Answers
Note: Please note that you missed adding the option points. So, I am solving the entire function to determine the points and the vertex which would anyways clear your concept.
Answer:
The vertex is located at (3, 7)
some of the points will make the table such as:
x 0 1 2 3 4
y -2 3 6 7 6
The graph is attached below.
Step-by-step explanation:
Given the table
[tex]y\:=\:6x-2-x^2[/tex]
The given equation is of the form quadratic function y = ax² + bx + c. Thus, it represents the Parabola.
As the leading coefficient of the parabola is -2, thus the Parabola opens down.We know that the vertex would be the highest point on the Parabola graph if the graph (Parabola) opens down.
Thus, the given Parabola has the vertex point at the highest point of the Parabola as shown in the attached figure.
Finding the Vertex:
y = -x² + 6x - 2
comparing with y = ax² + bx + c
a = -1, b = 6, c = -2
Finding the x-coordinate of the Vertex
x = -b / 2a
x = [-6] /[2(-1)]
x = [-6 ] / [-2]
x = 6/2
x = 3
Thus, the x-coordinate of the vertex : x = 3
Now substituting x = 3 in the equation y = -x² + 6x - 2 to determine the y-coordinate of the vertex
y = -x² + 6x - 2
y = -(3)²+6(3)-2
y = -9 + 18 - 2
y = 18 - 11
y = 7
Thus, the y-coordinate of the vertex : y = 7
Therefore, the vertex is located at (3, 7)
Now, finding some other points lie on the Parabola
y = -x² + 6x - 2
Putting x = 0 in the main function
y = -(0)² + 6(0) - 2
y = 0 + 0 - 2
y = -2
Thus, the y-intercept lies on (0, -2)
Putting x = 1 in the main function
y = -x² + 6x - 2
y = -(1)² + 6(1) - 2
y = -1 + 6 - 2
y = 3
Thus, the point (1, 3) lies on the Parabola
Putting x = 2 in the main function
y = -x² + 6x - 2
y = -(2)² + 6(2) - 2
y = -4 + 12 - 2
y = 6
Thus, the point (2, 6) lies on the Parabola
Putting x = 3 in the main function
y = -x² + 6x - 2
y = -(3)² + 6(3) - 2
y = -9 + 18 - 2
y = 7
Thus, the point (2, 7) lies on the Parabola
Putting x = 4 in the main function
y = -x² + 6x - 2
y = -(4)² + 6(4) - 2
y = -16 + 24 - 2
y = 6
Thus, the point (4, 6) lies on the Parabola
Hence, some of the points will make the table such as:
x 0 1 2 3 4
y -2 3 6 7 6
The graph is attached below.
Related Questions
find the value of x in each of the given triangles.
Answers
Answer:
x= 12°
Step-by-step explanation:
The angle measures in the triangle are given as;
A = 4x
B= 5x
C= 6x
The sum of angle measures in a triangle add up to 180°
Applying the statement in an equation as;
4x + 5x + 6x = 180°
15x = 180°
x= 180° / 15
x = 12°
Calculate the marked price of a sweater purchased at Rs. 1075 allowing 14% discount. ( please do proper answer )
Answers
Answer: $1225.50
Step-by-step explanation:
Purchase price = $1075
Discount Percent = 14%
Discount = 14% × $1075
= 0.14 × $1075
= $150.50
Marked price = Purchase price + Discount
= $1075 + $150.50
= $1225.50
A system of linear equations is shown below.
2x – 3y = 15
-2x + y = -1
Choose a method (Elimination or Substitution) to solve the system of equations. Solve and explain your process.
Answers
Choose all the factors of 5. (Check all that apply.)
4
1
3
2
5
plz i need help
Answers
Answer:
1 and 5
Step-by-step explanation:
only 1*5 equals 5
At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?
Answers
Answer:
37.5%
Step-by-step explanation:
OOF DIS COMPLICATED
I messed up big timeeeeeeeee
A lot of percent problem are very simple by just assuming values, especially in case the answer is also a percentage.
If there are 100 birds, 20% are tagged so 20 are tagged.
Out of the rest 80, 30 should be tagged so that a total of 50% are tagged.
