A toy company is releasing a new catapult for water balloons that launches them at 9.8 meters per second from a stand 0.6 meters tall. The function f(x) = −4.9x2 + 9.8x + 0.6 describes the path of the water balloon, where x is the amount of time since the launch. While the mathematical range is y ≤ 5.5, how does the reasonable range compare?

Answers

Answer 1

9514 1404 393

Answer:

  reasonable range: 0 ≤ y ≤ 5.5

Step-by-step explanation:

Unless the balloons are being launched from a building or the edge of a cliff, we generally expect f(x) ≥ 0. This limits the "reasonable range" to ...

  0 ≤ y ≤ 5.5


Related Questions

Pls help and show workings

Answers

Answer: x = 11

Step-by-step explanation:

same as the last question, set them as equal and solve. here's my work:

5x - 1 = 4x + 10

5x - 1 (+ 1) = 4x + 10 (+ 1)

5x = 4x + 11

5x (- 4x) = 4x (- 4x) + 11

x = 11

Judy is selling small candles at the fair for $4 each and large candles for $6 each. She collected $144 selling a
total of 28 candles. How many of each candle did she sell? Use x for the small candles and y for the large
candles.

Answers

12 small candles, 16 large candles.

HOW TO SOLVE

Let x = the number of small candles sold
Let y = the number of large candles sold

You are given two pieces of information:

(1) Number of candles sold: x + y = 28
(2) Revenue based on cost per candles sold: 4x + 6y = 144

Two equations, two unknowns - Solving by substitution (x = 28 - y)

4 * (28-y) + 6y = 144
112 - 4y + 6y = 144
112 + 2y = 144
2y = 32
y = 16

If y = 16, back substitute to find x = 12

Double check using revenue generated:

4x + 6y = 144
4(12) + 6(16) =? 144
48 + 96 = 144

Howard buys 5 pounds of apples at $2.50 per pound and 3 pounds of grapes at $1.50 per pound. Write an expression that shows the total cost of the fruit. Then, find the total cost.

Expression

The fruit cost

Answers

Answer:

5($2.50)+3($1.50)=17

Step-by-step explanation:

you you just need to put up quantity by side of the bar pound it goes in the brackets that will give you the answer when you multiply that or something fruits value.

[tex]\boldsymbol{\$\,17}[/tex]

Algebraic ExpressionAn algebraic expression is one that is composed of integer constants, variables, and algebraic operations.A mathematical operation is a mathematical action. A mathematical operation includes addition, subtraction, multiplication, division, and calculating the root.

Cost of [tex]5[/tex] pounds of apples at [tex]\$2.50[/tex] per pound [tex]=\$\,(5\times 2.50)[/tex]

Cost of [tex]3[/tex] pounds of grapes at [tex]$1.50[/tex] per pound [tex]=\$\,(3\times 1.50)[/tex]

Therefore,

Total cost of the fruit [tex]=\$\,(5\times 2.50)+\$\,(3\times 1.50)[/tex]

                                   [tex]=\$\,12.5+\$\,4.5\\=\$\,17[/tex]

So, total cost of the fruit is [tex]\boldsymbol{\$\,17}[/tex]

Find out more information about expression here:

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Michael has $10 to put in a savings account . He has two options for a saving account : Option 1 will add $ 100 to his account each week . - Option 2 will double the amount in his account at the end of each week . a) Write a function in terms of x to model each option of savings . b) Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike. Determine which option (s) will enable him to reach his goal. Justify your answer.

Answers

Answer:

Option 1:

He starts with $10, and for each week, we add $100

Then his balance as a function of weeks will be:

f(w) = $10 + $100*w

option 2.

Again, we start with $10, and for each week that passes this is doubled, then the equation will be:

g(w) = $10*(2)^w

Now, we want in week w = 7 to have at least $700, then we need to replace w by 7 in both equations and see which one is better.

option 1:

f(7) = $10 + $100*7 = $710

With option 1 he will have enough

option 2:

g(7) = $10*(2)^7 = $1280

Again, he will have more than $700 in week 7, and we can clearly see that this option is better.

Pls help and show workings due asap

Answers

Step-by-step explanation:

l^2=15^2+6^2

l^2=225+36

l^2=261

l=√261

What is 89 x 780 I need to know it please help.

Answers

Answer:780x89= 69,420

Simple math!

Step-by-step explanation:

69,420 hope this helps shug!

The following points are dilated at a center at point C by each of the following scale factors.
Plot and label the image points.

