Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters then sights the top of the steep cliff at a 30 degree angle if Sarah is 1.8 meters tall how tall is the cliff to the nearest meter ?

Answers

Answer 1

Answer:

Cliff is 45 m tall.

Step-by-step explanation:

Given:

Height of Sarah = 1.8 m

Angle of elevation = 60°

Angle of elevation 50 m back = 30°

As shown in the figure we have two right angled triangles SPQ and SPR.

Let the height of the cliff be [tex]h[/tex] meters and [tex]h= h_1+h_s[/tex].

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ.                                        In ΔSPR.

[tex]tan(60) = \frac{h_1}{x}[/tex] ...equation (i)        [tex]tan (30)=\frac{h_1}{x+50}[/tex]  ...equation (ii)

Dividing equation (i) and (ii)

[tex]\frac{tan(60)}{tan(30)} = \frac{h_1}{x} \times \frac{x+50}{h_1}[/tex]

[tex]3 = \frac{x+50}{x}[/tex]

[tex]3x=x+50[/tex]

[tex]3x-x=50[/tex]

[tex]2x=50[/tex]

[tex]x=\frac{50}{2}[/tex]

[tex]x=25[/tex] meters

To find [tex]h_1[/tex] plugging [tex]x=25[/tex] in equation (i)

[tex]h_1=x\times tan(60)[/tex]

[tex]h_1=25\times 1.73[/tex]

[tex]h_1=43.25[/tex] meters

The height of the cliff from ground :

[tex]h= h_1+h_s[/tex]

[tex]h= 43.25+1.8[/tex]

[tex]h=45.05[/tex] meters

The cliff is 45 m tall to the nearest meter.

Sarahs Stands On A Ground And Sights The Top Of A Steep Clift At A 60 Degree Angle Of Elevation She Then

Related Questions

Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y = 2x - 3
y = -2x + 5

A.) (-2,5)
B.) (-2,-7)
C.) (2,1)
D.) (2,-3)

Answers

Answer:

4

Step-by-step explanation:

Answer:

The answer is C. (2,1)

Step-by-step explanation:

What is the value of x 4 + 0:5y 3 when x = 2 and y = 4?

Answers

Answer:

Step-by-step explanation:

x^4+0.5y^3=2^4+0.5x4^3

=16+0.5x64

=16+32

=48

I need the answer ASAP !!!!

Answers

I hope this helps you

x^2+2.(-3).x+(-3)^2

(x-3).(x-3)

(x-3)^2

pls help i’ll give u a brainlest

Answers

Answer:

(13×14×6)/3= 364 centimeter cube

I answered wrongly cuz forgot to divide by 3

my mistake

Answer:

4263m^3

Step-by-step explanation:

So for number 2, that is a right rectangular pyramid. The formula is lwh/3.

The length is 21, the width is 21, and the height is 29. So the volume is 4263.

Suppose that Marvin rolls a pair of fair six-sided dice. Let A be the event that the first die lands on a 4 and B be the event that rolls doubles
P(A), the probability that the first die lands on 4?
P(B), the probability that Marvin rolls doubles?
P(A and B) the probability that the first die lands on 4 and Marvinv rolls doubles?
DEPENDENT OR INDEPENDENT?

Answers

Answer:

1/6

1/6

1/36

Independent

Step-by-step explanation:

Make a chart with 36 outcomes of a pair of six sided dice.

Count the amount that starts with 4, which is 6. 6/36 = 1/6

Doubles. Count the pairs, basically both numbers are the same. 6 outcomes out of total is 1/6.

Last one.

(1/6)^2 = 1/36

These are independent, because the first die landing on 4 doesn't have anything to do with making the die becoming doubles.

Let p be a prime number such that p>2. Use the proof by contradiction to show that at least one of numbers p−1 and p+1 is divisible by 4.

Answers

p can be 11
-11 is a prime number because it can only be divided by 11 or 1
- 11 + 1 is 12
- 12 is divisible be 4

p can also be 13
-13 is a prime number because it can only be divided by 13 or 1
- 13 minus 1 is 12
- 12 is divisible by 4

Mark, Chase, and Beatrice are running a 100-meter race. Which list represents the sample space of all the possible ways in which the three runners can win first, second, and third places? If there were four runners and three positions to be won, what would the sample size be?

A.

The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.

B.

The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 24.

C.

The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.

D.

The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 16.

Answers

the answer is B: 24

i know it

Are you winning or losing?