30/80 = 37.5%
(The huge number given is unnecessary, just to make you waste your valuable time. Read the question again to realize that it is not needed.)
The percent of the untagged birds that must be tagged so that half of all birds in the refuge are tagged is 37.5%.
Untagged birds percentage:First step
Currently Tagged birds= 54210 ×20/100
Currently Tagged birds=10842
Second step
Untagged birds=54210 - 10842
Untagged birds=43368
Third step
Untagged birds percentage:
Untagged birds percentage=( 54210/2)-10842/43368
Untagged birds percentage=(27105-10842)/43368
Untagged birds percentage=16263/43368
Untagged birds percentage=0.375×100
Untagged birds percentage=37.5%
Inconclusion the percent of the untagged birds that must be tagged so that half of all birds in the refuge are tagged is 37.5%.
Learn more about percentage here:https://brainly.com/question/24304697
Kevin bought 15 bananas for 4.50. How much does 1 banana cost?
Answers
Answer:
$0.30
Step-by-step explanation:
Divide 4.50 by 15.
Attendance at baseball games
Answers
Enjal paid Rs 15,255 for smart phone with 10% discount and 13% vat. Find marked price of that smart phone.
Answers
Answer:
The marked price of the smart phone is Rs 15,000.
Step-by-step explanation:
We proceed to explain step by step how to determine the marked price of the smart phone:
1) Divide the resulting price by the VAR factor:
[tex]C' = \frac{C''}{1 + \frac{r}{100} }[/tex] (1)
Where:
[tex]C''[/tex] - Resulting price, measured in rupees.
[tex]C'[/tex] - Price of the product after discount, measured in rupees.
[tex]r[/tex] - VAT rate, measured in percentage.
If we know that [tex]C'' = 15,255\,INR[/tex] and [tex]r = 13[/tex], then the price of the product after discount is:
[tex]C' = \frac{15,255\,INR}{1+\frac{13}{100} }[/tex]
[tex]C' = 13,500\,INR[/tex]
2) Divide the price of the product after discount by the discount factor:
[tex]C = \frac{C'}{1-\frac{r'}{100} }[/tex] (2)
Where:
[tex]C[/tex] - Marked price of the product, measured in rupees.
[tex]r'[/tex] - Discount rate, measured in percentage.
If we know that [tex]C' = 13,500\,INR[/tex] and [tex]r' = 10[/tex], then the marked price of the product is:
[tex]C = \frac{13,500\,INR}{1-\frac{10}{100} }[/tex]
[tex]C = 15,000\,INR[/tex]
The marked price of the smart phone is Rs 15,000.
solve the system of linear equations using subsitution. {y=2x-1. {y=x-8
Answers
Answer:Linear Algebra Examples ... Linear Algebra. Solve by Substitution y=x+3 , y=2x-1 ... Eliminate the equal sides of each equation and combine. ... Subtract 1 1 from 8 8 . ... The solution to the system of equations can be represented as a point.
Step-by-step explanation:
The perimeter of the rectangle is 28 units.
What is the value of w?
Answers
Answer:
5 units
Step-by-step explanation:
im pretty sure i did the calculations right
Use the drop-down menus to complete each equation so the statement about its solution is true. I’ll give brainliest :))
Answers
Step-by-step explanation:
5 - 4 + 7x + 1 = 7x + 2.
If there are no solutions, then it is of the form 7x + c, where c is any real number besides 2.
If there is 1 solution, then it is of the form mx + c, where m is any real number besides 7 and c is any real number.
If there are infinitely many solutions, then it is of the form 7x + 2.
Evaluate the expression if s = 5 and t = 7.
4s +t
A.19
B.23
C.27
D.33
Answers
Answer:
C. 27
Step-by-step explanation:
4s + t
4(5) +7
20 + 7
27
5x - 3(x - 2) - x math and stuff
Answers
Answer:
x + 6
Step-by-step explanation:
5x-3(x-2)-x
5x-3x+6-x
5x-3x-x+6
x+6
Can you please list how I do this and what the answer is I need help on it and I’ve been struggling for 20 minutes now
Answers
First thing's first, 20/4=5. This portion of the equation would be completed first because D comes before A and S in PEMDAS. this leaves you with 17+5-5. 17+5=22, and 22-5=17.