(a) A is dilated by a scale factor of 3.
(b) B is dilated by a scale factor of 2.
(b)D is dilated by a scale factor of 1 1/3
(d) E is dilated by a scale factor of 0.5.

Answers

Answer:

(a) A is dilated by a scale factor of 3.

Step-by-step explanation:

where the imagine

Geometric proofs of segments
Again..
Given: B is the midpoint of AC
C is the midpoint of BD
Prove: AD=3AB

This one hurts to look at

Answers

Answer:

The proof is shown below.

Step-by-step explanation:

Given: B is mid point of AC and C is mid-point of BD.

To prove: AD=3AB

It is given that B is mid-point of AC.

⇒ AB = BC               ...(1)

Also, C is mid-point of BD.

⇒ BC = CD               ...(2)

From (1) and (2),

AB = BC = CD

Now, AD = AB + BC + CD

⇒ AD = AB + AB + AB             (∵ AB = BC = CD )

Hence proved.

8. Solve for x:
3x + 8x = 44
A x= 4
B x= 44/11
C x= 11
D x=33

Answers

Answer:A

Step-by-step explanation:

just try putting 4 into x and you will see

3x +8x=44
11x=44
11x/11=44/11
X= 11


C x=11

Identifying the Graph of an Inequality
Which is the graph of 4x + 2y < 3?
y
4
TY
NA
2
2
2
21
x
41
2
4
-4-2
2.
4
-4
2.
4
2
4
-2
-2
x

Answers

Answer:

The point-slope form of the equation of a line is ...

 y -h = m(x -k)

for a line with slope m through point (h, k).

Comparing this to the given equation, you see that ...

 h = -2, m = 1, k = -4

The line has a slope of 1 and goes through the point (-4, -2). This information is useful for graphing.

__

You can also rearrange the equation to slope-intercept form by subtracting 2 from both sides.

 y = x +2

This has a slope of 1 and crosses the y-axis at y=2. It graphs the same as the above.

The graph of 4x + 2y < 3 is the region below the line 4x + 2y = 3.

The graph is given below.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

The graph of 4x + 2y < 3 is the region in the coordinate plane that satisfies the inequality.

To graph this inequality, we can start by graphing the line 4x + 2y = 3.

This line has a slope of -2 (because it can be written in the form

y = (-2x/1) + (3/2)), and a y-intercept of (0, 3/2).

We can plot this point on the y-axis and use the slope to find other points on the line.

For example, if we move one unit to the right from the y-intercept, we will move down two units (since the slope is -2), giving us the point (1, 1/2). Similarly, if we move one unit to the left from the y-intercept, we will move up two units, giving us the point (-1, 5/2).

We can connect these points to graph the line.

Therefore,

The graph of 4x + 2y < 3 is the region below the line 4x + 2y = 3.

Learn more about inequalities here:

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What is the median in this set of data?
14, 19, 26, 28, 18, 21, 30, 27

Answers

Answer:24

Step-by-step explanation:

Since the numbers in the middle are 21 and 27, you add both and divide by 2 to get the number in the middle of those 2.

Answer:

24

Step-by-step explanation:

it is the median in the set.

5x + 25 ° solve for x and find the measure of

Answers

Answer: 5(x+5)

Step-by-step explanation:

5(x+5)

Explanation:

Factor out 5 from the expression

The students in the music club sold tickets to their spring concert. The table shows the
amount of money raised and the number of tickets sold by each of four students.
What is the constant of proportionality for the sales?

Answers

Answer:

Step-by-step explanation:

You divide the tickets sold and money raised and your supposed to get 5 on all of them . Answer : 5

The constant of proportionality for the sales is 1/5. Therefore, option D is the correct answer.

What is a proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

The given table shows the amount of money raised and the number of tickets sold by each of four students.

The constant of proportionality for the sales is

Fawn: 15/85 =1/5

Ryan: 13/65 =1/5

Daisy: 9/45 =1/5

Doug: 6/30 =1/5

Therefore, option D is the correct answer.

To learn more about the proportional relationship visit:

brainly.com/question/12917806.

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Find the slope of the graph

Answers

2/3 (i’m not amazing at slope but i believe it is 2/3)

Answer:

[tex]-\frac43[/tex]

Step-by-step explanation:

Hello!

Slope is calculated by the formula [tex]\frac{Rise}{Run}[/tex].

Rise is the change in y between two pointsRun is the change in x between two points.

The two points I'm picking is (0,0) and (3,-4).

The change in y (0 and -4) is -4.The change in x (0 and 3) is 3.

