A water taxi travels around an island in a path that can be modeled by the equation y =0.5(x - 16). A water skier is skiing along a path that begins at the point
(6,6) and ends at the point (8. - 4).
a. Write a system of equations to model the problem.
b. Is it possible that the water skier could collide with the taxi? Explain

Answers

Answer 1

I realize that the equation is different, but do it in the same way, it'll help! It is given that the water​ taxi's path can be modeled by the equation y =0.5(x - 14)^2. ​Therefore, this is one of the equations in this system. Find a linear equation that will model the path of the water​ skier, which begins at the point (6,6) and ends at the point (8,-4). The slope is (-5). Use the slope and one point on the line to find the​ y-intercept of the line.  The​ y-intercept of the line that passes through the points (6,6) and (8,-4) is (0,36). Thus, the equation is y=-5x+36. Now, to determine if it is possible for the water skier to collide with the​ taxi, we have to determine if there is a solution to the system of equations. To determine if there is a solution to the system of​ equations, solve the system using substitution.​ First, write the equation that models the water​ taxi's path in standard form. y=0.5(x - 14)^2-->0.5x^2-14x+98. Use substitution. Substitute for  y in the equation and then solve for  x. As the expression on the left side of the equation cannot easily be​ factored, use the Quadratic Formula to solve for x. Do x=-b(plusorminus)sqrrtb^2-4ac/2a. Identify a, b, and c. a=0.5, b=-9, and c=62. Substitute into the Quadratic Formula. If there is a negative number under the radical, there are NO solutions. Thus, the path of the water skier will never cross the path of the taxi.

In conclusion: It is not possible that the water skier could collide with the taxi as the two paths never cross.


Related Questions

18 vocabulary words learned in 2 hours; 27 vocabulary words learned in 3 hours

Answers

Answer: They are equivalent

Step-by-step explanation:

Here is the complete question:

18 vocabulary words learbed in 2 hours 27 vocabulary words learned in 3 hours Are they equivalent? Why

From the question, we are informed that 18 vocabulary words are learned in 2 hours. The number of words learned per hour will be:

= 18/2

= 9 words per hour.

27 vocabulary words learned in 3 hours. The number of words learned per hour will be:

= 27/3

= 9 words per hour.

Since they both have identical number of words learned per hour, it means that they're equivalent.

A mayor estimates that 4,000 people will attend the first day of the county fair. A total of 8,400 people actually attend the first day of the fair. What is the percent error of the mayor’s estimate? Round the answer to the nearest tenth percent, if necessary.

Answers

Answer:

110%

Step-by-step explanation:

4000   100

8400     ?

8400x100

   4000

210% of the expected people showed up

Original price: $10 New price: $7
Is it a discount,
Or a mark up.

Answers

Answer:

discount

Step-by-step explanation:

goes under og price

Answer: 17

Step-by-step explanation:

Enter a range of values for x.

Answers

Can you give a picture of whatever your asking ?

In a class of 65 students, 10 students liked Maths but not English and 20 students liked
English but not Maths. If 5 students did not like both, how many students liked both subjects?​

Answers

Answer: 30 students liked both.

step-by-step explanation: If there are 65 students and 10 liked math but not english you subtract 10 from 65, you get 55. You continue to the next one, 55-20= 35, now there are 35 students but 5 of those students don't like either, so 35-5=30, meaning there are 30 students that like both english and math. I hope this helps.

please answer i will give you brainiest!!!!!!!!!!!!!!!!!!

Answers

Answer:

I'm pretty sure it's A because its showing that the line starts from 1 and goes up if that makes sense.

Answer:

B

Step-by-step explanation:

x < 1 means that x is lesser than 1. A shows x is more than 1 so it is wrong. C shows x is more than -1 which is not entirely true since x could be more than -1, but not less than 1. However, the line in C stretches all the way to 8 which is more than 1 so it is wrong.  D shows that x is lesser than -1, but x could have been 0 or -1, so it is not true either.

I WILL GIVE BRAINLIEST FOR FASTEST AND CORRECT ANSWERS!!
Alex was biking along a 48 mile trail. First half of the time he was biking twice as fast as the second half of the time. If he spent 4 hours on the road, how fast was he biking at first?

Answers

Answer:

The speed in the first part is 16 mph.

Step by step explanation:

The total distance is 48 miles. The total time is 4 hours.

In the second part of the trip, he was traveling at speed s for distance d for 2 hours.

