In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles. How far apart are the police station and the fire station?

Answer: 13.8 m

Step-by-step explanation:

Given

From point A, angle of elevation is [tex]19^{\circ}[/tex]

From point B which is 18 m closer, it changes to [tex]32^{\circ}[/tex]

Suppose the height of tree is h

From figure, we can write

[tex]\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}[/tex]

Similarly

[tex]\Rightarrow \tan19^{\circ}=\dfrac{h}{x+18}\\\\\Rightarrow h=(x+18)\tan 19^{\circ}\\\text{Substitute the value of h}\\\Rightarrow x\tan 32^{\circ}=x\tan 19^{\circ}+18\tan 19^{\circ}\\\Rightarrow x(\tan32^{\circ}-\tan 19^{\circ})=18\tan 19^{\circ}\\\\\Rightarrow x=\dfrac{18\tan 19^{\circ}}{\tan32^{\circ}-\tan 19^{\circ}}\\\\\Rightarrow x=22.09\approx 22.1\ m[/tex]

Deduce the value of h

[tex]\Rightarrow h=22.092\times \tan 32^{\circ}\\\Rightarrow h=13.8\ m[/tex]

Thus, the height of the tree is 13.8 m

Answer:

The output is -2 when the input is 3.

Step-by-step explanation:

You're actually being asked to evaluate y = -2x + 4 at x = 3.  x is the 'input' and y is the 'output.'

At x = 3, y = -2(3) + 4 = -2

The output is -2 when the input is 3.

Answer:

x = 5*|y|

Step-by-step explanation:

We know that the function is something of the form:

x = |a*y|

We know this because the vertex of the function is in the point where the value of the absolute part is zero, this is when y = 0

and:

x = |a*0| = 0

(0, 0)

Now let's look another point where the graph passes through to find the value of a.

We can see that the graph also passes through the point (5, 1) and (5, -1)

Then, when y = 1, we must have x = 5

Replacing these in our equation we get:

x = |a*y|

5 = |a*1|

5 = |a|

then we can have

Then we can rewrite:

x = |a*y| = |a|*|y| = 5*|y|

x = 5*|y|

The correct option is the last option.

Answer:

the third option

Step-by-step explanation:

Answer:

Step-by-step explanation:

m = - 2

b = 4

x - intercept = 2

Answer:A≈1075.21

d Diameter

37

d

r

r

r

d

d

C

A

Using the formulas

A=

π

r

2

d=

2

r

Solving forA

A=

1

4

π

d

2

=

1

4

π

37

2

≈

1075.21009

Step-by-step explanation:

Answer:

10.2956

Step-by-step explanation:

The distance  between (4,6) and (9,15) is √87.

The distance between the points P ([tex]x_1, y_1[/tex])and Q ([tex]x_2, y_2[/tex]) is

PQ = √[tex](x_2 - x_1[/tex]) ² + ([tex]y_2 - y_1[/tex])² , which is called the distance formula.

Given coordinates: (4,6) and (9,15)

Using distance formula:

=√[tex](x_2 - x_1[/tex]) ² + ([tex]y_2 - y_1[/tex])²

= √[tex](9 -5[/tex]) ² + ([tex]15 -6[/tex])²

=√[tex](4[/tex]) ² + (9)²

= √16 + 81

=√87.

Hence, the distance between  (4,6) and (9,15) is √87 units.

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Given:

Distance between two villages = 14 km

Map scale = 1:25000

To find:

The distance between the two villages on the map.

Solution:

Let the distance between the two villages on the map be x.

Map scale is 1:25000. So,

[tex]\dfrac{x}{14}=\dfrac{1}{25000}[/tex]

[tex]x=\dfrac{1}{25000}\times 14[/tex]

[tex]x=0.00056[/tex]

Therefore, the two villages are 0.00056 km apart on map.

Answer:

True

Step-by-step explanation:

An angle is formed by two rays with a common endpoint. Each ray is called an arm of the angle. The common endpoint is called the vertex of the angle.

