A village P is 10km from a lorry station,Q on a bearing 065°.another village R is 8km from Q on a bearing 155°.calculate; a.the distance of R from P to the nearest kilometer and b.the bearing of R from P to the nearest degree.

Answer:

y = - 4

Step-by-step explanation:

Locate x = - 1 then follow the line down until it meets the curve and read the corresponding value on the y- axis at this point.

For x = - 1, y = - 4

Answer:

B.

Step-by-step explanation:

Again, to find the equation of the line, we need to find the slope and y-intercept. First, let's find the slope. Let (-1,5) be x₁ and y₁ respectively and (1,3) be x₂ and y₂, respectively. So:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{1--1}=\frac{-2}{2}=-1[/tex]

So the slope is -1.

Now, to find the y-intercept, we can use the point-slope form. I'm going to keep using (-1,5) as the coordinate. Thus:

[tex]y-y_1=m(x-x_1)\\y-5=-1(x-(-1))\\y-5=-(x+1)\\y-5=-x-1\\y=-x+4[/tex]

This is slope-intercept form. We want the answer to be in standard form, where:

[tex]Ax+By=C[/tex]

A, B, and C are integers (and, conventionally, A is positive).

Thus, we need to rearrange the terms:

[tex]y=-x+4\\y+x=4\\x+y=4[/tex]

The answer is B.

Answer:

151200 possible combinations

Step-by-step explanation:

There are 10 digits 0 - 9  ( 0,1,2,3,4,5,6,7,8,9)

There are 10 choices for the first digit

10

There are 9 choices for the second digit

9

There are 8 choices for the third digit

8

and so on  since we can only use each digit once

10 *9*8 *7 *6*5

151200 possible combinations

Note how the triangles here have the angles between the marked sides. The tickmarks indicate which pair of sides are the same length. The SAS sequence has "A" in the middle of the two "S" letters to mean that the angles are between the sides.

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

Extra info:

The first pair of triangles can be proven congruent by SAS.

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.

Here, we have,

In the first pair of triangles the included angle of a triangle are equal to two sides and the included angle of another triangle, therefore by SAS postulate the two triangles are said to be congruent.

In the second figure, the pair of triangles are congruent by ASA postulate not SAS.

In the third figure, the pair of triangles are not congruent by any postulate or theorem [Because there is no SSA rule].

In the fourth figure, the pair of triangles are congruent by SSS postulate not SAS.

Hence, The first pair of triangles can be proven congruent by SAS.

learn more on congruent click:

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Answer:

590mph

Step-by-step explanation:

Speed with wind = 5525÷ 8.5

= 650mph

speed against wind = 4505÷8.5

= 530mph

speed without wind = (650mph+530mph)÷2

= 590mph

Answer:

The new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.

Step-by-step explanation:

The image related to the exercise is necessary, to be able to solve therefore the attached one.

We have the following information:

Perimeter of the triangle = 58 units

Hypotenuse = 24 units

We have that the other two sides are equal and have x units, therefore we have the following:

x + x + 24 = 58

2 * x = 58-24

2 * x = 34

x = 34/2

x = 17

Now the triangle rotates around line k , and then it will result in a cone, which is a three-dimensional shape.

Therefore, the new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.

Answer:

Cone with a radius of 17 units

Answer:

1607

Step-by-step explanation:

The mean (or average) of a data set is the sum of all of the data divided by the number of data in the set. In this case, that would be:

(1606 + 1607 + 1606 + 1607 + 1607 + 1609) / 6

= 9642 / 6

= 1607

Answer: 1,607

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

Work is attached below.

Answer:

-7/2

Step-by-step explanation:

We can find the slope by using the slope formula

m = (y2-y1)/(x2-x1)

  = ( -3 -11)/( 2- -2)

  = ( -14)/ ( 2+2)

  = -14/4

  = -7/2

Answer:

The distance between two cities is 60 miles.

