PLEASE HELP!! Brainliest to first answer
Part A: An archer shoots an arrow into the sky where the motion of the arrow can be modeled by the equation() = −5^2 + 20 + 4. Where t is time in seconds and f(t) is height in feet. Find how long it will take the arrow to hit the ground using an algebraic method. Round to the nearest tenth if necessary. Show all of your reasoning used with this algebraic method.
Part B: Using the information in Part A, find how high the arrow will go at its maximum height, and how long it takes for this to occur using an algebraic method. Show all of your reasoning used with this algebraic method. Round to the nearest tenth if necessary.
Answer:
The arrow will take 4.19 seconds to hit the ground
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
Step-by-step explanation:
The quadratic function is f(t) = -5t² + 20t + 4, where
f(t) is the height in feet
t is the time in seconds
If the arrow hit the ground that means h(t) = 0
→ Substitute h(t) by 0 and use the quadratic formula to find t
∵ h(t) = 0
∴ 0 = -5t² + 20t + 4
→ Switch the two sides
∴ -5t² + 20t + 4 = 0
→ Multiply all terms by -1 to make the coefficient of t² positive
∴ 5t² - 20t - 4 = 0
→ The quadratic formula is [tex]t=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] , where
a is the coefficient of t²b is the coefficient of tc is the numerical term∵ a = 5, b = -20, c = -4
∴ [tex]t=\frac{-5+-\sqrt{(-20)^{2}-4(5)(-4)}}{2(5)}[/tex]
∴ [tex]t=\frac{-5+-\sqrt{400+80}}{10}[/tex]
→ Find the values of t in decimal
∴ t = 4.19 seconds OR t = -0.19 ⇒ refused because it is negative
∴ The arrow will take 4.19 seconds to hit the ground
The graph of this quadratic function is a parabola with maximum vertex (h, k), where
h = [tex]\frac{-b}{2a}[/tex]k = f(h)To find the maximum height and the time taking for this to occur find h and k where k is the maximum height and h is the time for this to occur
∵ f(t) = -5t² + 20t + 4
∵ a = -5 and b = 20
∴ h = [tex]-\frac{20}{2(-5)}=-\frac{20}{-10}=2[/tex]
∴ The time for the maximum height is 2 seconds
→ Now use it to find k
∵ k = f(h)
∴ k = f(2)
∵ f(2) = -5(2)²+ 20(2) + 4
∴ f(2) = -5(4) + 40 + 4
∴ f(2) = -20 + 40 + 4
∴ f(2) = 24
∴ k = 24
∴ The maximum height is 24 feet
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
How would you write 0.5.... as a decimal?
Answer:
0.5 is already a decimal.
Fraction: 1/2
Percent: 50%
Step-by-step explanation:
Solve:
x/4 - x/8 = 5
Answer:
x=40
Step-by-step explanation:
x/4 - x/8
LCM of 4,8=8
x/4x2/2 - x/8=5
2x/8 - x/8 =5
x/8=5
transpose
x=5x8
x=40
hope this helps
please mark as brainliest
14.625 as a mixed number?
Answer:
14 5/8
Step-by-step explanation:
10 : 35 fraction in simplest from
What is 10/35 Simplified? - 2/7 is the simplified fraction for 10/35.
-BBBM
Which conversions go from a smaller unit to a larger unit? Select all that apply.
centimeters to millimeters
decimeters to meters
hectograms to kilograms
liters to centiliters
Answer:
decimeters to meters
Step-by-step explanation:
There are 10 decimeters in a meter.
Answer:
decimeters to meters
hectograms to kilograms
Step-by-step explanation:
2x-2y= 14 standard to slope and intercept form
2x - 2y = 14
-2y = 14-2x
y= -7 + x
y = x - 7
Help plz it’s algebra 2 vertex forms of quadratic function
Answer:
I did the entire thing I attached the picture for it !! hope this helps !!
I didnt do 5 and 7 cause I forgot how to do those!!
Find the slope between the given points. REMEMBER: Slopes must be simplified.
(-10, 13). (5.-3)
Answer:
The slope is m= -16/15
what is 5280 divided by 60
Answer:
88
Step-by-step explanation:
Write the quotient as a power
Answer:
a^20
Step-by-step explanation:
a^21-a^1
a^20
If a person walks 1/4 mile in 10 minutes, how far will that person walk in one hour?
Answer:
one and a half or 1/2 hours
3. What is the measure of angle ABE?
Answer:
50°
Step-by-step explanation:
Both angles are congruent
Answer:
The measure of angle ABE is 50 degrees because it is a vertical angle to CBD.
Step-by-step explanation:
PLEASE HELP! WILL MARK BRAINLIEST!
Answer:
-25
Step-by-step explanation:
(-6) (-5) - (-5)
-30 -(-5)=-25
choose the graph of the translated parent function f(x)=cos(x) where it is translation 3 units up
Answer:c
Step-by-step explanation:move up 3 units on the y axis and create the graph
7. Which number is not a perfect square?
A. 81
C. 169
B. 125
D. 289
Answer:
B. 125
Step-by-step explanation:
square roots:
81 = 9
169 = 13
125 = 11.180..
289 = 17
i will make you brainlliest whoever answers this right and will give you points Please help me i am having a hard time
Evaluate 14 + (-8) ÷ 2 · -3.
26
-9
-30
15
14 + (-8) / 2 x -3
Follow order of operations: divide and multiply from left to right:
-8/2 = -4 x -3 = 12
Now you have 14 + 12
The answer is 26
Answer:
26
Step-by-step explanation:
14+(-8) ÷ 2 (-3)
14+ (-4)(-3)
14+12
26
What is the slope of a line perpendicular to the line whose equation is
6x - 5y = -40. Fully reduce your answer.
Answer:
Slope = - 5/6
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
6x - 5y = - 40 Equation
Step 3:
- 5y = - 6x - 40 Subtract 6x on both sides
Step 4:
y = 5/6x - 80 Divide 5 on both sides
Step 5:
m = Slope
Answer:
Slope = - 5/6
Hope This Helps :)
The equation for line w is y = 2x – 3. Line d contains the point (4, -1) and is parallel to line w. Which equation
describes line d?
Answer:
y = 2x - 7
Step-by-step explanation:
y = 2x - 3
Gradient of line w = 2
Gradient of line d = 2
i.e line w and d are parallel.
Equation of line d is:
y - (-1) = 2(x - 4)
y + 1 = 2x - 8
y = 2x - 7
Please help. Only help if you know the answer
Answer:y-7=-9/8(x-0)
Step-by-step explanation:
Answer:
y -7 = -9/8 (x-0)
Step-by-step explanation:
i hope it help
Which of the figures is a concave polygon?
Answer:
B
Step-by-step explanation:
Answer:b
Step-by-step explanation:
–25y – 35
plz tell me step by step
Knhrh theme jejrjrh eiie
Answer:
what
Step-by-step explanation:
find the equation of the line shown
how do you do this ?
Answer:
y=1/2x+0.5
Step-by-step explanation:
The slope is 1/2, which you can see by looking at the change of y/x. The y intercept is 0.5, which can be seen on the y axis.
Ryan and his brother are at a carnival. They separate from each other at the ferris wheel at 1:00 PM, and they agree that they will each meet back at the ferris wheel from time to time to see whether the other is ready to leave. Ryan checks the ferris wheel every 15 minutes. His brother checks in every 24 minutes. At what time will they meet at the ferris wheel again. (Hint: Don't forget you're looking for a time)
Answer:
3:00pmStep-by-step explanation:
The idea hear is to find the least common multiples of 15 and 24
Given that they separated at exactly 1:00pm
the multiples are
15= 15,30,45,60,75,90,105,120
24= 24, 48,72,96,120
the multiples common is 120
Therefore they will meet in 120minute, which is 2 hours time \
hence the time will be 3:00pm
what does x equal to?
Answer:
27.3
Step-by-step explanation:
x = (36.4 x (49 - 28))/21 = 27.3
In his motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing spot, a distance of 264 mi, in 6 hr. Returning, he finds that the trip downstream, still at top speed, takes only 5.5 hr. Find the rate of Bill's boat and the speed of the current. Let x = the rate of the boat in still water and y = the rate of the current.
Answer:
The values are [tex]x = 46 miles /hr [/tex]
[tex]y = 4 \ miles / hr[/tex]
Step-by-step explanation:
From the question we are told that
The distance covered is d = 264 miles
The time taken is [tex]t_1 = 6 hours[/tex]
The time taken for the return trip is [tex]t_2 = 5.5 \ hours[/tex]
Generally during the trip toward fishing spot , the velocity is mathematically represented as
[tex]v_t = \frac{d}{t_1 } = x - y[/tex]
=> [tex]v_t = \frac{264}{6 } = x - y[/tex]
=> [tex]x - y = 44 \cdots 1 [/tex]
Generally during the return trip , the velocity is mathematically represented as
[tex]v_r = \frac{d}{t_2} = x+ y[/tex]
=> [tex]v_r = \frac{264}{5.5} = x+ y[/tex]
=> [tex]48 = x+ y\cdots 2[/tex]
add equation 1 and 2
[tex]2x = 92[/tex]
=> [tex]x = 46 miles /hr [/tex]
substituting this into equation 1
[tex] 46 - y = 44 \cdots 1 [/tex]
=> [tex]y = 4 \ miles / hr[/tex]
help asap i need this todayy
What role does Geometric formulas have in our lives??
Which equation shows a proportional relationship between x and y?
y = 16
y = 7x
y=−7x−2
y = 9x + 1
The equation that shows a proportional relationship is y = 7x.
How to find the equation that is proportional?Two variables have a proportional relationship if all the ratios of the variables are equivalent.
In other words, a proportional relationship is one in which two quantities vary directly with each other.
Therefore, a proportional relationship can be represented as y = kx.
where
k = constant of proportionalitythe variables are x and yTherefore, y varies directly as x in a proportional relationship.
Hence, the equation that shows proportional relationship is y = 7x as 7 is the constant of proportionality. y and x are the variables.
learn more on proportional relationship here: brainly.com/question/20213987
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Answer:
y = 7x
Step-by-step explanation:
the proportional relationship is y = 7x as 7 is the constant of proportionality. y and x are the variables.