Answers

I think you are winning

Answer:

You are winning

Step-by-step explanation: If you drop in $2 a day for 10 weeks you have spent $20. You have won $75 from the slots which leaves you with a gain of $55.

You miss 6 out of 25 questions on an science quiz 5 out of 20 questions on an math quiz. Which Quiz has an higher percent of correct answers.

Answers

5 wrong out of 20 would be higher

The science quiz has a higher percentage of correct answers.

To determine which quiz has a higher percent of correct answers, we need to calculate the percentage of correct answers for each quiz.

Science Quiz:

You missed 6 out of 25 questions. Therefore, you answered 25 - 6 = 19 questions correctly.To find the percentage of correct answers, use the formula:
[tex]Percentage = \frac{Number\ of\ correct\ answers}{Total\ Questions}*100[/tex]For the science quiz:[tex]Percentage = \frac{19}{25}*100 = 76\%[/tex]

Math Quiz:

You missed 5 out of 20 questions. Therefore, you answered 20 - 5 = 15 questions correctly.For the math quiz:[tex]Percentage = \frac{15}{20}*100 = 75\%[/tex]

Comparison

The science quiz has a higher percentage of correct answers (76%) compared to the math quiz (75%).

Explain the differences between solids that are polyhedra and solids that aren’t polyhedra.

Answers

Answer:

A polyhedron is a solid shape with flat sides, while a non polyhedron is a solid shape which has curved sides.

Step-by-step explanation:

A polyhedron, can be seen as a solid shape with many plane figures, forming its sides. Examples of polyhedrons are cuboids, squares and pyramids. As you can see, these solid shapes have flat sides.

On the  other hand, a non polyhedron is a solid shape that has curved surfaces. Examples include: cones, spheres and cylinders.

Hence polyhedron: No curved surface

Non polyhedron: curved surface

Final answer:

Polyhedral solids are composed of flat polygonal faces and have geometrically regular shapes, while non-polyhedral solids can have curved surfaces and irregular shapes, such as spheres and cylinders.

Explanation:

Differences Between Polyhedral and Non-Polyhedral Solids:

Solids that are polyhedra have flat faces, straight edges, and sharp vertices. Polyhedral solids are a category of solids composed of polygons that are joined together at their edges and vertices. The most common examples of polyhedra include cubes, pyramids, and prisms. These solids have a geometrically regular shape and are often symmetrical.

In contrast, solids that are not polyhedra may have curved surfaces, and irregular shapes, and do not consist exclusively of flat polygonal faces. Common examples of non-polyhedral solids include spheres, cylinders, and cones. These shapes are not limited by flat surfaces and can have continuous curved surfaces.

While polyhedral solids can be easily mathematically described by the polygons that comprise their faces, non-polyhedral solids often require more complex geometry, such as calculus, to describe their curved surfaces.

A bacterial culture starts with 400 bacteria and grows at a rate proportional to its size. After 2 hours there will be 800 bacteria.
1) Express the population, P(t) after t hours as a function of t
2) Using your equation from above, what will the population be after 8 hours?
3) Using your equation from above, after how many hours will the population reach 2270 bacteria?

Answers

Answer:

P(t) = 400×2^(t/2)64005.0

Step-by-step explanation:

The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.

1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.

  population = (initial population) × (growth factor)^(t/(growth period))

where the "growth period" is the period of time in which the population is multiplied by the "growth factor".

Here, we're given ...

  (initial population) = 400

  (growth factor) = 800/400 = 2

  (growth period) = 2 . . . . hours

So, our population function can be written as ...

  P(t) = 400×2^(t/2)

__

2) Putting t=8 into the formula, we get ...

  P(8) = 400×2^(8/2) = 400×16 = 6400

After 8 hours, the population will be 6400.

__

3) Fill in the given number and solve for t.

  2270 = 400×2^(t/2)

  2270/400 = 2^(t/2)

Taking logs, we have ...

  log(227/40) = (t/2)log(2)

  t = 2×log(227/40)/log(2) ≈ 5.009

After 5.0 hours, the population will reach 2270.

The partial factorization of x2 – 3x – 10 is modeled with algebra tiles.

Answers

Add together to get -3
Multiply together to get -10
Can you think of the two numbers?

Try 2 and -5:
2+-5 = -3
2*-5 = -10.

