29009905
#SPJ4
Find the area of the figure, round to the nearest hundredth.
Answers
The area of the given figure is 51.63 m².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
In the given combination figure, there are three geometrical shapes rectangle, triangle and semicircle.
Now, in triangle base =3 m and height =5 m
So, area of a triangle = 1/2 ×Base×Height
= 1/2 ×3×5
= 7.5 m²
In rectangle length= 6 m and width =5 m
Area of rectangle = Length×Width
= 6×5
= 30 m²
In semicircle, radius =6/2 =3 m
Area of a semicircle = πr²/2
= 3.14×3×3/2
= 14.13 m²
Total area = 7.5+30+14.13
= 51.63 m²
Therefore, the area is 51.63 m².
Learn more about the area here:
https://brainly.com/question/27683633.
#SPJ1
edurado has $24 saved. if he saves $8 each week how much money will he have in 5 weeks
Answers
Answer:
Step-by-step explanation: 40$
The value of 5 × (7 + 3)2 ÷ 4 this expression is
PLEASE HELP
Answers
Answer: 25
Step-by-step explanation:
This quarter Joseph has earned grades of 81, 89, 80, 84, 89, and 85 on his math quizzes. Based on these scores, he claims to have an average quiz grade of 89. Explain why this claim might be considered inaccurate
Answers
The claim might be considered to be inaccurate because Joseph's actual average quiz grade for math is 85
How to find the average ?When given a set of numbers of variables, the average variable can be found by dividing the sum of the variables by the number of variables in the set.
For Joseph therefore, the average of the quiz grades that he has from his math quizzes would be :
= ( 81 + 89 + 80 + 84 + 89 + 85 ) / 6
= 508 / 6
= 84. 6
= 85
This shows that Joseph's claim of an average of 89 in his math quizzes is therefore inaccurate.
Most likely, what Joseph thought he meant was that the mode of his math quizzes was 89 as the mode refers to the variable that appears the most in a set.
Find out more on average at https://brainly.com/question/20118982
#SPJ1
If the following relation is a function, which
ordered pair could be the missing point?
{(-4, 3), (5, -1), (0, 2), (x, y)}
A. (5, 7)
B. (1, -3)
C. (0, -6)
D. (-4, 0)
Answers
{(-4, 3), (5, -1), (0, 2), (x, y)} set of ordered pairs (1, -3) could represent a linear function.
What are Functions?In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
For option A:
m=1+2/3-1=3/2
m=3/2
m=7-4/8-5=3/3=1
Slopes are not same
For option B:
m=3-6/-3+6=-3/3=-1
m=0-3/0+3=-1
m=-4/3
Slopes are same
Slopes are same at every point, so this set of ordered pairs could represent a linear function
Hence, the correct option is B.
To know more about functions, visit:
brainly.com/question/11624077
#SPJ1
What are 4 examples of data types?
Answers
The 4 examples of data types are Integer - a whole number that can be positive, negative, or zero. Float - a number with decimal points. String - text or characters. Boolean - a true or false value.
Data types are the different kinds of data that can be stored in a computer system. They are used to define the type of data a variable can hold.
The four most commonly used data types are Integer, Float, String, and Boolean.
An Integer is a whole number that can be either positive, negative, or zero. Integers are used for counting and manipulating whole numbers.
A Float is a number with decimal points. It is used for storing numerical values that require a more precise representation.
A String is a set of characters and text. It is used for storing textual information such as names and addresses.
A Boolean is a true or false value. It is used for evaluating logical expressions and making decisions based on certain conditions.
Overall, data types are used to specify the kind of information that a variable can store and to ensure that data is stored in a consistent and organized manner.
Learn more about datatype here
brainly.com/question/29977626
#SPJ4
In 1945, a person made $3.20 for working an 8-hour day. model a division problem to determine how much a person made per hour in 1945. what is the hourly wage?
Answers
Answer:
$0.40 per hour
(This is 40cents per hour)
Step-by-step explanation:
The "hourly wage" is a rate, a ratio, a comparing of two numbers. We are comparing dollars and hours. So we have information given in the problem about the $ and hours. Compare these two numbers and then simplify. Because we need the hours, on the bottom, to be 1 hour. "Per hour" means per ONE hour.
dollars/hours
= $3.20/ 8hours
Divide.
= $0.40/1 hour
This is the hourly wage, $0.40 (or 40cents) per hour.
Find the slope of the line that passes through the points \left(10,8\right)(10,8) and \left(4,12\right)(4,12).
Write your answer as a simplified fraction.
