The amount of time it would take for the rock to hit the ground is 1.25 seconds.
Given the following data:
Initial velocity = 16 ft/secHeight = 5 ft.Scientific data:
Acceleration due to gravity (g) = 9.8 [tex]m/s^2[/tex]To determine the amount of time it would take for the rock to hit the ground, we would apply the parabolic function:
How to calculate the time.Mathematically, the parabolic function is given by this formula:
[tex]h(t) = -16t^2 +ut+h_0[/tex]
Where:
U is the initial velocity.a is the acceleration.[tex]h_0[/tex] is the height.t is the time.Substituting the given parameters into the formula, we have;
[tex]0 = -16t^2 +16t+5\\\\16t^2-16t-5=0\\\\(4t+1)(4t-5)=0[/tex]
Taking the positive value of t, we have:
[tex]4t-5-0\\\\4t=5\\\\t=\frac{5}{4}[/tex]
t = 1.25 seconds.
Read more on time here: brainly.com/question/24728358
E Homework: 2.3 Linear Inequalities
Question 14, 2.3.101
Part 1 of 2
Assume that in 2005 consumers used credit and debit cards to pay for 43% of all purchases. This percentage is projected to be 58% in 2011.
(a) Find a linear function that models the data, where x is the year and P(x) is the percentage.
(b) Estimate when this percentage was between 48% and 53%.
(a) P(x) =
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Linear functions are functions that change at a constant rate
The linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]
The equation of the linear functionFrom the question, we have the following ordered pairs
(x,P(x)) = (2005,43%) and (2011,58%)
Start by calculating the slope (m)
[tex]m = \frac{P(x2) - P(x1)}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{58\% - 43\%}{2011 - 2005}[/tex]
Evaluate the differences
[tex]m = \frac{15\%}{6}[/tex]
Evaluate the quotient
[tex]m = 2.5\%[/tex]
The linear function is then calculated as:
[tex]P(x) = m(x - x_1)+ P(x_1)[/tex]
So, we have:
[tex]P(x) = 2.5\%(x - 2005) + 43\%[/tex]
Rewrite as:
[tex]P(x) = 0.025(x - 2005) + 0.43[/tex]
This gives
[tex]P(x) = 0.025x -50.125 + 0.43[/tex]
[tex]P(x) = 0.025x -49.695[/tex]
Hence, the linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]
Read more about linear functions at:
https://brainly.com/question/15602982
.
Solve the equation -8(x + n) = x for n.
Answer:
-x/8 - x
Step-by-step explanation:
Answer:
n = -(9/8)x
Step-by-step explanation:
Solve for n:
-8(x + n) = x-8x - 8n = x-8n = 9xn = -(9/8)x-Chetan K
Need help with homework
Answer:
5. the other angle has to be 2x because of the other lines being equals so
2x+2x+x-15=180
5x-15=180
5x=195
x=19
6. the other two angle is ajacent to the other two so
3x+17+3x+17+x-9+x-9=360
8x+16=360
8x=344
x=43
7. this ones pretty simple
2x-4+3x+5+2x+11=180
7x+12=180
7x=168
x=24
8. this one to
x+x+4+3x-9=90
5x+5=90
5x=85
x=17
Hope This Helps!!!
A tank has length 6m, breadth 5m and height 3m.Find the volume of the tank.If it is full of water, Find the volume of water in litres.
Solution:
Given:
Volume of tank = Length x Breadth x HeightLength = 6mBreadth = 5mHeight = 3mLet's substitute the values of Length, Breadth, and Height to obtain the volume of the tank.
Volume of tank = Length x Breadth x Height=> Volume of tank = 6 x 5 x 3=> Volume of tank = 90 m³Now, let's convert meters into liters.
1 cubic meter = 1000 liters=> 90 m³ = 1000 x 90=> 90 m³ = 90000 litersHoped this helped!
2) What is the most precise name for a quadrilateral ABCD with vertices A(-2,4), B(5,6), C(12,4), D(5,2)?
parallelogram
rhombus
quadrilateral
rectangle
3) What is the most precise name for a quadrilateral ABCD with vertices A(4,4), B(5,8), C(8,8), D(8,5)?
square
rhombus
kite
parallelogram
Answer:
2 rhombus
3 parallelogram
please help! thanks in advance!
You have $50 in savings. Two months later, you have $80. After the third month, you have $95. You plan to continue to save the same amount each month. What will be in saving after 12 months?
Answer:
230
Step-by-step explanation:
multiply 12 by 15 and add it onto the 50 to get your answer!
Have a good day!
28 less than twice a number is equal to the number. What is the number?
