Answer:
A) 48 feet
B) 4 seconds
C) 0.54 seconds and 3.46 seconds
Step-by-step explanation:
So we have the function:
[tex]h(t)=64t-16t^2[/tex]
Which represents the height h(t) of the ball after t seconds.
A)
To find the height of the ball 1 second after it has been thrown, substitute 1 for t. Thus:
[tex]h(1)=64(1)-16(1)^2[/tex]
Simplify:
[tex]h(1)=64-16[/tex]
Subtract:
[tex]h(1)=48[/tex]
So, after 1 second, the height of the ball is 48 feet above the ground.
B)
To find out how many seconds after being thrown does the ball hit the ground, we'll set h(t) to 0. 0 means that it will be 0 feet above ground level: in other words, on the ground. So:
[tex]0=64t-16t^2[/tex]
Solve for t. Factor out a 16t:
[tex]0=16t(4-t)[/tex]
Zero Product Property:
[tex]16t=0\text{ or } 4-t=0[/tex]
Solve for t:
[tex]t=0\text{ or } t=4[/tex]
We'll ignore the first zero. So, the ball lands after 4 seconds of being thrown into the air.
C)
To find out at what time(s) the ball is 30 feet above the ground, set h(t) to 30 and solve for t:
[tex]30=64t-16t^2[/tex]
First, divide everything by 2 to simplify things:
[tex]15=32t-8t^2[/tex]
Subtract 15 from both sides:
[tex]-8t^2+32t-15=0[/tex]
Now, to find the zeros, we can use the quadratic formula. a is -8, b is 32, and c is -15. Thus:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute:
[tex]x=\frac{-32\pm\sqrt{32^2-4(-8)(-15)}}{2(-8)}[/tex]
Simplify:
[tex]x=\frac{32\pm\sqrt{544}}{16}[/tex]
Use a calculator. Approximate:
[tex]x\approx0.5422\text{ or } x\approx 3.4577[/tex]
So, the ball is 30 feet above the ground after 0.54 seconds and 3.46 seconds.
And we're done :)
Jack picks 5 pounds of apples in 8 minutes. Jill picks 6 pounds of apples in 10 minutes. Working together at these rates, how many pounds of apples will they pick in 40 minutes?
A scientist creates a colony of bacteria in a dish. This type of
bacteria duplicates itself per minute.
If at 9am the experiment started with a single cell and at 9:13
the dish was half-full, at what time will the dish be full?
Answer: 9:14
Step-by-step explanation: So if he started if 1 bacteria, it becomes 2 bacteria at 9:01, etc. So at 9:13, it is 2^13 and if that is half, that means 2^14 is when it is full so 9:14.
The dish will be full at 9:14 am.
Given, the bacteria duplicates itself per minute.
The experiment started with a single cell at 9 am and at 9:13 am the dish was half full.
So it is clear that after 13 minutes of experiment started the dish was half full.
Now, let here is only 1 bacteria in the dish which is duplicating per minute,so after 1 minute it becomes 2 after that it becomes 4 and after that it becomes 8. Hence it is clear from the example the bacteria doubles itself in powers of her minute. ([tex]2^x[/tex]) here x is the number of minute.
Since after 13 minutes the dish was half full, it means there are [tex]2^{13}[/tex] bacteria in the dish. hence the full dish is [tex]2^{14}[/tex] bacteria. so the bacteria will take 1 more minute for the dish to be full.
Hence at 9:14 am the dish was full.
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Name: Graphing in the Coordinate Plane
PLS I NEED YOUR HELP
Basically all you have to do is go over (left from the center 5 spots) to -5 and up 3. You do x before y always. Then you put a p there because that is point p. I hope this helps you
[tex]0.05x^{2}[/tex]how do i evaluate 0.05
The graph shows the speed of a ball in free fall for 10 seconds. Which is the constant of proportionality shown in the graph? It's on TTM.
Answer:A
Step-by-step explanation:
[easy points] what is the verbal expression to this equation
Answer:
b
Step-by-step explanation:
BECAUSE x-25 = 3
shows something mines 25 that equals 3
CAN SOMEONE PLEASE HELP ME ASAP PLEASEEEE!!!
Answer: being similar means they are in the same ratio. so x = 12
Step-by-step explanation:
first put it into a ratio, 4/x =2/6 and answer it like an equation.
