The graph below represents the path of a grasshopper as it jumps which type of function models the data on the graph
Answers
Answer:
Quadratic
Step-by-step explanation:
Given function is a quadratic function.
There are many key features in a quadratic graph such as the zeroes (x-intercepts, also known as the roots), y-intercept, axis of symmetry, and the vertex.
The graph of a quadratic function is a parabola, which has several important properties:
Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the parabola, depending on whether the parabola opens upward or downward, respectively.
Axis of symmetry: The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. It passes through the vertex and is perpendicular to the directrix.
Directrix: The directrix is a horizontal line that is located at a distance equal to the distance between the vertex and the focus. It is perpendicular to the axis of symmetry and reflects the parabola onto itself.
Focus: The focus is a point on the axis of symmetry that is located at a distance equal.
As we can see that given graph has two roots and it is symmetric to the line parallel to the y-axis.
From the graph we know this is a quadratic function { a parabola with respect to symmetry and axis symmetry}
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Related Questions
Write an algebraic expression to represent the pay (in dollars) for working "x" hours at a rate of eight dollars and seventy-five cents per hour. A) 8.75x B) 875x C) 8.75 x D) 875 x
Answers
What does the b value represent? in Exponential Functions
A. Initial amount
B. Rate of growth/decay
C. Independent variable
D. Dependent variable
Answers
C
Hope it helped :)
Solve the following systems of 3-variable linear equations.
50 points
Answers
Answer:
x = 9/25
y = 7/25
z = 4/25
Step-by-step explanation:
2x + y = 1 .......(1)
3y + z = 1 ........(2)
x + 4z = 1 ........(3)
Elimination 1 and 2
2x + y = 1 | ×3 |
3y + z = 1 | ×1 |
6x + 3y = 3
3y + z = 1
___________--
6x - z = 2 .............. (4)
Elimination 3 and 4
x + 4z = 1 | ×6 |
6x - z = 2 | ×1 |
6x + 24z = 6
6x - z = 2
___________--
25z = 4
z = 4/25
Elimination 3 and 4
x + 4z = 1 | ×1 |
6x - z = 2 | ×4 |
x + 4z = 1
24x - 4z = 8
___________+
25x = 9
x = 9/25
Subsitution 1
2x + y = 1
2(9/25) + y = 1
18/25 + y = 1
y = 1 - 18/25
y = 25/25 - 18/25
y = 7/25
Answer:
x = 9/25
y = 7/25
z = 4/25
Step-by-step explanation:
:D
An author signed copies of her newest book for 57 minutes until the bookstore closed at 5:00 What time did the author begin signing books?
4:03
4:57
5:03
5:57
Answers
Answer:
4:03
Step-by-step explanation:
If a rational exponent represents the cube root of x^m, where m is a positive integer, how does the rational exponent change as m increases?
The rational exponent ______ as m increases.
a. increases
b. decreases
Answers
Answer:
Option B
Increases
Step-by-step explanation:
to solve this problem, let us plug in figures to replace the variables in the equation.
Let y be equals to the rational exponent which represents the cube root of x^m,
The equation is given as y =[tex]\sqrt[3]{x^{m}}[/tex]
let x= 3
and m =, 3, 4, and 5
when m = 3, we have [tex]y =\sqrt[3]{3^{3}} =3[/tex]
when m = 4, we have [tex]y =\sqrt[3]{3^{4}} =4.33[/tex]
when m = 5, we have [tex]y =\sqrt[3]{3^{5}} =6.24[/tex]
As we can see, the values of y are increasing. Hence, we can say that the value of the rational exponent increases as y increases
Final answer:
As the positive integer m increases in the rational exponent expression for the cube root of [tex]x^m[/tex], the rational exponent itself increases. This is because the base x is being raised to a higher power, exemplified by [tex]x^{2/3[/tex] compared to [tex]x^{3/3[/tex], showing an increase in expression value.
Explanation:
If a rational exponent represents the cube root of [tex]x^m[/tex], where m is a positive integer, the form used to represent this is [tex]x^{m/3[/tex]. As m increases, the value of the expression increases because the base (x) is being raised to a higher power. Therefore, the correct answer to how the rational exponent changes as m increases is it increases.