Therefore, (x+2)(x-5) is the answer :)

Factoring out in algebra simplifies expressions such as quadratic equations into products of binomials or linear factors, sometimes using complex coefficients to achieve this if necessary.

The process of factoring out involves finding the numbers or expressions that divide evenly into the original expression. In the case of quadratic expressions like [tex]x^2 - 3x - 10[/tex], we look for two binomials that multiply together to give us the original quadratic. In algebra, a common method of factoring is looking for two numbers that multiply to give the constant term (in this case -10) and add up to the coefficient of the middle term (in this case -3). These two numbers are the factors of -10 that we use to split the middle term.

For example, the factors of -10 that add up to -3 are -5 and 2. Using these numbers, we can write [tex]x^2 - 3x - 10[/tex] as (x - 5)(x + 2). This is called factoring by grouping, wherein we factor common terms out of pairs of terms and then factor further if possible.

In the context of complex numbers, all second-order polynomials can be factored into linear factors. For instance, [tex]x^2 + 1[/tex] can be factored as (x - i)(x + i), utilizing complex roots i and -i. The fundamental theorem of algebra assures us that any polynomial can be factored completely into linear factors using the complex number system.

In triangle ABC a=8. b=6, and angleC= 60°. Find the measure of angleA
16 degrees
46 degrees
74 degrees
106 degrees

Answers

Answer: The correct answer is 74˚

Which of the following is a trinomial?
O A. 7+X
O B. v3x+1
O C. x+3
D. 3x2 + 4x+1
su

Answers

Answer:

D. 3x2 + 4x+1

Step-by-step explanation:

This answer is a trinomial because there are 3 terms being used, 3x2, 4x, and 1.

If this answer is correct, please make me Brainliest!

The answer for this question is D.

what is the cost of a new trampoline cover that needs to cover a trampoline with a diameter of 8 feet if the material cost 6.75 per square foot?

Answers

Answer: The cost of the trampoline cover would be $339.12

Step-by-step explanation: The radius of the trampoline is 4 feet (Diameter divided by 2 equals radius).

The trampoline cover will effectively cover the entire area of the trampoline and the area is given as

Area of circle = πr²

Area of circle = 3.14 x 4²

Area of circle = 3.14 x 16

Area of circle = 50.24 square foot

However the material costs $6.75 per square foot, which means the total cost of the trampoline cover would be derived as

Total area x cost per square foot = cost of trampoline cover

50.24 x 6.75 = Cost of trampoline cover

$339.12 = Cost of trampoline cover

Answer:  The cost of the new trampoline cover is $339.29

Step-by-step explanation:

Hi, we have to calculate the area of the trampoline cover.

Since it has a circle form with a 8 ft diameter.

Area of a circle = π r^2

Since the radius (r) is equal to the diameter (d) divided by 2

R = d/2 = 8/2 =4

Replacing in the formula:

A = π 4^2 = 50.26 square ft

Since the material cost 6.75 per square foot

Cost = 6.75 x 50.26 = $339.29

I need help please. Solve by the method of substitution, and could you please show/explain how? Im stumped. Thanks

Answers

Answer:

D x+9 = 2x+1

Step-by-step explanation:

y = x+9

y = 2x+1

Substitute x+9  for y in the second equation

y = 2x+1

x+9 = 2x+1

This answers the question

To finish the problem

Subtract x from each side

x+9-x =2x-x+1

9 = x+1

Subtract 1 from each side

9-1 =x+1-1

8=x

Now find y

y = x+9

y = 8+9

y=17

10
A person is selected randomly. What is the probability that the person was born on a
Sunday? *
14.3%
20%
80%
85.7%

Answers

the answer is 14.3%


because if u times it by 7 u get 100 because there is 1/7 percent chance it it will be sunday then any other day of the week

A bag contains 5 blue marbles, 2 blavk marbles, and 3 red marbles. A marble is randomly drawn from the bag. The probability of not drawing a black marble is ___. The probability of drawing a red marble is ___.

Answers

Answer:

20% black marble 30% red marble

Final answer:

The probability of not drawing a black marble is 4/5. The probability of drawing a red marble is 3/10.

Explanation:

To find the probability of not drawing a black marble, we need to find the ratio of the number of marbles that are not black to the total number of marbles. In this case, there are 5 blue marbles and 3 red marbles, so the total number of marbles is 5 + 2 + 3 = 10. The number of marbles that are not black is 5 + 3 = 8. Therefore, the probability of not drawing a black marble is 8/10 or 4/5.

To find the probability of drawing a red marble, we need to find the ratio of the number of red marbles to the total number of marbles. In this case, there are 3 red marbles out of a total of 10 marbles. Therefore, the probability of drawing a red marble is 3/10.

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97. Find the price of the adult's
ticket and the price of a child's ticket

Answers

Answer:

all work pictured and shown

The price of the adult's ticket and the price of a child's ticket are $20 and $19 respectively.

What is a system of linear equations?

A "system" of equations is a set or collection of equations that you deal with all together at once.

Given that, Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97.

Let the price for adult be a and for children be c,

Establishing the equations,

3a+4c = 136.......(i)

2a+3c = 97.........(ii)

Solving the equations,

Multiplying the equation 1 by 3 and equation 2 by 4 and subtracting,

(9a+12c = 408) - (8a+12c = 388)

a = 20

c = 19

Hence, the price of the adult's ticket and the price of a child's ticket are $20 and $19 respectively.

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David is an enthusiastic cyclist. He uses an app on his phone to track each of his cycling sessions. What was the shortest he cycled

Answers

Answer:

There is no picture

Step-by-step explanation:

There is no picture but the answer would be the shortest amount of time.

The answers are as follows:

15.05 miles2 :09:125 hours 19 minutes 18 secondsWhat is unit Conversion?

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

Given :

28/4/18:

Time : 1 :03 : 25

Fastest mile = 02 : 25

Distance = 15.05 miles

03/5/18:

Time : 2:06: 41

Fastest mile = 02 : 53

Distance = 28.70 miles

08/5/18:

Time : 2 :09:12

Fastest mile = 02 : 45

Distance = 26.39 miles2

1.)As, per the data

15.05 < 26.39 < 28.70

Shortest distance cycled = 15.05 miles

and, 1 :03 : 25 < 2:06: 41 < 2 :09:12

Longest = 2 :09:12

Total time, in hours

=1 :03 : 25 + 2:06: 41 + 2 :09:12

=(1 + 2 + 2)

= 5 hrs

In minutes

= 03 + 06+ 09

= 18 minutes

For seconds,

25 + 41 + 12

= 78 seconds

= 1 minute 18 seconds

Hence, Total time = 5 hours 19 minutes 18 seconds.

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simplify 3 square root of 4/ 3 square root of 5

Answers

The final simplified expression is 2 over the square root of 5, represented as  [tex]\( \frac{2}{\sqrt{5}} \).[/tex]

Let's break it down step by step:

1. Simplify the square roots:

[tex]- \(\sqrt{4}\) equals 2 because \(2 \times 2 = 4\). So, \(\sqrt{4} = 2\).[/tex]

  - We have [tex]\(\sqrt{5}\)[/tex] in the denominator, which cannot be simplified further because 5 is a prime number and doesn't have any perfect square factors.

2. Substitute the simplified square roots:

  - After simplifying [tex]\(\sqrt{4}\)[/tex] to 2, the expression becomes [tex]\(\frac{3 \times 2}{3\sqrt{5}}\).[/tex]

3. Cancel out the common factor:

  - Both the numerator and the denominator have a factor of 3. So, we can cancel out 3 from both sides:

[tex]\[\frac{3 \times 2}{3\sqrt{5}} = \frac{2}{\sqrt{5}}\][/tex]

4. Final simplification:

  - The expression [tex]\(\frac{2}{\sqrt{5}}\)[/tex] is simplified as far as it can go because the square root of 5 cannot be simplified further.

So, the simplified expression is [tex]\(\frac{2}{\sqrt{5}}\).[/tex]

please help will give brainliest and 80 points

Answers

Answer:

Start

A2

B2

B1

C1

C2

D2

D3

D4

C4

END

Step-by-step explanation:

Start (A3)

x is equal to 141 because they are alternate interior angles.

A2. x is equal to 39 because they are corresponding angles.

B2. x would be supplementary to 41 because the angle that x supplements is corresponding to 41.

41 + x = 180 due to the linear pair postulate. Therefore, x = 139.

B1. x would be supplementary to 82 because they are consecutive exterior angles.

82 + x = 180 due to the linear pair postulate. Therefore, x = 98.

C1. x = 102 due to the vertical angles theorem.

C2. x would be supplementary to 130 because the angle that x supplements is equal to 130 (Alternate Exterior Angles).

130 + x = 180, x = 50.

D2. x = 74, corresponding angles.