4/x=2/6 (cross multiply)
24=2x
x=12
Answer:
x = 12
Step-by-step explanation:
The only full "pair" of sides is 2 on the little polygon and 6 on the big polygon. The relationship between them is 3. 2 × 3 = 6
Now, apply this to the pair we are using: 4 × 3 = x
4 × 3 = 12, so x equals 12.
simplify the expression
Answer:
[tex]\sqrt[3]{215}[/tex]
Decimal Form: 5.99072641
Look down for explanation
Step-by-step explanation:
[tex]\sqrt[3]{215}[/tex]
You have to simplify.
[tex]= \sqrt[3]{215}[/tex].
Decimal Form: 5.99072641
Now you have the answer to your question!
Hope this helps!
What is the solution to this equation?
5x + 9 - 3x = 18 + 15
A. x= 3
B. x = 8
C. x = 12
D. x = 21
Answer:
21
Step-by-step explanation:
5x-3x=18+15-9
2x=42 /:2
x=21
the positive square root of 28?
Answer:
is 4 i think
Step-by-step explanation:
PLZZZZZZZZZZZ HELP!!!!!!!!!!!!!!!!
Answer:
A. Graph B
Step-by-step explanation:
The reasoning is because the 2 lines are parallel; therefore, it is impossible for them to overlap or intersect, which is the only way a solution can be found. Parallel lines can never have a solution. Hope this helped!
Plz help would the answer be -30
Answer:
Yes
Step-by-step explanation:
-27+(-3) can be simplified to -27-3
-27-3= -30
Answer: Yes you are correct. The answer is -30
Explanation:
We are adding 2 negatives. So we effectively add the positive versions of each number, and then make the result negative.
You can think of it in terms of money: you start off 27 dollars in debt and then borrow 3 more dollars to be a total of 27+3 = 30 dollars in debt.
Or you can think of it like you're under the ocean. Writing -27 could mean you're 27 feet below sea level. Adding on -3, ie subtracting 3, would then move you down 3 feet to get to 27+3 = 30 feet below sea level.
Please help :) which angles are supplementary
Answer:
The first one BED and DEA. AEC and BEC.
Step-by-step explanation:
Supplementary angles are 2 angles that when added equals 180. Also, if there are no numbers given, the 2 angles should make a straight line when next to each other.
c.
A train is traveling 1 mile every 75 seconds. If the train continues at this rate, then how
far will it travel in two hours?
Answer:
96 miles.
Step-by-step explanation:
2 hours = 2*60*60 = 7200 seconds.
So the required distance = 7200/75
= 96 miles.
Answer:
96 miles
Step-by-step explanation:
i did this a few months ago (coincidence I think not)
What number divided by 9 is greater than 700?
Answer:
Any number greater than 6,300
Step-by-step explanation:
Find the inverse of the function: f ( x ) = 1 5 x + 4 Group of answer choices f − 1 ( x ) = 4 x − 5 f − 1 ( x ) = − 5 x − 4 f − 1 ( x ) = x − 4
Answer:
D
Step-by-step explanation:
So we have the function:
[tex]f(x)=\frac{1}{5}x+4[/tex]
To find the inverse, simply switch x and f(x), change f(x) to f⁻¹(x), and solve for it. Thus:
[tex]x=\frac{1}{5}f^{-1}(x)+4[/tex]
Subtract 4 from both sides:
[tex]x-4=\frac{1}{5}f^{-1}(x)[/tex]
Multiply both sides by 5:
[tex]f^{-1}(x)=5x-20[/tex]
So that's our inverse :)
So, our answer is D
Answer:
D
Step-by-step explanation:
Identify the property of equality that makes Equation 1 and Equation 2 equivalent.
Equation 1
4.2x – 1.5 = 1.7x + 8.3
Equation 2
42x - 15 = 17x + 83
We use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.
Given,
Equation 1 - 4.2x – 1.5 = 1.7x + 8.3
Equation 2 - 42x - 15 = 17x + 83
We have to Identify the property of equality that makes Equation 1 and Equation 2 equivalent.
We have,
Equation 1 - 4.2x – 1.5 = 1.7x + 8.3
Equation 2 - 42x - 15 = 17x + 83
If we multiply 10 on both sides of the equation, we get
10 (4.2x – 1.5) = 10 (1.7x + 8.3)
10 x 4.2x - 10 x 1.5 = 10 x 1.7x + 10 x 8.3
42x - 15 = 17x + 8.3
We get,
42x - 15 = 17x + 8.3 which is equivalent to equation 2.
This property is called the multiplicative property of equality.
Thus we use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.
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Evaluate the expression if x = 3, y = 4 and z = 5. 6y - 2xy
Answer:
the answer is 0
Step-by-step explanation:
6 (4) -2 (3)(4)
24-24=0
Please help me with my homework :(
13. -5/6
14. -7/8
15 -7/10
Step-by-step explanation:
The reduce feature on a copy machine is set at 84%. The picture being copied is 4.5 inches wide. What will be the width of yhe reduced picture?
Answer:
The answer is 3.825 inches, the reduced picture will be 84% of the size of the original
Answer:
3.78 inches
Step-by-step explanation:
if the original length is 4.5 and we are making it 84 percent of that size we multiply 4.5 times 84 percent(that is 0.84).
If we type in 4.5 * 0.84 on a calculator the answer comes back as 3.78
so the answer is 3.78 inches
Help please Thanks homework help
Answer:
30
Step-by-step explanation:
3x+x=4x
40+20=60
180-60=120
120/4=30
A refrigerator sells for $1201. If the sales tax rate is 6.8%, what is the total price that you would pay for the fridge?
The answer is $1282.66
Explanation:
The sales tax rate (in this case 6.8%) is paid as part of selling a product. Also, to find the final price of a product, find the tax rate (percentage) of the price of the product and add this number to the price. The process to know the final price of the fridge is shown below:
1. Determine the 6.8% of $1201
1.1. Write the values
1201 = 100
x = 6.8
1.2. Cross multiply and solve the equation
x100 = 8166
x= 8166 ÷ 100
x = 81.66
2. Add this value to the original price
$1201 + $ 81.66 = $1282.66 (Total price including the sales tax)
Here is a polygon on a grid. An L shaped figure on a square grid. Draw a scaled copy of this polygon that has a perimeter of 30 units. What is the scale factor? Explain how you know.
Answer: the perimeter of this L shaped figure is 10 units, so scaling it by 3× would make the perimeter 30 units. so the scale factor is 3
The scale factor of the figure is 3 units.
We need to draw a scaled copy of this polygon that has a perimeter of 30 units and also we need to find the scale factor.
What is the scale factor?The scale factor is the ratio of one figure's side length to the other figure's corresponding side length.
If the sides of a polygon are changed by a scale factor 'a' then its perimeter is also changed by the same scale factor.
Now, scale factor = Scaled perimeter/Actual perimeter
From the figure, the perimeter of the figure is 10 units.
So, scale factor = 30/10 =3 units
Therefore, the scale factor of the figure is 3 units.
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What type of number is pie/2 ?
Answer:
its a irrational number
People drive, on average, 11,979 miles per year. About how many miles each week is that?
(Type a whole number or decimal rounded to the nearest tenth as needed)
Answer:
230.4
Step-by-step explanation:
11,979 divided by 52 is 230.365384615.
230.365384615 Rounded gets the answer
The last one Please answer asap im still crying
Answer:
He has 12 ten dollar bills
Step-by-step explanation:
Let t = number of 10 dollar bills
f = number of fifty dollar bills
t+f = 25 since he has 25 bills
solving for f
f = 25 -t
Then we know he has 770 dollars
10t+50f = 770
Using f = 25-t in the above equation
10t + 50 ( 25-t) = 770
Distribute
10t+ 1250 - 50t = 770
Combine like terms
-40t+1250 = 770
subtract 1250 from each side
-40t - 1250-1250 = 770-1250
-40t = -480
divide each side by -40
-40t/-40 = -480/-40
t =12
He has 12 ten dollar bills
Add 15,7,.5 step by step please I'll mark u brainlest PLEASE
Answer:
27
Step-by-step explanation:
15+5=20
20+7=27
Answer: 27
Step-by-step explanation:
15+5=20
20+7=27
The difference between a number x and 17 is 22
Answer:
X-17=22
X=22+17
X=39 this is the answer
A chemist has 42 grams of aluminum. There are for aluminum. How many milliliters of aluminum does the chemist have?
Answer:
4,200 g. of aluminum
Step-by-step explanation:
42x100=4,200
The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum
How to determine the amount of aluminum?The mass is given as:
Mass = 42 grams
The density of aluminum is:
Density = 2.7 g/cm³
So, we have:
Volume = Density/Mass
This gives
Volume = 2.7/42
Evaluate
Volume = 0.06429cm³
Convert to ml
Volume = 0.06429ml
Hence, the chemist has 0.06429ml of aluminum
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The information below represents the costs of Maggy’s home ownership. what does Maggy spend on average per month related to her home? Mortgage $1,309 per month
$2,152.58.
You can add the per month straight up, but you have to divide the annual costs by 12 (12 months in a year). Add all the numbers together, and you get (roughly) 2,152.58.