Answer:
The function which represents the graph is:
[tex]y=-\left(x\:-\:2\right)^2+\:3[/tex]
Hence, option B is correct.
The graph is also attached.
Step-by-step explanation:
From the graph, it is clear that:
The vertex = (2, 3)
The y-intercept = (0, -1)
Let us check the equation
[tex]y=-\left(x\:-\:2\right)^2+\:3[/tex]
Determining the y-intercept:
The value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
substituting x = 0 in teh equation
[tex]y=-\left(x\:-\:2\right)^2+\:3[/tex]
[tex]y=-\left(0\:-\:2\right)^2+\:3[/tex]
[tex]y=-2^2+3[/tex]
[tex]y=-4+3[/tex]
[tex]y=-1[/tex]
Thus,
The point representing the y-intercept is: (0, -1)
Determining the vertex:
The vertex of an up-down facing parabola of the form ax² + bx + c is:
[tex]x_v=-\frac{b}{2a}[/tex]
As the equation is
[tex]y=-\left(x\:-\:2\right)^2+\:3[/tex]
Rewriting the equation [tex]y=-\left(x\:-\:2\right)^2+\:3[/tex] in the form ax² + bx + c:
[tex]y=-x^2+4x-1[/tex]
The Parabola params are:
[tex]a=-1,\:b=4,\:c=-1[/tex]
Thus,
[tex]x_v=-\frac{b}{2a}[/tex]
[tex]x_v=-\frac{4}{2\left(-1\right)}[/tex]
[tex]x_v=2[/tex]
Now plug in [tex]x_v=2[/tex] in the equation to find [tex]y_v[/tex]
[tex]y_v=-x^2+4x-1[/tex]
[tex]\:y_v=-\left(2\right)^2+4\left(2\right)-1[/tex]
[tex]y_v=-4+8-1[/tex]
[tex]y_v=3[/tex]
Therefore, the vertex of the equation is: (2, 3)
Hence, the function which represents the graph is:
[tex]y=-\left(x\:-\:2\right)^2+\:3[/tex]
Hence, option B is correct.
The graph is also attached.
Help a sista oooouuuttt!!!
Volunteers recently planted a new tree in the town square, and its leaves are doubling in number each month. This
will last for only 3 more months, until the end of summer. If the tree began with 246 leaves, how many leaves will it
have before autumn?
Answer:
1968
Step-by-step explanation:
246×2=492(First month)
492×2=984(Second month)
984×2=1968(Third month)
Length of x
A.6
B.10
C.6.2
D.8
2/12 + 5/8 help me please
Answer:
19/24
Step-by-step explanation:
Write using an exponent.
–5 • –5 • –5 • –5
A. (–4)5
B. 4–5
C. –54
D. (–5)4
Answer:
D
Step-by-step explanation:
Is the circumference of a circle that the diameter is 9.4 cm
Answer:
To find the radius we must multiply by two to get 18.8
Then we multiply 18.8 for PIEEEEEE
3.14x18.8= 59.03
Step-by-step explanation:
I hope this helps!!!!! Please mark me brainliest.
The equation p = −5x2 + 100x − 250 models the profit p in dollars from selling pizza, where x is the price per pizza in dollars. What is the highest price you can charge per pizza to profit $100?
The highest price per pizza in a profit of $100 is approximately $15.48
The profit equation is given by:
p = -5 [tex]x^2[/tex] + 100x - 250
Substitute p = 100 and solve for "x":
100 = -5 [tex]x^2[/tex]+ 100x - 250
To solve this quadratic equation, it can be rearranged it to standard form [tex](ax^2 + bx + c = 0)[/tex]
[tex]5x^2- 100x + 350 = 0[/tex]
Now, we can solve the quadratic equation using the quadratic formula:
[tex]x = \dfrac{(-b\pm \sqrt ({b^2 - 4ac)}}{2a}[/tex]
In our equation, a = 5, b = -100, and c = 350. Substitute these values into the formula:
x =[tex]\frac{(\sqrt{(-100)^2 - 4 \times 5 \times 350}}{2\times5}[/tex]
x= [tex]\dfrac{{100 \pm\sqrt{3000}}}{10}[/tex]
Thus, the two possible solutions for "x":
[tex]x_1[/tex] =[tex]\dfrac{100 + \sqrt{3000}}{10}[/tex]
[tex]x_2[/tex] =[tex]\dfrac{100 - \sqrt{3000}}{10}[/tex]
Calculating the values:
[tex]x_1[/tex]≈ 15.48
[tex]x_2[/tex] ≈ 4.23
The highest price per pizza that results in a profit of $100 is approximately $15.48 (rounded to two decimal places).
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Janet has a bag of marbles. The bag contains 10 blue, 5 green, and 1 orange marble. She will randomly select 1 marble from the bag. What is the probability that Janet will elect a green marble?
Answer:
5/16
Step-by-step explanation:
Answer:
The probability that Janet will elect a green marble is that if she shake them up and down. When she puts her hand in she has the move her hand around giving her the chance that she might pick a green marble.
