Two cruise ships left the same port. After two hours, Ship A is 30 miles west and 18 miles north of the port and Ship B is 10 miles west and 27 miles south of the port. If there is a tug boat located one-fifth of the way from Ship A to Ship B, find the location of the tug boat relative to the port.

*see attachment for the figure referred to

Answer/Step-by-step explanation:

1. PN = 29

MN = 13

PM = ?

[tex] PN = PM + MN [/tex] (Segment addition postulate)

[tex] PN - MN = PM [/tex] (subtract MN from each side)

[tex] 29 - 13 = PM [/tex] (substitute)

[tex] 16 = PM [/tex]

[tex] PM = 16 cm [/tex]

2. PN = 34, MN = 19, PM = ?

[tex] PN = PM + MN [/tex] (sediment addition postulate)

[tex] PN - MN = PM [/tex] (subtract MN from each side)

[tex] 34 - 19 = PM [/tex] (substitute)

[tex] 15 = PM [/tex]

[tex] PM = 15 cm [/tex]

3. PM = 19, MN = 23, PN = ?

[tex] PN = PM + MN [/tex] (Segment addition postulate)

[tex] PN = 19 + 23 [/tex] (substitute)

[tex] PN = 42 cm [/tex]

4. MN = 82, PN = 105, PM = ?

[tex] PN = PM + MN [/tex] (segment addition postulate)

[tex] PN - MN = PM [/tex] (subtract MN from each side)

[tex] 105 - 82 = PM [/tex] (substitute)

[tex] 23 = PM [/tex]

[tex] PM = 23 cm [/tex]

5. PM = 100, MN = 100, PN = ?

[tex] PN = PM + MN [/tex] (Segment addition postulate)

[tex] PN = 100 + 100 [/tex] (substitute)

[tex] PN = 200 cm [/tex]

Answer: [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Convert from decimal to fraction.

0.75 = 3/4. That is your answer.

Answer:

3/4 i believe.

Step-by-step explanation:

Answer:

-2/7x+3

Step-by-step explanation:

1/7x+6-4/7x-3

-3/7x+3

Answer:

false

Step-by-step explanation:

since its the absolute value it will be equal to 14

Answer:

I = 91.125

Step-by-step explanation:

Given that:

[tex]I = \int \int_E \int zdV[/tex] where E is bounded by the cylinder [tex]y^2 + z^2 = 81[/tex] and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and [tex]y^2 + z^2 = 81[/tex]

∴ [tex]z^2 = 81 - y^2[/tex]

[tex]z = \sqrt{81 - y^2}[/tex]

Thus, z lies between 0 to [tex]\sqrt{81 - y^2}[/tex]

GIven curve x = 0 and y = 9x

[tex]x =\dfrac{y}{9}[/tex]

As such,x lies between 0 to [tex]\dfrac{y}{9}[/tex]

Given curve x = 0 , [tex]x =\dfrac{y}{9}[/tex] and z = 0, [tex]y^2 + z^2 = 81[/tex]

y = 0 and

[tex]y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9[/tex]

∴ y lies between 0 and 9

Then [tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy[/tex]

[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy[/tex]

[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy[/tex]

[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy[/tex]

[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy[/tex]

[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy[/tex]

[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy[/tex]

[tex]I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}[/tex]

I = 91.125

Answer:

Step-by-step explanation:

MP, same thing

Answer:

MP

Step-by-step explanation:

PM is the same thing as MP just flipped around. So, they are equal to each other.

Hope This Helps :)

Answer:

Sixty-four , one eighty six, three hundred

Step-by-step explanation:

That’s it.-,

Answer:

sixty four million, one-hundred eighty-six thousand three hundred

Step-by-step explanation:

Answer:

Basically each part of the first complex number gets multiplied by each part of the second complex number. You are multiplying 2 binomials.

(15 + 56i(7 + 4i)

= 105 + 60i + 392i + 224i^2

= 105 + 452i - 224 ( because i^2 = -1)

= - 119 + 452i

Step-by-step explanation:

let me know if this helps!

Answer:

Step-by-step explanation:

The formula for the area of a triangle of base b and height h is A = (1/2) (b)(h).