For example, consider x to equal 8, and compare [tex]x^{2/3[/tex] (the cube root of 8 squared) to [tex]x^{3/3[/tex] (the cube root of 8 cubed).
As m increases from 2 to 3, the exponent changes from 2/3 to 3/3 (or 1), and thus the result of the expression goes from 4 to 8, illustrating that the expression's value increases with m.
Hannah can type 450
words in 6 minutes.
How many words per
minute can she type?
Answers
Answer:
75
Step-by-step explanation:
That means she type 450/6 minutes. Take 450 and divide it by 6.
450/6 = 75
WILL MARK BRAINLIEST! help pleaseee
The manager of a local cable company has hired an advertising agency to find out which is the most popular cartoon channel on cable. Which population should the agency sample to get the most reliable information?
Answers
I know I’m two years late, but for those in the future…
~
↓answer choices↓
A.) Cable subscribers.
B.) Employees of the cable company.
C.) Adults listed in the local telephone directory.
D.) Employees of the advertising agency.
~
The correct answer is:
A.) Cable subsricbers.
~
What is the range of the following data set?
56, 78, 124, 34, 67, 91, 20
Answers
Answer:
104
Step-by-step explanation:
Range is the max value - the min
124 - 20 = 104
By visual inspection, determine the best-fitting regression
model for the data plot below.
Answers
Given:
Given that the graph of the regression model.
We need to determine the type of the best - fitting regression model.
Model of the graph:
From the graph, it is obvious that the points in the graph does not follows a straight line and thus the graph is not a linear model.
Also, from the graph, we can see that the points in the graph follows a curve pattern.
This curve pattern in the graph indicates that the graph follows an exponential curve.
Therefore, the best - fitting regression model for the given data plot is exponential model.
Hence, Option C is the correct answer.
[ 2,-3,4,-1] - [-2,7,11,0]=[a,b,c,d]
Answers
Answer:
[4, -10, -7, -1] = [a, b, c, d]
Step-by-step explanation:
Operations of addition and subtraction on lists are generally performed term by term.
[2-(-2), -3-7, 4-11, -1-0] = [a, b, c, d]
[4, -10, -7, -1] = [a, b, c, d]
*WILL MAKE BRAINLIEST*
What is the scale factor of this dilation?
a) 1/5
b) 1/2
c)1
d) 2
Answers
Answer: 1/2
Step-by-step explanation: The scale factor of the dilation is 1/2 because it's 1/2 of the other triangle. As you can see it used to be 10, but now it's 5.
Have a good day :D
Answer:
From Triangle ABC to Triangle A'B'C', the scale factor is 1/2
b) 1/2
Step-by-step explanation:
Side Length of Line Segment AC is 8 units
Side Length of Line Segment AB is 6 units
Side Length of Line Segment of BC is 10 units
Side Length of Line Segment A'C' is 4 units
Side Length of Line Segment A'B' is 3 units
Side Length of Line Segment B'C' is 5 units
Checking:
A'C'/AC=4/8=1/2 simplified
Hence, the answer is 1/2 as the scale factor for the dilation.
Lucia and Marcus are playing a board game. They roll 2 dice (number cubes) to see who goes first. The person who rolls the highest sum gets to go first. If there is a tie, they each roll the dice again. Lucia went first and she rolled a 4 and a 1. Find the probability that Marcus will not get to go immediately after he rolls the dice. Show all of your work below. Express your answer as a fraction in simplest form, a decimal and a percent
Answers
Answer:
5/18, 0.278, 27.8%
Step-by-step explanation:
In this problem, we basically want to find the probability that Marcus will have a total sum of the 2 dices less than Lucia.
In her throw, Lucia gets a 4 and a 1, so she gets a total sum of 5.
Therefore, we want to find the probability that Marcus will get 5 or less.
The possible combinations that can be obtained when throwing 2 dices are 36 (6 x 6).
Of all these 36 combinations, those that gives a sum of 5 or less are:
1 +1 = 2
1 + 2 = 3
2 + 1 = 3
1 +3 = 4
3 + 1 = 4
1 + 4 = 5
4 + 1 = 5
2 + 2 = 4
2 + 3 = 5
3 + 2 = 5
So, a total of 10 combinations.
