Two observers are standing on shore 20 mile apart at points A and B and measure the angle to a sailboat at a point C at the same time. one observer is 10 miles from the sailboat and the other observer is 25 miles from the sailboat. round to the nearest degree

The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.

Let the equation of the line be y = ma + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx +c is given as y = -(1/m)x + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation is given below.

3x – y = 10

y = 3x – 10

Then the equation of the perpendicular line is given as,

y = –(1/3)x + d

The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.

More about the equation of a perpendicular line link is given below.

https://brainly.com/question/14200719

#SPJ1

Answer:

[tex]m^{15} n^{9}[/tex]

Step-by-step explanation:

The translation observed by shape A after reflection is

Translation refers to a linear movement used in describe repositioning of image during transformation

Transformation is the generally the repositioning of an image. Transformations are usually described in a cartesian plane for ease of comprehension.

The shape A after reflection had a new position. The new position was moved downwards, in the y direction by 2 units representing -2

The shape was further moved to the left 5 units in the x direction  representing -5

Hence we say that c = -5 and d =  -2

This describes the position of the image now labeled shape B

Learn more on translation here: https://brainly.com/question/1046778

#SPJ1

Answer:

x = 7 , ∠ A = 36°

Step-by-step explanation:

since ∠ ADB ≅ ∠ CBD ( alternate angles )

and ∠ ABD ≅ ∠ CDB ( alternate angles )

then ABCD is a parallelogram

the opposite angles of a parallelogram are congruent , so

∠ C = ∠ A , that is

8x - 20 = 3x + 15 ( subtract 3x from both sides )

5x - 20 = 15 ( add 20 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Then

∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°

Answer: x = 7 and m∠A = 36

Step-by-step explanation:

Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB

This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C

⇒3x +15 = 8x - 20

⇒3x + 15 - 3x = 8x - 3x -20

⇒5x = 20 + 15

⇒x = 7

Now m∠A = (3X7) +15 = 36

A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

___________________________

Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

5:2 means that it is divided into 7, and we do not move two positions from (7,7)

X axis

7- (-7) = 14

14/7 = 2

7-2*2 = 3

Y axis

7-(-6)= 13

13/7 =

7 - 2* (13/7) = 49/7 - 26/ 7 = 23/7 = 3 2/7

______________________________

Answer

(3, 3 2/7)

The probability that a randomly selected band member is a senior given that he or she plays the trumpet is 34.78%.

Probability is defined as the likeliness of an event to happen. It can be calculated by dividing the total desired outcomes by the total outcomes.

P = desired outcomes / total outcomes

Of the 108 band members, if 23 play the trumpet, and 8 are seniors who play the trumpet, then the probability that a randomly selected band member is a senior given that he or she plays the trumpet is 8 divided by 23.

P = 8/23 x 100

P = 34.78%

Learn more about probability here: https://brainly.com/question/6649771

#SPJ4

Answer:

                         8

3x² + 2x - 2 - ----------

                      3x + 8

Step-by-step explanation:

                 3x² + 2x - 2

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

3x + 8     |  9x³ + 30x² + 10x - 24

                 -9x³ - 24x²     ↓

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

                             6x² + 10x

                             -6x² - 16x    ↓

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

                                       -6x - 24

                                       +6x + 16

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

                                               -8

I hope this helps!

The ordered pair which is a solution to the given linear equation is (-5, -4)

Linear equations are equations that has a leading degree of 1. The standard linear equation is given as Ax + By = C.

Given the linear equation below;

-2x+9y=-26

We need to determine the ordered pair that gives a solution to the linear expression.

For the coordinate point (4, 4)

-2(4) + 9y = -26

9y = -26 + 8

9y = -18

y = -18/9 = -2

This shows that (4, 4) is not a solution.

For the coordinate point (-4, -4)

-2(-4) + 9y = -26

9y = -26 - 8

9y = -34

y = -34/9

This shows that (-4, -4) is not a solution.

For the coordinate (-5, -4)

-2(-5) + 9y = -26

9y = -26 - 10

9y = -36

y = -4

This shows that (-5, -4) is a solution of the linear equation.

Learn more on linear equation here: https://brainly.com/question/14323743

#SPJ1

Answer:

5°C

Step-by-step explanation:

hope this helps, i used your formula :D

The equivalent expression of the given expression 60x - 24 using distributive property and greatest common factor is 12(5x-2).

Distributive property is a property with which we multiply the sum or difference of two numbers with a number. For example:

a×(b+c) = a×b + a×c

a×(b-c) = a×b - a×c

The greatest common factor is a number which is common multiple of all the given numbers.

Now, solve the given expression 60x - 24

The factors of terms

60x = 12 × 5x

24 = 12 × 2

The greatest common factor is 12, so we take 12 common and the given expression can be written as

60x - 24

= 12 × 5x - 12 × 2

= 12(5x - 2)

Hence, the equivalent expression is 12(5x-24)

To learn more about distributive property here

https://brainly.com/question/5637942

#SPJ1

Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.

