Answers
Answer:
The ball reached its maximum height of ([tex]11\ yards[/tex]) in ([tex]1\ second[/tex]).
Step-by-step explanation:
This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.
The first step in completing the square is to group the quadratic and linear term:
[tex]h(t)=-5t^2 + 10t + 6\\\\h(t) = (-5t^2 + 10t) + 6[/tex]
Now factor out the coefficient of the quadratic term:
[tex]h(t)=-5(t^2 -2t) + 6[/tex]
After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:
[tex]h(t) = -5(t^2 -2t) + 6\\\\h(t) = -5(t^2 -2t + 1 -1 ) + 6[/tex]
Now take the balancing term out of the parenthesis:
[tex]\\\\h(t)=-5(t^2 -2t + 1) + 6 + ((-1)(-5))[/tex]
Simplify:
[tex]h(t) = -5(t^2 -2t + 1) + 6 + 5\\\\h(t) = -5(t-1)^2 + 11[/tex]
The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is:
[tex](1, 11)[/tex]
Related Questions
A square painting has a side length of 13 inches.
What is the area of the painting?
Answers
Answer:
169
Step-by-step explanation:
13*13=169
Answer:
169
Step-by-step explanation:
length x width = area
since it is a square, all sides are equal.
13 x 13 = 169
Find KJL (5x-2) (9x-62)
Answers
Answer:
45x^2-328x+124
Step-by-step explanation:
what is the intersection point of function f and g
Answers
Answer:3,15) and (-1.5, 1.5)
Step-by-step explanation:
If g(x) = 2x² - 3
-6x+5y=1
6x+4y=-10
what is the answer to this problem by elimination
Answers
Answer:
x= -1 and y= -1
Step-by-step explanation:
Answer:
(-1,-1)
Step-by-step explanation:
-6x+5y=1
6x+4y=-10
Add the two equations together to eliminate x
-6x+5y=1
6x+4y=-10
---------------------
9y = -9
Divide by 9
9y/9 = -9/9
y= -1
Substitute back into one of the equations to find x
-6x+5y=1
-6x +5(-1) = 1
-6x -5 = 1
Add 5 to each side
-6x -5+5 = 1+5
-6x = 6
Divide by -6
-6x/-6 = 6/-6
x = -1
(-1,-1)
A test has 25 true/false questions. If 64% of the answers are true, how many of the test questions are true?
Answers
Answer:
16
Step-by-step explanation:
First, let's find 64% of 25. We do this and get:
[tex]\frac{64}{100}\cdot25=\frac{1600}{100}=16. \text{ so our answer is \boxed{16 \text{ problems are true}}}[/tex]
−6 7/8÷(−3 3/4)
Help me pls :{
Answers
---:
convert both into improper fractions
-55/8 and -15/4
turn both into a positive bc two negatives
then flip 15/4 to 4/15
simplify
11/2 * 1/3 =
11/6
hope this helps
Which number is in the solution set of this equation? 7x − 9 = 40
Answers
Answer: the answer is 7
Step-by-step explanation: add 9 to both sides, eliminating -9 so now you have 7x=49 divide both by 7 and you get x= 7 check it by inputing 7 for x, 7(7)-9=40
7(7)=49 next 49-9= 40
it checks out, so x= 7
find the 9th term of the geometric sequence 6,-24,96...
Answers
Answer:
A9 = 393216
Step-by-step explanation:
the first thing that will help you solve this question is finding the common ratio between each terms
the first thing that I like to do that usually helps is to take the second term (-24) and divide it by the first term (6) --> this will usually help you spot the common ratio fairly quickly
in your case, the common ratio is -4
- you can also check this by following my note above and then multiplying the second term by the common ratio to see if it matches the third term, which it does!
so now you can go about this two different ways
1. solve directly for the 9th term
2. use the nth term formula for geometric sequences
METHOD 1:
if you continue to multiply by -4 to solve for each term you would end up with:
6, -24, 96, -384, 1536, -6144, 24576, -98304, 393216
and you will recieve 393216 as your answer
METHOD 2:
the nth term formula is An = A1*r^(n-1)
where An = the nth term of the sequence
A1 = first term of the sequence (6)
and r = common ratio
using this formula, you would get:
A9 = 6(-4)^8
A9 = 393216
I hope this helped :)
How many triangles can a heptagon be divided into? 3 5 4 6
Answers
Answer:
5 triangles.
Step-by-step explanation:
Answer:
5 or 4
Step-by-step explanation:
find the perimeter of the polygon
Answers
So it should be 22
4+4+7+7 = 22
Each marble bag sold by Henry's Marble Company contains 5 purple marbles for every 4 orange marbles. If a bag has 20 orange marbles, how many purple marbles does it contain?
Answers
Answer:
25
Step-by-step explanation:
If it's 5 for every 4 and the bag has 20, 4*5 = 20 and you'd have to do that to the 5 as well to get 5*5=25.
10. Find the slope of the line.
Answers
Answer:
-2/1
Step-by-step explanation:
Answer:
67
Because I just know
What does the discriminant determine?
Answers
Plx help me! Brainlist!
Answers
Answer:
Its A. have a good day
Step-by-step explanation:
Hegarty please help me
Answers
Answer:
wait let me try and see this carefully and then I will help you
the radius of a circle is 8 what is the area of the circle? pls show work
Answers
Answer:
201.06
Step-by-step explanation:
A=πr2=π·82≈201.06193
Answer:
201.14 ≈ 201 unit²
Step-by-step explanation:
Area of circle = πr², where π is either 3.14 or 22/7 or 355/113. Mostly it is 22/7.