Step-by-step explanation:

Time taken to travel from B to A = 2 hours

Time taken to travel from A to B = 1.5 hours

Current speed = 5 mph

Let the speed of ferry in still water = u mph

When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).

Let the distance between the two cities A and B = D miles

While moving with the current, speed = [tex](u+5)\ mph[/tex]

While moving against the current, speed = [tex](u-5)\ mph[/tex]

Formula for Distance = Speed [tex]\times[/tex] Time

Distance traveled in each case is same i.e. D.

So,

[tex]D = (u+5) \times 1.5 = (u-5) \times 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = \dfrac{175}{5}\\\Rightarrow u = 35 \ mph[/tex]

Now,

[tex]D = (u+5) \times 1.5\\\Rightarrow D =(35+5) \times 1.5\\\Rightarrow D =(40) \times 1.5\\\Rightarrow \bold{D =60\ miles}[/tex]

So, the distance between two cities is 60 miles.

Answer:

I believe that the answer is 60 miles

Step-by-step explanation:

Answer:

17.7 percent

Step-by-step explanation

You find the area of the trapezoid and rectangle. You divide the area of the trapezoid by the rectangle. then move the decimal 2 places to the right.

Answer:

The correct option is;

A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25

Please find attached the graphs of the table data

Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x,               -3,                 -1,                 2,                5,                10

y,              -4.5,              -3.0,             -1.5,             0.0,              1.5              

-4.5/-3  = 1.5 ≠ -3.0/-1 = 3

No direct variation

Table 2      

x,             -5.5,               -4.5,            -3.5,            -2.5,             -1.5

y,              10,                   8,                 6,              4,                  2

10/(-5.5) = -20/11  ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3              

x,              -5.5,               -5.5,             -5.5,           -5.5,            -5.5

y,              -3,                    -1,                 2,                5 ,              10                  

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x,              -3,                    -1,                2,                  5,             10

y,              -7.5,                 -2.5,            5.0 ,              12.5,         25  

 -7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists        

Answer:

so D

Step-by-step explanation:

Answer: about 13u

Step-by-step explanation:

Distance can be calculated as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(6-(-7))^2+(4-8)^2}\\\\\\\sqrt{(13)^2+(-4)^2}\\\\\\\sqrt{185}\\\\13[/tex]

Hope it helps <3

Answer:

$20 i think

Step-by-step explanation: have a good day bye bye yup yup

Answer:

(x+6) / 6

Step-by-step explanation:

(3x+18) /18

Factor out 3 from the numerator

3(x+6) /18

Cancel a 3 from the numerator and denominator

(x+6) / 6

Answer:

4a) 110 square centimetres

4b) 127 square centimetres

6) 292 square centimetres

8) 800 tiles

Step-by-step explanation:

4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:

a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:

A = 12 * 15 = 180 square centimetres

The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:

a = 10 * 7 = 70 square centimetres

Therefore, the area of the shaded part is:

A - a = 180  - 70 = 110 square centimetres

b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:

A = 13 * 11 = 143 square centimetres

The unshaded part has dimensions 8 cm by 2 cm. Its area is:

a = 8 * 2 = 16 square centimetres

Therefore, the area of the shaded part is:

A - a = 143 - 16 = 127 square centimetres

6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.

The frame has dimensions 24 cm by 18 cm. Therefore, its area is:

A = 24 * 18 = 432 square centimetres

The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:

a = 14 * 10 = 140 square centimetres

Therefore, the background area of the space not covered by the photograph is:

A - a = 432 - 140 = 292 square centimetres

8) The floor has dimensions 8 m by 4 m. The area of the floor is:

A = 8 * 4 = 32 square centimetres

Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:

a = 0.2 * 0.2 = 0.04 square metres

The number of tiles that are needed is the area of the floor divided by the area of each tile:

A / a = 32 / 0.04 = 800 tiles

Answer:

Step-by-step explanation:

[tex]8a - 5b - (6a - 9b)[/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression.

