A ranger in a lookout tower spots two fires on the campground below. Fire A is 75 meters east
and 40 meters south of the tower. Fire B is 37 meters west and 64 meters south of the tower.
If there is a fire hydrant located three-fourths of the way from Fire A to Fire B, find the location
of the fire hydrant relative to the tower.

Answers

Answer 1

Answer:

the fire hydrant is 9 meters west and 58 m south of the tower

Step-by-step explanation:

Fire A and Fire B can be represented as a point in the Cartesian coordinate with the tower as the origin. Fire A is 75 meters east  and 40 meters south of the tower, It can be represented as (75, -40).  Fire B is 37 meters west and 64 meters south of the tower,  It can be represented as (-37, -64).

If a point O(x, y) divides a line segment AB in the ratio n:m, with A([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]), the point O(x, y) is at:

[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1\\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]

The fire hydrant (x, y) divides Fire A(75, -40) and fire B(-37, -64) in the ratio 3:1(three fourth), hence:

[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1=\frac{3}{4}(-37-75) +75=\frac{3}{4}(-112)+75=-84+75\\x=-9 \\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1=\frac{3}{4}(-64-(-40))+(-40)= \frac{3}{4}(-18)-40=-18-40\\y=-58[/tex]

The fire hydrant is at (-9, -58). That is the fire hydrant is 9 meters west and 58 m south of the tower

Answer 2

The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters.

How to locate the coordinates of the hydrant relative to the tower

In this question we should use the vectorial formula for a line segment to determine the coordinates of the hydrant relative to the tower ([tex]\vec C[/tex]), in meters:

[tex]\vec C = \vec A + r\cdot (\vec B - \vec A)[/tex] (1)

Where:

[tex]\vec A[/tex] - Coordinates of the fire A relative to the tower, in meters. [tex]\vec B[/tex] - Coordinates of the fire B relative to the tower, in meters. [tex]r[/tex] - Distance ratio.

Now we determine the location of the hydrant: ([tex]\vec A = (75, -40)\,[m][/tex], [tex]\vec B = (-37, -64)\,[m][/tex], [tex]r = \frac{3}{4}[/tex])

[tex]\vec C = (75,-40) + \frac{3}{4}\cdot [(-37,-64)-(75,-40)][/tex]

[tex]\vec C = (75,-40) + \frac{3}{4} \cdot (-112,-24)[/tex]

[tex]\vec C = (75,-40) + \left(-84, -18\right)[/tex]

[tex]\vec C = \left(-9, -58 \right)\,[m][/tex]

The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters. [tex]\blacksquare[/tex]

To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13188123


Related Questions

X2 - 13x + 40 = 0

Hey, I got this on my math homework and I need help with figuring out how to solve it

Answers

Answer:

x=8   x=5

Step-by-step explanation:

X^2 - 13x + 40 = 0

What two numbers multiply to 40 and add to -13

-8*-5 = 20

-8-5 = -13

( x-8) (x-5) =0

Using the zero product property

x-8=0    x-5 =0

x=8   x=5

x² - 13x - 40 = 0

To solve this polynomial equation, we will first factor the left side.

On the left, we have a special type of trinomial

that can be factored as the product of two binomials.

X² breaks down as x · x and we are looking for

the factors of 40 that add to the middle term, -13.

Since the middle term is negative, we use negative factors of 40.

The factors that work are -8 and -5.

So we have (x - 8)(x - 5) = 0.

If (x - 8)(x - 5) = 0, that means that either x - 8 = 0 or x - 5 = 0.

Solving for x in each equation, we have x = 8 or x = 5.

We can write this as the set of numbers {8, 5}.

Which question relates to setting a​ long-term financial​ goal?   
Choose the correct answer below.
A.
When would I like to buy a new​ car?
B.
How much does it cost to buy a movie ticket and snacks at the​ theater?
C.
On which day of the month is my credit card bill sent​ out?
D.
What is the late payment fee on my car​ loan?

Answers

A. When would I like to buy a new car
a when would i like to buy a car

The probability of a student passing
an examination is 2/3
If the student
takes three examination, what is the
Probability that he will not
pass
any of them.​

Answers

Answer:  1/27

===============================================

Explanation:

2/3 is the probability of passing a test, so 1/3 is the probability of failing

Note how 2/3 and 1/3 add to 3/3 = 1 to represent 100%

The probability of failing 3 tests in a row is (1/3)^3 = (1/3)*(1/3)*(1/3) = 1/27 assuming each test event is independent from one another.

-------

Side note: the probability of passing at least one test is 1-1/27 = 26/27 and the probability of passing all three tests in a row is (2/3)^3 = 8/27

Solve 16x + 9 = 9y – 2x for y.
y =

Answers

y= 2x + 1, hope this helps
Y= 2x + 1 I tried lol

Write the equation of the line PERPENDICULAR to y = 3/2x + 6 that passes through the point (-3, 4).

Answers

Answer:

Step-by-step explanation:

perp. -2/3 slope

y - 4 = -2/3(x + 3)

y - 4 = -2/3x - 2

y = -2/3x + 2

What two numbers should be placed in the blanks below so that the difference between the
consecutive numbers is the same?
13,_,_,34

Answers

Answer:

20,27

Step-by-step explanation:

let 13,a,b,34 be consecutive numbers.

a=13

l=34

n=4

l=a+(n-1)d

34=13+(4-1)d

34-13=3d

21=3d

d=21/3=7

a=13+7=20

b=20+7=27

Answer:

  20, 27

Step-by-step explanation:

The difference 34-13 = 21 must be divided into three equal parts. Each is 21/3 = 7.

The numbers are 13+7 = 20, 20+7 = 27. As a check, 27 +7 = 34

The missing numbers are 20 and 27.


1. Multiply the following polynomials to write an equivalent expression.
Part A: -7x2y2 (8x2y – 5xy + 11xy2 – 31)
Part B: (t3 – 5t) E+2 – 3t)
Part C: (4x2 – 7x + 5)(2x - 5)
Part D: (3m2 - 5m + 2)2

Answers

Answer/Step-by-step explanation:

A. [tex] -7x^2y^2(8x^2y - 5xy + 11xy^2 - 31) [/tex]

[tex] -7x^2y^2(8x^2y) - (-7x^2y^2)(5xy) + (-7x^2y^2)(11xy^2) - (-7x^2y^2)(31) [/tex] (distributive property)

[tex] -56x^4y^3 + 35x^3y^3 - 77x^3y^4 + 217x^2y^2 [/tex] (note: - × - = + and - × + = -)

B. [tex] (\frac{4}{5}t^3 - 5t)(\frac{1}{4}t^2 - 3t) [/tex]

[tex] (\frac{4}{5}t^3)(\frac{1}{4}t^2 - 3t) - 5t(\frac{1}{4}t^2 - 3t) [/tex] (distributive property)

[tex] \frac{4*1}{5*4}t^3*t^2 - \frac{4*3}{5}t^3*t - \frac{5*1}{4}t*t^2 + 15t^2 [/tex]

[tex] \frac{1}{5}t^5 - \frac{12}{5}t^3 - \frac{5}{4}t^3 + 15t^2 [/tex]

Combine like terms

[tex] \frac{1}{5}t^5 - \frac{73}{20}t^3 + 15t^2 [/tex] (note: -12/5 - 5/4 = -73/20)

C. (4x² - 7x + 5)(2x - 5)

4x²(2x - 5) - 7x(2x - 5) + 5(2x - 5) (distributive property)

8x³ - 20x² - 14x² + 35x + 10x - 25

Combine like terms

8x³ - 34x² + 45x - 25

D. (3m² - 5m + 2)²

= (3m² - 5m + 2)(3m² - 5m + 2)

= 3m²(3m² - 5m + 2) - 5m(3m² - 5m + 2) + 2(3m² - 5m + 2) (distributive property)

= 9m⁴ - 15m³ + 6m² - 15m³ + 25m² - 10m + 6m² - 10m + 4

Combine like terms

= 9m⁴ - 15m³ - 15m³ + 6m² + 25m² + 6m² - 10m - 10m + 4

= 9m⁴ - 30m³ + 37m² - 20m + 4

For income tax​ purposes, a man uses a method called​ straight-line depreciation to show the loss in value of a copy machine he recently purchased. A man assumes that he can use the machine for years. The following graph shows the value of the machine over the years. What loss in value occurred during the first​ year?

Answers

Answer: $500

Step-by-step explanation:

The vertical axis of the graph represents the value of the copy machine and the horizontal axis represents the years.

Using the line, one can see that in the first year, the value of the machine went from $7,000 to $6,500.

The loss in value is therefore;

= 7,000 - 6,500

= $500

The needed graph is attached.

Angles, angles everywhere! Big ones, little ones, right
ones too! But this angle is something new. It has two
rays that meet at a vertex, and it measures 180
degrees. How complex! What angle am I? Draw me.

Answers

Answer:

Straight angle

<----------------------------->

You can determine if an angle is a straight angle only if it is 180 degrees. You can also draw it by drawing a straight line and drawing an arrow facing outward at each end.

A rectangle or prism has dimensions of 2 cm x 2 cm x 3 cm what is the surface area

Answers

Answer:

32 cm²

Step-by-step explanation:

SA = 2(lw + lh + hw)

      = 2(2x2 + 2x3 + 3x2)

      = 2(4 + 6 + 6)

      = 2(16)

      = 32 cm²

a vegetable farmer fills 2/3 of a crate with 5/7 of a pound of tomatoes. how many lbs can fit in one crate​

Answers

Answer:

1 1/14 lbs

Step-by-step explanation:

We can use ratios to solve

2/3 crate        1 crate

----------------- = -----------------

5/7 lb                 x lbs

Using cross products

2/3x = 5/7 *1

Multiply each side by 3/2

3/2 * 2/3 x = 3/2 * 5/7

x = 15/14

x = 1 1/14

Answer:

[tex]\huge\boxed{\sf 1 \ crate = \frac{15}{14} \ lbs}[/tex]

Step-by-step explanation:

[tex]\sf \frac{2}{3}\ of \ a\ crate = \frac{5}{7} \ of \ a\ pound \\\\We \ need \ to \ find\ the \ weight \ of \ one \ crate\\\\So, Multiplying \ both \ sides \ by \ the\ reciprocal \ of \ \frac{2}{3} \ i.e. \frac{3}{2} \\\\1 \ crate = \frac{5}{7} * \frac{3}{2} \ lbs\\\\1 \ crate = \frac{5*3}{7*2} \ lbs\\\\1 \ crate = \frac{15}{14} \ lbs[/tex]

Complete the table
30x – 6y = -6x2

Answers

Answer:

-0.5

Step-by-step explanation:

30x - 6x = -6(2)

24x           -12

24              24

x         =      -.5

Solve for x.

16 = -2x - 1

x = -8
x = -7
x = 7
x = 8

Answers

Step-by-step explanation:

16=-2x-1

17=-2x

x=-17/2

x=-8.5

(this one isn't in the correct order but it's one of the answers ¯\_(ツ)_/¯

16 = -2x - 1

-8=x-1

-7=x

x=-7

3. Round 9995.2 to the nearest ten. Explain in your
own words the reasoning behind why we round
the number the way we do. Use a number line to
support your explanation

Answers

Answer:

10000

Step-by-step explanation:

First, highlight parts of the question. Since it says round to the nearest ten, draw a number line to start. Start by drawing a number line from 9990 to 10000. Whenever a number has the digit from 5 till any number less than 10, you round up. If the number you are trying to round to any digit is less than 5, then you can round down. Since the part of the number that is important for the question is 5.2, we round above. You get 10000 from this.

Jamal owes $424.04 on his credit card. He returns two items, one for $49.95 and the other for $50.42.
Then he makes purchases of $39.19 and $37.41. What is the new balance on the card?

Answers

Answer:

$400.27

Step-by-step explanation:

owes $424.04

returns an item for $49.95

-424.04 + 49.95 = -374.09

he now owes $374.09

returns an item for $50.42

-374.09 + 50.42 = -323.67

he now owes $323.67

makes a purchase of $39.19

-323.67 - 39.19 = -362.86

he now owes $362.86

makes a purchase of $37.41

-362.86 - 37.41 = -400.27

he now owes $400.27

How much string would you need to go around the bottom of a hat shaped like a cone if the radius is 4 inches? (Use 3.14 for π)

Answers

Answer:

25.12 inches

Step-by-step explanation:

To find the circumference or the perimeter of a circle it is the diameter times pi. (pi = 3.14) Or you can do radius times 2 times pi.

Answer is 4 times 2 times 3.14 which is 25.12

Answer as a fraction (please help)

Answers

48/188≈ 0.255319
Alternative form: 12/47

A 6- foot roll of waxed paper costs $3.60. What is the price per inch?

Answers

Answer:

0.3

Step-by-step explanation:

1 foot = 12 inches so 3.60/12=0.3

A coin flipped 10 times and the results is recorded. What is the probability of getting exactly 5 tails?

Answers

Answer:

50%

Ste50p-by-step explan%ation:

Solve the equation for y

Answers

the answer is C). y= 1/4x + 2

If 4 times a number is 156, then 1/3 of the number is

Answers

4 divided by 156 is 39. 39 divided by 1/3 is 13

Answer:

[tex]\huge\boxed{\sf \frac{x}{3} = 12}[/tex]

Step-by-step explanation:

Let the number be x

4x = 156

Dividing both sides by 4

x = 36

Dividing both sides by 3

[tex]\frac{x}{3}= \frac{36}{3}[/tex]

[tex]\frac{x}{3} = 12[/tex]


Express each rational number in decimal form.
[tex] \frac{3}{4} [/tex]

Answers

Answer:

.75

Step-by-step explanation:

there is only 1 number

0.75

The decimal forms of rational numbers either end or repeat a pattern. To convert fractions to decimals you just divide the top by the bottom — divide the numerator by the denominator — and if the division doesn't come out evenly, you can stop after a certain number of decimal places and round off.

Find the value of x.

X=8

X=10

X=16

X=20

Answers

Answer:

D. 20

Step-by-step explanation:

Find the required diagram to the question in the attachment.

From the diagram it can be seen that the distance of the lines projecting from the centre of the circle to the line segment is equal i,e they are both 8. This means that the length of both chords given will be equal. For the known chord length, it can be seen that the line perpendicular to the chord cuts them at the centre. and since both sides of the chord are parallel, the other sides too will be 10 making the total length to be 10+10 = 20.

Since the length of the known chord is equal to the length of the unknown chord x, hence, the value of x will also be 20

Answer:

D. x=20

Step-by-step explanation:

correct on EDGE2021

Brayden is working two summer jobs, making $18 per hour lifeguarding and making $9 per hour clearing tables. In a given week, he can work no more than 19 total hours and must earn a minimum of $270. If Brayden worked 14 hours lifeguarding, determine the minimum number of whole hours clearing tables that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.

Answers

Answer: The amount he earns from lifeguarding = $252 ($18×14). The total amount he needs to make a week is $270.

$270-$252=$18, he needs to earn $18 more from clearing tables.

$18÷9=2, so the minimum number of whole hours clearing tables is 2

Can someone please help me on this one!

Answers

Answer:

The answer is (1,-1)

Step-by-step explanation:

The best approach for this problem is to plug in the coordinates into the given inequality.

[tex]7x-3y\geq 10\\[/tex]

(3,4) ------> [tex]7(3)-3(4)=9[/tex]

9 is less than 10 so, we can rule this one out.

(1,0) -------> [tex]7(1)-3(0)=7[/tex]

7 is less than 10 so, we can rule this one out.

(1,2) -------> [tex]7(1)-3(2)=1[/tex]

1 is less than 10 so, we can rule this one out.

(1,-1) -------> [tex]7(1)-3(-1)=10[/tex]

10 is equal to 10, so this is the answer.

Hope this helps!

As mentioned by Mark there are an unlimited number of pairs that satisfy your equation. So let us see how you can characterize these solutions

if 7x - 3y > 10 then

7x > 10 +3y

Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6

then by substitution

7  must be > 10+ 3*6

or 7x must be > 28

or x must be > 4

So all pairs such that x is > 4 and y = 6 are solutions.

I can create an infinite number of pairs choosing any number for y. Likewise I could have chosen x and solved the problem for y. In the above example I chose 6 for y to make the division easy. I could have chosen any number(real or integer) for y and solved the equation for x  to derive appropriate  pairs

Which step is incorrect when solving the equation 2(x+9)=4(x+7)+2?
Choose the first step that made an error.

1. 2(x+9)=4(x+7)+2

2. 2x+18=4X+28+2

3. 2x+18=4x+26

4. -8=2x

5. -4=x
(i think it's step 3)

Answers

Answer:

3. 2x+18=4x+26

Step-by-step explanation:

2(x+9)=4(x+7)+2

2x+18=4x+28+2

2x+18=4x+30

The step that made an error in solving this linear equation is step 3.

Hope this helps ;) ❤❤❤

What is 30/35 in simplest form? ​

Answers

What is 30/35 Simplified? - 6/7 is the simplified fraction for 30/35.

Answer: 6/7

Step-by-step explanation:

is is 6 2/7 rational or irrational
is -19 rational or irrational
is -√100 rational or irrational​

Answers

Step-by-step explanation:

6 2/7is rational

-19is rational but next I dont know

if x and 3x are linear pair then find the value of x.

Answers

Answer:

x = 45°

Step-by-step explanation:

x + 3x = 180°

--> 4x = 180°

--> x = 180 / 4 = 45°

Step-by-step explanation:

x+3x=180 (sum of linear pair=180)

or, 4x =180

or, x = 180/4

therefore x =45

Someone help me on this.

Answers

Answer:

[tex]-57-39i[/tex]

Step-by-step explanation:

So we have the expression:

[tex](7+2i)(-9-3i)[/tex]

FOIL:

[tex]=7(-9)+7(-3i)+2i(-9)+2i(-3i)[/tex]

Simplify:

[tex]=-63-21i-18i-6i^2[/tex]

Recall that i² is just -1. Thus:

[tex]=-63-21i-18i-6(-1)[/tex]

Simplify:

[tex]=-63-21i-18i+6[/tex]

Combine like terms:

[tex]=(-63+6)+(-21i-18i)[/tex]

Add:

[tex]=-57-39i[/tex]

And we're done!

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