Since the probability of an event is:
[tex]p(A)=\frac{s}{n}[/tex]
where
s is the number of successfull outcomes
n is the number of total possible outcomes
Here we have
s = 10
n = 36
Therefore the probability here is
[tex]p=\frac{10}{36}=\frac{5}{18}=0.278 = 27.8\%[/tex]
Given the function f(x)=x^2-4x-1 determine the average rate of change of the function over the interval -4
Answers
Answer:
- 1
Step-by-step explanation:
The average rate of change in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [4, 7 ], thus
f(b) = f(7) = 7² - 4(7) - 1 = 49 - 28 - 1 = 20
f(a) = f(- 4) = (- 4)² - 4(- 4) - 1 = 16 + 16 - 1 = 31
average rate of change = [tex]\frac{20-31}{7+4}[/tex] = [tex]\frac{-11}{11}[/tex] = - 1
Complete the steps to find the area of the trapezoid.
Area of rectangle = v square units
Area of triangle 1 = L M square units
Area of triangle 2 = square units
Area of triangle 3 = square units
Area of trapezoid = square units
Answers
Answer:
256
24
16
96
120
Step-by-step explanation:
The area of the trapezoid is 256, 24, 16, 96, and 120.
What is surface area? The area is the sum of the areas of all its faces.The areas of the base, top, and lateral surfaces i.e all sides of the object. It is measured using different area formulas and measured in square units and then adding all the areas. The area of a solid object is a measure of the total area that the object covers.A Rectangle is a four sided-polygon, having all of the internal angles equal to ninety degrees. the two aspects at every nook or vertex, meet at right angles. the alternative aspects of the rectangle are identical in duration which makes it specific from a rectangular.Area= Lenght x wide
Perimeter= 2(lenght+wide)
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Leonora is factoring a trinomial. The factors of the trinomial are shown on the model.
An algebra tile configuration. 7 tiles are in the Factor 1 spot: 1 is labeled + x and 6 are labeled negative. 3 tiles are in the Factor 2 spot: 1 is labeled + x and 2 are labeled +. 0 tiles are in the Product spot.
Which trinomial did she factor?
A.x2 + 4x – 12
B.x2 + 2x – 6
C.x2 – 8x – 6
D.x2 – 4x – 12
Answers
Answer:
D
Step-by-step explanation: just trust me
The trinomial Leonora factored is x²+2x-6. Therefore, option B is the correct answer.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
From the given figure (see attachment),
Here, x×x+x+x-1-1-1-1-1-1
x²+2x-6
Therefore, option B is the correct answer.
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Will give brainliest!!! Determine the answer to (−5) + 4 and explain.
Answers
Answer:
The answer is -1 because adding onto a negitive number makes the number go towards 0
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
So, if you have 5 negatives (A) and 4 positives (B) and pair them together:
A B A B A B A B A
You'll see that you have one extra A or -1 leftover.
So, -5 + 4 = -1
PLEASE I REALLY NEED HELP
Answers
Answer:
x=10
Step-by-step explanation:
Triangle MNP is identical to Triangle QRP.
(x+8)÷24=28÷(3x-9)
28x+224=72x-216
44x=440
x=10
what are the next two numbers in the pattern 8, 18, 38, 78
Answers
Answer:
158 & 318
Step-by-step explanation:
8+10=18
18+20=38
38+40=78
78+80=158
5x2=10
10x2=20
20x2=40
40x2=80
Answer:
158, 318
Step-by-step explanation:
A particular type of Gasoline is suppose to have a mean octane rating greater than 90%. Five measureaments are taken of the octane rating, as follow:
90.1 88.8 89.5 91.0 92.1
Can you conclude that the mean octane rating is great er than 90%?
Answers
Answer:
Yes
Step-by-step explanation:
The mean octane rating will be 90.3
Hope this helps!
Answer:
Yes
Step-by-step explanation:
The mean is just the average, and it's calculated by adding up all the data set numbers and dividing that sum by the number of numbers:
(90.1 + 88.8 + 89.5 + 91.0 + 92.1) / 5 = 451.5 / 5 = 90.3
Our average/mean is 90.3%, which is clearly greater than 90%. So, yes, we can conclude that the mean octane rating is greater than 90%.
Hope this helps!
QT
is the midsegment of the trapezoid PRSU.
