[tex]y = -2x^2 + 8x + 3[/tex]
Using the model above, it is found that it lands on the ground after 4.35 seconds.The equation of a quadratic function of vertex (h,k) is given by:
[tex]y = a(x - h)^2 + k[/tex]
The vertex is the maximum point, which is (2,11), hence [tex]h = 2, k = 11[/tex]. Then:
[tex]y = a(x - 2)^2 + 11[/tex]
The initial height is of 3 feet, then when [tex]x = 0, y = 3[/tex], and this is used to find a.
[tex]y = a(x - 2)^2 + 11[/tex]
[tex]3 = 4a + 11[/tex]
[tex]4a = -8[/tex]
[tex]a = -\frac{8}{4}[/tex]
[tex]a = -2[/tex]
Then:
[tex]y = -2(x - 2)^2 + 11[/tex]
In standard format, the model is:
[tex]y = -2x^2 + 8x - 8 + 11[/tex]
[tex]y = -2x^2 + 8x + 3[/tex]
It hits the ground when [tex]y = 0[/tex], so:
[tex]-2x^2 + 8x + 3 = 0[/tex]
[tex]2x^2 - 8x - 3 = 0[/tex]
Which has coefficients [tex]a = 2, b = -8, c = -3[/tex]. So
[tex]\Delta = b^2 - 4ac = (-8)^2 - 4(2)(-3) = 88[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + sqrt{88}}{4} = 4.35[/tex]
[tex]x_1 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - sqrt{88}}{4} = -0.35[/tex]
Time is positive, so it lands on the ground after 4.35 seconds.
A similar problem is given at https://brainly.com/question/17987697
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Answer:
thanks for the points........
Answer:
wt f ok?
Step-by-step explanation:
These triangles are similar. Find the missing
length.
Answer:
h=57
Step-by-step explanation:
The triangles seem to have a pattern, which is that the numbers on the left are multiplied by 1.5 to get the numbers on the right. We figured this out by doing 42/28 and 54/36 (which are the corresponding numbers), which would both equal 1.5. Now to find h we would do the opposite of divide which is multiply, we would do 38*1.5 and get 57.
please help meh i dont know the answer
A line passes through the point (2, 4) and has a slope of -5/2
Answer:
y = -5/2 + 12
Step-by-step explanation:
hello if yall can help me please...
Answer:
A. 2
Step-by-step explanation:
4 to 6 to 8 to 10 to 12
what is the differences in length between a 1 1/4 inch butten and a 3/8 inch button
Answer:
7/8
Step-by-step explanation:
Helpppppppp please it’s due today
Answer:
Option B, would be the correct option as she sets it in the attic window. I hope this helps you! :)
Find the unknown sizes of angles:
X=92
X+Y=180
Y=180-92
Y=88
Z=Y=88
:)
Step-by-step explanation:
We have,
x = 92 ( vertically opposite angles) 92 + y = 180 { linear pair}So that ,
y = 180-92y = 88°And ,
y = z ( VOA) z = 88°In a class of 25 students; 15 students like Mathematics, 6 like English and 4
like Spanish. Express as a fraction in its simplest form the students who like
Mathematics.
Help plz
Answer:
3/5
Step-by-step explanation:
we got 15 students who like math in 25 student
the fraction is 15 over 25 , 15/25 , when you simplify by 5 the simplest form gonna be 3 over 5, 3/5For BRAINILY
Please answer fast
Answer:
37
Step-by-step explanation:
S+S+106⁰=180⁰(sum of angles of triangle)
2S=180⁰-106⁰
S=74⁰/2
S=37⁰
Encuentre el valor de x en la siguiente ecuación 6x = 4x + 6
Answer:
[tex]6x = 4x + 6 \\ 6x - 4x = 6 \\ 2x = 6 \\ x = \frac{6}{2} \\ \boxed{x = 3}[/tex]
Answer:
x = 3
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
I will give you brainliest if you solve the math question
Answer:
y = 50, x = 74
Step-by-step explanation:
the total degrees must equal 180. In the left triangle, we are given 80 as in of them. 180-80=100 degrees left in the triangle there are two equal angles left, so we divide 100/2 and get 50, so y=50. In the triangle on the right, there are two equal angles of 53 degrees. So 53x2=106. 180-106= 74 degrees left. x is the only angle left, so x=72
For the function f(x)=5(x+10), find
f −1(x).
