Two cargo ships spot a signal fire on a small island. The captains know they are 140 feet
away from each other and using angle measuring device they can determine the angle from
cach of their ships to the signal fire. The angle at ship A is 82º and the angle at ship B is 78°.
How far is it from Ship B to the signal fire at point C?
Hint: Use Law of Sines:
sin A = sinB = sin C
82
B
a.
b.
48.9 feet
400.4 feet
c. 405.3 feet
d. 673.4 feet

Answer:

C) a = 6, b = 4

Step-by-step explanation:

6 + 4 = 10

6 - 4 = 2

To solve the system, we first add both equations to find 'a = 6'. Then, substitute 'a' in one of the original equations to get 'b = 4'. The solution is 'a = 6' and 'b = 4', corresponding to answer choice C).

To solve the system of equations:

We can add the two equations to eliminate the variable b. By adding them, we get:

2a = 12

Divide both sides of the equation by 2:

a = 6

With the value of a known, substitute a = 6 into either of the original equations. For example, substituting it into the first equation:

a + b = 10

6 + b = 10

b = 10 - 6

b = 4

Therefore, the solution to the system of equations is a = 6 and b = 4, which corresponds to answer choice C).

father is 50

Julia's age : a year-old

Wendy is twice the age of Julia

= > Wendy = 2a year-old

Dad's age : b year-old

" The man is now five times as old as Wendy " b / 2a = 5 <=> b = 10a

" In four years he will be six times as old as Julia " :

( B + 4 ) / (a + 4 ) = 6 + 4 = 6. <=> b (a + 4 )

<=> B = 6a +20

I have two equations :

6a + b = 20

b = 10a

= > 10a = 6a + 20 - > a = 5

- > B = 10a = 50

Answer:

50

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

2^-2=0.25

Answer:

The rug's area is equal to 49π m².

General Formulas and Concepts:
Geometry

Area of a Circle Formula: A = πr²

Step-by-step explanation:

Step 1: Define

Identify given.

r = 7 m

Step 2: Find Area

∴ the family room circular rug with a circle radius of 7 meters has an area of 49π m². And we have solved our problem!

---

Topic: Geometry

Explanation of the number of generations and minutes it would take for gossip to reach everyone in a school.

The total number of students in the school: 2016

Number of students each person tells: 4

Generations needed: Log base 4 of 2016 is approximately 4.033.

Number of minutes: Each generation is 10 minutes, so 4.033 generations would be approximately 40.33 minutes.

Graph: As the number of generations increases, the number of people reached grows exponentially.

Answer:

Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3

Step-by-step explanation:

i) the pre-image co-ordinates is  Y(6, -12)

ii) the coordinates of the image is Y' (2, -4)

iii) therefore we can clearly see that if we divide the coordinates of the pre-image (6,-12) by 3 then we get the coordinates of the image(2,4).

Therefore this is a dilation with scale factor of 1/3.

Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3

Final answer:

The transformation from the pre-image point Y(6, -12) to the image point Y'(2, -4) is a dilation with a scale factor of 1/3.

Explanation:

Given an image point Y'(2, -4) of a transformation and the pre-image point Y(6, -12), we can determine the type of transformation and the scale factor. The transformation is a type of change that affects the position, size, or shape of a figure. To find out the type of transformation and the scale factor, we compare coordinates.

Since the x-coordinate changed from 6 to 2, it has been reduced by a factor of 3 (6 divided by 3 equals 2). The y-coordinate changed from -12 to -4, which also has been reduced by a factor of 3 (-12 divided by 3 equals -4). This consistent reduction indicates that the transformation is a dilation. The objects are shrunk uniformly in both dimensions by the scale factor.

The correct answer is therefore dilation with scale factor 1/3.

