Answer: I and III
Step-by-step explanation:
The graphs of f and g have the same axis of symmetry. The graph of f has a maximum point, and the graph of g has a minimum point. The graph is a result of a reflection of the graph pf g across the x-axis. The correct options are 1, 3, and 4.
What is quadratic function?A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.
We can use the fact that the points (3,2) and (7,2) are on the graphs of both functions to find out which of the given statements are true.
Let's start by using the fact that the graphs of the functions f and g pass through the points (3,2) and (7,2).
Since the y-coordinate is the same for both points, we can set the equations of the functions equal to 2 and solve for the unknown coefficients.
For the downward-opening quadratic function f, the equation is of the form:
[tex]f(x) = a(x - h)^2 + k[/tex]
Where (h,k) is the vertex of the parabola. Since f opens downward, the coefficient a is negative.
Using the point (3,2), we get:
[tex]2 = a(3 - h)^2 + k[/tex]
Using the point (7,2), we get:
[tex]2 = a(7 - h)^2 + k[/tex]
Subtracting the second equation from the first, we get:
[tex]0 = a[(3 - h)^2 - (7 - h)^2][/tex]
Simplifying this expression, we get:
0 = a[(3 - h + 7 - h)(3 - h - (7 - h))]
0 = a[-4(h - 5)]
Since a is non-zero (otherwise the parabola is not quadratic), we get:
h = 5
Plugging in h = 5 and using one of the equations above, we can solve for k:
[tex]2 = a(3 - 5)^2 + k[/tex]
2 = 4a + k
k = 2 - 4a
Therefore, the equation of the quadratic function f is:
[tex]f(x) = a(x - 5)^2 + (2 - 4a)[/tex]
Using the same method for the upward-opening quadratic function g, we get:
[tex]g(x) = b(x - 5)^2 + (2 + 4b)[/tex]
Where b is positive.
Now, let's check which of the given statements are true:
The graphs of f and g have the same axis of symmetry.
Since the vertex of f is (5, 2 - 4a) and the vertex of g is (5, 2 + 4b), the x-coordinate of the axis of symmetry for both functions is 5. Therefore, statement 1 is true.
The graphs of f and g have the same x-intercepts.
The x-intercepts of f are given by:
[tex]0 = a(x - 5)^2 + (2 - 4a)\\4a = a(x - 5)^2[/tex]
x - 5 = ±√(4/a)
x = 5 ± 2√(a)
The x-intercepts of g are given by:
[tex]0 = b(x - 5)^2 + (2 + 4b)[/tex]
-4b = [tex]b(x - 5)^2[/tex]
x - 5 = ±√(-4/b)
x = 5 ± 2i√(b)
Thus, since a and b have opposite signs, the x-intercepts of f and g are different. Therefore, statement 2 is false.
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HELPP WILL GIVE BRAINLIEST NO LINKS
The width of a rectangle room is 80 percent of its length. WHat is the area of the room?
Answer:
180 squared ft
Step-by-step explanation
80% = 80/100 = 40/50 = 4/5
L = 15
W= 4/5 of 15 = 12
Area = LxW
Area = 15x12 = 180 squared ft
21.13 x 78.29 =
pls help <3
Answer:
1654.267
Hope this helps!
Please Help Out
The Screenshots are Bellow!
pls help me ! (Links=report)
Answer:
WHeres the questionnn???????
Step-by-step explanation:
The ratio x + y : x - y is equal to 2 : 1.
Write an equation for x in terms of y.
Answer:
x=3y
Step-by-step explanation:
ATQ
(x+y):(x-y)=2
or, x+y=2x-2y (crossmultiply)
or, 0= 2x-x-2y-y
or, x- 3y=0
or, x=3y is required equation
Find the value of x. PLZZZ HELP MEEE
9514 1404 393
Answer:
128°
Step-by-step explanation:
End angles of a trapezoid are supplementary.
x° = 180° -52° = 128°
x = 128
Answer:
Solution :-According to the question
The supplementary theorem
x + 52 = 180
x = 180 - 52
x = 128⁰
Value of x is 128⁰
[tex] \\ [/tex]
Determine if the two expressions are equivalent and if so name the property that is being used.
52-(43-6) & (52-43) - 6
Answer: i really dont know
Step-by-step explanation: but 46
Plsss i need help boys and girls lol FRL :)
Answer:
The answer is D.
Step-by-step explanation:
Sci-Fi + Comedy = 60.
Other + Action = 59.
So, that makes it D.
Hope this helps. :)
what are the values of x and y
Answer: Step-by-step explanation:
35+y+y=180
2y=180-35=145
y=72.5°=72°30'
y+y+x=180
145+x=180
x=35°
Answer:
X is 35
y is 72.5 I think
sorry if wrong
Step-by-step explanation:
At 12:15, the end of the minute hand of a clock is 8 feet above the ground. At 12:30, it is 6.5 feet off the ground How long is the minute hand of the clock? And How high is the center of the clock from the ground
Answer:
Length of minutes hand= 1.5 feet
Height of the center of the clock from the ground= 8 feet
Step-by-step explanation:
At 12:15, the end of the minute hand of a clock is 8 feet above the ground.
