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Gilligan sees a ship coming close to the shore he’s standing on.

he wants to determine the distance (segment SD) from the ship to the shore.

he walks 130ft along the shore from point D to point C and marks the spot.

then he walks 23ft further and marks point B.

he turns 90° and walks until his location (point A), point C, and point S are collinear.


Answer the following questions making sure to show all your work.


(A) can Gilligan conclude that triangle ABC and triangle SDC are similar? why or why not?


(B) suppose AB = 150ft. what is the distance from the ship to the shore? show all your work and round your final answer to the nearest tenth of a foot.

[tex] \sf \dashrightarrow(x - 4) {}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \sf \dashrightarrow {x}^{2} + {4}^{2} + 2 \times 4 \times x[/tex]

[tex] \\ \\ [/tex]

[tex] \sf \dashrightarrow {x}^{2} + 16 + 8x[/tex]

Answer:

78 units²

Step-by-step explanation:

Area of rectangle

Area of triangle

Total area

Answer:

450%

Step-by-step explanation:

Divide 9/2 to get 4.5, then multiply this by 100 to get 450%

Good Luck!

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Answer:

Samira earns $5 dollars per hour.

Step-by-step explanation:

$22.50 divided by 4.5 hours = $5 dollars

Answer:

  90.7

Step-by-step explanation:

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(S) = RT/ST

  ST = RT/sin(S) = 63/sin(44°) ≈ 90.7

The length of ST is about 90.7 units.

Answer:

132.25π m²

Step-by-step explanation:

Answer: Class room dynamics includes student behavior, emotions and imagination. It also includes teacher's ways of presenting academic materials and student interactions. It helps in creating a positive class room culture. Effective teaching and learning cannot take place in a poorly managed classroom.

Step-by-step explanation:

The null hypothesis and the research hypothesis respectively refers to;

A: Population; Sample

Null hypothesis is defined as a working hypothesis making a claim about the population parameter in question. This means it deals with an overall Population.

Whereas, the alternative hypothesis also called the research hypothesis is one that seeks to disapprove or validate the null hypothesis and as such it is based on the results taken from a sample of a given population from which the null hypothesis is based.

Read more about Null hypothesis and Alternative Hypothesis at; https://brainly.com/question/15980493

Answer:

See below.

Step-by-step explanation:

A measurement could be a distance or a length, or a weight, or a volume. All those quantities are expressed as positive numbers.

For example, what is the distance from New York to Los Angeles?

Answer: 2,800 miles

What is the length of a book?

Answer: 8 inches

How much does John weigh?

Answer: 150 lb

All those numbers are positive.

There is one measurement that is often a negative number. That is a temperature.

Answer:

Angles are measured in degrees ( °), using a protractor. The protractor was invented by Joseph Huddart in 1801. It was a more complex form of protractor.

Answer:

Approximately 8.234 inches.

Step-by-step explanation:

The area for a sphere is 4πr²

=> r² = 213 : 4 : π = approx. 16.95
=> r = sqrt (16.95) = approx. 4.117

=> d = 4.117 x 2 = approx. 8.234 inches

hope this helps :o

Answer: -7

Step-by-step explanation:

The equation is in slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept

Therefore, the m value is -7 and it is the slope

Answer:

For multipication, it would be 5x2, 1x10, and 2x5.

Step-by-step explanation:

You can use fractions to find the answer to this question.

Step-by-step explanation:

15,12$

3,5$ × 4,42meter =15,12

Answer:

100

Step-by-step explanation:

45 degrees from I to H +55 degrees from H to G

The three workers working in different shifts, and the number of gold

nuggets found in three days give a system of three equations.

Response:

1) Kate finds 4 nuggets per hour, Kevin finds 1 nugget per hour and Greg finds 5 nuggets per hour.

2) Kevin

Let a, b, and c represent the number of nuggets per hour that Kate, Kevin, and Greg finds, we have;

Kate, Kevin, and Greg works for 6, 7, and 4 hours respectively on Monday

On Tuesday, we have; 5, 5, and 6 hours respectively

On Wednesday, we have; 4, 8, and 6 hours respectively

Which gives the following system of simultaneous equations;

6·a + 7·b + 4·c = 51...(1)

5·a + 5·b + 6·c = 55...(2)

4·a + 8·b + 6·c = 54...(3)

Subtracting equation (2) from (3) gives;

4·a - 5·a + 8·b - 5·b + 6·c - 6·c = 54 - 55 = -1

3·b - a = -1

a = 3·b + 1

Which gives;

6·(3·b + 1) + 7·b + 4·c = 25·b + 4·c + 6 = 51

25·b + 4·c + 6 = 51

5·(3·b + 1) + 5·b + 6·c = 20·b + 6·c + 5  = 55

20·b + 6·c + 5 = 55

Similarly;

Which gives;

4 × (50 - 20·b) = 6 × (45 - 25·b)

200 - 80·b = 270 - 150·b

150·b - 80·b = 270 - 200 = 70

70·b = 70

a = 3·b + 1

a = 3 × 1 + 1 = 4

[tex]c = \dfrac{45-25\times 1}{4} = \mathbf{ 5}[/tex]

2.) The person that can be fired is the one that finds the least number of gold nuggets per hour, which is Kevin

Learn more about simultaneous equations here:

https://brainly.com/question/867837

Answer:

6

Step-by-step explanation:

substitute the given values into the expression

4[tex]a^{4}[/tex] - 2b² + 40

= 4[tex](2)^{4}[/tex] - 2(7)² + 40

= 4(16) - 2(49) + 40

= 64 - 98 + 40

= - 34 + 40

= 6

[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]

[tex]\bold{\underline{ Given }}[/tex]

[tex]\bold{\underline{ To \: Find }}[/tex]

[tex]\bold{\underline{ Let's \: Begin }}[/tex]

[tex]\sf{ 2x - 3y = -6 ...eq(1)}[/tex]

[tex]\sf{ x + 3y = 12 ...eq(2)}[/tex]

Multiply eq( 2 ) by 2 :-

[tex]\sf{ 2( x + 3y = 12 )}[/tex]

[tex]\sf{ 2x + 6y = 24 }[/tex]

Subtract eq(1) from eq(2) :-

[tex]\sf{ 2x + 6y -( 2x - 3y) = 24 -(-6)}[/tex]

[tex]\sf{ 2x + 6y - 2x + 3y = 24 + 6 }[/tex]

[tex]\sf{ 9y = 30 }[/tex]

[tex]\sf{ y = 30/9}[/tex]

[tex]\sf{\red{ y = 10/3}}[/tex]

Now, Subsitute the value of y in eq( 1 ):-

[tex]\sf{ 2x - 3(10/3) = -6 }[/tex]

[tex]\sf{ 2x - 10 = -6 }[/tex]

[tex]\sf{ 2x = -6 + 10}[/tex]

[tex]\sf{ x = 4/2}[/tex]

[tex]\sf{\red{ x = 2}}[/tex]

Hence, The value of x and y is 2 and 10/3

Answer:

80

Step-by-step explanation:

I took the test

The measure of the fifth angle will be 80°. Then the correct option is B.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Let 'n' be the number of sides of the polygon. Then the sum of the interior angles of the polygon is given as,

Sum of angles = (n - 2) × 180°

The sum of the interior angle of the pentagon is given as,

Sum of angles = (5 - 2) × 180°

Sum of angles = 3 × 180°

Sum of angles = 540°

And the diagram is given below. The equation is given as,

x + 90° + 90° + 140° + 140° = 540°

x + 460° = 540°

x = 540° - 460°

x = 80°

The measure of the fifth angle will be 80°. Then the correct option is B.

More about the polygon link is given below.

https://brainly.com/question/17756657

#SPJ6

Answer:

1152

Step-by-step explanation:

Look at the picture I put in

The time that Rudy finished the race was 11:10: 10 am.

The time that Teresa's group finished the race was 10:50:08 am.

The formula that can be used to determine the time is Time = distance / average speed

Teresa's group = 26.6 / 16 = 1.6625 = 1 hour 40 minutes 10 seconds = 11:10: 10 am

Rudy's group = 16.6 / 12.5 = 1.328 = 1 hour 20 minutes 8 seconds = 10:50:08 am

To learn more about average speed, please check: https://brainly.com/question/21734785

Answer:

x=14

Step-by-step explanation:

This shape is a pentagon, as it has 5 sides. The formula to find the sum of the interior angles of a polygon is:

(n-2)*180

In this case n represents the number of sides. We can plug 5 into the equation to get...

(5-2)*180=3*180=540

Since all sides are equal, all angles are equal too therefore one angle is equivalent to...

540/5=108

This means...

9x-18=108

Add 18 to both sides

9x-18+18=108+18

9x=126

Divide both sides by 9

x=14

Answer:

x = 14

Step-by-step explanation:

This is a pentagon and there are five sides in a pentagon. All of the sides degrees added together makes 540.

Since the angles are the same and the average angle of every pentagon is 108, then 9x - 18 = 108.

108 + 18 = 126

9x = 126

9x/9 = 126/9

x = 14

Answer:

slope = 4

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, - 7 ) and (x₂, y₂ ) = (3, 9 )

m = [tex]\frac{9-(-7)}{3-(-1)}[/tex] = [tex]\frac{9+7}{3+1}[/tex] = [tex]\frac{16}{4}[/tex] = 4

Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:

[tex]P = 100\% \times [(1 .03)^t - 1][/tex]

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

As a percentage, the increase is modeled by:

[tex]P = 100\% \times [(1 + r)^t - 1][/tex]

In this problem, the growth rate is of r = 0.03, hence:

[tex]P = 100\% \times [(1 + 0.03)^t - 1][/tex]

[tex]P = 100\% \times [(1 .03)^t - 1][/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

Step-by-step explanation:

The formula states that

S. I=P*R*T/100

R=S. I*100/P*T

Simple Interest= Amount - principal

Simple Interest = 130000 - 50000

Simple Interest = 80000

R= 80000*100/50000*20

R= 800000/100000

R=8%