Answer:

The area of rectangle ABCD is [tex]18\ units^2[/tex]

Step-by-step explanation:

Plot the figure to better understand the problem

we have the vertices

A(-4, -2), B(-2, -2), C(-2, 7), D(-4, 7)

see the  attached figure

The area of the rectangle is equal to

[tex]A=LW[/tex]

where

L is the length

W is the width

In this problem we have

[tex]L=BC=7-(-2)=9\ units[/tex] ---> difference of the y-coordinates

[tex]W=AB=-2-(-4)=2\ units[/tex] ---> difference of the x-coordinates

substitute

[tex]A=(9)(2)=18\ units^2[/tex]

Final answer:

The area of rectangle ABCD is calculated as 18 square units by finding the product of its width (2 units) and height (9 units).

Explanation:

The area of rectangle ABCD with vertices A(-4, -2), B(-2, -2), C(-2, 7), and D(-4, 7) can be calculated by finding the lengths of the sides AB and BC. The length of AB (width) is the difference in the x-coordinates of A and B, which is |-2 - (-4)| = 2.

The length of BC (height) is the difference in the y-coordinates of B and C, which is |7 - (-2)| = 9. Therefore, the area of rectangle ABCD is the product of the width and height, which is 2 * 9 = 18 square units.

363 gallons of water is in Tank A

Solution:

Water tank A has a capacity of 550 gallons and is 66% full

Let, w = 550

p = 66 % = 0.66

The percent equation is: a = p . w

where,

"a" is the gallons of water in Tank A

p is the percent in fraction or decimal form

w is the capacity of tank A

Therefore,

[tex]a = 0.66 \times 550\\\\a = 363[/tex]

Thus 363 gallons of water is in Tank A

Answer:

The number of 1/5 liter glasses that Lin can fill is [tex]7\frac{1}{2}[/tex]

Step-by-step explanation:

we know that

To find out how many 1/5 liter glasses can Lin fill with a 1 1/2 liter bottle of water, divided 1 1/2 by 1/5

so

[tex]1\frac{1}{2} :\frac{1}{5}[/tex]

Convert mixed number to an improper fraction

[tex]1\frac{1}{2}=1+\frac{1}{2}=1\frac{1*2+1}{2}=\frac{3}{2}[/tex]

substitute

[tex]\frac{3}{2} :\frac{1}{5}[/tex]

Multiply in cross

[tex]\frac{5*3}{2*1}=\frac{15}{2}=7.5[/tex]

Convert to mixed number

[tex]7.5=7+\frac{1}{2}=7\frac{1}{2}[/tex]

Lin can fill 7.5 glasses of water from a 1 1/2 liter bottle. However, if only full glasses are counted, Lin can fill 7 full glasses.

The question asks how many 1/5 liter glasses can be filled with a 1 1/2 liter bottle of water. To answer this, we need to perform a division of the total volume of the water by the volume of each glass.

First, express both quantities in the same units, in liters. The bottle has 1 1/2 liters, which is the same as 1.5 liters. Now, divide the total volume of the water by the volume of one glass:

1.5 liters / (1/5 liter per glass) = 1.5 * 5 = 7.5 glasses.

Therefore, Lin can fill 7.5 glasses of water from a 1 1/2 liter bottle, if we consider that partial glasses can be filled. If only full glasses can be filled, Lin can fill 7 full glasses.

Answer:

look at the picture shown

Answer:

Step-by-step explanation:

The answer is B) B :)

Answer:

The answer is B

Step-by-step explanation:

According to USA Test prep it says so, but i didn't quite get the explanation so bear with me. Thank you :)(:

Answer:

THE DIFFERENCE OF THE NUMBERS IS 6~ likely

THE SUM ON EACH DIE IS 5~ unlikely

THE NUMBER ON EACH DIE IS A WHOLE NUMBER~ Certain

THE NUMBER ON EACH DIE IS LESS THAN 6~ likely

THE SUM OF THE NUMBERS IS 14 OR GREATER~ impossible

Answer:

1.Therefore the solution of given system is (3,4)

2.Therefore the solution of given system is (-1,2)

Step-by-step explanation:

1.

Given the system

2x +3y =18...........(1)

-2x+5y =14...........(2)

Adding the equation (1) and (2)

2x+3y-2x+5y= 18+14

⇔8y = 32

⇔[tex]y = \frac{32}{8}[/tex]

⇔y = 4

Putting the value of y in equation (1)

2x + 3. 4=18

⇔2x+12 =18

⇔2x = 18-12

⇔2x = 6

⇔x =3

Therefore the solution of given system is (3,4)

2.

Given the system

3x +4y = 5..........(a)

2x +7y =12...........(b)

Equation (a) ×2 - equation (b)×3

2(3x+4y)- 3(2x+7y) = 2.5 -12.3

⇔6x + 8y -6x -21y = 10-36

⇔ -13y = -26

⇔[tex]y=\frac{-26}{-13}[/tex]

⇔y = 2

Putting the value of y in equation (a)

3x +4.2 =5

⇔3x = 5 -8

⇔3x = -3

⇔x = -1

Therefore the solution of given system is (-1,2)

Answer:

  the numbers are 7 and 11

Step-by-step explanation:

If you add the smaller to the sum of numbers, you have the sum of the greater and twice the smaller. That is ...

  18 + smaller = 25

  smaller = 25 -18 = 7

  larger = 18 -7 = 11

The two numbers are 7 and 11.

_____

If you like, you can write two equations. Let x and y represent the smaller and larger numbers, respectively.

  x + y = 18

  2x + y = 25

Subtract the first equation from the second:

  (2x +y) -(x +y) = (25) -(18)

  x = 7

  y = 18-x = 18-7 = 11

The numbers are 7 and 11.

The value of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]

Explanation:

The expression is [tex]12abx^{2} -(9a^{2} -8b^{2} )x-6ab=0[/tex]

Multiplying the term x withing the bracket, we get,

[tex]12abx^{2} -9a^{2} x+8b^{2} x-6ab=0[/tex]

Grouping the terms, we have,

[tex](12abx^{2} -9a^{2} x)+(8b^{2} x-6ab)=0[/tex]

Taking out the common terms in each bracket, we get,

[tex]3ax(4bx -3a)+2b(4bx-3a)=0[/tex]

Simplifying, we get,

[tex](3ax+2b)(4bx -3a)=0[/tex]

Equating each term to zero, we get,

[tex]\begin{aligned}3 a x+2 b &=0 \\3 a x &=-2 b \\x &=-\frac{2 b}{3 a}\end{aligned}[/tex]   and [tex]\begin{aligned}4 b x-3 a &=0 \\4 b x &=3 a \\x &=\frac{3 a}{4 b}\end{aligned}[/tex]

Hence, the values of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]

Answer:

8 because 32÷8=4,48÷8=6,80÷8=10

The least possible number of coins Pirate Jack has, is 81 coins.

Step-by-step explanation:

Given,

When the coins are divided into 7 equal piles, 4 coins are left.

When the coins are divided into 11 equal piles, 4 coins are left.

We will take LCM of both 7 and 11.

7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, ....

11 = 11, 22, 33, 44, 55, 66, 77, 88, ...

The least common multiple of 7 and 11 is 77.

As 4 coins are left, therefore, we will add those coins.

Total possible coins = 77+4 = 81

The least possible number of coins Pirate Jack has, is 81 coins.

Keywords: LCM, addition

Learn more about addition at:

#LearnwithBrainly

Answer:

205

Step-by-step explanation:

Were gonna start by writing an equation (121+184+x)/3=170 because were adding a 3rd value to the average and x is going to be our value that were looking for. If you solve that, you get 205. Hope this helps.

For Ben to have an average of at least 170 in his third game, he must bowl a score of 205.

To find out what Ben must bowl in his third game to have an average of at least 170, we can use the formula for average: average = total score/number of games.

In this case, Ben has played two games and wants to have an average of 170. So we can set up the equation: 170 = (121 + 184 + x) / 3, where x represents his score in the third game.

To solve for x, we can multiply both sides of the equation by 3 to get rid of the fraction: 510 = 121 + 184 + x.