[tex]8a - 5b - 6a + 9b[/tex]

Collect like terms

[tex]2a + 4b[/tex]

Factor out 2 from the expression

[tex]2(a + 2b)[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

2(a + 2b)

Step-by-step explanation:

2 bcoz vertically opp

the one in front of 3, I can't see that number maybe 4

because corresponding angles

yea that's all

Answer:

4√mn/m^2

Step-by-step explanation:

√16n/m^3

= √16n/√m^3

= √4x4xn/√mxmxm

= 4√n/m√m

Rationalize by multiplying the numerator and the denominator by the denominator, which is a surd:

= (4√n x √m)/(m√m x √m)

= 4√mxn/m√mxm

= 4√mn/mxm

= 4√mn/m^2

Answer:

22

Step-by-step explanation:

Let the first number be x.

Let the second number be y.

(x+y)/2 = 11

x-y=4

Solve for x in the second equation.

x = 4 + y

Put x as 4 + y in the first equation and solve for y.

(4+y+y)/2 = 11

4 + 2y = 22

2y = 18

y = 9

Put y as 9 in the second equation and solve for x.

x = 4 + 9

x = 13

Find the sum of the numbers x and y.

x + y

13 + 9

= 22

Answer:

[tex]22[/tex]

Step-by-step explanation:

let the numbers be x and y

[tex] \frac{x + y}{2} = 11 \\ x - y = 4[/tex]

so,

[tex] \frac{x + y}{2} = 11 \\ x +y = 11 \times 2 \\ x + y = 22[/tex]

So they asked to find the sum of the two numbers

And the answer is 22

Answer:

2 and 1/6 feet

Step-by-step explanation:

To do this you would just put aside 17 and 14 and you would subtract 5/12 by 5/8. To subtract these you would just find the lcm which is 48 and that would be denominator and to make the top the same as the bottom you would just multiply how much it took the denominator and multiply the numerator. So to subtract them you would get 20/48 for 5/12 and 30/48 for 5/8. When you subtract them you get -10/12 so then you will subtract 17 and 14 which is 3 then you will subtract 3 - 10/12 and you would get 2 and 2/12 which can simplify to 2 1/6 feet

The difference in the lengths of alligators in zoos and Florida is 2.79 feet.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Given that

The length of an alligator in a Zoo = 14 5/8 feet.

The length of an alligator in Florida =  17 5/12 feet.

Convert fractions into decimals, and we get

The length of an alligator in a Zoo = 14.625 feet.

The length of an alligator in Florida =  17.416 feet.

So the difference in their lengths = 17.416 - 14.625

So the difference in their lengths = 2.79 feet

Therefore, the difference in the lengths of alligators in zoos and Florida is 2.79 feet.

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Answer:

[tex]x = 10[/tex]

Step-by-step explanation:

If we have our proportion set up like this:

[tex]\frac{5}{n} = \frac{16}{32}[/tex]

Then using the cross products property, we can find the value of n.

The property states that the two numbers that are diagonal to each other DIVIDED by the number diagonal to the variable will equal the variable.

So:

[tex]32\cdot5 = 160\\160\div16 = 10[/tex]

Hope this helped!

Answer:

20

Step-by-step explanation:

use the cos or sin function to solve

Step-by-step explanation:

using 30°

we use cos

using 60

we use Sin

Answer:

D.  [tex]\boxed{x = 5}[/tex]

Step-by-step explanation:

Let the number be x

Condition:

[tex]\frac{1}{10} x + 2 = \frac{1}{2} x[/tex]

[tex]\frac{x}{10} -\frac{x}{2} = -2\\LCM = 10\\Multiplying \ both \ sides \ by \ 10\\x - 5(x) = -2(10)\\x -5x = -20\\-4x = -20[/tex]

Dividing both sides by -4

x = 5

Answer:

[tex]\boxed{5.0}[/tex]

Step-by-step explanation:

Let the number be [tex]x[/tex].