Here A = 28 in^2, so 28 in^2 = (1/2)(8 in)(7 in), or

                                    28 in^2 = 28 in^2

Answer:

The answer is ab-3a+5b-15

Step-by-step explanation:

apply de disruptive property by multiplying each term a+5by each term b-3

Hope this helps :)

Answer:

here you go ab-3a+5b-15

Answer:

40,000

Step-by-step explanation:

15000+25000=40000

Answer: 40,000

Step-by-step explanation:

25,000 + 15,000 = 40,000

Hope this helps

Plz mark brainliest

Answer:

Step-by-step explanation:

Area of a trapezoid is given by

where

a and b are the bases

h is the height

From the question

A = 135 m²

a = 20m

b = 7 m

Substitute the values into the above formula and solve for the height

That's

Divide both sides by 27

That's

We have the final answer as

Hope this helps you

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

Explanation:

Initially there are 15+18+12 = 45 marbles total. He selects 3 marbles (2 reds, 1 blue).

Assuming he doesn't put the three marbles back, this means there are now 45-3 = 42 marbles overall. The yellow count hasn't changed since the first three marbles do not involve yellow. We have 12 yellow out of 42 which leads to the fraction 12/42 to represent the probability of getting yellow.

Reduce 12/42 to get 2/7. You divide both parts by the GCF 6.

-------

Side note: if he did put the marbles back, then the probability of getting yellow would be 12/45 = 4/15

The correct answer is

tenths

Answer:

Thousandth

Step-by-step explanation:

Answer:

eqn 1. ( k + a = 500 )

Step-by-step explanation:

In eqn. 1 , both 'k' & 'a' have co-efficient as 1. But in eqn. 2 , 'k' has co-efficient as 3 & 'a' has co-efficient as 10.

Answer: b. Median

Step-by-step explanation:

The most common measures of central tendency are :

a. Mode - It is used in nominal data.

b. Median - It is used as central tendency when data is skewed or having outliers in the data.

c. Mean - It is the best measure of central tendency when data does not have outliers because it affect mean badly.

Given, Prices of item have a skewed distribution with outliers in the left tail.

That means , the  best measure of central tendency to summarize this data set is median.

So, the correct option is b.

Answer:

Samuel slept for 1/4 of the distance.

Step-by-step explanation:

The information provided are:

Consider that the total distance covered was 1.

Then from the first point we know that Samuel fell asleep after covering a distance of 1/2.

It is provided that he woke up only after covering half of the remaining distance.

That is, he slept for 1/4 of the remaining distance.

Thus, Samuel was asleep for 1/4th of the entire trip home.

Answer:

hope this helps

Step-by-step explanation:

I don't know I have a similar one but I also don't know that one

Step-by-step explanation:

Answer:

The following are the solution to this question:

Step-by-step explanation:

The average frequency of each of the four new word processing applications, that can be determined as well as the computer expertise of the consumer, which can be calculated as low and medium. Its information could then be displayed in a table of 3×3, and we'll use ANOVA 2 ways to demonstrate those two comparisons.

Answer:

r=5 or r=−5

Step-by-step explanation:

Answer:

fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

2c(a+b) = 2 . 4 . (12 + 9) = 2 . 4 . 21 = 8 . 21 = 168

x = - 6

x + 3 = - 3

x = - 3 - 3

x = - 6

Answer:-6

Step-by-step explanation:

X+3=-3

X=-3-3

X= -6

Answer:

A. $18.45

Step-by-step explanation:

17 miles * .85 = 14.45 + 4.00 = 18.45

Answer:

Area of triangle ADC  is 54 square unit

Step-by-step explanation:

Here is the complete question:

Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .

Step-by-step explanation:

Please see the attachment below for an illustrative diagram

Considering the diagram,

BC = BD + DC = 14

Let BD be [tex]x[/tex] ; hence, DC will be [tex]14-x[/tex]

and AD be [tex]y[/tex]

To, find the area of triangle ADC

Area of triangle ADC  = [tex]\frac{1}{2} (DC)(AD)[/tex]

= [tex]\frac{1}{2}(14-x)(y)[/tex]

We will have to determine [tex]x[/tex] and [tex]y[/tex]

First we will find the area of triangle ABC

The area of triangle ABC can be determined using the Heron's formula.

