Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary and to produce the graph
Answer step by step
A. Y = (x - 2)^2 - 3
B. Y = (x + 2)^2 - 3
C. Y = - ( x - 2 )^2 - 3
D. Y = 1/2 ( x + 2)^2 - 3
The equation that best represents the parabola given in this problem is:
A. y = (x - 2)² - 3.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (2, -3), hence:
h = 2, k = -3.
And:
y = a(x - 2)² - 3.
When x = 0, y = 1, hence:
1 = 4a - 3
4a = 4
a = 1.
Hence the equation is given by:
A. y = (x - 2)² - 3.
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
#SPJ1
answer the question in the photo
Answer: input is h, output is k
Step-by-step explanation: inserting a number into h will give you your outcome of k in the solution
Answer:
Step-by-step explanation:
If the smaller of two numbers is one-half of the larger number and the sum of the two numbers is 75
Step-by-step explanation:
let the larger number=n
then the smaller number=½n
We conclude from the question that
n+½n=75
3/2n=75
3n=150
n=150/3=50
Therefore the larger number=50 and the smaller number=½×50=25
What is the common ratio between successive terms in the sequence?
1.5, 1.2, 0.96, 0.768,
The common ratio between successive terms in the sequence is 1. 25
What is common ratio?
Common ratio is defined as the ratio of each term of a geometric sequence to the term before it.
It is also known as the constant factor between consecutive terms of a geometric sequence.
It is the number multiplied or divided by at each interval.
Given the sequence;
1.5, 1.2, 0.96, 0.768,
The common ration is;
= 1. 5/ 1. 2
= 1. 25
Thus, the common ratio between successive terms in the sequence is 1. 25
Learn more about common ratio here:
https://brainly.com/question/1509142
#SPJ1
What are the missing numbers in the following pattern ?
1, 9 , 25, 49 , -------- , 121 , 169 , ------- , 289 , ----------.
Answer:
81, 225, 361
Step-by-step explanation:
Givien f(x) = 5x+4, solve for x when f(x) = -6.
Answer: -26
Step-by-step explanation:
5 x -6 = -30
-30 + 4 = -26
5(-6) + 4 = -26
PLS ILL GIVE U A LOT OF POINTS
Step-by-step explanation:
(3.5q³k^4)³ (2q²k³)²
(42.875 q^9 k^12) (4 q^4 k^6)
171.5 q^13 k^18
The answer is C.
If line KM bisects angle JKL, angle JKL = 92 degrees, and angle MKL = (5x+1) degrees, find the value of
The value of the variable x is found to be x = 9.
What is termed as angle bisector?In geometry, an angle bisector is a line that divides an angle into two equal angles. A bisector is something that divides a shape or thing into two equal portions. An angle bisector is a ray that divides an angle into two equal components of the same measurement.A bisected angle divides the two sides in equals.
JKM = LKM
As, both are equal.
Then, each of these angles are 1/2 the angle JKL.
1/2 JKL = MKL
1/2 ×( 92) = 5x + 1
Further simplifying;
46 = 5x+1
Subtract 1 from each side
46-1 = 5x
45 = 5x
Divide each side by 5
45/5 = 5x/5
x = 9
Thus, the value of the unknown variable is found to be x = 9 units.
To know more about the angle bisector, here
https://brainly.com/question/14399747
#SPJ9
The population of pine bluff is 654 and is increasing at the rate of 7 per year
If the population of pine bluff is 654 and is increasing at the rate of 7 per year, then the equation will be y=654+7x and the population after 3 years will be 675.
Given that the population of pine bluff is 654 and is increasing at the rate of 7 per year.
We are required to find the equation which shows the population and the population after 3 years.
Equation is basically the relationship between two or more variables that are expressed in equal to form and can be solved to find the value of variables. It may be linear equation, quadratic equation, cubic equation and many more depending on the power of the variables that are present in the equation.
Suppose the number of years be x.
The equation which shows the population after x months be:
y=654+7x
To find the population after 3 years, we can use x=3 in the equation.
y=654+7*3
y=654+21
y=675
Hence if the population of pine bluff is 654 and is increasing at the rate of 7 per year, then the equation will be y=654+7x and the population after 3 years will be 675.
Learn more about equation at https://brainly.com/question/2972832
#SPJ9
A qualitative forecasting technique that is useful for identifying what consumers like and dislike about a product is?
A qualitative forecasting technique that is useful for identifying what consumers like and dislike about a product is Market research.