At 12:15 the minutes hand is making a radius along the diameter of the clock which means it is at the center of the clock. In other the center of the clock is 8 feet above the ground.
At 12:30, it is 6.5 feet off the ground .
This tells length of the minutes hand the clock which is the distance from the ground minus the distance off the ground
= 8-6.5= 1.5 feet
The center of the clock is 8 feet from the ground.
The length of the minute hand is 1.5ft, the distance of the center of the clock from the ground is 8ft
To solve this problem, we have to apply logical reasoning here.
Length of the Minute HandTo calculate the length of the minute hand, we just have to subtract or find the difference between the minute and from the ground at 12:30 to the minute hand at 12:15.
This will give us
[tex]12:15 - 12:30 = 8 - 6.5 = 1.5ft[/tex]
Distance of the Center of the clock from the groundThe distance of the center of the clock from the ground can be gotten from the distance from the ground at 12:15. This is because at 12:15, the minute hand is at the same horizontal line with the center of the clock and this makes the distance of the center of the clock from the ground is 8ft.
From the above,
The length of the minute hand is 1.5ft The distance of the center of the clock from the ground is 8ftLearn more on clocks here;
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Andres signed up for a streaming music service that costs $14 per month. The service
allows Andres to listen to unlimited music, but if he wants to download songs
for
offline listening, the service charges $0.50 per song. How much total money would
Andres have to pay in a month in which he downloaded 20 songs? How much would
he have to pay if he downloaded s songs?
Answer:
$24.00
Step-by-step explanation:
x = per month
y = per song
t = total
Equation:
t = 14x + 0.5y
t = 14(1) + 0.5(20)
t = 14 + 10
t = 24
In the diagram, AE = x + 5, ED = 12, BE = x, and EC = 4. Solve for x.
PLS HURRY TIMED
Answer:
there is no img given
Step-by-step explanation:
pls mark as brainliest
L = 9.1 in
W = ? in
H = 6 in
Volume = 141.96 in3
Answer:
It should be 2.6
Step-by-step explanation:
141.96 ÷ 6 =23.66
23.66 ÷ 9.1 =2.6
Determine if the work below is correct.
NO FILES OR LINKS OR PHOTOS PLEASE
Answer:
Correct
Step-by-step explanation:
To find the volume of a rectangular prism, the formula is [tex]lwh[/tex].
5 · 9 · 3.2 = 144
So, the answer and work are all correct.
Good luck :)
A rectangular lawn is 14 meters by 21 meters. It would cost $6.32 per meter to install a fence around
the lawn. How much would it cost to put a fence around the lawn?
$
Answer:
$442.40
Step-by-step explanation:
14x2=28
21x2=42
42+28=70
70x6.32=442.4
Arquimedes, Euclides e Ptolomeu têm, juntos, R$ 1 990,00. Arquimedes possui R$ 190,00 a mais do que Euclides e esse, dispõe de R$ 120,00 a mais do que Ptolomeu. Determine quantos reais cada um deles possui.
Responder:
Ptolomeu = 520
Euclides = 640
Arquimedes = 830
Explicação passo a passo:
Deixar :
Quantidade que Ptolomeu tem = x
Quantidade de Euclides = x + 120
Quantidade que Arquimedes tem = x + 120 + 190
Valor total que todos eles têm = $ 1990
Portanto,
x + x + 120 + x + 120 + 190 = 1990
3x + 430 = 1990
3x = 1990 - 430
3x = 1560
x = 520
Ptolomeu = 520
Euclides = 520 + 120 = 640
Arquimedes = 640 + 190 = 830
Can someone help please ?
Answer:
Step-by-step explanation:
12.8/2 = 96 / 2 = 48
the answer is the first one
have a nice day!Solve for x. please i need know
Answer:
x = 18
Step-by-step explanation:
Vertically opposite angles are equal.
x + x + x + 90 = 144
3x + 90 = 144
Subtract 90 from both sides
3x = 144 - 90
3x = 54
Divide both sides by 3
x = 54/3
x = 18
Malik is solving the equation x2 – 10x – 11 = 0 using the complete the square method. Here is Malik's work: Line 1 p^2 -10p-11=0 Line 2 p^2 -10p+25=11+25 Line 3 (p-5)^2 =36 Line 4 p-5=36 or p-5=-36 Line 5 p=41 p=-31 Line 6 the solution is p=41 or p=-31 Malik checks his answer and realizes he has made a mistake. On which line did Malik make his mistake? Explain Malik's mistake using the complete the square method in 1-3 complete sentences.
Completing the square method rearranges the equation to have the
square of linear equation and constant on both sides of the equation.
Responses:
The mistake is made in line 4The mistake is in not taking the square root of both sidesWhich is the correct completing the square method?The given equation is; x² - 10·x - 11 = 0
Line 1: p² - 10·p - 11 = 0
Which gives;
p² - 10·p = 11
Adding 25 to both sides gives;
Line 2: p² - 10·p + 25 = 11 + 25
11 + 25 = 36
Factorizing p² - 10·p + 25 = (p - 5)·(p - 5) = (p - 5)²
Line 3: (p - 5)² = 36
Which gives;
p - 5 = ±√36
Line 4: p - 5 = √36 = 6 or p - 5 = -√36 = -6 (Line that has a mistake)
Line 5: p = 6 + 5 = 11, or p = -6 + 5 = -1
Line 6: p = 11 or p = -1
The line Malik made a mistake is on line 4The mistake made is that in line 4, the root of both sides of the equation, rather than only the left side of the equation is to be taken.The constant on the left and side is then subtracted from the positive
and negative value of the square root of the right hand side to give two
results.
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Donovan and Timothy solved two different division problems. Who solved the problem correctly?
A cylinder has a height of 11 inches. Its volume is 4,973.76 cubic inches. What is the radius of the cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
12 inches
Step-by-step explanation:
Given data
Height= 11 inces
Volume= 4,973.76 cubic inches.
The expression for the volume of a cylinder is
V= πr^2h
substitute
4,973.76= 3.14*r^2*11
4,973.76= 34.54r^2
r^2= 4,973.76/ 34.54
r^2= 144
Square root both sides
r=√144
r=12 inches
Find the Prime Factorization of 32, using the Factor Tree.
Answer:
32 = 2x2x2x2x2
Step-by-step explanation:
32 = 2 x 16
16 = 2 x 8
8 = 2 x 4
4 = 2 x 2
Find the number of possible outcomes in the sample space.
A padlock's combination is four digits long.
Please show your work
Answer:
10,000
Step-by-step explanation:
Highest 4 digit number: 9999
Lowest possibility: 0000
9999-0000=9999
The 0000 is 1 number
9999+1=10,000
Answer:
1000 possible combinations
Step-by-step explanation:
For the padlock combination code, each number can be one of 10 (0-9).
This means there are 10 possibilities for the first digit, 10 for the 2nd, 10 for the 3rd, and 10 for the 4th.
If we combine all these possibilities between the different digits we get:
10 x 10 x 10 x 10 = 1000 different combinations.
Hope this helped!
A weight of 270 pounds falls
Answer:
240
Step-by-step explanation:
Answer:
240
Step-by-step explanation:
A completely full cylindrical storage tank of Ski with a diameter of 60 feet and a
height of 50 feet sprung a leak. You are able to catch the liquid in rectangular prisms
with the dimensions 5ft by 6ft by 10ft. How many rectangular prisms are needed?
Justify your answer by writing sentences and showing your work.
Answer:
471Step-by-step explanation:
Volume of liquid in the tank:
V = πr²h = πd²h/4V = 3.14*60²*50/4 = 141300 ft³Volume of each prism:
V = lwh V = 5*6*10 = 300 ft³Number of prisms needed:
141300/300 = 471hiii please help i’ll give brainliest:)
Answer:
Homer
Homer wrote the Odyssey and The Iliad
Answer:
Homer
Step-by-step explanation:
Solve the inequality.
6x + 10 + 10x < 4(4x + 3)
Answer:
X = all #'s
why?
6x+10+10x < 4(4x+3)
Combined liked terms
16x + 10 < 16x +12
you can see that there is X on both sides and the lowest one has a +10 and the highest has a +12 so it will always be greater by 2
Answer:
undeterminate (all real numbers are a solution)
Step-by-step explanation:
1) multiply 4 by 4x and 3
6x + 10 + 10x < 16x + 12
2) added up the terms with x
16x + 10 < 16x + 12
3) add at the two members -16x
10 < 12
4) notice the 10 is ever < 12, so the inhequality is undetermined
The binomial (x + 5) is a factor of x2 + 8x + 15. What is the other factor? (x + 3) (x + 7) (x + 12) (x + 13)
Answer: [tex]x+3[/tex]
Step-by-step explanation:
Given
[tex](x+5)[/tex] is a factor of [tex]x^2+8x+15[/tex] , that is
If [tex]x^2+8x+15[/tex] is divided by [tex](x+5)[/tex], it yields 0 remainder
Solve the quadratic equation
[tex]\Rightarrow x^2+8x+15=0\\\Rightarrow x^2+3x+5x+15=0\\\Rightarrow (x+3)(x+5)=0\\\Rightarrow x=-3,-5[/tex]
Therefore, [tex]x+3[/tex] is another factor of the quadratic equation.
Answer:
x+3
Step-by-step explanation:
its A or first option or (x+3)
What two whole ,postive numbers that have a one -digit answer ehen multiplies and a two digit answer when added
Answer:
The two positive whole number that have a one -digit answer ehen multiplies and a two digit answer when added are 9 and 1
Step-by-step explanation:
The two positive whole number that have a one -digit answer ehen multiplies and a two digit answer when added are 9 and 1
When 9 and 1 are added, we get 10 (two digit number)
When 9 and 1 are multiplied, we get 9 (one digit number)