Answer:
[tex]\huge\boxed{\text{1. } h(t) = -5(t-3)^2 + 45}[/tex]
[tex]\huge\boxed{\text{2. 3 seconds}}[/tex]
Step-by-step explanation:
If we're looking for the point at with the ball reaches its highest point, we want to find the graph's vertex. In order to get the equation into a form with the vertex in it, we need to convert the equation into vertex form. This is an equation in the form [tex]y=a(x-h)^2 + k[/tex], h being the x value of the vertex, and k being the y value of the vertex.
In order to convert our equation, [tex]-5t^2+30t[/tex] into vertex form, we can algebraically manipulate it to get it into the form we want.
[tex]-5t^2 +30t[/tex] [tex]-5 \cdot t^2 + 30t[/tex] (Separate the -5 from the t^2)[tex]-5(t^2-6t+0)[/tex] (Factor out a -5)[tex]-5(t^2 -6t + (-3)^2 - (-3)^2 + 0)[/tex] (Completing the Square)[tex]-5((t-3)^2 - (-3)^2 + 0)[/tex] (Binomial Formula)[tex]-5((t-3)^2 - 9)[/tex] (Simplify)[tex]-5(t-3)^2 + 45[/tex] (Factor the -5 back in)Therefore, our equation with the vertex in it is [tex]-5(t-3)^2 + 45[/tex]. To find the vertex, we can examine the equation to find the values of h and k in the formula [tex]y=a(x-h)^2 + k[/tex] (where the vertex coordinates are (h, k)).
It seems that h is 3 and k is 45. Therefore, the coordinate of the vertex is (3, 45). Since it asks for how many seconds after being hit does the ball reach its highest point, we would take the x value since x represents seconds. This is 3. Therefore, the ball reaches its highest point after 3 seconds.
Hope this helped!
f(x) =2x squared - 5x - 3 g(x) = x squared + 6x - 1 what is h(x), if h(x) = g(x) - f(x)
Answer:
-2x^2 + x^2 +11x +2
Step-by-step explanation:
f(x) = 2x^2-5x -3
g(x) = x^2 + 6x -1
h(x) = g(x) - f(x)
x^2 + 6x -1 - 2x^2 +5x +3
-2x^2 + x^2 +11x +2
1) A recipe for a fruit drink calls for 2 cups of fruit juice for every 5 cups of water. Look at each drink mix. Does each drink mix
follow the recipe?
Yes
No
A 4 cups of fruit juice and 10 cups of water
Yes
No
B 0.5 cup of fruit juice and 1 cup of water
Yes
No
с
1 cup of fruit juice and 2.5 cups of water
Yes
No
D
7 cups of fruit juice and 17 cups of water
Answer:
yes, no , yes, no in order
Step-by-step explanation:
Find the value of (x) in the triangle shown below.
Solve the equation y=10x + 28.75
Answer:
x=y/10-2.875
slope=10
y= (0,28.75)
Standard form; 40x-4y=-115
Step-by-step explanation:
Not sure which answer you're looking for, but hope this helps!
Which graph represents the function f(x) = (x – 5)2 + 3?
Answer:
A
Step-by-step explanation:
Edge 2021
Angel and his 2 sisters shared 1/2 cup of baby carrots. How many cups did they each get?
Answer:
1/6 cup
Step-by-step explanation:
1/2 is to be split evenly between 3 people (Angel and his 2 sisters) so our equation is
1/2 ÷ 3 = 1/6
So, they each get 1/6 cup of baby carrots
Answer:
[tex]\frac{1}{6}[/tex] cups each.
Step-by-step explanation:
There is 1/2 of a cup of baby carrots available.
Angel and his 2 sisters would mean that there are 3 of them in all. Divide 1/2 with 3:
[tex]\frac{\frac{1}{2}}{3} = \frac{1}{2} * \frac{1}{3}[/tex]
Multiply across:
[tex]\frac{1}{2} * \frac{1}{3} = \frac{1}{6}[/tex]
Each person received [tex]\frac{1}{6}[/tex] of a cup.
~
PLS HELP ASAP!!!!!!!!!!!
Jude graphed the inequality s
Is his graph correct? Explain why or why not.
