The solution to the quadratic equations are
a) The number of seconds for the ball to reach the ground is t = 5 seconds
b) The number of seconds to reach the maximum height T = 2 seconds
c) The maximum height of the ball is h ( 2 ) = 144 feet
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as h ( t )
Now , the equation will be
h ( t ) = -16t² + 64t + 80 be equation (1)
a)
The number of seconds for the baseball to reach the ground be t
The height when the ball reaches the ground will be h = 0
Substituting the value of h ( t ) = 0 , we get
0 = -16t² + 64t + 80
On simplifying the equation , we get
16t² - 64t - 80 = 0
Divide by 16 on both sides of the equation , we get
t² - 4t - 5 = 0
On factorizing the equation , we get
t² + t -5t - 5 = 0
t ( t + 1 ) - 5 ( t + 1 ) = 0
( t - 5 ) ( t + 1 ) = 0
The value of t is time and it is not negative
So , when ( t - 5 ) = 0
Adding 5 on both sides of the equation , we get
t = 5 seconds
b)
The number of seconds the baseball to reach the maximum height be T
And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola
T = ( -b / 2a )
On simplifying the equation , we get
T = ( -64 / ( 2 ( 16 )
T = -64 / 32
T = 2 seconds
c)
The maximum height of the baseball is when T = 2
Substituting the value of t = 2 in the equation , we get
h ( t ) = -16t² + 64t + 80
h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80
On simplifying the equation , we get
h ( 2 ) = -64 + 128 + 80
h ( 2 ) = 64 + 80
h ( 2 ) = 144 feet
Hence , the equation is solved
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First use the digits in the box to create the largest possible number. Then use the same digits to create the smallest possible number. Then find the difference between the two numbers.
Answer:
What are the digits in the box?
Step-by-step explanation:
Which story shows 1/3 divided by 5?
Mark has $500 in his savings account. If he saves $25 each month, how many months will it take him to have $1000.
Answer: 20, I believe
Step-by-step explanation: You already have 500 which is half of 1000. 500 divided by 25 equals 20.
Select the correct answer.
Identify the expression equivalent to 4(x + x + 7) - 2x+8 - 4 by substituting x = 1 and x = 2.
ОА.
6x +11
OB. 3(x + 7)
OC. 2(3x + 16)
OD.
3x + 16
Reset
Next
Answer:
c
Step-by-step explanation:
The expression equivalent to this expression is 2(3x+16)
Data;
x = 1x = 2Equivalent ExpressionThe given expression is 4(x+x+7) -2x + 8 -4
Let's simplify this
[tex]4(x+x+7) -2x +8 - 4\\4(2x+7) -2x +4 = 8x + 28 - 2x + 4 = 6x + 32[/tex]
This can be simplified as
[tex]6x+ 32 = 2(3x + 16)[/tex]
The expression equivalent to this expression is 2(3x+16)
Learn more on equivalent expression here;
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Safeway has ginger ale on sale at 12 cans for $4.00 and Giant has the same brand
of ginger ale on sale for 20 cans for $6.00. Which store has the better deal?
Answer:
Giant
Step-by-step explanation:
Giant: .30c a can
Safeway: .33c a can
Write an equation for the following line.
10
-10
10
-101
1) -5n – 4n ?????????????????????????????????????????
Answer: =−9n
Step-by-step explanation: hope this help
-5n-4n
=-5n-4n
=-5n+-4n
=-n+-n+-n+-n+-n+-n+-n+-n+-n
=-9n
Pleasee help wit this
Answer:
Step-by-step explanation:
f(-9)=2(-9)²+5(-9)+20
= 162-45+20
= 137
Answer:
137
Step-by-step explanation:
f(-9) = 2(-9)^2 + 5(-9) + 20
= 162 - 45 + 20
= 137
Will mark BRAINLIEST!!
What is - 1 1/15 + (- 3/5) =
solve each equation by substituting. y=-3x+5
5x-4y=-3
not different problems they are in the same problem
Answer:
(1, 2 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 5 → (1)
5x - 4y = - 3 → (2)
Substitute y = - 3x + 5 into (2)
5x - 4(- 3x + 5) = - 3 ← distribute and simplify left side
5x + 12x - 20 = - 3
17x - 20 = - 3 ( add 20 to both sides )
17x = 17 ( divide both sides by 17 )
x = 1
Substitute x = 1 into (1) for corresponding value of y
y = - 3(1) + 5 = - 3 + 5 = 2
solution is (1, 2 )
Answer:
x = 1 and y = 2
Step-by-step explanation:
y + 3x = 5 -------------> (1)
-4y + 5x = -3 -------------> (2)
(1) * 4
=> 4y + 12x = 20 --------> (3)
(3) + (2)
=> 0y + 17x = 17
=> 17x = 17
by dividing both sides by 17
=> x = 1
by putting x = 1 into (1)
=> y + 3*1 = 5
=> y + 3 = 5
=> y = 5 - 3
=> y = 2
Richard and Teo have a combined age of 49. Richard is 13 years older than twice Teo's age. How old are Richard and Teo?