D3. x = 83, corresponding angles.

D4. x = 95, corresponding

C4. x is supplementary to 18 because of the consecutive interior angles theorem.

x = 162

END

Ariel and her family are going to order one large circular pizza that has a diameter of
20 inches and one small circular pizza that has a diameter of 12 inches.
Which measurement is closest to the difference between the area of the large pizza and the
area of the small pizza in square inches?

Answers

Final answer:

The difference between the area of the large pizza (20-inch diameter) and the small pizza (12-inch diameter) is about 201.06 square inches. We calculated this by finding the area of each pizza using the formula for the area of a circle, and then subtracted the smaller area from the larger.

Explanation:

The subject of this question is Mathematics, specifically the concept of area for circles. To calculate the difference between the areas of the two pizzas, we first have to find the area of each pizza individually.

The formula for the area of a circle is A = πr^2, where r is the radius of the circle. For the large pizza with a diameter of 20 inches, the radius is 20/2=10 inches, so its area would be A = π * (10^2) = 314.16 square inches.

For the smaller pizza with diameter of 12 inches, the radius is 12/2 = 6 inches. So, the area of the small pizza is A = π * (6^2) = 113.10 square inch.

Now, to get the difference between the two areas, we subtract the smaller area from the larger area: 314.16 square inches - 113.10 square inches = 201.06 square inches. This is the difference between the area of the large pizza and the small pizza.

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I know why but I can’t explain it and it won’t except my explanation someone help!

Answers

he can because the first rectangle is using 6 blocks straight across,but the second still equals 6 just 2 layers of 3 and that equals 6

find the mode of the following data: 9,15,17,18,6,20,8,5,18,18,10,5,14,12,10,7

Answers

Answer:

18

Step-by-step explanation:

mode is the number that occurs the most

Answer:

18

Step-by-step explanation:

I just identified the numbers and saw 18 the most

Solve the following system via substitution.
m = 2n + 30
2m - n = 39

Answers

Answer:

m=16

n=-7

Step-by-step explanation:

Answer: n=-7, m=16

Step-by-step explanation:

2772, 3663, 2970,4275, 5841, 3564 which of the numbers has to be excluded?

Answers

Answer:4275

Step-by-step explanation:4275 will be removed because in the other numbers ,the numbers formed by the first two digits plus the number formed by the second two digits is 99 which does not happen in the case of 4275.

27=9 72=9

36=9 63=9

A system of equations is shown below.

Equation A: 5x +9y = 12

Equation B: 4x – 3y = 8

Which method eliminates one of the variables?

1) Multiply equation A by and add the result

to equation B.

2) Multiply equation B by 3 and add the result to

equation A.

3) Multiply equation A by 2 and equation B by - 6

and add the results together.

4) Multiply equation B by 5 and equation A by 4

and add the results together.

1on

Answers

Multiply equation B by 3 and add the result to

equation A.

Option 2 is correct

Multiply equation B by 3 and add the result to A

How to Solve linear equations?

When we are given two equations we can solve them by eliminating one variable, and equating the value of one variable to another or by using a matrix.

How to Eliminate One Variable?Let us assume two-equation ax+by = c and px+qy = d, now suppose we want to eliminate x from this two-equation, then we cross-multiply the x coefficients and then subtract them or add them considering the final coefficients of x, we multiply the equation by a multiple of their LCM So multiplying equation ax+by= c by p we get: apx+bpy=pc similarly we mulitply (-a) in equation px+qy=d we get -apx-aqy= -ad If we add the new equation we get y(bp-aq) = pc-ad and we have eliminated x successfully. for eliminating y we would have used coefficients of y.Solving the question

If we want to eliminate y in the given equation we will, LCM of (9,3) is 9 we can multiply B by 3 and add to A.

Hence Option 2 is correct.

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Heather has a bag with 16 red blocks, 11 bile blocks, 9 purple blocks, 15 green blocks, 8 yellow blocks, and 20 orange blocks. If she
was to draw a block out of the bag, record the color and replace the block back in the bag, repeating 500 times, what would most
likely be the probability of drawing a green block (round to the nearest hundredth)?
Answer:0.19

Answers

Answer:

it would be 0.25

Step-by-step explanation:

I think the answer would be 0.19

(Hope this helps!)

8 times the sum of 2 and 15

Answers

Answer:

136

Step-by-step explanation:

15 plus 2 is 17,then multiplied by 8

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