If RS=2w+21, QT=4w+27, and PU=w+38, what is the value of w?
Answers
Answer:
w=1
Step-by-step explanation:
QT=(RS+PU)/2
4w+27=(2w+21+w+38)/2
3w+59=2*(4w+27)=8w+54
8w-3w=59-54
5w=5
w=1
Final answer:
After setting up an equation for the average, we calculated that the value of w is 5.
Explanation:
The question involves solving for a variable w in the context of a trapezoid and its midsegment.
We know that a midsegment of a trapezoid is parallel to the bases and its length is the average of the lengths of the two bases.
Given RS=2w+21, QT=4w+27 (midsegment), and PU=w+38, we set up the equation (2w+21 + w+38)/2 = 4w+27, since the length of the midsegment QT is the average of the lengths of the bases RS and PU.
Simplifying this equation:
Add the like terms of the bases: (2w + w) + (21 + 38) = 3w + 59.Divide the sum by 2 to find the average: (3w + 59) / 2.Set this average equal to the midsegment QT: (3w + 59) / 2 = 4w + 27.Multiply each side by 2 to get rid of the fraction: 3w + 59 = 2(4w + 27).Expand the right side of the equation: 3w + 59 = 8w + 54.Subtract 3w from both sides: 59 = 5w + 54.Subtract 54 from both sides to solve for w: w = 5.Therefore, the value of w is 5.
The locus of points idea allows you to define geometric objects just by determining whether or not two distances are equal.
Answers
Answer:
True
Step-by-step explanation:
Final answer:
The statement is True: the locus of points concept is used in geometry to define shapes based on the equality of distances, such as an equidistant curve from a line, or a circle at a fixed distance from a point.
Explanation:
The statement "The locus of points idea allows you to define geometric objects just by determining whether or not two distances are equal" is True. The locus of points is a concept in geometry that represents a set of points that satisfy certain conditions. For instance, the locus of points at a given distance from a straight line is known as an equidistant curve, and when this distance is from a point, it forms a circle. Euclidean geometry often assumes that distances are consistent and measurable, idealizing the real world where we use rules and compasses to define distances and constructs. Concepts like parallelism and measurement systems, as found in axioms, help to build an understanding of geometric relations on lines. Moreover, the validity of geometric propositions can be questioned in real-world applications as geometry serves as an abstraction of physical space.
Relative to the circle with the equation x^2 + y^2 = 4 how has the circle with the equation (x+5)^2 + (y-6)^2 = 4 been shifted, what is the radius of the circle
Answers
Answer:
the circle is shifted -5 on the x and +6 on the y. Center is (-5,6). Radius = 2.
Step-by-step explanation:
F—1(-2)
F(-4)
F(f-1(-2))
Answers
Answer:
= -2
Step-by-step explanation:
F(f^-1(x)) = x so in the case of yur question the -2 is in the place of the x in the explanation
The value of [tex]f^{-1}[/tex](-2) is -4 , f(-4) is -2 and f[ [tex]f^{-1}[/tex](-2)] is also -2.
What is the inverse of a function?The inverse of a function is basically a reverse function or undo of the function.
For example y = f(x) then inverse will be x = f(y).
It means in the inverse function we need to interchange x and y.
Another example y = 3x² ⇒ x = √(y/3) will be the inverse.
Given the function,
f(x) = 1/2x and [tex]f^{-1}[/tex](x)= 2x
Now,
[tex]f^{-1}[/tex](-2) = 2(-2) = -4
f(-4) = 1/2 (-4) = -2
Now,
Operation of f is that it will come x variable down,
So,
f[ [tex]f^{-1}[/tex](-2)] = f(-4)
f(-4) = -2
Hence "The value of [tex]f^{-1}[/tex](-2) is -4 , f(-4) is -2 and f[ [tex]f^{-1}[/tex](-2)] is also -2".
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The given question is incomplete, complete question is ;
Use f(x) = 1/2x and f-1(x)= 2x to solve the problems. f1(-2) f(-4) f(f-1(-2))
Select the property that allows m + 0 to be written as m.
commutative - addition
distributive
associative - multiplication
symmetric
commutative - multiplication
associative - addition
identity - addition
Answers
Answer:
identity - addition
Step-by-step explanation:
Properties of Numbers
Addition
Closure:
If a R and b R, then a + b is a unique element of R.