Answer:
No, Jude’s graph is incorrect. The inequality symbol is “less than,” so -9 is not included. He should have used an open circle on -9.
^ sample response
sorry that im late on this, but i hope it helps anyone else : )
Answer:
No , Jude’s graph is incorrect . The inequality symbol is “ less than , ” so - 9 is not included . He should have used an open circle on - 9 .
Step-by-step explanation:
sample response on EDGE
What is the end behavior of the graph of f(x) = -0.25x2 – 2x + 1?
End behavior means what are the y-values doing as the x-values both increase and decrease without bound.
This is a parabola (degree 2) with a negative leading coefficient (−0.25). Therefore both ends of the graph will be going towards negative infinity.
As x increases, f(x) decreases.
As x decreases, f(x) decreases.
Since the highest degree of the given function, f(x) = -0.25x² – 2x + 1 the end behavior of the graph will be down.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that,
f(x) = -0.25x² – 2x + 1
A polynomial function's end behavior defines how the graph acts as x gets closer. The leading term of the function—that is, the term with the highest n-value for a × n, where n is a positive integer and an is any nonzero number—allows us to infer the function's final behavior.
The highest degree of the given function is 2. When the function is plotted on the graph we get the graph shows downward behavior when x gets closer.
Thus, since the highest degree of the given function, f(x) = -0.25x² – 2x + 1 the end behavior of the graph will be down.
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
PLEASE HELP ME ANSWER THIS I WILL GIVE FREE THANKS
Answer:
C: Two solutions
Step-by-step explanation:
If you try to solve the problame you can find to solution's
Hope this Help's
Answer:
lol too bad laurenercsp6fpli
Step-by-step explanation:
In a survey of 3,300 people who owned a certain type of car, 660 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car ?
Answer:
20%
Step-by-step explanation:
660:3300*100 =
(660*100):3300 =
66000:3300 = 20
how many 1/3's are in 3
Answer:
9
Step-by-step explanation:
1/3 times9=3
Bryan wants to buy a new pair of jeans. If the jeans were originally $45.00, but are on sale with a 20% discount, how much will Bryan have to pay for the jeans?
Answer:
20% of 45= 9 so you would subtract 9 from 45 getting you 39
Step-by-step explanation:
45-9=39 he would have to pay $39
Suzi starts her hike at 275 feet below sea level. When she reaches the end of the hike, she is still below sea level at −135 feet. What was the change in elevation from the beginning of Suzi's hike to the end of the hike?
Answer:
Have a nice day!
Step-by-step explanation:
Answer:
140
Step-by-step explanation:
Hi there!
This problem may seem tricky because of the negative sea level, os let’s set up an equation.
[tex]-275+x=-135[/tex] where x = the change in elevation.
Using orders of operations, add 275 to both sides and you will end with
x = 140
Her change in elevation is 140 feet.
I hope this helps!
2x -6x2 -7 write the polynomial in standard form
Answer: It would be 2x-19
Step-by-step explanation:
Which set of points would result in a slope of 1/4
(2,8) and (1.4)
(8.2) and (1, 4)
(8, 2) and (4,1)
(2,8) and (4,1)
Answer:
C) ( 8,2) and (4,1)
The slope of the line
[tex]m = \frac{1}{4}[/tex]
Step-by-step explanation:
Explanation:-
Given that the set of points ( 8,2) and (4,1)
ThesSlope of the line
[tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
[tex]m = \frac{1-2 }{4-8 }= \frac{-1}{-4} = \frac{1}{4}[/tex]
The slope of the line
[tex]m = \frac{1}{4}[/tex]
When simplifled, the value of the expression (15 - 11) 2 + 64 +4 is equal to
10
4
24
18
Answer:
I genuinely dont see the answer lol
Step-by-step explanation:
P - Parenthesis
E - Exponent
M - Multiply
D - Divide
A - Add
S - Subtract
[tex](15 - 11)2 + 64 + 4 \\ (4)2 + 64 + 4 \\ 8 + 64 + 4 \\ 72 + 4 \\ 76[/tex]
(Giving brainliest to correct answer)
Need quick
28 POINTS ANSWER RIGHT
Congruence
Answer:
BE =DE
BEC=DEC
AEB AED
Step-by-step explanation:
not that hard lol
A large tank is partially filled with 100 gallons of fluid in which 40 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 30 minutes. (Round your answer to two decimal places.