Given a triangle with a,b, and c

[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where [tex]s = \frac{a+b+c}{2}[/tex]

For the given triangle ABC

Let [tex]a[/tex] = AB, [tex]b[/tex] = BC, and [tex]c[/tex] = CA

Hence, [tex]a = 13, b= 14,[/tex] and [tex]c = 15[/tex]

∴ [tex]s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21[/tex]

Then,

Area of triangle ABC = [tex]\sqrt{(21)(21-13)(21-14)(21-15)}[/tex]

Area of triangle ABC = [tex]\sqrt{(21)(8)(7)(6)}[/tex] = [tex]\sqrt{7056}[/tex]

Area of triangle ABC = 84 square unit

Now, considering the diagram

Area of triangle ABC = Area of triangle ADB + Area of triangle ADC

Area of triangle ADB = [tex]\frac{1}{2} (BD)(AD)[/tex]

Area of triangle ADB = [tex]\frac{1}{2}(x)(y)[/tex]

Hence,

Area of triangle ABC =  [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]

84 =   [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]

∴ [tex]84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)[/tex]

[tex]84 = 7y\\y = \frac{84}{7}[/tex]

∴ [tex]y = 12[/tex]

Hence, [tex]y =[/tex] AD = 12

Now, we can find BD

Considering triangle ADB,

From Pythagorean theorem,

/AB/² = /AD/² + /BD/²

∴13² = 12² + /BD/²

/BD/² = 169 - 144

/BD/ = [tex]\sqrt{25}[/tex]

/BD/ = 5

But, BD + DC = 14

Then, DC = 14 - BD = 14 - 5

BD = 9

Now, we can find the area of triangle ADC

Area of triangle ADC  = [tex]\frac{1}{2} (DC)(AD)[/tex]

Area of triangle ADC  = [tex]\frac{1}{2} (9)(12)[/tex]

Area of triangle ADC  = 9 × 6

Area of triangle ADC  = 54 square unit

Hence, Area of triangle ADC  is 54 square unit.

it says if

ax^2+bx+c=0

a<0

answer is D because, there is (-) near of x^2

Answer:

Third option choice

Step-by-step explanation:

Notice that the angle is in the second quadrant, where the cosine is negative, the sine is positive and the tangent negative. In particular given the value of the cosine you are located at the angle 150 degrees, which gives a sine of 1/2 and a tangent given by [tex]-\sqrt{3} /3[/tex]

Therefore the third option is the correct one.

Answer:

B. $79 + 0.1($79)

Step-by-step explanation:

Given that;

the shipping cost for an order = 1/10 multiply by the cost of the items bought;

i.e.  [tex]\dfrac{1}{10}\times x[/tex]

where

x = cost of items ordered for.

This implies that:

[tex]\implies[/tex] x + 0.1x

The objective is to determine the expression for the total cost of an order which is $79

x = 79

Then,  the total cost of an order is

$79 + 0.1($79)

Answer: The smaller of the numbers is 2 and the larger is 4.

Step-by-step explanation: 2x3-2=4. 2+4-2=4

Answer:

The bigger number is 1 and the smaller number is also 1

Step-by-step explanation:

One number is 2 less than 3 times another

x + 2 = 3y

If their sum is decreased by 2 the result is 4

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

x + 3y = 4

x = 4 - 3y

Substituting value of x, 4 - 3y , in x + 2 = 3y

4 - 3y + 2 = 3y

6 - 3y = 3y

6 = 3y + 3y

6 = 6y

Divide both sides by coefficient of y, 6

y = 1

Substituting value of y, 1 in x + 2 = 3y

x + 2 = 3(1)

x + 2 = 3

x = 3 - 2

x = 1

Answer:

-1/2

Step-by-step explanation:

The slope of a line parallel is to another line is the same.

So the line in the picture has a slope of -1/2, and since the other line is parallel to the first one, its slope is also -1/2