Decide whether n = 9 is a solution to
the equation 2+n=7. Write yes or no
Answer:
No. The answer would be n=5
Step-by-step explanation:
You have to subtract the 2 from both sides to cancel it out on the left side. so you would be doing 7-2, not 7+2
PLEASE HELP
What is the gradient of this line?
Answer:
Gradient of the line is 1/2 or 0.5
Step-by-step explanation:
If we use the simple formula
UP divided by ACROSS
Then we can substitute our numbers in. I used the co-ordinates (0,2) and (2,3).
This makes 1/2, because it goes 2 across and 1 up from (0,2) to (2,3).
Answer: 2 (I am not sure if this is correct)
Step-by-step explanation:
11 of 11
The mass of the gold ever mined is 1.65 x 108 kilograms.
The mass of all the silver ever mined is 1.411 x 10 kilograms
How much more silver has been mined than gold?
Give your answer in standard form.
X/5 = -3 x=____ help
Helppppppppppppppppppp I’ll mark you brainlist
Answer:
1
Step-by-step explanation:
its subtracting 5 every step, 11, 6, 1, -4, -9
Answer:
1
Step-by-step explanation:
It does substract 5 every single time so it's
11 , 6 , 1 , -4 , -9 , -14 , -19 and so on.
Devon waxes 1/2 of his car with 1/3 bottle of car wax. At this rate, what fraction of the bottle will Devon use to wax his entire car?
Answer:
2/3 bottle of car wax
Step-by-step explanation:
If Devon waxes 1/2 of his car with 1/3 bottle of car wax then he only has half of his car to finish. Since 1/2 of his car used 1/3 of wax then the other half will only take 1/3 of car wax.
Hope this helps!
CAN YOU HELP ME PLEASE HURRY PLEASE HURRY :(
What is the perimeter 2x+3 as length and x-6 as width
What is the perimeter 2x+3 as length and x-6 as width
P = 2L + 2W
P = 2(2x+3)+2(x-6)
P = 4x+6 + 2x - 12
P = 6x - 6
#CarryOnLearning#LearningIsFunAnswer:
[tex]perimeter = 2(l + b) \\ = 2(2x + 3 + x - 6) \\ = 4x + 6 + 2x - 12 \\ = 6x - 6[/tex]
Please help will give brainliest
Answer:
C, D, F
Step-by-step explanation:
I hope it helps, sorry if any wrong.
Giving out 100 POINTS FOR THIS QUESTION!! Please don’t write nfoenwownw or something like that for the points!! I really need help! I WILL MARK BRAINLIEST!
What are the x-intercepts of the quadratic function shown?
A) (-1, -2)
B) (3,-4) and (-5,-4)
C) (1, 0) and (-3, 0)
D) (0, 1) and (0, -3)
Answer:
C) (1,0), and (-3,0)
Step-by-step explanation:
The parabola intercepts the x axis at points (1,0) and (-3,0).
your answer is
C) (1,0), and (-3,0)
have a good dayyy!
Amy had 60 carrots from her garden, she gives 18 to her friend, and 2 to her rabbits Cottonball. How many does Amy have now?
Answer:
She had 40 carrots.
Step-by-step explanation:
60 - 18 = 42 -2 = 40
Help please the problem is in the picture below.
Answer:
Step-by-step explanation:
C=pi times 4
C= 3.14 times 4
C=12.56
The midpoint of RS is point T. What are the coordinates
of point S?
5
4
3
R (-2,3)
01 - 3
0 1 )
2
1
45 -4 -3 -2 -1
2
3
4
5
X
O (8,4)
(10,-7)
-2
T(4-2)
-3
Answer:
( 10,-7)
i didn't understand what u wrote in choice
The coordinates of the point S of the line RS having midpoint T are found to be (10, -7).
What is mid point?In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
here, we have,
The points that are given to us are R(-2,3) and T(4, -2).
The point T is the mid point of the line segment RS.
If A(a, b) and B(c, d) are the two points then the mid point M of the two points will be,
M = ((a+c)/2), ((b+d/2))
So, using the above modified form of section formula we can find the coordinates of the point S.
Assuming point S to be x and y.
So, putting all the values,
(4, -2) = ((-2+x)/2), ((3+y/2))
Now, solving further, we get,
-1+x/2 = 4
-2+x = 8
x = 10
And,
3 + y = -4
y = -7
So, the coordinates are (10, -7).
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5 2/3 + 7 5/9 ples I nnmed help
Answer:
Step-by-step explanation:
Solution
=5 2/3 + 7 5/9
=3×5+2/3+9×7+5/9
=17/3+68/9
=119/9
=13.22
Hope it helped you.