Answer:
76.09 pounds
Step-by-step explanation:
From the information given:
[tex]R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)[/tex]
[tex]R_{in} =3 \ lb/min[/tex]
At a slower of 4 gal/min, the solution gets pumped out;
So,
[tex]R_{out} = \dfrac{4A}{100+(6-4)t }[/tex]
[tex]R_{out} = \dfrac{2A}{50+t }[/tex]
The differential of the equation is:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)[/tex]
For the linear differential equation, the integrating factor is determined as:
[tex]\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|[/tex]
[tex]= (50+t)^2[/tex]
Multiplying [tex](50+t)^2[/tex] with the above integration factor;
[tex](50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2[/tex]
[tex]\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2[/tex]
[tex](50+t)^2 A = (50 +t)^3 + c[/tex]
[tex]A = (50 +t) + c (50 +t )^{-2}[/tex]
By using the given condition:
A(0) = 40
40 = 50 + c (50)⁻²
10 = c(50)⁻²
OR
c = -10 × 2500
c = -25000
A = (50 + t) - 25000(50 + t)⁻²
The number of pounds of salt in the tank after 30 min is:
A(30) = (50+30) - 25000(50 + 30)⁻²
[tex]A(30) = 80 - \dfrac{25000}{6400}[/tex]
[tex]A(30) = 76.09 \ pounds[/tex]
Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.
Graph a line that contains the point (−6,1) and has a slope of 5
Answer:
y=5x+31
Plot points at: (-4,11), (-6,1), (-3, 16)
Step-by-step explanation:
y-1=5(x+6)
y-1=5x+30
y=5x+31
please help me please
The quotient of 56 and a number
Answer:
yes
Step-by-step explanation:
One step equation
-104=8x
Answer:
The answer you gave can only be solved if you know what the Variable is.
Step-by-step explanation:
A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true. To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself.
the point (- 7, 4) is reflected over the line x = - 3 . Then , the resulting point is reflected over the line y = x . Where is the point located after both reflections?
Answer:
(-10,-7)
Step-by-step explanation:
first reflect over x=-3
(-7,-10)
then reflect over y=x
(-10,-7)
It is not always possible to measure every individual in a population; what is the name of the representative group
Answer:
Sample
Step-by-step explanation:
The term that represents the description in the question is called sample.
Take for instance:
40 students selected from a class of 1001000 people selected from a population of 100000In the above descriptions:
40 and 1000 represent the samples while 100 and 100000 represent the populations, respectively.
Another example is when 10 cats are picked from an animal farm in order to study their eating pattern.
All these and many more represent sample.
The cost of a meal is $ 66. The sale tax rate is 8.5%. How much would the sale tax be?
Answer: $5.61
Step-by-step explanation: 8.5% of $66
Simplify the following expression.
13x+11y-3x+3y+9
Answer:
10x+14y+9Step-by-step explanation:
13x+11y-3x+3y+9
10x+11y+3y+9
10x+14y+913x + 11y - 3x + 3y + 9
This problem consists of combining alike parts of the equation. This means 13x and - 3x go together, 11y and 3y go together, and 9 has no other alike parts.
This shows that the answer (when combining like terms) is:
10x + 14y + 9
An individual rides a bike at a rate of 15 miles per hour for h hours. Write an equation that expresses the situation, let x be the independent variable and y be the dependent variable.
Answer:
15y+x
Step-by-step explanation:
How does a 90° counterclockwise rotation about the origin change the coordinates of a shape
Answer:
Step-by-step explanation:
it switches the x and y coordinates and places a negative on the new x
P=(x,y)
90° CCW rotation P'(-y,x)
Answer:
it switches the x and y coordinates and places a negative on the new x
P=(x,y)
90° CCW rotation P'(-y,x)
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!11
Cecilia records the weight change in her cat over 2 weeks. What number does she record as the total weight change for her cat?
LOOK AT THE ATTACHED PICTURE
Answer:
1 over 16
Step-by-step explanation:
I GIVEEE BRAINLLILST
I NEED HWLP
Answer:
3
Step-by-step explanation:
the smaller one has a height of 5
the larger one has aheight of 15
15/5 is 3
