Communities A,B and C are faced with acute water problem. The distance between communities A and B is 5km and that of A and C 7km. The angle between path AB and AC is 45degrees. If a well is dug for the three communities such that it would have equal distance to the path linking each communities. (a) Indicate by a way of sketching the exact place to dig the well? (b) Measure the distance between communities B and C?

Answers

Answer 1

Answer:

a) by finding the incentre

b) 5 km

Step-by-step explanation:

Let the communities A, B and C be shown by the three points of the triangle as shown in the figure below. As the angle between the path Ab and Ac is 45 degrees this is an isosceles triangle having two angles equal. As this is an isosceles triangle it must also have two sides equal .

a) the in center   point can be used to  have equal distance to the path linking each communities.

We take a compass and draw arcs on the two sides of the vertex and placing the compass on the arcs bisect each angle made by the triangles arms.

Joining the bisectors the lines meet at a point which is highlighted by a circle in the diagram.

This is the incentre which is equidistant from each vertex.

b) Using Pythagorus theorem

c² = a² + b²

7²= 5² + b²

b²= 24

b= 4.89= 5 km

The path between B and C is also 5 km.

Communities A,B And C Are Faced With Acute Water Problem. The Distance Between Communities A And B Is

Related Questions

hola , alguien me podria decir cuanto es x+y=47 , tomando en cuenta que 40 alumnos y 14 profesores van de viaje , y en el hotel que se quedaran , los alumnos dormiran en cuartos dobles (2 camas) y los profesores en sencillas (1 cama) , y sumando en total son 47 habitaciones y 79 camas , y la incognita x es las habitaciones sencillas y la incognita y son las habitaciones dobles

Answers

Answer:

Step-by-step explanation:

40s=40×2=x

14t=14×1=y

40s=80

x=80

14t=14

y=14

Function Homework f(x) g(x)

Answers

Answer:

5x-1

Step-by-step explanation:

A family built a house in a beach resort area. In 1990, the house was 430 ft from the water. With erosion, the house was 400 ft from the water in 2000. In what year will the house be only 250 ft from the water?

a. 1990

c. 2015

b. 2004

d. 2050

Answers

We develop an equation for the given situation by first writing the general equation for lines,

                                y = mx + b

Substituting to this given the values given above,

(1990)                      430 = b

(2000)                      400 = m(10) + 430

The value of m from the equation in 2000 is -3. Thus, the equation of that relates the variables is,

                              y = -3x + 430

Answer:

 

d.  2050

Step-by-step explanation:

What is the exact value of sin(157.5)?

Answers

Answer:

Its B edg

StartFraction StartStartRoot 2 minus StartRoot 2 EndRoot EndEndRoot Over 2 EndFraction

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

edge

hope this helped! :D

What Is the value of X?
Lines cut by a transversal line...

Answers

(2x–5)° + 45° = 180° (sum of consecutive interior angles

=> 2x + 40 = 180

=> 2x = 180– 40

=> x = 140 /2

=> x = 70

The required value of the x is 70 in the measures of the angle.

Given that Line m and n are parallel lines and intersect by a transversal line l.

When a transversal line intersects two other lines, it creates eight angles, four of which are called exterior angles and four are called interior angles.

From the sum of consecutive interior angles we have;

(2x–5)° + 45° = 180°

2x + 40 = 180

2x = 180– 40

x = 140 /2

x = 70

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Dora, the school lunch manager, says that it takes 225 oranges to make 5 gallons of orange juice how many oranges does Dora need to make one gallon?

Answers

Answer:

45

Step-by-step explanation:

Since

5 : 225 = 1 : X

Then we know

225/5 = X/1

Multiplying both sides by 1 cancels on the right

1 × (225/5) = (X/1) × 1

1 × (225/5) = X

Then solving for X

X = 1 × (225/5)

X = 45

Therefore

5 : 225 = 1 : 45

Answer:45

Step-by-step explanation:well all you do is divide 5 from 225

When simplifying the expression in part H, how many times will the sign change on the positive term? Will the final expression be positive or negative?

Answers

Answer:

There are two -1s in the expression, so the sign of the positive term will change two times: positive → negative → positive. So, the final expression will be positive.

Step-by-step explanation:

Answer:

There are two -1s in the expression, so the sign of the positive term will change two times: positive → negative → positive. So, the final expression will be positive.

Step-by-step explanation:

An ice cream shop charges customers a set amount for one scoop of ice cream, plus a charge per topping. If two toppings would cost a total of $3.99, and 4 toppings $4.99, what is the rate per topping?

