Two boats started to move towards each other from two boat stations, located 30 miles apart. One boat moved at a speed of 3 miles per hour, the other moved twice as fast. How soon will the boats meet?

Answers

Answer 1

Answer:

The boats will meet in 3.33 hours.

Step-by-step explanation:

The position of each boat can be modeled by a first order equation.

I am going to say that the first boat is at the position 0, and moving in the positive direction with a speed of 3 miles per hour. So

[tex]A(t) = 0 + 3t[/tex]

They are moving in oppositie directions, and initially are 30 miles apart. This means that the second boat starts at the position 30, and moves in the negative direction at the rate of 6 miles an hour. So

[tex]B(t) = 30 - 6t[/tex]

How soon will the boats meet?

This is t when:

[tex]A(t) = B(t)[/tex]

[tex]3t = 30 - 6t[/tex]

[tex]9t = 30[/tex]

[tex]t = \frac{30}{9}[/tex]

[tex]t = 3.33[/tex]

The boats will meet in 3.33 hours.


Related Questions

help me plzzzzzzz!!!!

[tex] {y}^{2} + 14 = 3 {y}^{2} \times 5[/tex]​

Answers

Answer:

[tex]y=1,\:y=-1[/tex]

Step-by-step explanation:

[tex]y^2+14=3y^2\cdot \:5\\\y^2+14-14=3y^2\cdot \:5-14\\y^2=15y^2-14\\y^2-15y^2=15y^2-14-15y^2\\-14y^2=-14\\\frac{-14y^2}{-14}=\frac{-14}{-14}\\y^2=1\\\\y=\sqrt{1},\:y=-\sqrt{1}\\y=1,\:y=-1[/tex]

Answer:

y = ± 1

Step-by-step explanation:

Given

y² + 14 = 3y² × 5, that is

y² + 14 = 15y² ( subtract y² from both sides )

14 = 14y² ( divide both sides by 14 )

1 = y² ( take the square root of both sides )

± [tex]\sqrt{1}[/tex] = y , that is

y = ± 1

Thus y = - 1 or y = 1

what is the area of this triangle?

Answers

Answer:

1099.589 ft^2

Step-by-step explanation:

idk what happen to my answer but some bozo delete my answer but ehre you go again for any who has the same question:)

what percent of 420 is 70​

Answers

Answer:

16.67

Step-by-step explanation:

Answer:

16.67

Step-by-step explanation:

70:420*100 =

(70*100):420 =

7000:420 = 16.67

translate (-4,5) up 3 units
then reflect the result over the y-axis
what are the coordinates of the final point?

Answers

Answer:

4,8

Step-by-step explanation:

reflecting over y axis is flipping to the other side. and you are going up 3 points so 5+3 is 8. and negative four turns to positive four

A submarine at a depth of 675 feet below the surface rose to 1/3 this depth. Which of the following represents the new depth of the submarine below the surface?

Answers

Answer:

225

Step-by-step explanation:

Take 675/3 to find one third of its current depth. That gives you your answer. Does that make sense?

How to determine the function with the graph?

Answers

i think it’s f (x)= 1

if the sides of a triangle and area is given. How to find perimeter​

Answers

Answer:

add it up to see if it's 180

Answer:

Well since you have the sides you would add up all of the sides to find the perimeter.

Step-by-step explanation:

(x - 3)² + (x - 1)² = 8
Identify the center and radius of each

Answers

Answer:

The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]

Step-by-step explanation:

I am going to assume you meant to write

[tex](x-3)^2+(y-1)^2 = 8[/tex]

Since if both variables were x it would not be a circle:

Then you can find the center and radius using the general formula of a circle:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where the center is at (h,k) and r is the radius

Therefore:

The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]

What are the domain and range of the logarithmic
function f(x) = log7X? Use the inverse function to
justify your answers.

Answers

Answer:

The domain of f is x > 0.

The range of f is all real numbers.

The domain of the inverse function is all real numbers.

The range of the inverse function is y > 0.

The domain of f is the same as the

range of the inverse function.

The range of f is the same as the

the domain of the inverse function.

Step-by-step explanation:

this is the sample answer, make sure you rewrite in your own words!

The domain and the range of a function are the set of input and output values of the function

The domain and the range of the function are set of real numbers greater than 0

The function is given as:

[tex]f(x) = log_7(x)[/tex]

The above function is a logarithmic function.

From the properties of a logarithmic function, we have:

The x-values are always greater than 0The y-values are always greater than 0

This means that, the domain and the range of the function are set of real numbers greater than 0

Read more about domain and range at:

https://brainly.com/question/10197594

What is the end behavior of the polynomial function?

Answers

Answer:

D) as x approaches neg. infinity, y approaches neg. infinity

Step-by-step explanation:

This is because you get to negative x infinity which is towards the right, you see that the y value is going down sharply as well towards the direction of negative infinity in y direction (x direction is right to left and y direction is up and down)

Answer:

D one Edge 2021 ;))

Step-by-step explanation:

So do i divide by 2 each time?

Answers

Divide by two if you are dividing by two...

What is the y-intercept of the quadratic function f(x) = (x-8)(x+3)

Answers

Answer:

-24

Step-by-step explanation:

To find the y intercept, plug x in as 0.

Answer:

-24

Step-by-step explanation:

Y intercept is where graph cuts the y axis and it satisfies x=0

So put x=0 in your equation

F(0)= -8 x 3

F(0)= -24

Therefore y-intercept= -24

3. Find x, y, and z.


y
18°
64°​

Answers

Answer:

[tex]y = 18 \: \: degrees[/tex]( vertically opposite angles)

[tex]x = 64 \: \: degrees[/tex]

[tex]y + z + x = 180 \\ 18 + z + 64 = 180 \\ 82 + z = 180 \\ z = 180 - 82 \\ z = 98 \: \: degrees[/tex]

EMERGENCY!!!! EXTRA POINTS! I HAVE POSTED THIS QUESTION 5 TIMES AND HAD TO REPORT ALL RESPONSES! I ACTUALLY NEED HELP!
The amusement park in Riverdale charges a $10 entrance fee plus $1 per ride. The amusement park in Esterdamb charges a $5 entrance fee and $2 per ride. For how many rides will the cost be the same for both amusement parks? x= # of rides
Number of rides_____?
Cost_____?

Answers

Answer:

5 rides $15

Step-by-step explanation:

.

Answer:

omg riverdale is my favorite show!

Step-by-step explanation:

The measure of an angle is 17°. What is the measure of its complementary angle?

Answers

Answer:

73°

Step-by-step explanation:

the measure of two complementary angles add up to 90

so We need to solve this equation to get the measure of its complementary angle :

x + 17 = 90

then

x = 90 - 17

  = 73

Find the greatest common factor of 24, 40 and 60
Please answer asap ty!!

Answers

Answer:

4

Step-by-step explanation:

Answer:

GCF=4

Step-by-step explanation:

It's 4

24/4=6

40/4=10

60/4=15

You can't go any higher because there is no GCF of 6, 10, and 15.


Which problem is being modeled on the number line?

Answers

I don’t see a number line but I can help

Answer:

Step-by-step explanation:

What is the distance between the points (4, 5) and (10, 13) on a coordinate plane?

A. 10 units
B. 14 units
C. 12 units
D. 8 units

Answers

Answer:

10

Step-by-step explanation:

Distance = √(x2-x1)² + (y2-y1)²

d = √(10-4)² + (13-5)²

d = √6² + 8²

d = √36+364

d = √100

d = 10

A rectangular prism has a length of 12in, a height of 5in, and a width of 8in. What is its volume, in cubic in?

Answers

Answer: The volume is 480 in^3

Step-by-step explanation:

v= lwh

v= 12 * 5 * 8

v= 480 in^3

Answer:

Volume of the rectangular prism = [tex]480in.^{3}[/tex]

Step-by-step explanation:

Formula for the volume of a rectangular prism= Ah, where A= base area

                                                                                               & h= height

Base area(A)= Length×Width

                    = 12in.×8in.

                    = [tex]96in.^{2}[/tex]

Since height=5in.,

Volume= [tex]96in.^{2}[/tex]×5in.

            = [tex]480in.^{3}[/tex]

Hope this helps!!!

Pls mark as brainliest

Need Help Asap offering 10 Points!!!!

Answers

Answer:

13 minutes 30 seconds.

Step-by-step explanation:

You just divide 10.8 by 0.8...

10.8÷0.8=13.5

what is the solution of this equqtion? 1w= -17​

Answers

Answer:

-17

Step-by-step explanation:

1w= -17

(1)(-17)=

-17

Answer:

-17

Step-by-step explanation:

in this situations, we normally divide both sides by the number next to the unknown.

1w is the same as saying w

so,

w = -17

find the two values that x can have if x2-12=37​

Answers

Answer:

[tex]x2 - 12 = 37[/tex]

Step-by-step explanation:

Add 12 to both sides:

[tex]x2 - 12 + 12 = 37 + 12[/tex]

Simpilfy:

[tex]x2 = 49[/tex]

Simplify:

[tex]2x^{2} = 49[/tex]

Simplify:

[tex]\frac{2x^{2} }{2} = \frac{49}{2}[/tex]

[tex]x^{2} = \frac{49}{2}[/tex]

For x^2 = f(a) the solutions are x = [tex]\sqrt{f(a)} , - \sqrt{f(a)}[/tex]

x = [tex]\sqrt{\frac{49}{2} } , x = -\sqrt{\frac{49}{2} }[/tex]

-[tex]\sqrt{\frac{49}{2} } = -\frac{7\sqrt{2} }{2}[/tex]

x = [tex]\frac{7\sqrt{2} }{2} , x = -\frac{7\sqrt{2} }{2}[/tex]

Hope I helped, may I get brainliest and a thanks?

Thank you, have a good day! =)

Answer:

[tex]x = 7 \\ x = - 7[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 12 = 37 \\ {x}^{2} = 37 + 12 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ x = - 7[/tex]

Pleaaaase hellp me will mark u brainly for both answers!!!
Thank u if u do really appreciate it.

Answers

Answer:

1. Option A is correct (A = length x width)

2. Option B is correct ( A = base x height/2)

Hope this helps

:)

On your birthday you receive a new TV valued at $1199. The value of the TV decreases by 25% each year. What will its value be 4 years from now?

Answers

Answer: 74.93

Step-by-step explanation:   if you heard of the line equals line method this should be able to help you.  

299.75                     25%

---------------=------------------  

$1199                     100%      

so you cross multiply 1199 and 25 and then divide it by 100.   which would be 299.75 that is the price per 1 year then you divide that value by 4 and that will be your answer.  

299.75 divided by 4= 74.93  

hope this helps

Answer:

379.37

Step-by-step explanation:

I just did it the manual way

1199-25%=899.25

(25% of 1199 is 299.75)

899.25-25%=674.44

(25% of 899.25 is 224.81)

674.44-25%=505.83

(25% of 674.44 is 168.61)

505.83-25%= 379.37

(25% of 505.83 is 126.5)

I just took a test with this question

Determine the volume of the cylinder

Answers

Answer:

about 904.78

Step-by-step explanation:

πr^2h pi(6)^2 * 8

find the variable: n/14=3

Answers

Answer:

n=42

Step-by-step explanation:

3. Which of the following represents a function?
O (5, 1), (5,2), (5, 3), (5, 4)
O (-1,2), (-2, 1), (-1, -2), (-2,-1)
O (3, 4), (-3, 2), (3, 8), (5,5)
O (2, 3), (4, 3), (-2, -3), (-4,-3)

Answers

Answer: D is a function.

Step-by-step explanation:

A function need to have exactly one output to each input.

Answer: D. (2, 3), (4, 3), (-2, -3), (-4,-3)

Step-by-step explanation: This represents a function because they're the opposing of each other. Hope this helps happy holidays! :)

I need help with this :/ pls help

Answers

Answer:

When you divide by 10^3, the decimal point moves three places to the right. When you multiply by 0.001, the decimal point moves three places to the right. So, both equal .0777

Step-by-step explanation:

Someone help me please

Answers

Step-by-step explanation:

Step 1:  Convert degrees into radians

[tex]\frac{degrees}{1}*\frac{\pi }{180}[/tex]

[tex]\frac{52}{1}*\frac{\pi}{180}[/tex]

[tex]\frac{52\pi}{180}[/tex]

[tex]\frac{13\pi}{45}[/tex]

Step 2:  Find the arc length

[tex]S = r\theta[/tex]

[tex]S=(3)(\frac{13\pi}{45})[/tex]

[tex]S = \frac{39\pi}{45}[/tex]

[tex]S=\frac{13\pi}{15}[/tex]

Answer: Option B

Please answer i'll give brainlist
AD and BE are diameters. What is the measure of arc EDC
A. 125 degrees
B. 145 degrees
C. 235 degrees
D. 215 degrees

Answers

Answer:

a

Step-by-step explanation:

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