Answer:
13×2=26
Maybe i can help u a little
Answer:
teo is 18 and Richard is 31
Step-by-step explanation:
hope it helps you
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Find the missing side length
Answer:
b
Step-by-step explanation:
Triangle V P M. Angle V is 52 degrees, angle P is 78 degrees, angle M is x degrees.
Answer:
[tex]x = 50[/tex]
Step-by-step explanation:
[tex]52 + 78 + x = 180[/tex]
[tex]130 + x = 180[/tex]
[tex]x = 180 - 130[/tex]
[tex]x = 50[/tex]
A bank account with an initial deposit of $4,000 and an interest rate of 4% increases by 4% each year. The balance (B) as a function of time in years (t) can be described by an exponential function: B(t) = 4,000(1.04)t
What parameter would change if the interest rate were changed to 7%?
Parameter
(select)
would change if the interest rate were changed to 7%.
10x - 4y for x = 14 and y = 5 PLEASE!
Answer:
120
Step-by-step explanation:
10(14)-4(5)
=140-20
=120
Answer:
120.
Step-by-step explanation:
10(14)-4(5)
140-20
120.
Is 1,48 rational or irrational
Answer:This number is classified as rational
Step-by-step explanation: Have a great day!
Bella went to Yard Depot multiple times. Each time she was there, Bella bought a gardening hat and y pairs of gardening gloves. The expression shown below represents the total amount of money, in dollars, Bella spent at Yard Depot. a(by + c) C. Explain what a, b, and c each mean in terms of the situation.
Answer:
a is how many times bella went 2 yard depot
b is how many gardening gloves she bought
c is how many gardening hats she bought
2 It is 7:40 A.M. Delilah's bus arrives
at 7:53 A.M. It takes her 10 minutes
to get to the bus stop. Will she
catch her bus?
yourloos nosos 3 sovios
to
no 18119
What time will she get to the bus
stop?
9
SRB
Answer:
no she will be 3 min late
Step-by-step explanation:
what is the equation?
Answer:
y=22x
Step-by-step explanation:
If x=1 and y=22 then y=22x
2.
Write a rule for the linear function in the table.
x f(x)
–1 –5
2 –2
5 1
8 4
A. f(x) = x – 4
B. f(x) = 3x
C. f(x) = x + 4
D. f(x) = x – 5
Answer:
C. f(x) = x + 4
Step-by-step explanation:
If a circle has an area of 49 squared, what is its exact radius?
Answer:
27.7
Step-by-step explanation:
Area = πr²
49²/π = r²
r = 49/√π = 49/1.77 = 27.7
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Option C it is sure
,
A
trust me looooooooooll
Hey please help me!
Whats 12y + 2x = 24 ???
Answer:
y=2 x=0
Step-by-step explanation:
12x+2x=24
12 times 2+ 2 times 0
=24
what is the value of x in the triangle??
Answer:
x=40°
Step-by-step explanation:
Every triangles area equals 180
75+65=140
180-140=40
Answer:
40
Step-by-step explanation:
All angles in a triangle add up to 180°.
65° + 75° + x° = 180
140° + x° = 180°
-140 -140
x° = 40°
PLEASE HELP!!! (i will give brainliest)
Step-by-step explanation:
[tex] {9}^{2} = {6}^{2} + {x}^{2} \\ 81 = 36 + {x}^{2} \\ {x}^{2} = 45 \\ x = 6.71 \: ft[/tex]
6.71 is answer ok plz MARK me as BRAINLIST
Verdadero o falso a) al reducir a comun denominador las fracciones se sustituyen por otras equivalentes
Answer:
Verdadero
Step-by-step explanation:
Verdadero, cuando cambias dos fracciones para darles un denominador comun la fraccion entera se sustituye para otra que tiene el mismo valor numerico que la original. Por ejemplo tenemos una fraccion 2/6 en la cual tenemos que cambiarle el denominador a uno comun con otra fraccion que es 18. Entonces sustituyemos la fraccion por la siguente fraccion 6/18. Esta nueva fraccion es equivalente a la original y los dos tienen el mismo valor numerico...
2 / 6 = 0.333
6 / 18 = 0.333
will give brainliest at the right answer
Answer:
1.) 40.0 2.) 75.00 3.) 140.00 4.) 200.00 5.) 500.00 6.) 1300.00 7.) 70.0000
8.) 10.00 9.) 245.00 10.) 900.00
why do countries, make alliances, in wartime? please someone help me!
Answer:
Most of the time, it is because they need the military aid or the resources that a certain country needs. That's kinda what the UN is all about is aiding each other in times of war
Step-by-step explanation:
Answer:
Because when make allies, they have someone to have their back.
Step-by-step explanation:
For example, If you're in a fight, you're gonna need backup. In war, you need as many people as you can to take down the villain (your opponent). Which means people, ammo, guns, bombs, support, and inside spies. All of this helps and will be easier to defeat the person per-say.
what is the range for a x intercept of (5,0) and a y intercept of (0,3)
Answer:
(5,0)=x1,y1
(0,3)=x2,y2
so the range will be x1-x2/
what is 146 / pi as a fraction
Answer:
Step-by-step explanation:
[tex]\frac{146}{\pi}\\ \\ \text{Pi is irrational and cannot be expressed as a ratio of two integers.}\\ \\ \frac{146}{\pi}\approx 46.47[/tex]