Jenny cut her pizza into 8 equal slices and ate some of them. Billy cut his
pizza into less than 8 equal slices, but ate the same amount of pizza as
Jenny. Use the circles below to show or explain in words how many slices
Jenny and Billy could have eaten. (2 pts)
Answer:
Billy could have cut his pizza into 7,6,5,4,3,2, or 1 slices of pizza
Step-by-step explanation:
Billy ate less than 8 slices of pizza so billy could have sliced his pizza into any number that is less than 8
HELP ME PLEASE I WILL BE SOOOO THANKFUL
Type the missing number in this sequence:
2, 8, 32, 128, ___ , 2,048
Answer:
512....................
Solve the system
9x^2 + 4(y - 2)^2 = 36
x^2 = 2y
Answer: y = 2 and x = 2
Step-by-step explanation:
[tex]9x^2+4(y-2)^2=36\\x^2=2y[/tex]
First, get the entire thing in terms of y, because you cant solve for two variables at the same time. They gave us the fact that x^2 = 2y
[tex]9(2y)+4(y-2)^2=36\\18y+4(y^2-4y+4)=36\\18y+4y^2-16y+16=36\\4y^2+2y-20=0[/tex]
What two numbers multiply to equal -80 but add to equal 2? That is +10 and -8.
[tex]4y^2+2y-20=0\\(4y^2-8y)+(10y-20)=0\\4y(y-2)+10(y-2=0)\\(4y+10)(y-2)=0\\y=-5/2\\y=2[/tex]
Now solve for x by plugging in y to the easier equation
[tex]x^2=2(-5/2)\\x\neq \sqrt{-5}[/tex]
If I didn't make a mistake, this should be the only answer. In the case of y = -5/2, you would get an imaginary x-value. Therefore y cannot equal -5/2
[tex]x^2=2(2)\\x=2[/tex]
The solution of the expression are,
x = 2.28 , y = 2.62
Or, x = 3.9i , y = - 7.62
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
9x² + 4 (y - 2)² = 36 .. (i)
x² = 2y .. (ii)
Substitute the value of x² from (ii) in (i);
9x² + 4 (y - 2)² = 36
9 × 2y + 4 (y - 2)² = 36
18y + 4 (y - 2)² = 36
9y + 2 (y - 2)² = 18
9y + 2 (y² + 4 - 2y) = 18
9y + 2y² + 8 - 4y = 18
2y² + 5y + 8 - 18 = 0
2y² + 5y - 10 = 0
y = - 5 ± √5² - 4×2×- 10 / 2×2
y = - 5 ± √ 25 + 80 / 2
y = - 5 ± √ 105 / 2
y = - 5 ± 10.24 / 2
y = - 5 + 10.24 / 2
y = 5.24/2
y = 2.62
y = - 5 - 10.24 / 2
y = - 15.24 / 2
y = - 7.62
From (ii);
x² = 2y
x² = 2 × 2.62
x² = 5.24
x = 2.28
x² = 2y
x² = 2 × - 7.62
x² = - 15.24
x = 3.9i
Thus, The solution of the expression are,
x = 2.28 , y = 2.62
Or, x = 3.9i , y = - 7.62
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I WILL GET A ZERO IF I DONT GET THIS RIGHT A) describe each two-dimensional figure cross section that results from slicing each three-dimensional figure
B)describe the two dimensional figure cross section that results from slicing the cylinder number 6 with a vertical cross-section
PLEASE HELP QUICK
Answer:
What is the two dimensional shape that is created when the shape provided is sliced horizontally? Explanation: A horizontal cut is a side to side cut. This shape is a right rectangular pyramid, which has a base of a rectangle and sides in the shape of triangles; thus, a horizontal cut would make a rectangle.
Step-by-step explanation:
what’s the answer (multiple choice) m
Answer: I think it’s A but I’m not really good with square roots.
Step-by-step explanation:
Help me out please!!!! (Operations of Functions) Giving alot of points for this if you answer these both two correctly.
Answer:
1) 20
2) 4
Step-by-step explanation:
1)
I) Substitute t with 2:
2² + 5(2) + 6
II) Simplify/Evaluate:
2² + 5(2) + 6
4 + 10 + 6
14 + 6
20
2)
I) Setup the equation:
g(t) = 5t - 2 = 18
5t - 2 = 18
II) Solve it:
Reorder the terms:
-2 + 5t = 18
Add 2 to each side of the equation:
-2 + 2 + 5t = 18 + 2
Simplify:
0 + 5t = 18 + 2
5t = 18 + 2
5t = 20
Divide each side by 5:
t = 4
Hope I helped :)
find the slope of the line that passing through the points (5,-2) and (5,8)
Answer:
undefined
Step-by-step explanation:
In algebra, what is substitution?
Answer:
In algebra, the operation of substitution can be applied in various contexts involving formal objects containing symbols; the operation consists of systematically replacing occurrences of some symbol by a given value. Substitution is a basic operation of computer algebra.
Step-by-step explanation:
Hope I helped!
what does the intersection of two lines represent
Answer:
the solution for the two functions
Step-by-step explanation:
the coordinate that satisfies both equations