Answer: f-1(x) = x/5 - 10
Shortend: f(x)=5(x+10), f-1(x) = x/5 - 10
Steps:
The inverse can be found algebraically by switching x for y and y for x in the equation. You must then isolate y.
[tex]f(x)=5x+10\\y=5x+10\\x=5y+10\\x-10=5y\\\frac{x-10}{5} =y\\[/tex]
So, [tex]f^{-1} (x)=\frac{x-10}{5}[/tex]
What is the slope of the line graphed below
Answer:
mx + y = c slope = - 4 and y - intercept = 2 , then the equation of line is mx + y = c .
Step-by-step explanation:
If I am wrong sorry If I am right mark me brainliest
Determine whether the graphs of the equations are parallel, pependicular, or neither.
1
y = 1/3X + 2
y = 3x - 5
A. parallel
B. perpendicular
C. neither
Answer: perpendicular
Step-by-step explanation: You can do this (of course, you have to know the equations of the pairs of lines under consideration);
For each equation, put in form y = mx + b and compare their slopes (values of m).
If the m's are equal, the two lines are parallel;
if the product of the two m's equals -1, the two lines are perpendicular.
Find the value of x.
nick have collection of 80 cars.3/5 of his toys are bus.the rest are cars and bike.the number of cars are the three time the number of bikes.how many cars are there.
Answer:
24 cars
Step-by-step explanation:
out of 80 toys, 3/5 are buses- 80 * 3/5 is 48 so there are 48 buses
80 - 48 is 32, 32 of the rest of the toys are cars and bikes
we know that there are 3 times as many cars than bikes, so to find out how many cars and bikes there we can do 3n + n, where n is the number of bikes it also equals 4n
32 = 4n; n = 8
there are 8 bikes, so there are 24 cars
I need help please
And thank you
Answer:
-1, 3, and 5
Step-by-step explanation:
When mapping a function the inputs (x), the oval to the left, is the domain. The oval to the right, the output, is the range.
Suppose that 12 inches of wire costs 60 cents at the same rate how many inches of wire can be bought for 25 cents
Answer:
5 inches
Step-by-step explanation:
60÷12=5 cents ( 1 inches of wire )
25÷5=5 inches
if two angle of a right angle triangle are in the ratio 1:2,find them
Answer:
let the angles be x,2x
=>90+x+2x=180
=>3x=90
=>x=30
so, the angles are 30,60
let the angles be x,2x
=>90+x+2x=180
=>3x=90
=>x=30
so, the angles are 30,60
please help (view screenshot)
someone assist me please thank you
Answer:
I am pretty sure thats acute triangle but not 100%
can someone give me the coordinates that each option should be placed at??? hurry please!
Answer:
x = -10
Step-by-step explanation:
-2x - 10y = 20 (plug y=0)
-2x = 20
x = 20/-2
x = -10
Which angle in the isosceles triangles is the biggest?
Answer:
Since the two base angles are congruent (same measure), they are each 70°. If we are given a base angle of say 45°, we know the base angles are congruent (same measure) and the interior angles of any triangle always add to 180°.
Answer:
degrees
Step-by-step explanation:
Evaluate. -1/4(d+1) < 2
Please show how
Answer:
-1/4 (d+1)< 2
(d+1) × -1 < 2×4
(d+1) × -1 < 8
-d - 1 < 8
-d < 8 + 1
-d < 9
d > -9
d = { -8, -7, -6....., 0, 1, 2, 3, 4,....}
Step-by-step explanation:
brainliest plz
Graph the linear equation y = -2x -1
(hope this helps) :)
Step-by-step explanation: in the picture
please give me a brainliest answer
Ashley went to a store and bought 3 items. Each item cost $21. How much did she spend
Answer:
$63
Step-by-step explanation:
Solve for x: 16 = x + 32
Answer:
Step-by-step explanation:
-16
Answer:
x= -16
Step-by-step explanation:
Christopher buys 3 pizzas for £13.56. If all of the pizzas are the same price, how much does one pizza cost? Give your answer in pounds (£).
Answer:
£4.52
Step-by-step explanation:
£13.56/3
not sure how to do these. i need help with 13! needing it to be reduced just like y should be 8
Answer:
I'm not sure 710
Step-by-step explanation:
I'm not sure
Answer:
#14
y=5
x=14
Step-by-step explanation:
I did 14 for you
the two expressions with x equal each other since they are on the same side of their line, similar to eachother. Then plug in x into one of those expressions and do 180- your answer to get the angle for one of the y expressions since its on the other side of the line. both angles have to add up to 180.