To indirectly measure the distance across a lake, Nachelle makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter

To Indirectly Measure The Distance Across A Lake, Nachelle Makes Use Of A Couple Landmarks At Points

Answers

Answer 1

Answer:

207.68 m

Step-by-step explanation:

From the diagram,

ΔDEC is similar to ΔFGC

Therefore,

(DE)/(FG) = (DC)/(FC).............. Equation 1

make line DE the subject of the equation

DE = [(DC)(FG)/(FC)]................ Equation 2

From the diagram,

Given: DC = 190 m, FG = 142.1 m, FC = 130 m

Substitute these values into equation 2

DE = (190×142.1/130)

DE = 207.68 m

Hence the distance across the lake is 207.68 m

Answer 2

Applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m

Recall:

The corresponding side lengths of two triangles that are similar are always proportional to each other.

Thus:

ΔCDE  and ΔCFG are similar to each other

FG = 142.1 m

FC = 130 m

DF = 60 m

DC = 130 + 60 = 190 m

Therefore:

DE/FG = DC/FC

Substitute

DE/142.1 = 190/130

Cross multiply

[tex]DE = \frac{190 \times 142.1}{130} \\\\\mathbf{DE = 207.68 $ m}[/tex] (nearest hundredth).

Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m

Learn more about similar triangles here: https://brainly.com/question/11899908


Related Questions

Mrs Dlamini bought a 10kg bag of rice. She cooks 500g of rice per day. How many days will the bag of rice last her family​

Answers

Answer:

20 days

Step-by-step explanation:

10kg= 10,000g

10,000g/500g= 20 days

Answer:

20 days

Step-by-step explanation:

1 kg=1000 grams

10 kg=10000 grams

10000÷500

=20 days

The closed form sum of

$$12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]$$
for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ Find $an + b.$

Answers

Perhaps you know that

[tex]S_2 = \displaystyle\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}6[/tex]

and

[tex]S_3 = \displaystyle\sum_{k=1}^n k^3 = \frac{n^2(n+1)^2}4[/tex]

Then the problem is trivial, since

[tex]\displaystyle\sum_{k=1}^n k^2(k+1) = S_2 + S_3 \\\\ = \frac{2n(n+1)(2n+1)+3n^2(n+1)^2}{12} \\\\ = \frac{n(n+1)\big((2(2n+1)+3n(n+1)\big)}{12} \\\\ = \frac{n(n+1)\big(4n+2+3n^2+3n\big)}{12} \\\\ = \frac{n(n+1)(3n^2+7n+2)}{12} \\\\ = \frac{n(n+1)(3n+1)(n+2)}{12}[/tex]

Then

[tex]12\bigg(1^2\cdot2+2^2\cdot3+3^2\cdot4+\cdots+n^2(n+1)\bigg) = n(n+1)(n+2)(3n+1)[/tex]

so that a = 3 and b = 1.

The figure is not drawn to scale.

Answers

Answer:

93°, 89°, 93°

Step-by-step explanation:

∠1 and ∠4 are supplementary angles:

m∠1 + m∠4 = 180°; m∠1 = 93°

∠2 and ∠4 are vertical angles:

m∠2 = m∠4 = 87°

∠3 and ∠4 are supplementary angles:

m∠3 + m∠4 = 180°; m∠3 = 93°

In the figure below, triangle ABC is similar to triangle PQR:

A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.

What is the length of side PQ?

48
24
40
18

Answers

Answer:

The length of PQ is 24

Step-by-step explanation:

If you flip triangle PQR upside down the you can see which side corresponds to which. BC corresponds to QR and AB with PQ, the scalar is 6 because of BC (2) times 6 = QR (12). So you just have to do 4 times 6 which is 24.

HELP!!!!! PLEASE!!!!

Answers

53280 miles. If you multiply the mps by seconds in a minute (60) then minutes (48) you can get this answer easily

Find a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1

Answers

The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'

To prove, we will look at some situations:

If we add up the two digits of 18. We get,

[tex]1 + 8 = 9[/tex]

And we multiply 18 by 2 which is greater than 1. We get,

[tex]18[/tex] × [tex]2 = 36[/tex]

The sum remains the same i.e. [tex]3 + 6 = 9[/tex]

Similarly,

If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;

[tex]18[/tex] × [tex]3 = 54[/tex]

where (5 + 4 = 9)

Once more,

Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.

 [tex]18[/tex] × [tex]4 = 72[/tex]

[tex](7 + 2 = 9)[/tex]

[tex]18[/tex] × [tex]5 = 90[/tex]

[tex](9 + 0 = 9)[/tex]

Thus, 18 is the answer.

Learn more about 'numbers' here: brainly.com/question/1624562

In the PQRS triangle PQ=QR, QR side extended to S Show that PQ+RS=QS. -S Q R

pls explain too

Answers

Answer:

Step-by-step explanation:

from the picture:

QP = QR

and

QR = RS

so

PQ + RS = QS

what percentage is equal to 2/5?

a. 50%
b. 25%
c. 10%
d. 40%

Answers

Answer:

40%

Step-by-step explanation:

Percent is out of 100

2/5 * 20/20

40/100

40%

Answer:

Step-by-step explanation:

Divide 2 by 5 to get the decimal .4. Multiply that by 100 to get the percent:

40%, choice d.

Rewrite the expression in the form y^n. (y^-1/2)^4

Answers

Answer:

y^ -2

Step-by-step explanation:

We know that a^b^c = a^(b*c)

(y^-1/2)^4

y^(-1/2*4)

y^ -2

Answer:

Step-by-step explanation:

Write an expression in simplified form for the area of each rectangle. Width: 11 Length: 3x+2

Answers

Answer:

33x+22

Step-by-step explanation:

The area of a rectangle is

A = l*w where l is the length and w is the width

A = 11(3x+2)

Distribute

   = 33x+22

Area of rectangle = Length * Width

Length is 3x+2Width is 11

⇛Area = 11(3x+2)

⇛Area = 33x + 22

the ratio of boys and girls in a 4:3.If there are 20 boys, find the number of girls.​

Answers

Answer:

There are 15 girls.

Step-by-step explanation:

The ratio is 4:3, meaning there are 7 parts.

4 parts= 20 (Boys)

This means 1 part is 20 divided by 4.

1 part= 5

3 parts= Amount of girls.

3 x 5 = 15.

There are 15 girls.

Answer:

15

Step-by-step explanation:

Add:

boys : girls

     4 : 3 = 7

    20: ? = ?

Divide:

20 / 4 = 5

5 × 3 = 15

20: 15

So, there are 15 girls.

abc or d please help me!

Answers

A is the answer because the dot Is on point (10,3)

Answer:

A

Step-by-step explanation:

Cuz that’s the only graph that goes with the statement.

on this graph it’s saying the cost of 3 hair accessories is $10.

X = 3

Y = 10

Describe how (2 cubed) (2 superscript negative 4) can be simplified.

Answers

Answer:

1/2

Step-by-step explanation:

Given:

(2 cubed) (2 superscript negative 4)

= (2³)(2^-4)

= (2³) (1 / 2⁴)

= (2³ * 1) / 2⁴

= 2³ / 2⁴

Both numerator and denominator has the same base. Thus, pick one of the bases

Also, in indices, division sign can be translated to subtraction

Therefore,

2³ / 2⁴

= 2^3-4

= 2^-1

= 1/2¹

= 1/2

(2³)(2^-4) = 1/2

Answer:

D

Step-by-step explanation:

bc i said so

Consider the following points. (−4, −1) and (4, 2) Let Y'O' be the image of YO after a reflection across line . Suppose that ′ is located at (1, 4) and ′ is located at (−2, −4). Which of the following is true about line ?

Answers

The line was reflected about the line y = -x.

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

This question is solved using reflection concepts.

There are various kinds of reflections, 90º clockwise about the origin, 90º counterclockwise, among other, and each of them has a rule.

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

In this question:

Point (-4,-1) became (1,4).Point (4,2) became (-2,-4).

From this, we have the following rule: (x,y) -> (-y,-x)

Checking the rules, it can be said that the line was reflected about the line y = -x.

A similar question can be found at https://brainly.com/question/16130908

Which of the following is a rational number?
square root 97square root 98, square root 99, square root 100

square root 97
square root 98
square root 99
square root 100

Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Answers

Answer:

Square root of 100.  

Step-by-step explanation:

Step-by-step explanation:

We can write 10 as a fraction 10/1, therefore,[tex]\sqrt{}[/tex]100   is a rational number.

Part A : A rational no. between 5.2 and 5.5 is 5.3.  

It is rational because it can be expressed in the form  

p/q where p and q are integers and q is not equal to 0, which is 53/10

Part B: A rational no. between 5.2 and 5.5 is 5.29150262213

An irrational number between 5.2 and 5.5 is 5.29150262213. It is irrational because there is no pattern that repeats and it cant be written as a fraction of two whole numbers.

Answer:

Step-by-step explanation:

Square root of all prime numbers is irrational.

97 is an prime number. So √97 is an irrational number.

√98 = [tex]\sqrt{2*7*7}=7\sqrt{2}[/tex]  is an irrational number.

[tex]\sqrt{99}=\sqrt{3*3*11} =3\sqrt{11}[/tex] is an irrational number

√100 = 10 is a rational number.