Answers
3y + 2x = 44 is the equation of the line through (10, 8) and (4, 12).
What is the Equation of line?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
Given, two coordinates of a line [tex]\left(10,8\right) and \left(4,12\right)[/tex]
The slope of the line formula is:
[tex]m = \frac{y₂ - y₁}{ x₂ - x₁}[/tex]
Let's substitute our numbers.
[tex]m = -\frac{8 -12}{4-10}[/tex] = -4/6
The GCF of these two numbers is 2
So, our slope = -2/3
The general equation of a line is y = mx +c
Therefore the equation of the line is y = -2/3x + c
Since, this line passes through ( 10, 8 )
Hence, it must satisfy these coordinates
8 = -2/3 * 10 + c
44/3 = c
Thus the equation of the line is y = -2/3x +44/3
the equation of the line is 3y + 2x = 44.
Therefore, The equation of the line that passes through (10, 8) and (4, 12) is 3y + 2x = 44.
Learn more about Line here:
https://brainly.com/question/30003330
#SPJ1
Mr. Wilson and Miss Krietz have homerooms with the same perimeter. Miss Krietz's homeroom has a length 1 1/4 times the length of Mr. Wilson's homeroom. What is the width, w, of Miss Krietz's homeroom?
Answers
Answer: 12.5
Step-by-step explanation:
Let's first find the perimeter.
P = 2l + 2w
Since Mr.Wilson's perimeter equals Ms.Krietz's, we can use the same number for both.
P = 2(30)+2(20) = 100
Since the length of Ms.Krietz's homeroom is 1.25x the length of Mr.Wilson's, we can substitute that
l = 1.25(30) = 37.5
100 = 2(37.5) + 2w
100 = 75 + 2w
25 = 2w
w = 12.5
Jade buys a blouse and a skirt for of their original price. She pays a total of $31.50 for the two items. If the original price of the blouse is $18, what is the original price of the skirt?
Part A
Which equation represents the situation?
O 0.75= 31.50
(18)= 31.50
O 0.75(s 31.50)=18
O
Part B
(18+5)= 31.50
Use the Distributive Property to solve the equation.
Answers
The equation that represents the situation could be 3/4(18 + s) = 31.50 and the solution is s = 24 thus option (D) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
Part (A)
Given that;
Cost of skirt = s
cost of blouse = $18
She bought it at 3/4 of that cost,
The Total pay = 3/4 of the total cost
3/4(18 + s) = 31.50
Part (B)
By the distributive property of multiplication then we get;
3/4(18) + 3/4(s) = 31.50
3/4(s) = 31.50 - 13.5
3/4(s) = 18
s = 18 x 4/3 = 24
Hence "The answer is s = 24"
For more about the equation,
brainly.com/question/10413253
#SPJ1
A rectangular prism has a volume of 840 cubic inches. The height of the prism is 6 inches and the width
iS 10 inches. Find the length of the prism and explain how you found it.?
Answers
Answer:50400cm2
Step-by-step explanation:lxWxH
Answer:
The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.
Step-by-step explanation:
The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.
Seth uses 20 nails to make a birdhouse. He wants to make 60 birdhouses to sell at the county fair. There are 30 nails in a box. How many boxes will he need?…..Could someone tell me what type of operation I have to use?
Answers
To build 60 birdhouses, Seth will need 40 boxes of nails
What is proportion?A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)
Seth uses 20 nails for a birdhouse. This means that to build 60 birdhouses, Seth will need 60×20 = 1200 nails
In each box there are 30 nails;
This means that 1200 nails will contain 1200/30 boxes = 40 boxes.
Therefore the number of boxes of nails Seth will need to build 60 birdhouses is 40.
learn more about proportion from
https://brainly.com/question/19994681
#SPJ1
the _______ _______ is a statement of no change comma no effect comma or no difference.
Answers
The null hypothesis is a statement of no change, no effect, or no difference.
The null hypothesis is a statement or assumption that there is no relationship between two variables or no difference between two groups, and any observed differences are likely due to chance. It is often denoted as H0. In scientific research, the null hypothesis is usually tested against an alternative hypothesis, which proposes that there is a relationship or difference.
For example, in a medical study, the null hypothesis might be that a new treatment has no effect on a certain disease, while the alternative hypothesis is that the treatment does have an effect. The researcher would then collect data and use statistical methods to test the null hypothesis against the alternative hypothesis.
It's important to notice that a failure to reject the null hypothesis doesn't mean the null hypothesis is true, it only means that there isn't enough evidence to reject it.
Learn more about the null hypothesis here:
https://brainly.com/question/25263462
#SPJ4
Triangle ABC is being rotated 90° about the
origin. What will A' be if A was located at (7. 2)?
Answers
Answer:
A' (2, - 7 )
Step-by-step explanation:
under a rotation about the origin of 90°
a point (x, y ) → (y, - x ) , then
A (7, 2 ) → A' (2, - 7 )
Which quadrant or axis contains the point (−5, 3)?
Answers
Answer:
not sure
Step-by-step explanation:
not sure sqauredxfree bagdes
=answer
A ____________ is a table in which frequencies correspond to two variables.
A
▼
relative frequency table
Pearson correlation coefficient table
standard normal distribution table
contingency table
is a table in which frequencies correspond to two variables
Answers
Answer:relative frequency table
Step-by-step explanation:
Jacqueline is buying grapes and apples from the Walmart produce section. Grapes are $3 per pound and apples are $4 per pound. Jacqueline's mother gave her $20 to spend. To determine the combinations of grapes and apples that she can afford to purchase,
Jacqueline wrote the inequality 3x+4y<20 .
Define the variables Jacqueline used based on the context.
Let x represent
Let y represent
Explain why the inequality sign s makes sense in this context.
Graph the inequality 3x+4y< 20.
The ordered pair (3,-4) is a solution to the inequality 3x + 4y s 20. Explain why this is not a viable solution in the context of buying grapes and apples.
The ordered pair (4,2) is a point on the boundary line. Explain what the ordered pair represents in the situation.
Answers
Answer:
Step-by-step explanation:
This should help
Determine the scale factor. Pre-Image: (-5, 3), (-2, 3), (-2, 1), (-5, 1) Image: (-10, 6), (-4, 6), (-4, 2), (-10, 2)
Answers
The scale factor, given the pre - image and the image, can be found to be 2.
How to find the scale factor ?The scale factor is the measure that either increases or decreases the size of a shape. When the scale factor is an integer then the size of the shape increases.
When the scale factor is a fraction with a larger denominator than numerator, the shape decreases.
To find the scale factor, look at the relationship between a point on the pre - image and the corresponding point on the image. For the points, ( -5, 3 ) and ( -10, 6 ) the scale factor would be :
= -10 / -5 or, = 6 / 3
= 2 = 2
The scale factor is therefore 2.
Find out more on scale factor at https://brainly.com/question/2826496
#SPJ1
What is the coefficient of 5x² in 5x² 5x?
Answers
Answer:
Step-by-step explanation:
i think 1
Situations and Sequence Types Assignment
Answers
Answer:12+6=3=1.5
Step-by-step explanation:
A baseball player strikes out 3 times for every 2 hits he gets. If the player strikes out 15 times, how many hits does he get? If the player gets 46 hits, how many times does he strike out?
Answers
3/2 = 15/x
3 x 5 is 15 so 2 x 5 is 10.
So if the player strikes out 15 times, he hits 10 times.
3/2 = x/46
2 x 23 is 46 so 3 x 23 is 69.
So he strikes out 69 times. That’s interesting.
in how many ways can people be seated in a row of chairs if three of the people, john, wilma, and paul, refuse to sit in three consecutive seats?
Answers
The total number of ways to seat the people in a row such that John, Wilma, and Paul refuse to sit in three consecutive seats is 4320.
There are a few different ways to approach this problem, but one possible method is to use the principle of inclusion-exclusion.
We start by counting the total number of ways to seat the people in a row of chairs without any restrictions. Since there are n chairs, there are n! ways to seat the people in a row.
Next, we count the number of ways to seat the people in a row such that John, Wilma, and Paul are seated in three consecutive seats. Since there are n-2 chairs between the three chairs that John, Wilma, and Paul are not allowed to sit in, there are (n-2)! ways to seat the people in a row such that John, Wilma, and Paul are seated in three consecutive seats.
Finally, we use the principle of inclusion-exclusion to find the total number of ways to seat the people in a row such that John, Wilma, and Paul are not seated in three consecutive seats.
The total number of ways to seat the people in a row such that John, Wilma, and Paul are not seated in three consecutive seats is n! - (n-2)!
For example, if there are 7 chairs, the total number of ways to seat the people in a row such that John, Wilma, and Paul are not seated in three consecutive seats is 7! - (7-2)! = 5040 - 720 = 4320
So, the total number of ways to seat the people in a row such that John, Wilma, and Paul refuse to sit in three consecutive seats is 4320.
Learn more about inclusion-exclusion here: brainly.com/question/10927267
#SPJ4