Answer:

false

Step-by-step explanation:

two rays with don't have the same end point from an angle

Answer:

4 haha lol lol

Step-by-step explanation:

2+2 is 4 lol

Answer:

$7.50

Step-by-step explanation:

30 x 0.25= 7.50

Answer:

Number of milk chocolate in beg = 56

Step-by-step explanation:

Given:

Probability of randomly choosing a dark chocolate = 3/8

Number of dark chocolate = 21

Find:

Number of milk chocolate in beg

Computation:

Number of milk chocolate in beg = Number of dark chocolate / Probability of randomly choosing a dark chocolate

Number of milk chocolate in beg = 21 / [3/8]

Number of milk chocolate in beg = 21[8/3]

Number of milk chocolate in beg = 7[8]

Number of milk chocolate in beg = 56

Answer:

1140 square inches

Step-by-step explanation:

The rear window of DeMarcus's car is in the shape of a trapezoid. The bottom is 50 inches across and the top is 45 inches across. The window has a height of 24 inches. What is the area of the window?

Area of a Trapezoid

= 1/2(b1 + b2)h

b1 =

b2 =

h =

Hence, 1/2 (50 + 45) × 24

= 1/2 × 95 × 24

= 1140 Square inches

y=x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

Y=x

Step-by-step explanation:

it's a straight line passing by the center (0,0) at 45°

You can tell because Y is equal to X for every value of X and the points you posted fall in this case.

Answer:

-10d⁴ + 17d²s - 6s²

Step-by-step explanation:

Multiply using FOIL

First

-2d² * 5d² = -10d⁴

Outer

-2d² * -6s = 12d²s

Inner

s * 5d² = 5d²s

Last

s * -6s = -6s²

-------------------------

Together

-10d⁴ + 12d²s + 5d²s - 6s²

Combine like terms

-10d⁴ + 17d²s - 6s²

Answer: 5/12

Step-by-step explanation:

13-7 = 5

16-4 = 12

ohh dear u still have school i have a holiday for two months

Answer:

the answer is- g= 72/d minus f/d

Answer:

that is the procedure above

Answer:

311.01 in^3

Step-by-step explanation:

Volume of cylinder = pi*r^2*h

Volume of cylinder = pi*9*11=311.01 in^3

Answer:

No solution is possible

Step-by-step explanation:

You failed to provide the function.

This question cannot be answered,

No, 24 is not a possible output value.

The domains are -2, 0, 3, and 11.

The range is -1, 4, 14, and 38.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function is given in the figure.

The outputs are -1, 5, 14, and 38.

The domain of the function is -2, 0, 3, and 11.

The range of the function is -1, 5, 14, and 38.

Thus,

24 is not a possible output value.

Domains are -2, 0, 3, and 11.

Range are -1, 4, 14, and 38.

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Answer:

Step-by-step explanation:

9x - 3x

[When like terms are combined then as per statement they get subtracted]

= 6x (Ans)

9514 1404 393

Answer:

  5.92 inches on a side

Step-by-step explanation:

The new dimension is the original dimension multiplied by the scale factor.

  (8 in)(74%) = 5.92 in

Answer:

my last answer was why the sum of two known angles is equal to the exterior angle so now you can use the easier way:

add the two known angles.

41+107 = 148

that means the exterior angle is equal to 148

x=148

Step-by-step explanation:

Answer:

148

Step-by-step explanation:

The first thing that you want to do is find the missing angle on the inside of the triangle as that angle is supplementary (an angle that when put together it adds up to 180°). So,

In accordance to the triangle sum theorem all of the angles inside the triangle must add up to 180°. For this equation will call the missing interior angle n.

41+107+n=180

148+n=180

n=32

So with this we know that the interior angle is 32°, now all we have to do is subtract 180 by 32 as the X and angle n are supplementary angles

180-32 = 148°

And that is you’re answer!

Answer:

-9

Step-by-step explanation:

[tex]3^{-36}[/tex]= [tex]27^{-12}[/tex]

Answer:

Domain(-4,4) and Range:(-3,0)

Step-by-step explanation:

Because the graph goes through - 4 and 4

Answer:

y = 5/3x + 48

Step-by-step explanation:

y2 - y1 / x2 - x1

28 - 8 / -12 - (-24)

20 / 12

5/3

y = 5/3x + b

8 = 5/3(-24) + b

8 = -40 + b

48 = b

Answer:

I think its 4,5. Not entirely sure but it makes sense