Un camión admite en su interior 68,25 toneladas de patatas. Se cada caja de patatas pesa 22,75 Kg, ¿cuántas cajas de
patatas lleva el camión?
Answers
Answer:
El camión lleva 3000 cajas de patatas
Step-by-step explanation:
Proporciones
La capacidad de carga de un camión es de 68.25 Toneladas de patatas.
Como 1 tonelada es equivalente a 1000 Kg, expresamos la capacidad en Kg:
68.25 * 1000 = 68250 Kg
Cada caja de patatas pesa 22.75 Kg, luego el número de cajas que caben en el camión son:
68250/22.75 = 3000 cajas
El camión lleva 3000 cajas de patatas
Shelby purchases personalized stockings from Etsy for $15 per stocking. She has to pay $4.50 shipping. How many stockings can Shelby purchase for $50???
Answers
Answer:
3
Step-by-step explanation:
help me find the answer lol
Answers
Answer:
First/Top graph.
Step-by-step explanation:
First, we need to solve the inequality for n:
-6n + 5 < 11 (Given)
-6n < 6 (Subtracted 5 on both sides)
n > -1 (Divided -6 on both sides)
NOTE: Whenever you multiply or divide by a negative number when dealing with inequalities, the sign switches.
Now that we know that n > -1, we need to look for a graph that has an open circle on the point -1 and goes in the right direction.
Therefore, the first graph is the correct answer.
p l e a s e h e l p m e e e e
Answers
Answer:
i believe its c
Step-by-step explanation:
A ,B and C average is 45 ,b and C average is 40 then find b
Answers
This question is incomplete
Complete Question
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is :
Answer:
31 kg
Step-by-step explanation:
From the above question:
A ,B and C average is 45.
Hence, the total values of A, B, C is calculated as:
A + B + C /3 = 45
A + B + C = 45 × 3
A + B + C = 135
Also,
B and C average is 43
The total values of B, C is calculated as:
B + C /2 = 43
B + C = 43 × 2
B + C = 86
A and B average is 40
The total values of A, B is calculated as:
A + B /2 = 40
A + B = 40 × 2
A + B = 80
Hence:
A + B + C = 135
B + C = 86
A + B = 80
Hence, we can solve for A, we substitute 80 for A + B
80 + C = 135
C = 135 - 80
C = 55kg
B + C = 86
B + 55 = 86
B = 86 - 55
B = 31 kg
At a little-known vacation spot, taxi fares are a bargain. A 56-mile taxi ride takes 63 minutes and costs $50.40 You want to find the cost of a 34- taxi ride. What unit price do you need?
Answers
Answer:
the unit price that required is $30.60
Step-by-step explanation:
The computation of the unit price that required is shown below
For one mile, the cost is
= taxi ride cost ÷ distance covered
= $50.40 ÷ 56
= $0.90
Now for the cost of 34 mile taxi ride
= Unit cost × distance covered
= $0.90 × 34 mile
= $30.60
hence, the unit price that required is $30.60
We simply applied the above formula so that the correct cost could come
The same is to be considered
Jose worked 8 days for a total of 58.4 hours. If he worked the same number of hours each day, how many hours did he work in a day?
Answers
Answer:
7.3 or 7 hours.
Step-by-step explanation:
So i divided 58.4 by 8. And got 7.3.
8 x (7) = 56. So, 58 - 56 = 2. Put the decimal up. Now, 8 x (3) = 24. So, now you should have 7.3. But you could round it to 7. Depends.
A park has a 3m tall tetherball pole, and a 6.8m tall flagpole. The lengths of their shadows are proportional to their heights.
Answers
Complete question is;
A park has a 3 meter tall tether ball pole and a 6.8 m tall flagpole. The lengths of their shadows are proportional to their heights.
Which of the following could be the lengths of the shadows?
Choose 2 answers from the options attached.