In the first part of the trip he was traveling

at twice the speed, or 2s, for distance 48 - d, for 2 hours.

speed = distance/time

distance = speed * time

First part of trip:

48 - d = 2s * 2

d + 4s = 48 Equation 1

Second part of the trip:

d = s * 2

d = 2s =

Equation 2

Equations 1 and 2 form a system of equations in two unknowns, d and s.

d + 4s = 48

d = 2s

Substitute 2s for d in equation 1.

2s + 4s = 48

6s = 48 =

s=8

The speed in the second part is 8 mph.

The speed in the first part is 2s = 2(8) =

16.

The speed in the first part is 16 mph.

Check:

d = 2s = 2(8) = 16

48 - d = 48 - 16 = 32

The second part is 16 miles. The first part is 32 miles.

16 miles at 8 mph takes 2 hours.

32 miles at 16 mph takes 2 hours.

2 hours + 2 hours = 4 hours.

Our answer is correct.

Answer: The speed in the first part is 16 mph.

A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 420 feet. Determine the​ flag's length and width if the length is 110 feet greater than the width. Use pencil and paper. Write three situations to which you could apply the resulting system of equations.
What is the length of the flag?

Answers

Answer:38

Step-by-step explanation:

He comprado 10 rotuladores que me han costado 8 euros cuento costara cada rotulador

Answers

Answer:

0,8 euros

Step-by-step explanation:

Según la pregunta, 10 rotuladores cuestan ocho euros.

Ahora si

10 rotuladores cuestan 8 euros

1 marcador cuesta 1/10* 8 = 0,8 euros

Por tanto, cada marcador me costó 0,8 euros

I need help with this questions ASAP!

Answers

Answer:

Step-by-step explanation:

3100 ft per 50,000 years

31 ft per 500 years (Divided 100)

Convert ft to inches

372 in per 500 years

0.744 inches per year (Divided by 500)

What is the value of x?

Answers

triangles=180

70+30=100

so x has to equal 80

(mark brainliest if correct pls)

Sum of three angles in the triangle equals to 180.

70+30+x=180

100+x=180

x=180-100

x=80

Therefore, the answer is 80.

Write the equation of the graphs which have m=2, c = 1

Answers

Answer:

y = 2x + 1

Step-by-step explanation:

formula for equation of graph:

[tex]y = mx + c[/tex]

substitute m = 2 and c = 1 into the equation

[tex]y = 2x + 1[/tex]

Step-by-step explanation:

please see it my step work solution

A
Solve the triangle.
19.3
b
45°
105
B
a

Answers

The answer is 30 degrees

Solve -4h - 3 > 4 for h.


will give you brainliest

Answers

Answer:

h<-7/4

Step-by-step explanation:

Please help I really need it!! A student found out that 8% of the students in his school are left-handed.If there are 114 lefties, how many students are in his school?

Answers

Answer:

x = 1425

Step-by-step explanation:

Given that,

A student found out that 8% of the students in his school are left-handed.

Total no of lefties = 114

We need to find the total number of students in the school. Let they are be x.

ATQ,

8% of x = 114

[tex]\dfrac{8x}{100}=114\\\\x=\dfrac{114\times 100}{8}\\\\=1425[/tex]

Hence, there are 1425 students in the school.

What is the range of the function f(x)=2x−4 when the domain is {-3, 0, 4}?

Answers

I found: Domain: all real x ; Range: all real y

What is the radius of the base of the cylinder below?

A cylinder with height of 36 inches and diameter of 42 inches.

inches

Answers

Answer:

21

Step-by-step explanation:

Last year, Jackson made 24 one-cup servings of chili for a school party. This year, he will make ten times the amount of chili that he made last year. If there are 4 cups in 1 quart and 4 quarts in one gallon, how many gallons of chili will Jackson make this year?

Answers

Answer: 15

Step-by-step explanation:

You have to multiply what Jackson made last year (24 cups) times 10 which equals 240. after that you do 240 divided by 4, which equals 60, and 60 divided by 4 again, which gives us the answer (15) (hope you could understand that) Also sorry for not answering in time!

2(6x+5)=58
(solve for x)

Answers

x=4

explanation:
2(6x+5)=58
you distribute the 2 to the 6x and the 5 making the problem:
12x+10=58
you would then subtract 10 from both sides of the equation then making the problem:
12x=48
since we are trying to get x alone we would then divide each side of the equation by 12 leaving you with
x=4

what is 1+1 first person gets brainlst if u get wrong no brainlst

Answers

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

What is 12 1/2 x 4 2/3

Answers

Answer:

174 1/3

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

because may i pls have brainlest

Solve this pls. WILL AWARD BRAINLIEST TO BEST ANSWER!!!!!

Answers

Answer: 31.18

Step-by-step explanation:

The problem is focused on mainly the right triangle made up of points M, Q, and R.  This problem can be solved with the base formula, b = a · tan(β) where a = the length of line MR, β = m∠MQR, and b is the unknown length of RQ.  

Given:

RQ = 18 · tan(60°)

Point M is the midpoint of line PM and line MR.  Since MP is equal to 18, MR has to be 18 as well.  This means that the value of a is 18.

The vertex of ∠MQR is Q, which is 60°.

Step 1: Find the tangent of 60°

The tangent of 60° is √3

Step 2: Solve

RQ = 18 · √3

18 · √3 = 31.18

RQ is equal to 31.18

hii please help mee urgent :)

Answers

Answer:

The answer is C.

explanation:

The reason for answer (C) is because when looking for a function the (X) value cant repeat, but the (Y) can. In answer (C) the x-value 19 repeats.

sorry if its wrong, but pretty sure im right.

5x-2x(x-1)=???????????????????????????????​

Answers

Answer:

7x-2x"2

Step-by-step explanation:

Answer:

it is

7x-2x^2

Step-by-step explanation:

5x+2x-2x^2 = 7x-2x^2

if f(x)= x^2 and g(x) = 4f (x)-1 then which of the following is the value of g (-3)

view image below to see answer choices

Answers

Answer:

27

Step-by-step explanation:

Given

f(x)= x^2-2 and g(x) = 4f (x)-1

g(x) = 4(x^2-2) - 1

g(x) = 4x²-8-1

g(x) = 4x²-9

Get g(-3):

g(-3) = 4(-3)²-9

g(-3 = 4(9) - 9

g(-3) = 36-9

g(-3) = 27

true or false im dumb sorry

Answers

Answer:

False

Step-by-step explanation:

Tell me if you need an explanation

Answer:

it's false.

4×4×4= 64.

(x) = 3x + 5, what is the value of f (5)?

Answers

Answer:

the answer is 20 .put the 5 in place of x                                                                          

and u always remember that f(5) =f(x)

Step-by-step explanation:

58.6 km/h in cm/min solve and explain me ​

Answers

Answer:

PLEASE MARK AS BRAINLIEST!!!!!!!

58.6 kilometer/hour = 97666.666667 centimeter/minute

Step-by-step explanation:

How to Convert Centimeter/minute to Kilometer/hour

1 cm/min = 0.0006 km/h

1 km/h = 1666.6666666667 cm/min

Example: convert 15 cm/min to km/h:

15 cm/min = 15 × 0.0006 km/h = 0.009 km/h

CAN ANYBODY HELP ME WITH THIS JUST WITH 7 TO 12 PLEASE IT IS FOR AN GRADE!!

Answers

Answer: I think there is a mistake for the first one because I did the math and I got 200 added but then there are more answers to this one, I added all the others by 200 and got the next number but then when I got to 6,300 I can't get the 6,700. I get something else, I add 6,000 with 200, and then I get 6,200 instead of getting 6,300. Then I added that 6,200 and 200 and got 6,400. I am confused with the second one, can you please help me understand that one. The third one is also confusing, The one is 12 nuggets eaten per minute. The fifth I am not sure if that is a solvable question, The sixth one I am not sure but I think that it is 0.066667. The seventh one doesn't even make any sense to me.

Explanation: I am sorry this was so long, I was trying to make sense of these questions. Also if this is ALL wrong sorry for even trying.

-3(2x-3)= -5x+5 show your work

Answers

Answer:

x=4

Step-by-step explanation:

Hope this helps!

Plz, mark brainiest! ^.^

Answer:

x = 4

Step-by-step explanation:

Use the distributive property to distribute the -3 amongst the 2x and the -3 in the parenthesis. Once distributed you should have -6x + 9 = -5x + 5. Next, you want to get all like terms on the same side, and to do that you must swap the +9 and the -5x. When you swap these, you must 'flip' the sign and change 9 to -9 and -5x to 5x. Now the equation should look like this: -6x + 5x = -9 + 5.

Now just solve. After solving, it should look like this: -1x = -4. Now to get rid of the negatives. Just divide each side by negative one and your answer is x = 4.

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