In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

v₂ = v₁ + 200

Since Mattie and the turbopropeller plane travled at the same time, we have:

Time = distance/speed

Time = d₁/v₁ = d₂/v₂

Time = 140/v₁ = 540/v₁ + 200

Cross-multiplying, we have:

140(v₁ + 200) = 540v₁

140v₁ + 28,000 = 540v₁

Next, we would rearrange the equation by collecting like terms as follows:

540v₁ - 140v₁ = 28,000

400v₁ = 28,000

Speed of plane, v₁ = 28,000/400

Speed of plane, v₁ = 70 mph.

Read more on speed and distance here: https://brainly.com/question/25920823

#SPJ1

Answer: A square is a shape with four equal-length sides and four corners that are all right angles.

Part a

The domain is the set of x-values, which is [tex][1, \infty)[/tex].

Part b

The range is the set of y-values, which is [tex][-3, \infty)[/tex].

Part c

As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex].

Part d

The x-intercept is when y=0, which is [tex](2, 0)[/tex].

Part e

The absolute minimum is the lowest point, which has a y-coordinate of [tex]-3[/tex].

Part a

The domain is the set of x-values, which is .

Part b

The range is the set of y-values, which is .

Part c

As , .

Part d

The x-intercept is when y=0, which is .

Part e

The absolute minimum is the lowest point, which has a y-coordinate of

According to the combination method, there are 6 ways for the selection to be made if one worker is to be a receptionist, one a secretary, and one a technical typist.

Combinations:

A combination is all about grouping. The number of different groups which can be formed from the available things can be calculated using combinations.

The standard form for calculating the combinations is,

[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

where,

0 ≤ r ≤ n.

This formula is sometimes also called as ncr formula.

Given,

An executive hires 3 office workers from 8 applicants.

Here we need to find how many ways can the selection be made if one worker is to be a receptionist, one a secretary, and one a technical typist.

Here we have to split the problem like the following,

We know that the total number of office workers is 3.

Like, if one worker is to be a receptionist, the the combination is like,

So, the value of n = 3 and r = 1.

Then, according to the ncr formula,

=> ³C₁ = [tex]\frac{3!}{1!(3-1)!}[/tex]

=> 3!/1!2!

=> (3 x 2 x 1) / 1 x 2 x 1

=> 3

Similarly,  if one worker is to be a secretary,

Here the value of n = 2 (Because we have already select one person as receptionist) and r = 1

So,

=> ²C₁ = (2!)/1!(2-1)!

=> (2x1)/ 1 x 1

=> 2

Similarly,  if one worker is to be a technical typist,

Here the value of n = 1 (Because we have already select one person as receptionist) and r = 1

So,

=> ¹C₁ = 1

Therefore, the total number of possible ways are,

=> 3 x 2 x 1

=> 6

To know more about Combination here.

https://brainly.com/question/19692242

#SPJ1

Answer:

a) 95%

b) 2%

c) 16%

d) 98%

Explanation:

We have the following:

This is a normal distribution

Mean = 69

Standard Deviation = 6

a) Between 57 and 81%

The probability that a score is between 57 & 81 is given by the Area between (z = -2) & (z = 2):

b) Above 81%

The probability that a score is above 81% is given by the area of the graph greater than (z = 2):

c) Below 63%

The probability that a score is below 63% is given by the area of the graph lesser than (z = -1):

d) Between 51 and 81

The probability that a score is between 51 & 81 is given by the Area between (z = -3 & (z = 2):

The fraction 1/ (x- 3/6) can be simplified in its simplest form as  6/(6x -3).

From the question  were given the expression as  1/ (x- 3/6) , which have the numerator as 1 and the denominator as  (x- 3/6) , then

the denominator can be expressed as

(x- 3/6)

which can be  simplified as :

(6x -3)/6

then we can place it back to the normal equation as 1/ (6x -3)/6, since the equation now appear in form of inverse function, Then this can be expressed by simplifying it as  6/(6x -3).

Read more about fraction at:

https://brainly.com/question/11562149

#SPJ1

Answer:

a) 1.6×10∧-6

b)2×10∧7

Answer:

2

Step-by-step explanation:

1.9541 lets only worry about 1.95 because it rounds to this rounding up because its five will be 2

Answer : x = 30 degrees

< JKL and < MKQ are complementary

Let < MKQ = x

Angle JKL is twice the measure of angle MKQ

JKL = 2 x MKQ

Sum of a complementary angles = 90 degrees

< JKL + < MKQ = 90

< JKL = 2MKQ

Substitute the value of < jkl

2(<2MKQ + Since, Therefore,

2x + x = 90

3x = 90

Divide both sides by 3

3x / 3 = 90/3

x = 30 degrees

The equation of his allowance in slope-intercept form is y = 0.5x + 8

He received $18 in allowance the week he did 20 chores.