1/10 of x is added to 2, the result is half of x.

[tex]2+\frac{1}{10} x=\frac{1}{2} x[/tex]

[tex]2=\frac{1}{2} x-\frac{1}{10} x[/tex]

[tex]2=\frac{2x}{5}[/tex]

[tex]10=2x[/tex]

[tex]\frac{10}{2} =x[/tex]

[tex]5=x[/tex]

The number is 5.0

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

First we need the equation of line AB. Compute the slope through (-3,-1) and (4,4)

m = (y2-y1)/(x2-x1)

m = (4-(-1))/(4-(-3))

m = (4+1)/(4+3)

m = 5/7

This is the slope through points A and B, ie the slope of line AB.

To get the slope of line BC, we flip the fraction and change the sign.

Doing so has us go from 5/7 to -7/5. Note how 5/7 and -7/5 multiply to -1.

The slope of line BC is -7/5. Let m = -7/5.

--------

Use (x,y) = (4,4) along with m =-7/5 to find the equation of line BC

y = mx+b

4 = (-7/5)(4) + b

4 = -28/5 + b

20 = -28 + 5b ... multiply every term by 5 to clear out the fraction

20+28 = 5b

48 = 5b

5b = 48

b = 48/5

With m = -7/5 and b = 48/5, we go from y = mx+b to y = (-7/5)x+48/5

The slope intercept form for line BC is y = (-7/5)x+48/5

--------

Let's get this into standard form Ax+By = C

y = (-7/5)x+48/5

5y = -7x + 48 .... multiply everything by 5

7x+5y = 48 .... is one way to represent the equation in standard form

-7x - 5y = -48 ... your teacher has decided (for some reason) to multiply both sides by -1

Answer:

-5y-7y=-48

Step-by-step explanation:

distance between BC (4,4) C(x,y)

BC is perpendicular on AB (perpendicular line has opposite reciprocal slope)

slope of AB=y2-y1/x2-x1=4-(-1)/4-(-3)=5/7

slope of BC=-7/5

now input the value of B (4.4) and C(x,y)

y=mx+b

4=-7/5(4)+b

b=4+28/5

b=48/5

y=-7/5x+48/5

5y=-7x+48

5y+7x=48 multipy by -1

-5y-7y=-48

Answer:

2x2x7

Step-by-step explanation:

Answer:

I hope it will help you...

Answer:

(x-9)(x-6)

x= 9, x= 6

Step-by-step explanation:

Factored, and roots are:

Answer:

Volume of prism = 240 ft²

Step-by-step explanation:

Given:

Base of prism (B) = 10 ft

Length of prism (L) = 8 ft

Height of prism (H) = 6 ft

Find:

Volume of prism

Computation:

Volume of prism = [BHL] / 2

Volume of prism = [(10)(8)(6)] / 2

Volume of prism = [480] / 2

Volume of prism = 240 ft²

Answer:

y=2

Step-by-step explanation:

SEND + MORE = MONEY

notice that send and more have 4 digit ( means the number in thousands ,but the answer is 5 digit  means it is in 10000)

first word : 1000S+100E+10N+1 D

second word: 1000 M +100 O+10 R+1 E

the answer: 10000M+1000O+100N+10E+Y

if the answer is the sum of first word+second word:

(S E N D M O R E Y)

M in word Money can not be zero the range is [1,9]

S also can not be zero

  S   E    N    D    s=9 since E can not equal N it has to be 1+E=N

  9   5     6     7

+

  M   O   R     E     m=1 , then o =0

   1    0    8    5  

M   O    N    E  Y

1     0    6    5   2      

Answer:

Step-by-step explanation: to answer this question I need to know what 1 inch to a mile is. like    every one inch= 12 miles

Answer:

2

Step-by-step explanation:

Five and above, round up. Four and below, round down.

Answer:

2

Step-by-step explanation:

anything less then five is rounded down anything above 5 is rounded to the higher number