What methods are employed in a qualitative forecast?
The expert opinion approach, the Delphi method, and the market survey approach are the three main methods utilized in qualitative forecasting.
What are qualitative forecasting models, and when are they useful?
Qualitative forecasting techniques are based on the judgment and opinion of experts and consumers and are only appropriate in the absence of historical data. Market research, Delphi method, and informed opinion and judgment are a few examples of qualitative forecasting techniques.Learn more about qualitative forecasting
brainly.com/question/13289439
#SPJ4
A researcher reports t(22) = 5.30, p < .01 for an independent-measures experiment. how many individuals participated in the entire experiment?
For the entire independent-measures experiment 24 individuals are participated.
What do you mean by independent-measures experiment?Different participants are utilized in each condition of the independent variable in an experimental design known as an independent measures design, or between-groups. This indicates that a different group of participants is present for each condition of the experiment. A research strategy known as an independent measures design uses numerous experimental groups with subjects only being assigned to one group. Throughout the experiment, each participant is solely exposed to one independent variable condition. A drug trial for a novel medicine would serve as an example. This has the benefit of preventing order effects, which occur when participants behave differently as a result of the order in which conditions are done, often as a result of factors like boredom or exhaustion.
We are given the value t(22) = 5.30, p < .01
So here degree of freedom (df) is 22 and it is independent so there is two samples,
so df= n₁+n₂-2
⇒ 22 = n₁+n₂-2
⇒ n₁+n₂ = 24.
Thus for the entire experiment 24 individuals are participated.
To learn more about independent-measures experiment, click here:
https://brainly.com/question/17699654
#SPJ4
Joe moves a 10 kg weight 5 meters with a force of 50 N in 10 seconds. Leroy uses the same force to move the same weight the same distance in 7.5 seconds? Who has more power and why
Answer:
10 sec
Step-by-step explanation:
Write the inequality that represents the sentence, "Five less than a number is greater than 57."
Choose the correct answer below.
x-5>57
x-5257
x+5257
x+5> 57
.***
Answer:
Option A, or x-5>57
Step-by-step explanation:
30 POINTS
Write and solve an absolute value equation for the minimum and maximum times for an object moving at the given speed to travel the given distance. Absolute value 3 ft. 10 ft/s for 30 ft
Answer:
Step-by-step explanation:
12
How do the perimeters of the triangles compare? 24 cm 24 cm Original 24 cm 8 cm 8 cm Scaled 8 cm A. The scaled triangle's perimeter is 1/24 as long as the original triangle's perimeter. B. The scaled triangle's perimeter is 1/9 as long as the original triangle's perimeter. C. The scaled triangle's perimeter is 1/6 as long as the original triangle's perimeter. D. The scaled triangle's perimeter is 1/3 as long as the original triangle's perimeter.
The scaled triangles perimeter is 1/3 the size of the original triangles perimeter
What is Scaled traingle?All of the sides of the triangle known as the Scalene Triangle are of various lengths. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.
A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional planar object having three sides and three angles. There are three edges and three vertices on it.
According to the given values;
original:
hieght=24 slant= 24 lenght=24
Scaled:
hieght=8 slant= 8 lenght=8
Looking at the dimension of both triangles,
The relationship between the original and the scaled copy is : 1/3*original
Hence, the perimeter is:1/3*perimeter(original)
To know more about the perimeter of traingle ,visit;
https://brainly.com/question/22603791
#SPJ9
Create a polynomial that has 4 term, a degree of 6, a leading coefficient of -1 and a
Constant term of -5.5
Answer: Theorems About Roots of Polynomial Equations
Step-by-step explanation:
Theorems About Roots of Polynomial Equations
In the given case we can conclude that the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
To create a polynomial with 4 terms, a degree of 6, a leading coefficient of -1, and a constant term of -5.5, we can use the general form of a polynomial:
A "polynomial" is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers, combined using addition and multiplication. Polynomials are fundamental objects in algebra and are used to represent a wide range of mathematical relationships, including functions, curves, and various mathematical concepts.
P(x) = [tex]ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g[/tex]
Plugging in the given values, we have:
P(x) = [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5[/tex]
Remember that the degree of a polynomial is determined by the highest exponent of x.
In this case, the degree is 6.
The leading coefficient is the coefficient of the term with the highest degree, which is -1. The constant term is -5.5.