Part A:

5.3 is a rational number.

Rational can be written in p/q form and when divided the result will either terminating decimal or non terminating repeating decimal

Part B:

5.3020050......

Irrational numbers are non terminating non repeating numbers

Can some some help me with this one?

Answers

Answer: 7.5 x 10^3 is the answer.

Step-by-step explanation: First, 7.5 x 10^9 is 7500000000. Next, if you convert it to kilometers you would get 7500. And, 7.5 x 10^3 = 7500. Thus, that is the answer.

josh earns $415 a week plus 3% commision on any sales he makes. in a particular week, he gets paid $600. how much did he make in sales?

Answers

Answer:

$185 in commisions

Step-by-step explanation:

600 - 415 = $185

Answer:

6,166.666$ in total sales

Step-by-step explanation:

I. 600$, If 415$ is his earnings then 185 is commision [600 - 415 = 185]

II. Find 3% so 3/100 = 185/x

             3x = 18,500

               x = 6,166.666

Hope it help :)

Help plz!! Trig question

Answers

Answer:

5 meters tall.

Step-by-step explanation:

We know that angle A (the bird) is 55. The opposite side from this angle is 4.5 meters, since that is the distance she is from the tree. From this, we can set up an equation tan(55)=4.5/x and simplify it to x= 4.5/tan(55). This would be height x, but it is not accounting for the 1.5 meters the apple is off the ground, so you need to add 1.5 to the result. The final answer would be 4.65 but you need to round to the nearest meter so it would be 5.

Pleaseeeeee

Within 9 hours, the number of stars seen went from 190 to 33 as the sun started to rise. Find out how many stars are getting hidden by the sunlight each hour.

Answers

Answer:

Approximately 17

Step-by-step explanation:

Number of starts getting hidden in 9 hours = 190 - 33

= 157

Therefore the nun of starts getting hidden in 9 hours is 157

9 hours = 157 stars

1 hours = x

Cross multiply

9 × x = 157 × 1

9x = 157

Divide both sides by 9

x = 157 ÷ 9

x = 17.4

Therefore 17.4 stars are getting hidden every hour.

Answer:

17 4/9 stars per hour

Step-by-step explanation:

First find the decrease in the number of stars

190-33 = 157

Divide by the hours that passed

157/9

17 4/9 stars per hour

if 5^t = 0.04 ,then find the value of t

Answers

Answer:

t=-2

Step-by-step explanation:

Solve Exponent.

5t=0.04

log(5t)=log(0.04)(Take log of both sides)

t*(log(5))=log(0.04)

t=log(0.04)÷log (5)

t=−2

Man spends 1/5 of his salary on shoes and 2/3 on school fess what fraction of his salary is left

Answers

Answer: 2/15

Explanation :

1 - (1/5 + 2/3)
1 - (3/15 + 10/15)
1 - 13/15
15/15 - 13/15
= 2/15

e. What order will result in a final output of 36 when the initial input is 1/7?

Answers

Answer:

5

Step-by-step explanation:

7x5=35

the remainder is 1

=5.1

the nearest number is 5

Please help out explanation need it

Answers

Answer:

156m^2

Step-by-step explanation:

I dont know what you mean by "each figure," but if you need the surface area for the rectangular prism, then the answer is 156, because the top square has a surface area of 3*6, then it equals 18, and the bottom square is the same, so it is also 18, 18*2=36

The 4 rectangle on the side are all the same, and they are all 10x3 which is 30, so 30*4 because there are 4 rectangles, equals 120.

120+36=156. The surface area of the rectangle is 156m^2

a man is now 9 times as old as his daughter. in four years time he'll be five times as old as his daughter. what are their present ages​

Answers

Answer: The father is 36 right now and the son is 4

Step-by-step explanation: 9x4 is 36 and 36/9=4.

√2+1
b) Rationalize the denominator:
√2+1

Answers

Answer:

there is not a complete question here ...

[tex]\sqrt{2} +1[/tex] is not in a denominator to rationalize

if it were you would multiply the rational expression (the fraction)

by [tex]\frac{\sqrt{2} -1}{\sqrt{2} -1}[/tex] the result (in the denominator would end up being "2 -1"

which is 1

Step-by-step explanation:

Find the missing part.

Answers

Step-by-step explanation:

8²+10²= x²

64+100 =x²

164=x²

√164=√x²

square and squre root do cancel each other

x=√164

hope this helps

Answer:

x = [tex]\sqrt{164[/tex]

Step-by-step explanation:

In order to find the hypotenuse of a right triangle, you have to add,

[tex]8^{2} + 10^{2}[/tex]

which simplifies to,

64 + 100 =

[tex]\sqrt164[/tex]

Hope this helps! :)

What is the minimum of 52, 59, 61, 65, 65, 71, 72, 73, 74, 76, 83, 88, 92, 94, 97, 98, 101, 102, 103, 110

Answers

Answer:

52

Step-by-step explanation:

The minimum of the data set is the smallest number. Therefore, the minimum is 52.