=> area of circle = (22/7) (8)² unit²
=> area of circle = (22 x 64)/7 unit²
=> area of circle = 201.14 unit²
If we take π = 3.14
=> area of circle = (3.14)(8)² = 200.96 unit²
A toy manufacturer is shipping its newest product, an interactive talking globe, to a major toy store. The packaging for the globe is a rectangular prism that measures 2512 2512 inches high, 18 inches long, and 18 inches wide. The boxes for the globes are packaged into shipping crates that hold 8 globes each. What is the minimum volume of one shipping crate? Explain your answer in the space provided.
Answers
Answer:
6 511 104 in³
Step-by-step explanation:
Since we have 1 crate and 8 boxes fit into one crate.
So, volume of one crate, V' = 8 × volume of 1 box, V
Since the box is a rectangular prism of sides 2512 inches high, 18 inches long, and 18 inches wide, its volume, V = lwh where l = length of prism, h = height of prism and w = width of prism.
So, V = lwh = 18 in × 18 in × 2512 in = 813 888 in³
So, V' = 8 × 813 888 in³ = 6 511 104 in³
So, the minimum volume of the crate is 6 511 104 in³
can someone please help me with this? I'll mark brainliest for the right answer
Answers
What property is being used in 6 x (3+8) = 6 x 3 + 6 x 8?
Answers
Answer:
The distributive property
Step-by-step explanation:
[tex] \sqrt[4]{48x}^{4} [/tex]
Someone please help me this is so confusing, Please no links and do it step-by-step Thank you!!!
Answers
Answer:
48x
Step-by-step explanation:
[tex](\sqrt[4]{48x} )^{4}[/tex] = [tex]\sqrt[4]{(48x)^{4} }[/tex] = 48x
solve for x
x^9=12^2x12^7
Answers
Answer:
12Step-by-step explanation:
Hi!
Here is your answer,
I will explain in step by step,
[tex] {x}^{9} = {12}^{2} \times {12}^{7} [/tex]
Here we can simplify this further using this law,
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
So we will get,
[tex] {x}^{9} = {12}^{7 + 2} \\ {x}^{9} = {12}^{9} [/tex]
Since the powers are same we can cancel it out and we will get,
[tex]x = 12[/tex]
(Hope this answer helped :))
Engineers are designing a rollercoaster that at one point goes underground. The rollercoaster’s path underground is a large curve. The engineers use the function shown to model the elevation, ܧ ,in feet and ݐ , time, in seconds, of the rollercoaster’s path while it is underground.
Answers
Answer:
One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:
(x + 3)(x – 3) = 0. Using the zero factor property, you know this means x + 3 = 0 or x – 3 = 0, so x = −3 or 3
Step-by-step explanation:
One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:
(x + 3)(x – 3) = 0. Using the zero factor property, you know this means x + 3 = 0 or x – 3 = 0, so x = −3 or 3
Quadrilateral MNPQ is shown on the grid below.
What is the area, in square units, of the quadrilateral?
A) 182 square units
B) 4550 square units
C) 9100 square units
D) 91 square units
Answers
Answer:
42 square units
Step-by-step explanation:
Find the diagram attached
Area of the diagram = Area of the triangle + Area of rectangle
Area of rectangle = Length * Width
Area of rectangle = 3 * 6
Area of rectangle = 18 square units
Area of triangle = 1/2 * base * height
Get the base of the tringle using the pythagoras theorem;
b^2 = 10^2-6^2
b^2 = 100 - 36
b^2 = 64
b = 8units
height = 6 units
Area of the triangle = 1/2 * 8 * 6
Area of the triangle = 48/2
Area of the triangle = 24 square units
Area of the figure = 18+24
Area of the figure = 42 square units
A footballer attempted 30 goals during a match and only makes 12. What fraction of the attempted goals did he make?
Answers
Answer:
2/5
Step-by-step explanation:
you have to reduce each number by 6
Answer: 12/30 or 2/5
pls help will mark brainliest if correct
Answers
Answer:
its D Please put me as brain eat if correct
Por una tubería de 4.02 cm de diámetro circula agua a una velocidad de 1.9 m/s. En
una parte más estrecha el diámetro es de 3.61 cm. ¿Cuál es la velocidad que llevará el
agua en ese punto?Por una tubería de 4.02 cm de diámetro circula agua a una velocidad de 1.9 m/s. En
una parte más estrecha el diámetro es de 3.61 cm. ¿Cuál es la velocidad que llevará el
agua en ese punto?
Answers
Answer:
7.91
Step-by-step explanation:
I just took the quiz and i got an A
find the value of given expression
[tex] \sqrt{60 \times 60} [/tex]
Answers
Step-by-step explanation:
it is 3.600 this is my answer
Answer:
√(60×60)=√60²=±60 is your answer
Find the area and perimeter pls!!!
Answers
P = a + b + c =4.81 + 8.8 + 8.42 = 22.03
HURRY!! I need the answer. The assignment closes soon.
Answers
Answer: option 3
Step-by-step explanation:
evaluate the expression if g-=2, r=3, and t=. 3ab+c^2/a
Answers
Answer:
3ab+(c^2)/a
you can't really solve this because g and r is not in the equation.