Answers

Answer:

$0.50 per topping

Step-by-step explanation:

x + 2t = 3.99

x + 4t = 4.99

x + 2t = 3.99

2t = 3.99 - x

t = 1.995 - 0.5x

x + 4t = 4.99

x + 4(1.995 - 0.5x) = 4.99

x + 7.98 - 2x = 4.99

7.98 - x = 4.99

-x = -2.99

x = 2.99

t = 1.995 - 0.5(2.99)

t = 1.995 - 1.495

t = 0.50

The rate per toppings is given by the equation A = $ 0.50

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of the toppings be represented as A

Now , the equation will be

The cost of 2 toppings = $ 3.99

So , 2A = 3.99   be equation (1)

The cost of 4 toppings = $ 4.99

And , 4A = 4.99   be equation (2)

Subtracting equation (1) from equation (2) , we get

4A - 2A = 4.99 - 3.99

On simplifying the equation , we get

2A = 1.00

Divide by 2 on both sides of the equation , we get

A = $ 0.50

Therefore , the value of A is $ 0.50

Hence , the cost of one toppings is $ 0.50

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David is making mixed candy bags for trick-or-treaters. He has 45 gummy bears and 18 jelly beans left. He wants to put the same number of both types of candy into every bag. What is the largest number of candy bags he can make? ​

Answers

I think it is 9 if not I’m sorry

YALLLL I NEEDDDD HELPPPPPPP LOOK QT THE PICTURE PLZZZ

Answers

Answer:

Angle A = 65 degrees, Angle B = 78 degrees

Step-by-step explanation:

Since a triangle always has its vertices add up to 180 degrees to be a triangle, we can setup an equation on how to solve it. Adding all the vertices together into a formula to equal 180 degrees gives you 5x-5 = 180. Solving this equation will grant you an answer of x = 37 degrees, and taking this value and plugging it in for each requested angle is how to find the exact degree value. Angle A will just be 2(37) - 9, which ends up to be 65 degrees. Angle B is just 2(37) + 4, which becomes 78 degrees. (You can check the answer by taking all values and adding them together to equal 180. 78 + 65 + 37 = 180.) Hope that helps!

Answer: ∠A = 65° ∠B = 78°

The sum of all interior angles = 180°. So, set 180 equal to the angles you were given (in this case, 2x-9, 2x+4, and x), and solve for x.

180 = (2x-9) + (2x+4) + x (combine the like terms)

180 = 5x - 5 (isolate 5x by moving -5 to the other side)

5x = 180 + 5

5x = 185 (divide both sides by 5 to isolate for x)

x = 37°

Then, sub in the value of x (in this case, 37°) into ∠A and ∠B.

∠A = (2x-9) = 2(37)-9 = 65°

∠B = (2x+4) = 2(37)+4 = 78°

∴ ∠A = 65° and ∠B = 78°.

Help me solve this problem

Answers

Answer:

k = 3

Step-by-step explanation:

8k - (6k - 4) = 10

8k - 6k + 4 = 10

2k + 4 = 10

2k = 10 - 4

2k = 6

k = 3

Answer:

k=3

Step-by-step explanation:

8k-(6k-4)=10

Multiply everything inside of the parentheses by the negative.

8k -6k -4=10

Combine like terms

2k - 4 = 10

Subtract 4 from both sides

2k = 6

Divide by 2 on both sides

k-3

are 2x +4 = 10 and 3x +6 = 15 equivalent. equations? how do you know.​

Answers

Answer:

Yes, the two equations are equivalent.

Step-by-step explanation:

For the first equation, we will solve for x.

2x + 4 = 10

Subtract 4 from both sides...

2x + 4 = 10

      -4    -4

It then becomes

2x = 6

Then we divide by 2 on both sides.

2x = 6

2     2

Then the answer is...

x = 3

Now let's also solve for x on the second equation.

3x + 6 = 15

Subtract 6 on both sides to get x alone...

3x + 6 = 15

      -6    -6

Then it is..

3x = 9

Lastly, divide by 3 on both sides...

3x = 9

3     3

Then it becomes

x = 3.

Then we see that both equations have x = 3, meaning when both x's = 3, then both equations will be equivalent. I hope this helps, and I hope it is not wrong, but I don't think it is.

the sum of two numbers is -18. if the first number is 10 which equation represents this situation and what is the second number?​

Answers

The answer would be -28
10+ -28= -18

what fraction is -1/3 minus -5/12 equivalent to as a addition expression.

Answers

Answer:

-3/4 I think do

Answer:

To add or subtract two like fractions, simply add or subtract the numerators and put the result over the common denominator, so your answer is 0.08333333333

Step-by-step explanati

Need help for math! Open the picture above number 7 thank you

Answers

Answer:

1975....?

Step-by-step explanation:

3.860x10^3 - 1.885x10^3

can anyone help me with this question?

Answers

9514 1404 393

Answer:

  E.  37

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary:

  (4x -2)° +34° = 180°

  4x = 148 . . . . . . . . . . . divide by °, subtract 32

  x = 37 . . . . . . . . . . . . . divide by 4

Paralympics/Biking: List 3 ways math is used in biking
Please helppp

Answers

Answer: Calculating miles, calculating burned calories, and finding out your target heart rate.

Step-by-step explanation:

Answer:

Angles, the circumference of the wheel, and ratios for the gears

Step-by-step explanation:

Without these, a bike can't function.

Given f(x) = 3x – 2 what is f (2x)?

Answers

Answer:

6x - 2

Step-by-step explanation:

f(2x) = 3(2x) - 2

f(2x) = 6x - 2

Answer:

I think it is   ---->  m = 3

Step-by-step explanation:

Find the value of f(–2) for the function f(x) = 4x + 10.

A. –3
B. –2
C. 2
D. 18

Answers

Answer:

Step-by-step explanation:

f(-2) = 4(-2) + 10 = -8 + 10 = 2

answer is C

hey yall i need help again im just lazy but will mark brainlyest

Answers

Answer:

1) 1

2) 1

3) 5/6

4) 3/10

5) 5/6

6) 2/7

7) 3/8

8) 5/14

Simplify

3 /6 − 1/ 7 =

3 /6 − 1 /7 =

3 /6 + −1 /7 =

1 /2 + −1 /7 =

7 /14 + −2 /14 =

7+−2 /14 =

5 /14

(Decimal: 0.357143)

9) 2/9

10) 2/21

Step-by-step explanation:

Mr. Brown cuts 3/4 inch sections of wood to make a birdhouse roof. He cut 36 sections. How many inches did he cut?

Answers

Answer:

27 Inches

Step-by-step explanation:

PLEASE HELP ME! (80 POINTS UP FOR GRABS!!)

Which table has a constant of proportionality between y and x of 4?

A.
B.
C.

Answers

Answer: A

Step-by-step explanation:

Answer: A-

Step-by-step explanation:

When measuring volume what is the proper unit in science

Answers

Answer: liters

Step-by-step explanation:

Find the value of the variable that results in congruent triangles. Complete the explanation.
F
30°
30°
9 in.
9 in.
(2x) in.
(x + 4) in.
А
B
D
E
AC is congruent to DF, because AC
DF = 9 in. 2C is congruent
to ZF. EF
must correspond to BC. The triangles (select) » congruent by the (select) Triangle
Congruence Theorem only when x = |

Answers

Answer:

[tex] \overline{AC} [/tex] is congruent to [tex] \overline{DF} [/tex], because [tex] \overline{AC} = 9in [/tex], [tex] \overline{DF} = 8 in [/tex]. <C is congruent to <F. [tex] \overline{EF} [/tex] must correspond to [tex] \overline{BC} [/tex]. The triangles are congruent by the SAS Triangle

Congruence Theorem only when x = 4.

Step-by-step explanation:

From the figures given, ∆ABC and ∆DEF have an included corresponding angles measuring 30° each (<C and <F), and also a given corresponding side length of 9 in each (side AC and side DF). The other given as am expression, and hence the length is unknown. For these two ∆s to be considered congruent, using the SAS Triangle Congruence Theorem, we must have two sides and an included angle of ∆ABC equal to the corresponding sides of and an included angle of ∆DEF.

We already know that 1 of the given side corresponding side lengths are equal and also the include angles are equal, to find out what value of x that will make both unknown corresponding lengths equal, in other for the SAS to be true, set 2x equal to (x + 4) to solve for x.

Thus:

2x = x + 4

Subtract x from both sides

2x - x = 4

x = 4

Substituting x = 4 into 2x and x + 4 will give us equal lengths of 8 in respectively. Therefore, if x = 4, both triangles will be congruent based on the SAS Triangle Congruence Theorem.

The answer is:

[tex] \overline{AC} [/tex] is congruent to [tex] \overline{DF} [/tex], because [tex] \overline{AC} = 9in [/tex], [tex] \overline{DF} = 8 in [/tex]. <C is congruent to <F. [tex] \overline{EF} [/tex] must correspond to [tex] \overline{BC} [/tex]. The triangles are congruent by the SAS Triangle

Congruence Theorem only when x = 4.

294 is equal to the quotient of f and 373
Write the sentence as an equation

Answers

Answer:

f/373 = 294

Step-by-step explanation:

What is the equivalent expression to (8^-5/2^-2)^-4

Answers

Answer:

8^20 / 2^8

Step-by-step explanation:

when it is raised. you multiply it.

Question 9 of 10
Which expression is equivalent to -16 - 9?
A. -16+(-9)
B. 16+(-9)
C. 16+9
D. -16 +9

Answers

Answer:

b

Step-by-step explanation:

Nico earns $12.50 per hour as a math tutor. Show that the relationship between the amount he earns and the number of hours he tutors is a proportional relationship. What is the constant of proportionality (k). Then write the equation for the relationship.

Answers

Answer:

12.50k

Step-by-step explanation:

I came to this answer as k is the number of hours, and 12.50 is how much per hour.

Find the distance between the points. A(3, 0) and B((8,10)

Answers

Answer:

The distance is 5 square root of 5, or if it asks in decimal form it would be 11.180.

Step-by-step explanation:

To find the distance between any points, you must use the distance formula. When you plug in the points given, you end up with 11.180. I hope this helps!

Car A travels 127 miles in 4 hours. Car B travels 350 miles in 4 hours. Car C travels 583 miles in 14 hours. Which car has the fastest average speed?

Answers

B but look at the image to understand y

Answer:

B is the answer

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