Valeria purchases a can of chicken noodle soup and a can of tomato soup. The can of chicken noodle soup has a height of 4 inches and a radius of 2 inches. What is the volume of the can of chicken noodle soup?
Use ​≈3.14 and round your answer to the nearest whole number.
The can of tomato soup has the same volume, but a radius of 2.5 inches. What is the height of the can of tomato soup?
Use ​≈3.14 and round your answer to the nearest tenth.


Questions

Answers

Answer:

The height of the tomato soup can is 2.6 in.

Step-by-step explanation:

"The can of chicken noodle soup has a height of 4 inches and a radius of 2 inches."

We can find the volume of this can.

V = pi r² h

V = 3.14 * (2 in.)² * (4 in.)

V = 50.24 in.³

"The can of tomato soup has the same volume, but a radius of 2.5 inches."

Now we know the volume of the can, so we can find the height, h.

V = pi r² h

50.24 in.³ = 3.14 * (2.5 in.)² * h

50.24 in.³ = 19.625 in.² * h

h = (50.24 in.³)/(19.625 in.²)

h = 2.56 in.

Answer: The height of the tomato soup can is 2.6 in.

Answer:

:Volume of can of chicken noodle soup=50.24inch^3

:Height of can of tomato soup=2.56inches

Step-by-step explanation:

CHICKEN NOODLE SOUP :height=4inches

:radius=2inches

[ V=πr2h]

V=(3.14×2×2×4)=50.14

Now, Volume is same of both the can.

Volume of can of tomato soup=50.24;radius=2.5inches;

Height of can of tomato soup,

50.24=(3.14×2.5×2.5×h)

50.24=19.625h

h=50.24/19.625

=2.56inches

15 × u= 135
---------------

Answers

Answer:

15u = 135

Divide both sides by 15

u = 135/15 = 9

U is equal to 9

Hope this helps!

[tex]15 \times 4 = 135 \\ divide \: both \: sides \: of \: equcation \\ by \: 15 \\ \frac{15u}{15} = \frac{135}{15} \\ u = \frac{135}{15} \\ u = 9[/tex]

Triangle LMN is dilated by a scale factor of 2/3 to form triangle L’M’N. Side NL measures 48. What is the measure of side N’L’?

Answers

48 x 2/3 = 32. For dilation just multiply each side by the dilation factor.
Other Questions
Help Please !!A right triangle pyramid has a height of 10 inches and a base of 41.57 square inches. What is the volume, in cubic inches, of the pyramid? you are attempting to convince an audience that animal testing is morally wrong The soldiers sufferinjuries during the attack. meaning of education Identify the compound with ionic bonds.COH2ONeKClO2 what is photosynthesis? how did Asian Americans, Hispanic Americans, Women, and Dissenters react to the way they were treated in World War 1 Find and correct the mistake : 1. Animals were first dominated for food, and later become a source of skin, fur and wool. 2. He was doing a crossword puzzle while he is waiting for the train. 3. The children did their homework when their father came back from the office. 4. He played the guitar when someone opened the window and threw out a bucket of water. 5. What did you do between 9.00 and 10.00 yesterday? I was cleaning my house. I always clean my house on Sunday mornings. If an electric train moves south, which direction does the train smoke go?answer with intelligence. Help me please.. 1. How to increase the effectiveness of the institutional policy of nature protection and biodiversity? 2 cm = 7.5 m in the drawing the mall is 8.6 cm tall how tall is the actual mall 4. Name the federal cities in Russia. Choose the letter A, B, C or D the word that has the underlined part different from others. A. Cultural. C. LandlineB. Interact. D. Language Whats the chance of rolling the correct number 1-6500When every time you guess a number the number changes So if i guess 800 every time how many guesses to get the correct number When customers interact with technology and machines, the variability of the service encounter is reduced by Pls help in this maths problem how much cost Rs 1136 when it is 10% discount and 13% vat is added then find out the discount and Vat amount bell hooks describes how women's studies programs became a fruitful site for feminist thinking and theorizing, exposing and often converting masses of students to feminist ways of thinking about the world. However, there were some costs that she describes as well. What are some of the problems she points out with this shift?a. general audiences were neglected an important site for mobilizingb. elitist, jargony language discouraged popular reading of feminist textsc. feminist movements were deradicalized and depoliticized as they joined university bureaucraciesd. the experiences of privileged class women were for a time favored in feminist theorizinge. all of the above help, please please help is this correct?