Commutative:
a + b = b + a.
Associative:
a + (b + c) = (a + b) + c.
Identity:
a + 0 = a.
Additive Inverse:
a + (-a) = 0.
Answer:
identity - addition
Step-by-step explanation:
How do I tell if these are natural numbers, whole numbers, integers, or rational numbers? ( Photo for reference)
Answers
Step-by-step explanation:
1. divide -12 by -5
you get 2.4 this is a rational number
2. add 3/7 and -3/8 you get a long decimal so it's irrational
I want help ,i want an answer
;(
Answers
Answer:
9ft 39in
12×3=36
39-36=3
answer is 12ft 3in
Answer to #11: 12 ft 3 in
Answer to #12: 4 lb 9 oz
Answer to #13: 13 qt 1 pt
Answer to #20: 6 yd 2 ft 3 in
Answer to #21: 8 weeks 2 days 8 hours 44 min
Please give me brainliest, that was super hard
Solve using perfect square factoring patterns. y2 + 16y + 64 = 0 {8} {0, –1} {–8} {8, –8}
Answers
Answer:
y^2 + 16y + 64 = 0
(y + 8)(y+8) = 0
y + 8 = 0
y = -8
y + 8 = 0
y = -8
Step-by-step explanation:
a family has two cars. the first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. during one particular week, the two cars went a combined total of 725 miles, for a total gas consumption of 40 gallons. how many gallons were consumed by each of the two cars that week?
Answers
Car A consumes 25 gallon and car B consumes 15 gallon.
Step-by-step explanation:
Given,
The fuel efficiency of car A = 20 miles per gallon.
The fuel efficiency of car B = 15 miles per gallon.
In a week, two cars went 725 miles and consumed 40 gallons.
To find the consumption of each car in that week.
Let,
Car A consumed x gallon
Car B consumed y gallon.
According to the problem,
x+y = 40 ----- (1)
20x+15y = 725
or, 4x+3y = 145 -------- (2)
From (1) we get, x = 40-y
Putting the value of x in (2) we get,
4(40-y)+3y = 145
or, 160-4y+3y = 145
or, -y = 145-160
or, y = 15
From (1) we get, x = 40-15 = 25
Hence,
Car A consumes 25 gallon and car B consumes 15 gallon.
Find the mean, median, and mode of 3, 5, 1, 5, 1, 1, 2, 3, 15.
Answers
Answer:
Mean: 4
Median: 3
Mode: 1
Step-by-step explanation: For the mean, you have to add all the numbers and divide it by the amount of numbers there are to find the average (mean). For the median, you have to order the numbers from least to greatest and since there are 9 numbers and 9 is an odd number, you have to see which number is in the middle, 3 was in the middle for this problem. The mode is which number repeats the most, which was 1.
Answer:
Mean = 4, Median = 3, Mode = 1
Step-by-step explanation:
The mean is also the average. To find it you add all the numbers up and divide that by the # of numbers given.
[tex]\frac{3+5+1+5+1+1+2+3+1+5}{7} =\frac{28}{7}=4[/tex]
Median is the middle number when all the numbers are written out numerically including the doubles
1 1 1 2 3 3 5 5 15
Mode is the number that appears the most
in this case it is 1
Monday Night Football has been thrilling fans and topping the television ratings since 1969. As of the 1993 season, the San Francisco 49ers had appeared on Monday Night Football 35 times. The Miami Dolphins had appeared the most times, with 11 more appearances than the 49ers. How many times had the Dolphins appeared?
Answers
Answer:
The answer is 46. 35+11=46
Hope i could help! :D
Step-by-step explanation:
By the 1993 season, the Miami Dolphins had appeared on Monday Night Football 46 times.
Explanation:To solve this question, we are given that the San Francisco 49ers had appeared on Monday Night Football 35 times by the 1993 season. We are also informed that the Miami Dolphins had made 11 more appearances than the 49ers. Therefore, to find the total number of times that the Miami Dolphins had appeared, we simply need to add 11 to the 49ers' appearances.
So, 35 (49ers' appearances) + 11 (additional Dolphins' appearances) = 46.
This means that by the 1993 season, the Miami Dolphins had appeared on Monday Night Football a total of 46 times.
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