So, the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
Learn more about Polynomials here:
https://brainly.com/question/20121808
#SPJ3
Find the Inverse Function : Algebra 2
y = 2x² + 1
[tex]\displaystyle\\Answer:\ y=\sqrt{\frac{x-1}{2} } \ \ \ \ (x\geq 1,\ \ \ \ y\geq 0)[/tex]
Step-by-step explanation:
[tex]y=2x^2+1\\[/tex]
We change the argument and the value:
[tex]\displaystyle\\x=2y^2+1\\\\x-1=2y^2+1-1\\\\x-1=2y^2\\[/tex]
Divide both parts of the equation by 2:
[tex]\displaystyle\\\frac{x-1}{2}=y^2\\\\ \sqrt{\frac{x-1}{2} }=y \ -\ the\ desired\ inverse\ function\\\\[/tex]
The restrictions are imposed on the inverse function by on x:
[tex]x-1\geq 0\\x\geq 1[/tex]
The restrictions are imposed on the inverse function by on y:
[tex]y\geq 0[/tex]
Then the original function is defined on the sets:
[tex]x\geq 1,\ \ \ \ y\geq 0[/tex]
The initial function, a parabola, is constrained because of the inverse function; only in this case the functions are reciprocal.
in a sentence.
11) Kelsey has a $30 online gift voucher. She plans to buy as many books as she can. The cast of each book
is $3. There is also a single shipping charge of $2. How many books can she afford without spending more
than her gift voucher amount?
Answer:
Kelsey can buy 9 books.
Step-by-step explanation:
If Kelsey wants to buy as much books as possible with 30$, multiply 3$ by 9 (books) which is 27$.
30$-27$ is 3$ so she will have 3$ extra dollars to use for shipping. 2$ is the price for shipping so she will have an extra dollar.
I hope this was helpful! :) (Please rate/heart this if helpful)
For each complex number z, find arg z
z = 4/5 + 3/5i
The argument of complex number ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] ) is [tex]tan^{-1}[/tex]([tex]\frac{3}{4}[/tex])
Complex number:
A complex number is a result of adding a real and an imaginary number. A complex number has the formula a + ib and is usually represented by the symbol z. Both a and b are real numbers in this case. The value 'a' is known as the real part, which is denoted by Re(z), and the value 'b' is known as the imaginary part Im (z). ib is also known as an imaginary number.
Argument:
A complex number is represented in polar form by the equation r(cos[tex]\theta[/tex] +isin[tex]\theta[/tex]), where [tex]\theta[/tex] is the argument. Arg(z) denotes the argument function, where z is the complex number, i.e. z = x + iy. The complex argument can be determined by the following formula:
arg (z) = arg (x+iy) = [tex]tan^{-1}[/tex](y/x)
Here the given complex number is ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] )
arg (z) = arg ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] )= [tex]tan^{-1}[/tex]([tex]\frac{3}{4}[/tex])
Therefore,the argument of complex number ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] ) is [tex]tan^{-1}[/tex]([tex]\frac{3}{4}[/tex])
Learn more about complex number here:
https://brainly.com/question/20566728
#SPJ9
Each day a small business owner sells 200 pizza slices at $2.50 per slice and 85 sandwiches at $2.00 each. Business
expenses come to $60 per day. What is the owner's profit for a ten-day period?
The profit is S
The owner's profit for a ten-day period is equal to $ 6100.
We are given that:
Selling price of 1 pizza slice = $ 2.50
Number of pizza slice sold per day = 200
Selling price for pizza slices in a day = 200 × $ 2.50
SP ( pizza ) = $ 500
Selling price of 1 sandwich = $ 2
Number of sandwich sold per day = 85
Selling price for pizza slices in a day = 85 × $ 2
SP ( sandwich ) = $ 170
Selling price in 1 day = $ 500 + $ 170 = $ 670
Now, Cost price in 1 day = $ 60
Profit in 1 day = $ 670 - $ 60 = $ 610
Profit in 10 days = 10 × $ 610 = $ 6100
Therefore, the owner's profit for a ten-day period is equal to $ 6100.
Learn more about profit here:
https://brainly.com/question/19104371
#SPJ9
(3.6 x 105) / (1.2 x 103) =
3.0582524271844
Step-by-step explanation:
1.multiply the numbers:3.6×105=378
2.multiply the numbers:1.2 ×103=123.6
3.Divide the numbers:378/123.6=3.0582524271844
a building in a city has a rectangular base. the length of the base measures 65ft less than three times the width. the perimeter of this base is 910ft. what are the dimensions of the base?
The dimension of the base of the rectangular building is 340 x 135ft.
Perimeter of Rectangle:
The definition of perimeter of the rectangle is the total length or distance of its boundary on all sides.
The general formula to calculate the Perimeter of a rectangle is,
P = 2(l + w)
Where,
l represents the length of the rectangle
w represents the width of the rectangle.
Given,
The building in a city has a rectangular base. the length of the base measures 65ft less than three times the width.
The perimeter of this base is 910ft.
Now, we need to find the dimensions of the rectangular base.
According to the given details, the values of
L = 3W - 65
W = W
P = 910
Apply the values on the formula, then we get,
=> 910 = 2 * (L + W)
=> 910/2 = (L + W)
=> 455 = L + W
Apply the value of L,
=> 475 = 3W - 65 + W
=> 475 + 65 = 4W
=> 540 = 4W
=> 540/4 = W
=> W = 135
Apply the value of W as 135, in order to get the value of L,
=> L = 3*135 - 65
=> L = 405
=> L = 340
Therefore, the dimension of the rectangular base is 340 x 135 ft.
To know more about Perimeter of the Rectangle here.
https://brainly.com/question/2142493
#SPJ4
A line has no thickness, but it does have direction and ___ length.
(Fill in the blank)
A line has no thickness, but it does have direction and infinite length.
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
Given the variety of geometries in modern mathematics, the idea of a line is directly related to how the geometry is described. For instance, a line in the plane is frequently defined in analytic geometry as the collection of points whose coordinates satisfy a given linear equation, but in a more abstract context, such as incidence geometry, a line may be an independent object, distinct from the collection of points that lie on it.
In cartesian plane the general equation of a line is given by :
y=mx+c where the slope is denoted by m and the y-intercept by c.
To learn more about a straight line:
https://brainly.com/question/17188072
#SPJ9
Find the unit rate.
650 ft².
2
____
3
Combine the like terms to create an equivalent expression
-4r-2r+5
Answer:
-6r+5
Step-by-step explanation:
Combining the like terms
⇒-4r-2r+5
⇒-6r+5
Austin is mailing packages. Each small package costs him $2.60 to send. Each large package costs him $3.50. How much will it cost him to send 1 small package and 5 large packages?
Answer:
$20.1
Step-by-step explanation:
1 small package is $2.60
1 large package is $3.50
We multiply 3.5 * 5 since there are 5 large packages and we add 1 small package to get $20.1
Answer:
$20.10
Step-by-step explanation:
Let s = the cost of a small package and
l = the cost of a large package
1 small pakcage and 5 large package
1s+5l
Substitute s = $2.60 and l = $3.50
1($2.60) + 5(3.50)
= $20.10
Graph: y < 1/3x + 1/2
Answer: See attached.
Step-by-step explanation:
Since this inequality uses < and not ≤, we will be using a dashed line.
Next, we will shade "below" the line since this inequality uses the < aka less than.
Lastly, our y-intercept is [tex]\frac{1}{2}[/tex].
what are some properties of an isosceles triangle
Answer:
3 equal side 3 congruent angles of 60°
Step-by-step explanation:
what are some properties of an isosceles triangle
3 equal side 3 congruent angles
Nolvia sells copy machines, and her salary is $21,000 plus a 4% commission on sales. the equation s=21,000+ 0.04x
represents her salary s in dollars in terms of her total sales x in dollars.
part: 0/3
part 1 of 3
(a) how much money in sales does nolvia need to earn a salary that exceeds $40,000?
she needs to sell in excess of $
please help im getting timed
The amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000 is greater than or equal to $19,000.
Given that:-
Fixed salary of Nolvia = $21,000
Commission tax that Nolvia gets = 4 %
Linear equation of Nolvia's salary and commission tax = 21000 + 0.04x
Where,
s represents her salary
x represents total sales
We have to find the amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000.
The amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000 = 40000 - 21000 ≥ $ 19,000
To learn more about Linear equation, here:-
https://brainly.com/question/11897796
#SPJ4
Cindy and Richard leave their dorm in Charleston
at the same time. Cindy rides her bicycle north at a
speed of 18 miles per hour. Richard rides his bicycle
south at a speed of 14 miles per hour. How long will it
take them to be 96 miles apart?
Answer:
Hello,
Step-by-step explanation:
Let's suppose
t the time of the travel
d1 the distance rided by Cindy in miles
d2 the distance rided by Richard in miles
d1+d2=96
18*t+14*t=96
32*t=96
t=3 (hours)