Answer:
x = 28
Step-by-step explanation:
2x - 28 = x
-2x -2x
- 28 = - x
/-x /-x
28 = x
x = 28
Your family is going on vacation to Disney. It will cost your family $987 to travel there, plus $150 per day for tickets into the park. What is the greatest number of days you can stay at Disney while staying within their $3500 budget?
Answer:
They can stay 16 days.
Step-by-step explanation:
3500 - 987 = 2,513
2,513 divided by 150 = 16.7
*They can't stay 16.7 days, so you have to round down. Rounding up will go out of their budget.*
Checking answer:
16 x 150 = 2,400
2,400 + 987 = $3,387
- I'm sure this isn't how your teacher wants you to solve it but this is just how I solved it, I hope this helps!
Step-by-step explanation:
Equation: 987 + 150x = 3500
x represents the number of days the family is staying at the park.
Solve.
Subtract 987 from both sides:
[tex]150x = 2513[/tex]
Divide each side by 150:
[tex]x= 16.75[/tex]
16.75 is decreased to 16, it's impossible to stay for 16.75 days.
The family can stay in the park for 16 days.
Please please help f(x)7x1/5+6
Answer:
third answer
Step-by-step explanation:
solve for and isolate x by moving over all other numbers to the left and then take the fifth power to make x^1/5 = to x
Please solve for brainliest.
Answer: The first four terms are 33/4, 63/8, 15/2, and 57/8.
Step-by-step explanation: To make it easier, turn 8 1/4 into an improper fraction: 33/4. 33/4=66/8. Because the denominator is the same, it’s easier to subtract.
66/8 - 3/8 = 63/8
63/8 - 3/8 = 60/8
60/8 - 3/8 = 57/8
The first 4 terms in the sequence are 66/8, 63/8, 60/8, and 57/8. But we’re not done b/c we need to simplify. That means the first four terms are 33/4, 63/8, 15/2, and 57/8.
Huang buys 3 shirts that each cost the same amount, a pair of pants that cost $12, and he pays with a $100 bill. Which expression represents the amount of change Huang should receive? Select three options.
100 – (12(3x))
100 – (3x+12)
(100 – 12) – 3x
(100 – 12)(x+x+x)
100 – (x+x+x) – 12
Answer:
B, C, E
100 - (3x+12)
(100 - 12) - 3x
100 - (x+x+x) - 12
Step-by-step explanation:
they are all saying the same thing, just rearranged and the last one is 3x expanded
Chad used a number line to show the distance from the library to his house and the distance from the library to Kelli's house. How much farther is Chad's house than Kelli's house from the library? A number line from 0 to 1 is divided into 8 equal parts. Library is at 0, Kelli's House is at four-eighths, and Chad's House is at seven-eighths on the number line.
Chad's house is 3/8 units farther away than Kelly's house.
How to use the number line?By reading the number line, we can see that:
Library = 0Kelli's House = 4/8Chad's House = 7/8.These fractions are the positions of each location. We want to find how much farther is Chad's house than Kelli's house from the library, this is given by:
(Chad's house position - library position) - (Kelli's house position - library position)
Writting the fractions, we get:
(7/8 - 0) - (4/8 - 0) = 3/8
So Chad's house is 3/8 units farther away than Kelly's house.
If you want to learn more about fractions, you can read:
https://brainly.com/question/11562149
Answer: 3/8
Step-by-step explanation: 7/8 -4/8 equals 3/8
The water pipe of a house was leaking gallons of water per minute. What is the constant rate of water that is lost per minute according to the graph?
2.2,
Write the ratio 1 2/3: 2 2/3 in the simplest form.
,
Answer:
1:2
Step-by-step explanation:
this would be the answer as 1 2/3: 2 2/3 are the same as 1:2 if you cancel out the 2/3 from both sides.
Answer:
5 : 8
Step-by-step explanation:
1 [tex]\frac{2}{3}[/tex] : 2 [tex]\frac{2}{3}[/tex] ( change both mixed numbers to improper fractions )
= [tex]\frac{5}{3}[/tex] : [tex]\frac{8}{3}[/tex] ( multiply both parts by 3 to eliminate the fractions )
= 5 : 8
Julia pays $4.56 to ship a package that weighs 8 ounces. What is the cost to ship one ounce?
Answer:
1.7543859649. . . . . . . .. .
Answer:
$0.57
Step-by-step explanation:
$4.56/8 = 0.57
so the cost to ship one ounce is $0.57
the Sims family drove 5 miles to the store and 3 miles to their grandparent's house. How
many yards did they drive in all?
Answer:
yards: 14080
miles: 8
that's basically it
Answer:
14080 yards
Step-by-step explanation:
A yard is 1/1760 mile, meaning 1 mile = 1760 yards.