Then, we can combine the numbers on the right side: 510 = 305 + x.

Finally, subtracting 305 from both sides gives us: 205 = x.

Therefore, Ben must bowl a score of 205 in his third game to have an average of at least 170.

https://brainly.com/question/31317419

#SPJ2

a) Consecutive sides must be congruent, for SAND to be in a rhombus

For the word "SAND" to form a rhombus, certain conditions must be met based on the properties of a rhombus:

a) Consecutive sides must be congruent: True. In a rhombus, all sides are congruent, so consecutive sides must also be congruent.

b) Diagonals do not bisect the angles: False. In a rhombus, the diagonals bisect the angles. This is a property of rhombuses.

c) All interior angles add up to 360: False. In a rhombus, all interior angles are equal, but their sum is not necessarily 360 degrees. However, the sum of all interior angles in any quadrilateral (including a rhombus) is indeed 360 degrees.

Therefore, the correct statement is:

a) Consecutive sides must be congruent

The question is about calculating the center of mass for a triangular sandwich with a semicircular bite and determining the volume and uncertainty for a rectangular box.

The question asked concerns finding the center of mass of a triangular sandwich after taking a semicircular bite out of it, which is a problem related to geometry and mass distribution. When solving such problems, one would typically have to calculate the area of the original triangle and the area of the semicircular bite, then find the centroid of both shapes.

For the rectangular box's volume and uncertainty, this is a measurement and uncertainty calculation question. Here, one must apply the formula for the volume of a rectangle (length  imes width  imes height) and use the rules of propagation of uncertainty to calculate the overall uncertainty of the volume measurement.

Answer:

B. Less than a day

Step-by-step explanation:

From the question, the circuit board manufacturer produces 2000 board per hour.

Let x be the number of hours it will take to produce 16500 boards .

That’s

2000 boards = 1 hour

16500 boards = x hour

Cross multiply

xhour x 2000 = 1 x 16500

x hour = 16500/2000

x hour = 8.25 hours

8.25 hours is less than a day

Answer:

look at the picture shown

Answer:

c

Step-by-step explanation:

The true statement about triangle is: b. QR = 5.9 cm.

To understand what it means for two triangles to be congruent. When two triangles are congruent (△PQR ≌ △WVX), all corresponding sides and angles are equal.

Given:

For the triangles to be congruent, the corresponding sides and angles must be equal. Let's match the corresponding parts:

Given this correspondence:

QR must be equal to WX, so QR = 5.9 inches (Option b).

m∠R must be equal to m∠W, so m∠R = 28° (Option c).

m∠Q must be equal to m∠X, so m∠Q = 47° (Option d).

However, m∠R and m∠Q cannot both be correct choices simultaneously; only one can be correct because they refer to the same angle in each corresponding pair QR = 5.9 inches is the correct choice considering the triangle sides.

Complete question

In triangle VWX, VW=4.5 inches, WX=5.9 incheß, m∠ W=28° , and m∠ X=47°. If △ PQR≌ △ WVX , which statement is true?

a. QR=4.5cm

b. QR=5.9cm

c. m∠ R=28°

d. m∠ R=47°

Answer:

seems like you need to learn how to do your own work.  

Step-by-step explanation:

Ask instructor for help or go back to the book

Answer:

  -66, 80

Step-by-step explanation:

Let x represent the first number. Then the second number is 14-x, and the difference is ...

  x - (14-x) = -146

  2x = -132 . . . . . . add 14, collect terms

  x = -66 . . . . . . . . the first number

  14-x = 14-(-66) = 80 . . . . . . the second number

Answer:

-66 & 80

Step-by-step explanation:

Let the two numbers be x and y

x + y = 14 (1)

x - y = -146 (2)

Adding (1) & (2),

2x = -132

x = -66

y = 14 - x = 14 - (-66) = 14 + 66

y = 80

Answer:

x = 4, 6

Step-by-step explanation:

The line would go from 4 to 6 with closed circles at each point

(Add images of the lines provided if you need clarification)