For the given statement f(x)= a(x-h)² + k is the vertex form of a parabola.
If a < 0, h> 0 and k < 0 Option B is correct.
Vertex of a Parabola
The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.Given that:
f(x)= a(x-h)² + k
If a < 0, h> 0 and k < 0 then
f(x) = -1 (x - 1)^2 - 1
= -1([tex]x^{2} + 1^{2} - 2x[/tex]) - 1
= [tex]-x^{2} -1 + 2x[/tex] - 1
f(x) = -([tex]x^{2} - 2x + 2[/tex])
while making graph using the equation , we can find the vertex of f(x) is in quadrant 4 and has no y-intercepts.
Thus , the option B is correct.
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I’m having trouble with geometry, if anyone could help me i would appreciate it :)
You went shopping at a mall and bought a t shirt for $8.99 and a baseball hat for $12.99. What is the total cost of the items with 7.5% tax?
A. $21.98
B. $1.65
C. $38.46
D. $23.63
Find the sum of 318 nanoseconds and 96 microseconds
Step-by-step explanation:
1 microsecond is equal to 1000 nanoseconds.
Knowing this, we can multiply 96*1000 to get 96,000.
Then just add the additional 318 nanoseconds.
96,000+318=96,318 nanoseconds.
What are the solution to the equation (x+3)^2=7
Step-by-step explanation:
see attached. hope it's helps
If a car is traveling at 80 feet/second with 22 inch tires, how fast are the tires spinning in revolutions per second?
Answer:
43.6
Step-by-step explanation:
Harry has 25 sweets.
He gives 11 of the sweets to Nadia.
What fraction of the 25 sweets does Harry have now?
Answer: 14
Step-by-step explanation:
1. Harry has 25/25 sweets
2. Nadia takes 11/25 sweets
3. Your left with 14/25
Solve for x using the Quadratic Formula: x2 + 4x + 4 = 0 x = −2
Answer:
x=-2
Step-by-step explanation:
x^2+4x+4 = 0
(x+2)(x+2) = 0
x+2=0
x=-2
what is the x-intercept of the graph 4x-6y=12
Can you guys help me with this problem
It’s in the picture
Answer:
74
Step-by-step explanation:
Answer:
do length x with for both shapes then add together
Step-by-step explanation:
hope this helps
Can someone help me with this. Will mark brainliest.
Complete the recursive formula of the arithmetic sequence -3, -1, 1, 3,...
b(1)= "answer"
b(n)=b(n-1)+ "answer"
Given:
The given arithmetic sequence is:
[tex]-3,-1,1,3,...[/tex]
To find:
The recursive formula of the given arithmetic sequence.
Solution:
We have,
[tex]-3,-1,1,3,...[/tex]
Here, the first term is -3. So, [tex]b(1)=-3[/tex].
The common difference is:
[tex]d=-1-(-3)[/tex]
[tex]d=-1+3[/tex]
[tex]d=2[/tex]
The recursive formula of an arithmetic sequence is:
[tex]b(n)=b(n-1)+d[/tex]
Where, d is the common difference.
Putting [tex]d=2[/tex], we get
[tex]b(n)=b(n-1)+2[/tex]
Therefore, the recursive formula of the given arithmetic sequence is [tex]b(n)=b(n-1)+2[/tex], where [tex]b(1)=-3[/tex].
67. There are 15 clarinet players, 12 flute
players, and 7 saxophone players in a
marching band. How many ways can the
band director create a trio consisting of
one clarinet player, one flute player, and
one saxophone player?
A. 34 ways
B. 187 ways
C. 1,260 ways
D. 1,500 ways
Answer:
A
Step-by-step explanation: add 15+12+7
if im write can i get a brainliest? plss:>
The band director can create a trio in 1,260 different ways.
Hence, option C is correct.
Use the concept of permutations,
The formula for permutations is,
⇒ [tex]^{n}P_{r}[/tex] = n! / (n - r)!
Where n is the total number of items and r is the number of items we are selecting.
So in this case, we have,
⇒ n = 15 clarinet players
⇒ n = 12 flute players
⇒ n = 7 saxophone players
⇒ r = 1 clarinet player,
1 flute player, and 1 saxophone player
To find the number of ways we can create a trio with one player from each instrument, we need to calculate,
⇒ ([tex]^{15}P_{1}[/tex]) x ([tex]^{12}P_{1}[/tex]) x ([tex]^{7}P_{1}[/tex])
⇒ ([tex]^{15}P_{1}[/tex]) = 15! / (15 - 1)!
= 15! / 14!
= 15
This represents the number of ways we can choose one clarinet player out of 15.
([tex]^{12}P_{1}[/tex]) ) = 12! / (12 - 1)!
= 12! / 11!
= 12
This represents the number of ways we can choose one flute player out of 12.
[tex]^{7}P_{1}[/tex] = 7! / (7 - 1)!
= 7! / 6!
= 7
This represents the number of ways we can choose one saxophone player out of 7.
So the total number of ways we can create a trio consisting of one clarinet player, one flute player, and one saxophone player is,
⇒ 15 x 12 x 7 = 1,260
Therefore,
The band director can create a trio in 1,260 different ways.
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If y varies inversely with x and y = 8 when x = 10, then what is the constant of variation?
Answer:
Constant Variation = 80Step-by-step explanation:
Here,
Said that x and y vary inversely ,
So,
Then an increase in x causes corresponding decrease in y and vice-versa then to find the constant k will be:
xy = kHence,
Here y = 8 and x = 10
So their constant will be,
x × y = k
=> k = 8 × 10
=> k = 80
Therefore, the required constant is 80 (Ans)
HELP!!! answer quickly pls
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Each of the green lines has 3 times the length of the corresponding blue line. Thus the dilution factor is 3.
A rectangle has an area of 24 cm2. Function f gives the length of the rectangle, in centimeters, when the width is w cm.
Determine if each value, in centimeters, is a possible input of the function.
3
Answer:
Input is the value of w and the function f = 24/w as length x breadth = area of rectangle
Heart if this helped
I need help with these question! Please do step by step-
Number of bags of chocolate chip cookies = x = 0.133 bags
Number of bags of walnuts = 7.7 bags
For the people that are trying to help me, is this good?
Answer:
369.03
Step-by-step explanation:
The figure is a pyramid with a rectangular base
The formula is A+1/2ps
A=130 (Area of the base)
p=46 (perimeter of the base)
s=15 (slant height)
Haha posting the pics of me again cuz why not
1/10
for me i pick 5/10
Answer:
Step-by-step explanation:
10/10 cause everyone is
Answer:
AA by isaiah rashad
Step-by-step explanation:
good song
Just met a boy, just met a boy when He could over in my play pen♀️
If you want it I'm going to va va vroom vroom
Answer:
Um what
Step-by-step explanation:
simplify (2x^2+3)(x+4
Answer:
23+32−5+12 is the equaequation simplified
Step-by-step explanation:
Find the perimeter of the
polygon if ZB = ZD.
11.5 cm
B
D
12.5 cm
13.5 cm
Answer:
100cm
Step-by-step explanation:
From the given diagram;
Perimeter of the polygon = AB + BC+ CD + DA
Perimeter of the polygon = 11.5 + 12.5 + 12.5 + 13.5 + 13.5 + 12.5 + 12.5 + 11.5
Perimeter of the polygon = 24 + 26 + 26 + 24
Perimeter of the polygon = 50 + 50
Perimeter of the polygon = 100cm
Hence the Perimeter of the polygon is 100cm
Answer:
100 cm
Step-by-step explanation:
PLEASE HELP ME ANSWER THESE QUESTIONS. NO LINKS OR U WILL B REPORTED. ILL GIVE U THE BRAINLIEST TY!
A. Is there a more appropriate SI unit of measure to use to determine the surface area of the
playground equipment? Explain.
B. What would be a more appropriate imperial unit of measure for the surface area of this
playground equipment?
Answer:
A: Explanation: The surface area of a 3-D object is the sum of all the areas of all the 2-D surfaces of the object; so, its unit is the same as that of area. The SI unit of area is square metre (m2)
Please mark my answer as brainliest for further answers :)
Can someone help me please ?
Please help me, I'm behind and my teacher is making us take a quiz that I don't know anything about T_T
LMNP is rotated 180* clockwise around the origin.
Answer:
D
Step-by-step explanation:
If a shape is rotated 180* clockwise around the origin, then it is basically being flipped around which means that the current coordinates would be the opposite of what they currently are. So (3,4) would be (-3, -4).
I think that is the right answer but I'm not 100% sure sorry!
help pleaaaaaaaaaaaaaaaaaaaaaase
Answer:
26.85 in
Step-by-step explanation:
5+7+7 = 19
C 2πr/2 = 7.85
19+7.85 = 26.85
tombstone and bury me.. by the river they'll carry me. finally I been resting in peace.. finally, finally..
Answer:
rhymy
Step-by-step explanation:
scrieți divizorii întregi ai numerelor 6,9,15
Answer:
`15
Step-by-step explanation: i think
I'll give 20pts and Brainliest!
Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rectangle. The square plot of land has a side length of 6x³ feet, and the rectangular plot of land has a length of 3x⁵ feet and a width of 7x² feet. Use the properties of exponents to determine the expression that represents the area for each plot of land. Then analyze which plot of land has a larger area if x is 3.
The square plot of land has a larger area when x is 3.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To find the area of the square plot, we can use the formula for the area of a square: A = [tex]s^2,[/tex] where s is the length of a side of the square. In this case, the side length is 6x³ feet, so the area of the square plot is:
A = [tex](6x³)^2 = 36x^6[/tex]square feet
To find the area of the rectangular plot, we can use the formula for the area of a rectangle: A = lw, where l is the length of the rectangle and w is the width. In this case, the length is 3x⁵ feet and the width is 7x² feet, so the area of the rectangular plot is:
A = (3x⁵)(7x²) = 21x⁷ square feet
To analyse which plot of land has a larger area if x is 3, we can substitute x = 3 into the expressions for the areas of the plots:
Area of square plot[tex]= 36(3)^6[/tex] [tex]= 11664[/tex] square feet
Area of rectangular plot =[tex]21(3)^7 = 5103[/tex] square feet
Therefore, the square plot of land has a larger area when x is 3.
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Find the area of the shaded region. Round your answer to the nearest tenth.
5 in.
Answer:
10 is the number
Step-by-step explanation:
How many solutions does the equation 4x-7(x-2)=3x+2 have?
Answer:
one solution, x=2
Step-by-step explanation:
brainliest?