He received $12 in allowance the week he did 8 chores.

The ordered pairs will be (8,12) and (20,18)

The slope intercept form is

y = mx + b

Where m is the slope

b is the y intercept

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

m = (18-12)/(20-8)

m = 6/12

= $0.5 per chores

Now we have to find b,

Substitute the value of any ordered pair in the slope intercept form

12 = 0.5×8+b

12 = 4+b

b = 12-4

b = 8

Hence, the equation of his allowance in slope-intercept form is y = 0.5x + 8

Learn more about slope intercept form here

brainly.com/question/9682526

#SPJ1

The statements about triangles FAD and DCE which are translations of triangle ABC include the following:

A. Points B, A, and F are collinear.

(B.) The measure of angle BCA is the same as the measure of angle CED.

C. Line AD is parallel to line BC.

(E.) The measure of angle DAC is the same as the measure of angle BCA.

Generally, there are four (4) main types of transformation and these include the following:

In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.

Since triangles FAD and DCE both represent the translations of triangle ABC (see attachment), we can logically deduce the following information:

Read more on translation here: https://brainly.com/question/19880883

#SPJ1

Answer:

x = 114

Step-by-step explanation:

since the triangles are congruent then corresponding angles are congruent, then

∠ C = ∠ D , that is

x + 18 = 132 ( subtract 18 from both sides )

x = 114

for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,

T': (1, -3)

U': (2, 0)

V': (8, -2)

W': (7, -5)

In this question, we have been given a rectangle TUVW with vertices

T(-3,-1), U(0, -2), V(-2, -8) and W(-5, -7)

We know that for 90° counterclockwise rotation is (x, y) becomes (-y, x)

so, the coordinates of T' would be,

T' = (1, -3)

the coordinates of U' would be,

U' = (2, 0)

the coordinates of V' would be,

V' = (8, -2)

the coordinates of W' would be,

W' = (7, -5)

Therefore, for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,

T': (1, -3)

U': (2, 0)

V': (8, -2)

W': (7, -5)

Learn more about the counterclockwise rotation here:

https://brainly.com/question/1571997

#SPJ1

Answer:

26 pens

Step-by-step explanation:

Let P and R be the numbers of Pens and Rulers Saj purchases.

The cost of P Pens and R Rulers:

Pens = P(20p)

Rulers = R(60p)

P(20p) + R(60p) = £10

P(0.20) + R(0.60) = 10

R = 8

P(0.20) + (8)*(0.60) = 10

P(0.20) + 4.8= 10

P(0.20) = 5.2

P = (5.2/0.20)

P = 26 pens

CHECK:

8 Rulers = 8*(60p) = 480p

26 Pens = 26*(20p) = 520p

Total = £10

In a case whereby the the shortest side of a right triangle measures 6, and the longest side measures 10 the measurement of the unknown side is 8.

We can use this expression from trigonometry to know the third side of the triangle as:

a^2 + b^2 = c^2

Then since the longest side measures 10 which is the c side of the triangle then the unknown side can be calculated as :

10^2 - 6^2

The we can simplify as

100-36=64

Then [tex]\sqrt{64}[/tex] = 8.

Therefore, the second option is correct.

Read more about triangle at:

https://brainly.com/question/17335144

#SPJ1

Answer:

50 degrees

Step-by-step explanation:

Line CDF is 180 degrees

76 and 54 and some part of the 180 degrees

1. add 76+54 = 130

2. subtract 180-130 = 50

Answer:175/48

Step-by-step explanation:

A. The weight of the copies and the quantity of papers are proportional.

B. There is no proportion between the number of books and their weight.

Given,

A. All versions of the document are 8.5 by 11 inches in size.

We can readily determine the quantity of papers using direct proportion because all the paper has the same dimensions and weight.

As a result, the weight of the copies and the quantity of papers are proportional.

B. Each book has a distinct weight, as we know.

Since each book varies in weight, it is difficult to calculate the quantity of papers using a direct percentage.

Therefore, there is no proportion between the number of books and their weight.

Learn more about weight of paper here;

https://brainly.com/question/12000005

#SPJ1

Answer:

-7

Step-by-step explanation:

-7 is the greatest because it is closer to 0 on the number line.

We will investigate the equal distribution of ribbon amoung her friends.

Isis has a ribbon for crafts for a certain length ( L ):

Isis has ( n ) number of friends amoung which she wants to equally distribute the length ( L ) of her ribbon:

Under the assumption of equal distribution we can divide the total length of ribbon ( L ) amoung Isis ( n ) of friends to determine what length ( l ) each friend got:

So each friend of Isis got a piece of 40 cm length of the ribbon. So the length of the ribbon accumulated for 5 friends would involves the direct multiplication of 5 number of friends and length of each piece ( l ):

Therefore, the answer to the question is: