[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
Victor has 2 times as many trophies as dean . Together, victor and Dean have 27 trophies . How many trophies does victor have?
Answer:
18
Step-by-step explanation:
9 + 18 = 27
9 x 2 = 18
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.
Step-by-step explanation:
y coordinate
m = slope
x = x coordinate
b = y intercept
4/s-3 + s/2 = -2
Need help please
Step-by-step explanation:
Given equation is 4/(s-3) + (s/2) = -2
=> [(4×2)+s(s-3)]/2(s-3) = -2
=> (8+s²-3s)/(2s-6) = -2
=> 8+s²-3s = -2(2s-6)
=> 8+s²-3s = -4s+12
=> s²-3s+8+4s-12 = 0
=> s²+s-4 = 0
The standard form is s²+s-4 = 0
Tổng các góc của tứ giác bằng bao nhiêu
Answer:
tổng các góc của tứ giác bằng 360 độ
Step-by-step explanation:
ha? what language is that?
Find the slope of the line that passes through (10,10) and (1,2)
Answer:
8/9
Step-by-step explanation:
[tex]m = \frac{10 - 2}{10 - 1} = \frac{8}{9} [/tex]
A functionf(x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
Answer:
y = -1/2x + b meaning f(x) = -1/2x + b
Step-by-step explanation:
Use two points on the graph that you can find the value of or use Slope = raise/run
let use points (2,0) and (0, 1)
slope = (change in the y-value)/(change in the x-value.
slope = (1 - 0)/(0 - 2)
slope = 1/-2 or -1/2
Or starting at point (2, 0) the run(x movement) = -2 and the raise is 1.
slope = raise/run
slope = 1/-2 or -1/2
Using one point (2,0) and the slope of -1/2, substitute into the slope intersect form, y = mx + b, and solve for "b" .
y= mx + b
0 = -1/2(2) + b
0 = -1 + b
1 = b
Now write your equation: y = mx +b where m = -1/2 and b = 1
y = -1/2x +b
A dog kennel charges a daily boarding rate as shown on the graph. use the information to mark 5-8 as true or false. if false, rewrite the statement correctly. 1. The dog kennel charges $60 per day. 2. The equation y = 30x can represent the graph. 3.Third is It costs $200 to board a dog for 7 days 4. The graph will contain the coordinate (9,270) Please give me all answers to all questions or i will go into trouble
The relationship between the cost charged for the daily boarding of dogs
by the kennel is a directly proportional relationship.
The correct responses are;
1. The dog kennel charges $60 per day is; False
Correct statement; The dog kennel charges $30 per day
2. The equation y = 30·x can represent the graph; True
3. It costs $200 to board a dog for 7 days is; False
Correct statement; It costs $210 to board a dog for 7 days
4.The graph will contain the coordinate point (9, 270); True
Reasons:
Points on the graph of the given graph of the Cost to Number of days are;
(2, 60), (4, 120)
The slope of the graph is [tex]m = \dfrac{120 - 60}{4 - 2} = 30[/tex]
Equation of the graph is therefore; y - 60 = 30·(x - 2)
Which gives;
y = 30·x - 2×30 + 60 = 30·x
The equation of the graph is; y = 30·x
Therefore, the statement;
2. The equation y = 30·x can represent the graph is; TrueThe cost of the dog kennel a day is given by the value of 'y', when x = 1, as
follows;
Cost per day, y = 30 × 1 = 30
The cost per day = $30 per day
Therefore;
1. The dog kennel charges $60 per day is; FalseThe correct statement is; The dog kennel charges $30 per day
3. The statement; It costs $200 to board a dog for 7 days is; FalseThe amount it costs to board a dog for 7 days is y = $30×7 = $210
Therefore, the correct statement is; It costs $210 to board a dog for 7 days
4. When x = 9, we have; y = 30 × 9 = 270Therefore, the statement; the graph will contain the coordinate point (9, 270) is; True
Learn more here:
https://brainly.com/question/5281177
Can someone please show me y=2x-2 and x=4 on a graph please. ( IF U CAN PLEASE SHOW ME WHERE THE LINES GO THROUGH EACH OTHER ON A GRAPH)
i’m just stuck on #6, is it d or c???
FRANK has a paper clip.it has a mass of 9g and a volume of 3cm3.what is its density?
Answer:
3 g/cm³Step-by-step explanation:
The density of a substance can be found by using the formula
[tex]density = \frac{mass}{volume} \\[/tex]
From the question we have
[tex]density = \frac{9}{3} = 3 \\ [/tex]
We have the final answer as
3 g/cm³Hope this helps you
Let f(x) = x − 3 and g(x) = x + 11. Find f(x) ⋅ g(x).
x2 − 8x − 33
x2 − 8x + 14
x2 + 8x + 14
x2 + 8x − 33
Answer:
D) x^2 + 8x - 33
Step-by-step explanation:
I took the quiz and got a 100%
50 POINT QUESTION!!!!
f(x)=12x^(2)+4x-5
find the zeroes of the function...
Answer is in picture below
:)
In Pedro’s rose garden, 9 of the rose bushes are blooming and the other 6 rose bushes are not blooming. what is the ratio of the number of bushes that are not blooming?
Answer:9:6
Step-by-step explanation:
Can y'all help me this question ASAP this all I need
WILL GIVE BRAINLIEST TO ANSWER
Answer:
A , D , E
Step-by-step explanation:
Substitute x = 2 into f(x) and check if the result is 4
(a)
f(2) = 2² = 4 ← then f(2) = 4
(b)
f(2) = 2 + 6 = 8 ≠ 4
(c)
f(2) = 4(2) + 2 = 8 + 2 = 10 ≠ 4
(d)
f(2) = 2² = 4 ← then f(2) = 4
(e)
f(2) = 8(2) - 12 = 16 - 12 = 4 ← then f(2) = 4
C. Directions: Copy and answer. Write in the circle the final sum of
the given number.
1.
98
2.
40
3.
123
-13
47
150
70
1180
-59
321
1-300
다.
1
5.
1326
6.
109
66
11-51
39
139
7
7433
88
77
Answer:
98
Step-by-step explanation:
Please help me solve this ASAP please !
This is a Reflection :) Have a great day !
Kim has no more than $500 to spend on home repairs. HandyMan Co is charging her $125 for supplies needed and $25 per hour. Write and solve an inequality to show how many hours of repair she can afford.
Mathematics Ratio
Help plz
Answer:
480
Step-by-step explanation:
Check out the solution
=
?
(5
4
⋅b
−10
)
−6
[tex](5^{4} *\frac{1}{b^{10} }) ^{-6}[/tex]
[tex](\frac{5^{4} }{b^{10} } )^{-6}[/tex]
[tex]\frac{b^{60} }{5^{24} }[/tex]
Kayla bought 16 bagels. Each bagel cost $1.50. She paid a total of $20. Write an equation to determine how many bagels she bought.
express -121 in simplest form
Answer:
An expression is in simplest form when no terms can be combined. To express 3 + (2 × 5) in simplest form: First: perform the operation within parantheses. Next: perform the addition. thank me later
kuisssss
hi how are you?
[tex] \sf {3}^{2} \div 9 = [/tex]
pakai cara
Answer:
1
Step-by-step explanation:
[tex] {3}^{2} \div 9 = \\ =(3 \times 3) \div 9 \\ = 9 \div 9 \\ = 1 [/tex]
Moga Membantu ^-^
Answer:
The solution is 1
Step-by-step explanation:
3²÷9
= 9÷9
= 1
I don't understand this question can someone help me with this please, please explain!! and thank you for the help!! If u dont know try your best :D
Answer:
1. 4x=36
2. x+3 = 15
Step-by-step explanation:
so for 1 if one cupcake is $4.00 that means multiplying it by x gets you $36.00
and the 4 next to the x means multiplyand x is sam and 15 is marco sam is 3 years younger so x+3=15 and x being 12 <3 hope this helps
8 divided by 1 4/5 Arithmetic operation
Answer:
4.4
Step-by-step explanation:
Justify each step
-12p+45-7p
Answer:
Given, Associative, Commutative, Associative, Addition
Step-by-step explanation:
-12p + 45 -7p Given
-12p + (45 - 7p) Associative
-12p + (-7p + 45) Commutative
(-12p + -7p) + 45 Associative
-19p + 45 Addition
plsss help me with this:(((
Answer:
[tex] \frac{2 {a}^{2} }{3 {b}^{3} } \div \frac{6 {a}^{3} }{5 {b}^{2} } = \frac{2 {a}^{2} }{3 {b}^{3} } \times \frac{5 {b}^{2} }{6 {a}^{3} } = \frac{5}{9ab} \\ \\ \frac{ {x}^{2} - 5x + 6}{ {x}^{2} - 6x + 9} + \frac{4x - 12}{{x}^{2} - 6x + 9} \\ = \frac{{x}^{2} - 5x + 6 + 4x - 12}{{x}^{2} - 6x + 9} \\ = \frac{{x}^{2} - x - 6}{{x}^{2} - 6x + 9} \\ = \frac{(x - 3)(x + 2)}{(x - 3)(x - 3)} \\ = \frac{(x + 2)}{(x - 3)} \\ \\ \frac{3a}{a - b} - \frac{a + 2b}{a - b} \\ = \frac{3a - a + 2b}{a - b} \\ = \frac{2a - 2b}{a - b} \\ = 2\frac{a - b}{a - b} \\ = 2[/tex]
how would I solve this??
Answer:
y = 140
Step-by-step explanation:
you'd do:
y=25(7)-35
y=175-35
y=140
to double-check your math:
140 = 25(7)-35
both sides will equal 140 (or the same value) if done properly
Find the slope of the line
(18, 7) (8, 10)
Taylor has $150 to spend on small canvases and paints for her art classes. The art supply store sells a four-pack
of small canvases for $4.00 and paints for $6.25, including tax.
Which inequality represents this situation where is the number of four-packs of canvases and p is the number of
paints Taylor purchases?
O4c+ 6.25p < 150
O 40+ 6.25 > 150
O 6.25c+ 4p > 150
O 6.25c +4p < 150
Answer:A
Step-by-step explanation: