The day after the British burned most of the government building in Washington, DC, something shocking happened: (A) President Madison surrendered, (B) the Americans counterattacked and retook the city, (C) a strong hurricane hit the city.

The fire is a distance of 9.33 miles from Station A and 4.67 miles from Station B.

Let's denote the distance of the fire from station A as "x" and the distance of the fire from station B as "y".

From station A, the bearing of the fire is N 35° E. This means that if we draw a line connecting station A and the fire, the angle between this line and the north direction is 35°.

Similarly, from station B, the bearing of the fire is N 30° W. This means that the angle between the line connecting station B and the fire and the north direction is 30°.

Now, let's construct a triangle with vertices at Station A, station B, and the fire. The line connecting station A and station B represents the base of the triangle, and the lines connecting station A and the fire and station B and the fire represent the two sides of the triangle.

Since the triangle is isosceles (both sides are equal), the angles opposite the two sides will also be equal.

Let's denote the angle opposite side x as α and the angle opposite side y as β.

From the given bearings, we can determine the values of α and β:

α = 180° - 35° = 145°

β = 180° - 30° = 150°

Now, using the Law of Sines, we can set up the following ratios:

sin(α) / x = sin(β) / y

Solving for y, we get:

y = (sin(β) / sin(α)) * x

Substituting the known values, we have:

y = (sin(150°) / sin(145°)) * x

Using a calculator, we can evaluate the sin(150°) and sin(145°) to get:

y = (0.5 / 0.996) * x

y = 0.501 * x

Since the two stations are 14 miles apart, we know that x + y = 14.

Substituting the value of y from the previous equation, we have:

x + 0.501 * x = 14

1.501 * x = 14

x = 14 / 1.501

x ≈ 9.33

Now, to find the value of y, we can substitute the value of x into the equation:

y = 0.501 * x

y = 0.501 * 9.33

y ≈ 4.67

Therefore, the fire is 9.33 miles from Station A and 4.67 miles from Station B.

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The fire is approximately 38.7 miles away from station A and 38.4 miles away from station B.

To solve this problem, we can use trigonometry and create a diagram to visualize the situation.

Now, let's label the diagram. We'll use the following labels:

A: Fire-lookout station A

B: Fire-lookout station B

F: Fire's location

Next, we need to determine the angles and distances involved. From the problem statement, we know the bearing of the fire from station A is N 35° E, and the bearing of the fire from station B is N 30° W. Let's mark these angles on the diagram.

To find the distance of the fire from each station, we can consider the angles formed between the stations and the fire. The sum of these angles should be 180° since we have a straight line. Let's find the missing angles by subtracting the given angles from 180°.

For station A:

Angle A = 180° - 35° = 145°

For station B:

Angle B = 180° - 30° = 150°

Now, let's draw lines from each station to the fire, and label the distances as dA and dB.

We can use trigonometry (specifically, the tangent function) to find the distances dA and dB. Tangent of an angle is equal to the opposite side divided by the adjacent side.

For station A:

tan(145°) = opposite side (dA) / adjacent side (14 miles)

dA = 14 * tan(145°)

For station B:

tan(150°) = opposite side (dB) / adjacent side (14 miles)

dB = 14 * tan(150°)

Now, let's calculate these distances using a calculator.

dA = 14 * tan(145°) ≈ 38.7 miles

dB = 14 * tan(150°) ≈ 38.4 miles

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Answer:

y

Step-by-step explanation:

y\

Answer: 6.53 on khan academy

Step-by-step explanation:

Answer:

y=1/2x-7

Step-by-step explanation:

-9=1/2(-4)+b

-9=-2+b

b=-7

y=1/2x-7

Answer:

y=1/2x-2

Step-by-step explanation:

1. Find slop by subtracting y values over subtracting x values, which will get you the m value

-1+3 / 2+2 = 1/2

Answer:

0.20035667433

Step-by-step explanation:

Answer:

0.20035667433 , is the answer.

Step-by-step explanation:

Honestly whenever it comes to pi in maths , you can usually always use a calculator so on a calculator write in 'pi (5.6) *squared* x 2'

Answer:

x axis

Step-by-step explanation:

just remember it by saying x comes first then y

Answer:

x axis comes first.

Step-by-step explanation:

When pinpointing a point, find the x axis first, and then the y (x , y).

just add.................

197 + 27 = 224

hope this helps

Answer:

x = 9.2

Step-by-step explanation:

The scale factor is 2 from the triangle on the left to the triangle on the right

2*2 = 4

Multiply the scale factor times the number on the left to get the unknown on the right

2*4.6 =9.2

Answer:

74°

Step-by-step explanation:

The blue angle and the red angle are supplementary angles (meaning they add up to 180°) because these two lines are parallel. Therefore, 106° + ? = 180°, and the red angle is 74°. Hope this helps!

Answer:

71° will be your answer

Answer:

No

Step-by-step explanation:

If segment AB is tangent to the circle, then angle CBA will be a right angle, making triangle ABC a right triangle. If triangle ABC is a right triangle, it's sides will fit the Pythagorean theorem...

(leg)^2 + (leg)^2 = (hypotenuse)^2

Does 8^2 + 16^2 = 19^2 ?

64 + 256 does not equal 361!

Triangle ABC is NOT a right triangle, so segment AB is not tangent to the circle.

Answer:

A) 12 ounces for $0.89

Explanation:

$0.89 ÷ 12 = $0.07

$1.69 ÷ 18 = $0.09

$2.09 ÷ 24 = 0.087

Now we know the different prices for each ounce, as you can see the 12 ounces is definitely the best buy.

I hope this helps!

Answer:

2 apples....................

Answer:

2

Step-by-step explanation:

Tom has 5 apples

Mary takes 3 apples

subtract 3 from 5

3 - 5 = 2

Answer:

<LKH and <JKM

Step-by-step explanation:

<LKH and <JKM are vertical angles because they are vertically opposite.

Answer:

200 teachers

Step-by-step explanation:

Let t= teachers

t * 25% = basic math teachers

t *.25 = 50

Divide each side by .25

.25t/.25 = 50/.25

t =200

Answer:

200

Step-by-step explanation:

The 50 basic math teachers are 25% of all the teachers of the school.

You can use a proportion.

50 is to 25% as x is to 100%

50/25 = x/100

10/5 = x/100

5x = 100 * 10

5x = 1000

x = 200

There are 200 teachers.

I’m not sure what that meant.

Answer:

cool

Step-by-step explanation:

Answer:

(4,1)

Step-by-step explanation:

3x + 4y = 16

-4x - 3y = -19

4( 3x + 4y = 16)

3( -4x - 3y = -19)

Distribute

12x + 16y = 64

-12x - 9y = -57

Now subtract both equations

7y = 7

/7 on both sides

y = 1

Substitute y = 1 in one of the equations.

3x + 4y = 16

3x + 4(1) = 16

-4 on both sides

3x = 12

/3 on both sides

x = 4

Answer:

x = 4

y = 1

Answer:

x=8

Step-by-step explanation:

2.25x=1.5x+6

-1.5x     -1.5x

0.75x=6

3/4x=6

x=6*4/3

x=24/3

x=8

Answer:

8

Step-by-step explanation:

Look at the attachment

Answer:

she is expected to hit 18 out of the 30 pitches

Step-by-step explanation:

In this question, we are required to use experimental probability to make a prediction.

From the hits she has today, we can estimate the number of hits she might be getting tomorrow.

Since she made 12 hits out of 20 today, the probability that she has a hit will be 12/20 = 3/5

Now if she is having 30 pitches tomorrow, the expected number of hits would be the probability of getting a hit multiplied by the total number of pitches.

That would be 3/5 * 30 = 18 pitches

Answer:

a) 0.09

b) 2 ways

Step-by-step explanation:

a) Probability Pedro's shot will score will be given as) :

P(score) = 0.30

The probability he will score in 2 consecutive shots will be calculated as:

P(score) * P(score)

= 0.30 * 0.30

= 0.09

Therefore, probability he will score in 2 consecutive shots is 0.09

b) Jillian has 3 bracelets: X, Y, & Z as a gift. If bracelet Y is chosen first, the number of ways Jillian can give out the bracelets since bracelet Y is chosen first, she will have 2 bracelets remaining. So, number of ways to distribute these 2 bracelets are :

= 2!

= 2 * 1

= 2

Which could be in this order:

YXZ or YZX

Therefore, the number of ways if Y is chosen first is = 2 ways

Answer: A. 0.09

Just took test.

Answer:

50

Step-by-step explanation:

The slope is change in y divided by the change in x

Change in distance / change in hour

m = (400-200)/(8-4)

   = 200/4

  = 50

Answer:

1.5 hours

Step-by-step explanation:

We can write a ratio to solve

19 miles         57 miles

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

.5 hours          x hours

Using cross products

19x = 57*.5

19x =28.5

Divide each side by 19

19x/19 = 28.5/19

x =1.5

1.5 hours

I put the wrong answer don’t mind me

Answer:

Isosceles

Step-by-step explanation:

Two sides are equal to each other and not the same length as the other side, so it'd be an isosceles triangle.

Domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer:

Step-by-step explanation:

hmmm

Answer:

Height of cone is 5m

Step-by-step explanation:

Answer:

LM = 36

Step-by-step explanation:

A quadrilateral is a shape with 4sides. There are different type of quadrilateral such as square, rectangle, trapezium, parallelogram, kite and rhombus.

Perimeter of a quadrilateral is the addition of all 4 sides.

Since the shape is not specified neither is there a diagram, let's assume the quadrilateral is a square.

See attachment for diagram used in solving the question.

Perimeter of square = length+ length+ length+ length

= 4× length

Perimeter of quadrilateral ABCD:

640 = 4×length

Length = 640/4

Length = 160

Perimeter of quadrilateral LMNO:

144 = addition of all 4 lengths

144 = LM + MN + NO +OL

Since we are considering a square all the sides are equal.

LM = MN = NO = OL

144 = 4×LM

LM = 144/4

LM = 36

Answer:

[tex]y-3=\frac{1}{5} (x-2)[/tex]

Step-by-step explanation:

First you need to find the slope by using this formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{(4)-(3)}{(7)-(2)}\\m=\frac{1}{5}[/tex]

Now you can put it in point slope form which is: [tex]y-y_1=m(x-x_1)[/tex]

[tex]y-3=\frac{1}{5} (x-2)[/tex] is your answer.

Answer:

[tex]8\frac{1}{2}[/tex] cups

Step-by-step explanation:

To determine the quantity of snack mix Jared guest ate, we multiply the quantity of snack mix the guest ate by the quantity of snack mix Jared made. i.e we determine [tex]\frac{2}{3}of12\frac{3}{4}[/tex] by multiplying both fractions together

quantity of snack mix Jared guest ate = [tex]\frac{2}{3}of12\frac{3}{4}=\frac{2}{3}*12\frac{3}{4}=\frac{2}{3}*\frac{51}{4}=\frac{17}{2} =8\frac{1}{2}[/tex]

Answer:

Str (Texture aspect ratio) Str is a measure of uniformity of the surface texture

Step-by-step explanation:

Answer:

Step-by-step explanation:

Mean income of 99 people = $ 400

Sum of income of 99 people = 400 * 99 = $ 39600

Income of a woman = $ 1500

Income of 100 people = 39600 + 1500 = $41100

Mean of 100 people = 41100/100 = $411

411 - 400 = $11

Mean income increases by $11