5 miles + 3 miles = 8 miles
8 miles to yards = ?
8 x 1760 = 14080.
The Sims family drove 14.08k yds or 14080 yards.
Ted is installing lighting in a new block of 12 apartments . He will need 60 metres of cable for each apartment. Each mew spool holds 100 metres of cable . What is smallest number of new spools that Ted will need for his job
Answer: 8 spools
Step-by-step explanation:
There are 12 apartments, and each apartment will need 60 meters of cable, so 12×60= 720 meters of cable needed.
If each spool only has 100 meters and he needs 720 meters, then 720÷100= 7.2. So he would need to purchase at least 8 spools, and will have 80 meters left over.
help me with this pleasee
Which measurement is a reasonable length for 3 new pencils laid end-to-end?
A) 3 inches
B) 18 inches
C) 13 feet
D) 8 feet
What is an equation of the line that passes through the points (-4, -2) and (-8, 3)?
Answer:
[tex]y = -\frac54x -7[/tex]
Step-by-step explanation:
Slope:
[tex]\frac{3 - (-2)}{-8 - (-4)}[/tex][tex]-\frac{5}{4}[/tex]Y-intercept:
[tex]y = -\frac54x + b\\[/tex][tex]-2 = -\frac54(-4) + b[/tex][tex]-2 = 5 + b[/tex][tex]b=-7[/tex]y = -5/4x -7
-Chetan K
Verify trigonometric identiy
Answer:
see explanation
Step-by-step explanation:
Using the identity
cos²Θ = 1 - sin²Θ
Consider the left side
sin²Θ - cos²Θ
= sin²Θ - (1 - sin²Θ ) ← distribute parenthesis by - 1
= sin²Θ - 1 + sin²Θ
= 2sin²Θ - 1
= right side , thus verified
What is the total amount that Matthew’s bank will receive after lending him$8,000 for four years at an interest rate of 6 percent, compounded annually?
Identify a numerator that will make the number
sentence true.
3x blank/fifth=3
Answer:
Answer is 5
Step-by-step explanation:
You say 3 divided by 3 /5 = 5
Hope answer helps you
NEED HELP!!
can someone please help me this work? I am so confused with this math problem. Thank you
Answer:
SOH CAH TOA
Little triangle first - hypotenuse is 4, now we used this info help us find the opposite.
Opposite & Hypotenuse - Sin
Sin(45) = O/H
Sin(45) = O/4
x 4 both sides, to get Opposite
Opposite = 4 x Sin(45)
= 2 root 2
= 2.8284.......
Big Triangle next,
Opposite is 2.8284......
Y is the adjacent
Opposite & Adjacent - Tan
Tan (30) = O/A
Tan(30) = 2.8/A
x A
A x Tan(30) = 2.8
÷Tan(30)
A = 2.8 ÷ Tan(30)
A= 2 root 6
A= 4.8989...
So, y is 5 to 1 significant figure
Or
Y = 4.9 to 1d.p
(Haven't rounded anything in my calculation, even though it's shown that way, in my workings. So, you can follow along)
Hope this helps!
nee answer asap plz im stuck
Which point represents the least value on the number line?
Express alphabetically: Double the sum of p and q
Answer:
that would be:::
2(p+q)
A triangle has a perimeter of 66 feet. If the three sides of the triangle are n, 3n+3, and 4n - 9, what is the length of each side?
Separate multiple entries with a comma.
Answer:
9, 30, 27
Step-by-step explanation:
To find the perimeter, you must add up each side. In this scenario, we know that the perimeter is 66 feet. We also know the sides, which are n, 3n+3 and 4n-9.
So, we must add the sides to get 66 feet.
n+3n+3+4n-9=66
Combine like terms, and solve:
(n+3n+4n)+(3+-9)=66
8n+-6=66
8n-6=66
n=9
So if n=9, we can easily find the value of the other sides.
3(9)+3=30 feet.
4(9)-9=27 feet
So, the sides are 9, 30, and 27 feet (in order).
work out the area of the shape
Answer:
45cm^2
Step-by-step explanation:
we have two shapes in the diagram a square and a triangle so we find the area of each of them and add them together
finding the area of a square
we have area= s×s
area = 7×5
area = 35cm^2
finding the area of a triangle
1/2 ×b×h
1/2×4×5
area = 10cm^2
so we add together
total area = 35+ 10
area = 45cm^2
help geometry test is coming up and teacher hasn’t taught anything yet,(80% of grade)
Answer: I think it’s 647.96
Step-by-step explanation:
warning: this is not the exact value (it’s rounded)
First you find the height of the traingle
To do that, do pythagoras theorem
square root 36 squared minus 25.5 squared
then use formula for area of a triangle