Suppose you were to drop a stone down a well. A falling object obeys the equation s=16(t1)2 , where s is the distance fallen in feet and t is the time in seconds. Sound waves travel at a speed of about 1100 ft/sec, and the time it takes to travel a distance s is t2=s1100 . The total time it takes for you to hear the stone hit the water below equals the time it spent falling plus the time it takes the sound to reach your ear. What is the distance to the water's surface in the well if you hear the stone hit the water 4 seconds after dropping the stone?
Answer:
228.64 ft
Step-by-step explanation:
Given that the total time, t it takes for you to hear the stone hit the water below equals the time it spent falling, t1 plus the time it takes the sound to reach your ear t2.
Given that t = 4s and t = t1 + t2.
So t1 + t2 = 4 (1)
Also s = 16(t1)² and t2 = s/1100
Thus t2 = 16(t1)²/1000
From (1), t2 = 4 - t1
So 4 - t1 = 0.016(t1)²
0.016(t1)² + t1 - 4 = 0
(t1)² + 62.5t1 - 250 = 0
Using the quadratic formula to find t1,
[tex]t1 = \frac{-1 +/- \sqrt{1^{2} - 4 X -4 X 0.016} }{2 X 0.016}\\t1 = \frac{-1 +/- \sqrt{1 + 0.256} }{0.032} \\t1 = \frac{-1 +/- \sqrt{1.256} }{0.032} \\t1 = \frac{-1 +/- {1.121} }{0.032} \\t1 = \frac{-1 + 1.121 }{0.032} or t1 = \frac{-1 - 1.121 }{0.032}\\t1 = 0.121/0.032 or -2.121/0.032\\t1 = 3.78 s or -66.28 s[/tex]
Since t1 cannot be negative, t1 = 3.78 s
So, s = 16(t1)²
= 16(3.78)²
= 16(14.29)
= 228.64 ft
Please Please Please Help me with this math problem
Answer:
y=10(3/4)^x
10 and 3/4
Step-by-step explanation:
- 3 ( x + 4 ) = - 24
What is x?
*the dash in front of the numbers is a negative sign*
Let's solve your equation step-by-step.
−3(x+4)=−24
Answer:
x=4
4. Jake wants to make a garden with a border in the corner of his yard. He has lumber in several different lengths. Which three lengths could NOT be used to make a right triangle to fit into the corner of his yard? O 5 ft., 12 ft., 13 ft. O 9 ft., 12 ft., 15 ft. O 16 ft., 12 ft., 20 ft. 0 0 O 10 ft., 12 ft., 15 ft.
Answer:
10 ft., 12 ft., 15 ft.Step-by-step explanation:
Note that for a right triangle, the sum of the square of the hypotenuse is equal to the sum of square of the opposite and the adjacent.
Note that the hypotenuse is the longest side
Checking the given sides 10 ft., 12 ft., 15 ft.
Hypotenuse = 15ft (longest side)
Take the square of 15
15² = 225
Take the sum of square of other two sides
12²+10²
= 144 + 100
= 244
Since 225≠244, hence the three length could not be used to make a right triangle to fit into the corner of his yard
What is the solution to the system of equations? 4x + 2y = 1
5x = y - 18
Answer:
Step-by-step explanation:
X = -5/2
y = 11/2
Y= -2x + 1/2
Y= 5x + 18
Round to the hundredths place.
$4.56 for 18 cookies
13x - (10x + 11) + 6 = 13
PLEASE SHOW WORK
Answer:
x = 6
Step-by-step explanation:
Mary and Julie both have a goal of raising $1000 for charity. Mary raises $12 every 4 days. Julie raises $19 every 6 days.
Will Mary or Julie reach her goal first? Explain.
Answer:
Mary would have a rise of 12 and a run of 4, making her slope, or rate of change, $3 a day. Julie would have a rise of 19 and a slope of 6, making her slope, or rate of change, $3.17 a day. Since Julie is raising money at a faster rate, she would get to the goal of $1000 first.
Step-by-step explanation:
Answer:
Sample Answer: Mary would have a rise of 12 and a run of 4, making her slope, or rate of change, $3 a day. Julie would have a rise of 19 and a slope of 6, making her slope, or rate of change, $3.17 a day. Since Julie is raising money at a faster rate, she would get to the goal of $1000 first.
Step-by-step explanation:
BIG BRAIN
helpppppppppppppppppppppppppppp
Answer:
96
Step-by-step explanation:
First we have to see how the pattern is increasing.
How did the sequence of numbers get from -3 to 6?
Try adding first.
To get from -3 to 6, add 9.
Move on to the next nunber.
Can we get from 6 to -12 through the same pattern (adding 9)?
No, so addition is not the pattern.
Next try multiplication.
To get from -3 to 6, multiply -2.
Move on to the next number.
Can we get from 6 to -12 through the same pattern (multiplying by -2)?
Yes!
Check the other numbers.
-12 × -2 = 24
24 × -2 = -48
Do they meet the pattern?
Yes!
To find the next number in the sequence, use the pattern: multiply the previous number by -2.
-48 × -2 = 96
Answer:
36 i think , datsss confusin Asfkkkkkkk
Step-by-step explanation:
Dave bought some licorice for $1.80 a pound. He bought some trail mix for $4.00 and some bananas for $2.40. Dave spent a total of $10.00. How many pounds of licorice did he buy?
Answer:
2 pounds
Step-by-step explanation:
10-4-2.40=3.60
3.60/1.80= 2
Answer:
2 pounds
Step-by-step explanation:
7. Choose an appropriate variable for each situation. Then write and solve an
equation.
a. If I doubled the money in my savings account, I would have $150.62.
b. three times the hourly wage plus $7.65 in tips equals $27.90
Answer: See explanation
Step-by-step explanation:
a. Let the money in m savings account be represented by x.
If I doubled the money in my savings account, I would have $150.62. This means that:
(2 × x) = $150.62
2x = $150.62
Divide both side by x
2x/2 = $150.62/2
x = $75.31
The amount in the savings account is $75.31
b. Let the hourly wage be represented by x.
Three times the hourly wage plus $7.65 in tips equals $27.90. This will be:
(3 × x) + 7.65 = 27.90
3x + 7.65 = 27.90
3x = 27.90 - 7.65
3x = 20.25
x = 20.25/3
x = 6.75
The hourly wage is $6.75
para hacer un postre Carolina necesita 8 ingredientes para el segundo postre necesita 6 ingredientes de los cuáles 4 también entran en el primer postre¿cuántos ingredientes diferente necesita para hacer los dos postre ?
Answer:
ocupa 10 ingredientes diferentes
Answer:
ocupa 10 ingredientes diferentes
Help me Please!!!!!
Answer:
The function has an even degree
The function has a negative leading coefficient
^^^^ Hope this helps! :)
Help plsssss pls pls
Answer:
500
Step-by-step explanation:
if each ticket is 100 and he wants 5 u multiply em by each other and get 500
PLEASE HELP ASAP (8th grade question)
Answer:
m∠2=35°, m∠1=35°
Step-by-step explanation:
∠2 and ∠4 equal 180° when added, so 180-145=35
all angles of a triangle equal 180°, so 180-∠3-∠2=∠1
180-110-35= 35
Jenny bought gas for her car gas cost $3.45 per gallon Jenny bought 12.5 gallons what was the total of Jenny's gas
Answer: $43.13
Step-by-step explanation:
The cost of a gallon of gasoline is $3.45.
Jenny bought 12.5 gallons of said gasoline. Her total cost is therefore:
= Cost of a gallon * number of gallons purchased
= 3.45 * 12.5
= $43.13
Answer:
43.14
Step-by-step explanation:
which number line shows the solution to the inequality
5x + 3 ≥ - 17?
Answer:
C.
Step-by-step explanation:
Carter is deciding between two different movie streaming sites to subscribe to. Plan A costs $19 per month plus $2 per movie watched. Plan B costs $31 per month plus $0.50 per movie watched. Let AA represent the monthly cost of Plan A if Carter watches xx per month, and let BB represent the monthly cost of Plan B if Carter watches xx movies per month. Write an equation for each situation, in terms of x, and determine the interval of movies watched, x, for which Plan A is cheaper than Plan B.
Answer:
19x+2x=AA
31x+0.50x=BB
Step-by-step explanation:
Answer:
A = 2x +19
B = 0.50x + 31
Plan A is cheaper than Plan B when x < 8 movies
Step-by-step explanation:
2x + 19 = 0.50x + 31
1.5x = 12
x = 8
The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.
Given:
The LCM of two numbers is 14 times their HCF.
The sum of LCM and HCF is 600.
One number is 280.
To find:
The other number.
Solution:
Let HCF of two numbers be x.
The LCM of two numbers is 14 times their HCF.
LCM = 14x
The sum of LCM and HCF is 600.
[tex]14x+x=600[/tex]
[tex]15x=600[/tex]
[tex]x=\dfrac{600}{15}[/tex]
[tex]x=40[/tex]
So, HCF = 40 and the LCM is
[tex]LCM=14(40)[/tex]
[tex]LCM=560[/tex]
We know that, if a and b are two numbers, then
[tex]a\times b=LCM(a,b)\times HCF(a,b)[/tex]
One number is 280.
[tex]280\times b=560\times 40[/tex]
[tex]b=\dfrac{560\times 40}{280}[/tex]
[tex]b=2\times 40[/tex]
[tex]b=80[/tex]
Therefore, the other number is 80.
whoever guesses my birth month first gets the brainliest
4y + 15.5 = 45.5
what is y?
Answer:
Y=7.5
Step-by-step explanation:
Which expression is equivalent to 6x+8?
A 2(3x-4)
B 2(3x+4)
C 2(4x+6)
D 2(3x+8)
Answer:
B
Step-by-step explanation:
=> 6x+8
We see that 6 and 8 have following factors:
=> 2.3x+2.4
Taking 2 as common, we get
=> 2(3x+4)
This is equivalent to option B
7 Eva has 4 m of ribbon for wrapping gifts.
She needsm for each gift.
How many gifts can Eva wrap?
Answer: 6 gifts.
Step-by-step explanation:
I found the question elsewhere and it states that Eve needs 2/3 m for each gift.
Since Eve has 4 m, the number of gifts she can wrap is the 4 m she has divided by the 2/3 m required for each gift.
= 4 ÷ 2/3
= 4 × 3/2
= 12/2
= 6 gifts.
Note: When dividing by a fraction, you can multiply by it's inverse.
5+2(2x-3)+8x = -5x +2
5 -2(2x-3)+8x = -5x +2
show how you did it
Answer:
answer to top question: x = 3/17
answer to bottom question: x = -1
Step-by-step explanation:
distribute first
5 + 4x - 6 + 8x = -5x + 2
combine like terms
-1 + 12x = -5x + 2
12x = -5x + 3
17x = 3
x = 3/17
5 - 4x + 6 + 8x = -5x + 2
4x + 11 = -5x + 2
9x + 11 = 2
9x = -9
x = -1
The formula A = lw gives the area A of a rectangle with length l and width w. What is the area in square feet of a United States flag with a length of 13 feet and a width of 6 feet.
The area is ___ square feet.
Answer:
78
Step-by-step explanation:
You just plug in 13 as the length and 6 as the width
Then you multiply and get the answer
PLEASE HELP :)))
triangle similarity theorem
Answer:
9i
Step-by-step explanation
There are 42 pets at a local pet shop. Twenty-eight of the pets are fish, and the rest are birds. What is the ratio of fish to birds in the pet shop?
3 to 1
2 to 1
3 to 2
I don't know.
Answer:
Its 2 to 1. I just took the quizz!!!
Step-by-step explanation:
The ratio of fish to birds in the local pet shop is 2:1.
What are equivalent ratios?"Equivalent ratios are those that can be simplified or reduced to the same value. In other words, two ratios are considered equivalent if one can be expressed as a multiple of the other".
For the given situation,
Total number of pets in local pet shop = 42
Number of fish = 28, Then
Number of birds = [tex]42-28[/tex]
⇒ [tex]14[/tex]
Thus ratio of pets to fish = [tex]28:14[/tex]
Simplify the ratio to the smallest fraction
Dividing 14 on both sides,
⇒ [tex]2:1[/tex]
Hence we can conclude that the ratio of fish to birds in the local pet shop is 2:1.
Learn more about the equivalent ratios here
https://brainly.com/question/18074939
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To determine what effect the salespeople had on purchases, a department store polled 700 shoppers as to whether or not they had made a purchase and whether or not they were pleased with the service. Of those who had made a purchase, 130 were happy with the service and 119 were not. Of those who had made no purchase, 142 were happy with the service and 309 were not.
Find the probability that a shopper who was happy with the service had made a purchase (round off to the nearest hundredth).
Answer:
This problem has been solved: ... a department store polled 700 shoppers regarding whether or not they made a purchase and whether or not they were pleased ... Of those who made no purchase, 201 were happy with the service and 215 were not. ... We know that number of event of a purchase and a happy with service is.
Step-by-step explanation:
6. Find the measure of each
marked angle.
The measure of each marked angle is 60 degrees for the given figure, which are alternate exterior angles.
The angles are given as:
∠1 = 10x-20 and ∠2 = 7x+4
As we know that alternate exterior angles are described as the pair of angles formed on the outer side of the parallel lines and on opposite sides of the transversal when two parallel lines are crossed by a transversal.
By alternate exterior angles, it can be written as:
∠1 = ∠2
10x-20 = 7x+4
10x -7x = 4 + 20
3x = 24
x = 24/3
x = 3
From given angles:
80 - 20 = 60
56 + 4 = 60
Thus, the measure of each marked angle is 60 degrees.
Learn more about alternate exterior angles here:
https://brainly.com/question/23134598
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How do I solve these two complex fraction problems?