Therefore, the slope is [tex]-\frac43[/tex].

for each value of y , determine whether it is a solution to 3y<24.​

Answers

Answer:

1) No

2) Yes

3)No

4)Yes

Step-by-step explanation:

1) 3(8) is simplified to 24

But 24 < 24 is not a true statement because they are both equal.

2)  3(5) is simplified to 15

15 < 40 is a true statement because 15 is less than 24

3) 3(11) simplifies to 33

33 < 24 is not a true statement because 33 is more than 24

4) 3(6) simplifies to 18

18 < 24 is a true statement because 18 is less than 24

Hope this helped.

If you could help I would really appreciate it, but if not that’s fine. Thank you.

Answers

The answer is a! good luck

3x - 8 = 3(x - 4) + 1 halp pls​

Answers

Answer:

no solution

Step-by-step explanation:

3x-11=3x-8

3x=3x+3

0=3

Answer:

Step-by-step explanation:

The top answer is right.    

pls help ill give BRAINLIEST pls just show work lol

Answers

Answer:

s=2

Step-by-step explanation:

Simplify both sides of the equation.

8s−10=3(6−2s)

8s+−10=(3)(6)+(3)(−2s)(Distribute)

8s+−10=18+−6s

8s−10=−6s+18

Add 6s to both sides.

8s−10+6s=−6s+18+6s

14s−10=18

Add 10 to both sides.

14s−10+10=18+10

14s=28

Divide both sides by 14.

14s/14=28/14

s=2

Graph the equation Y = X -1

Answers

Answer:sorry for the delate

Step-by-step explanation:

Answer:

Simplifying
Y = x + -1

Reorder the terms:
Y = -1 + x

Solving
Y = -1 + x

Solving for variable 'Y'.

Move all terms containing Y to the left, all other terms to the right.

Simplifying
Y = -1 + x

What is another name for ray QR?
Options:
QS

NR

QN

NQ

RQ

Answers

Answer:

RQ

Because that is a word

1.Solve 3.2 + y = 8.7.
c
A
8.7
В.
5.5
C.
11.9
D.
-3.2

Answers

Answer:

B

Step-by-step explanation:

I hope this helps

Answer:

B(5.5)

Step-by-step explanation:

3.2+y = 8.7

      y = 8.7-3.2

      y = 5.5

100 points! I will mark brainliest! Only answer if you know it! Random answers WILL IN FACT be reported :)

Answers

Answer: First choice

Explanation:

2 lines are parallel unless both lines have the same slope and different y-intercept

If our line is y = 1/2x - 8

Then the other line should have (1/2)x as their slopes thus the first choice meet the requirement since it has same slope and different y-intercept.

Answer:

y = 1/2x - 8 this is it

Step-by-step explanation:

The sum of six and a number multiplied by
five is 11.

Answers

Answer:

ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg

Step-by-step explanation:

Step-by-step answer:

6+5n=11

6+5n-6=11-6

5n=5

5n/5=5/5

n=1

Plzzzzz give me Brainliest!!!!!  

its urgent pls answer
(2,8)
(4,2,)
(6,-4)
(9,-13)
Find the slope of the line.

Answers

Answer:

The slope would be (i believe, sorry if I am wrong)  3/-1. Rise over run.  So you would go up 3 and left 1.

Step-by-step explanation:

what is the answer to −9p − 6 = −141

Answers

Answer:

p = 15  

Hope this helps

Step-by-step explanation:

p=15 is what i got, good luck!!

Please help me with this question it is my first grade so I need to get it right on the answer if you’re positive you know

Answers

it's symmetrical because they both look alike on each sides

What is 4,490.9 rounded to the nearest hundred?

Answers

Answer:4,500

Step-by-step explanation:

Answer:

yeah, it is 4,500

Step-by-step explanation:

:))))))

What would the exponential growth model be for the given situation?

Answers

If you where to study this topic on yt it would be easier and answer is b

Which of the following triangles is NOT a right triangle?

Answers

Answer:

The first one

Step-by-step explanation:

The third triangle is not a right triangle.

What is a right triangle?

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angles is a right angle.

Given are triangles,

When we apply Pythagoras theorem in the third triangle,

9² ≠ 8²+6²

Hence, The third triangle is not a right triangle.

Learn more about right triangle, here;

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The quotient of ten and a number that is greater than four

Answers

A quotient is dealing with division and less than means subtraction. Let's say "a number" in this example is "x". So, we are going to divide x - 4 by 7 and set it equal to 10:

(x - 4) = 10
7
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