Answer:
Options B & D
Step-by-step explanation:
From the question, the proportional relationship between the height and shadow length is a direct proportionality. This means that an increase in the height, leads to an increase in the length of shadow and vice versa. Thus, the height to shadow length ratio is a constant.
Now, if we use x and y to denote length of shadow of tether ball pole and length of flagpole receptively, we will have;
3/x = 6.8/y
Let's make y the subject.
y = 6.8x/3
Looking at the options;
Option A: When x = 1.35 m, we have;
y = (6.8 × 1.35)/3 = 3.06 m
For Option B:
When x = 1.8 m,
y= (6.8 × 1.8)/3 = 4.08 m
For Option C:
When x= 3.75 m,
y = (6.8 × 3.75)/3 = 8.5 m
For option D:
When x = 0.6
y = (6.8 × 0.6)/3 = 1.36 m
For option E;
When x = 2,
y = (6.8 × 2)/3 = 4.533 m
From our calculations, the only values of y that correspond with the given value of y in the options are Options B & D
The distance between two cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers. What is the actual distance between these two cities in kilometers?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answers
Answer:
70 km
Step-by-step explanation:
[tex]\frac{3.5 cm}{x km}[/tex] = [tex]\frac{1cm}{20km}[/tex]
x = (3.5 cm × 20 km) ÷ 1 cm = 70 km
Answer:
70 km
Step-by-step explanation:
ZD, ZE, and ZF are the perpendicular bisectors of ABC. Use that information to find the length of each segment. Not that the figure is not drawn to scale.
Given:
ZD=44
ZA=87
FC=75
Find: ZC and AC
Answers
Answer:
wait I am solving. oklllllk
Answer:
ZA=85 ZB=85
Step-by-step explanation:
New York and Denver are in different time zones. When it is noon in New York, it is 10:00 a.m. in Denver. At 2:00 p.m. in New York, a train departs, and it arrives in Denver 45 hours later. What time is it in Denver when the train arrives?
Answers
Answer:
9:00 AMStep-by-step explanation:
Time in New York = noon = 12:00 PMTime in Denver = 10:00 AMTime difference = -2 hours
Train departs at 2:00 PMTravel time = 45 hoursTrain arrival time:
2:00 PM + 45 hours = 2:00 PM - 3 hours (plus 2 days) = 11:00 AMConverting to Denver time:
11:00 AM - 2 hours = 9:00 AMAnswer:
9:00 AM
Step-by-step explanation:
A general arranges his students to form a perfect square.He finds that in doing so 60 soldiers were left out if total number of soldiers be 8160 find the number of soldiers in each row
Answers
Answer:
90
Step-by-step explanation:
Given that :
Number of soldiers = 8160
Number left out = 60
Result of arrangement gives a perfect square ;
Hence, the number of soldiers which makes up the arrangement will be ;
Total number of soldiers - number left out
8160 - 60 = 8100
Hence 8100 soldiers were used to form a perfect square ;
Number of soldiers in a row :
√8100 = 90
Hence, we have 90 soldiers in a row
the roots of a quadratic function are -2 and -6
what are the two factors of the quadratic expression ?
x + 2 ; x - 2 ; x - 8 ; x + 8 ; x - 6 ; x + 6
Answers
Step-by-step explanation:
The factors are x + 2 and x + 6.
3.) T4.T4
Simply this for me to plz look at the pic
Answers
Answer:
t^8
Step-by-step explanation:
t^4 times t^4
exponents you add.
4 + 4 = 8
t^8
Lilliana is training for a marathon. She runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 4 laps on a running trail and then runs 8 more miles. On Tuesday and Sunday, she runs 6 laps on the trail and then runs 4 more miles. On Saturday, she just runs laps. How many laps does Lilliana run on Saturday?
Lilliana runs ??? laps on Saturday.
Answers
Answer: 17 3/4
Step-by-step explanation: because yes
Answer:
Actualy 17 3/4 is incorrect ( she actualy ran 8 laps on saturday)
Step-by-step explanation:
I dont feel like typeing out my math but i am correct because I had this same question on my homework.
i need help with this ?
Answers
Step-by-step explanation:
Notice that 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8...
The exponential function is y = 2^x.