Rachel is trying to find the length of the lake shown on the diagram. She knows that if the two triangles are similar, she can use a proportion to solve for the length. How can Rachel justify that the triangles are similar? What is the length of the lake? A) Corresponding sides of the two triangles have the ratio of 4:1, which proves SAS similarity.The length of the lake is 212 m. B) Corresponding sides of the two triangles have the ratio of 4:1, which proves SSS similarity. The length of the lake is 132 m.
C) Corresponding sides of the two triangles have the ratio of 3:1, which proves SSS similarity. The length of the lake is 159 m. D)
Corresponding sides of the two triangles have the ratio of 4:1, which proves AAS similarity. The length of the lake is 240 m.
Answers
Answer: B) Corresponding sides of the two triangles have the ratio of 4:1, which proves SSS similarity. The length of the lake is 132m.
Step-by-step explanation: Similar Triangles are triangles with corresponding sides proportional to each other.
One way to determine if two triangles are similar is a theorem called Side-Side-Side Similarity Theorem or SSS similarity and it states that two triangles are similar if corresponding angles are equal and corresponding sides are proportional.
The triangles below are similar and they obey this theorem because we observe that the angles are the same and the corresponding sides are proportional:
[tex]\frac{big}{small}=\frac{212}{53}=\frac{60}{15}=4[/tex]
So, the ratio of bigger triangle and smaller triangle is 4:1.
With that ratio and suppose length is represented as L:
[tex]\frac{L}{33} =4[/tex]
L = 132
The length of the lake is 132m.
Thus, the answer for this question is
1) The similarity of the triangles is proved by SSS similarty;
2) Ratio of proportion is 4:1;
3) Length of the lake is 132m;
Related Questions
A constant volume of cookie dough is formed into a cylinder with a relatively small height and large radius. When the cookie dough is placed into the oven, the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t, the height of the dough is 8 mm, the radius of the dough is 18 mm, and the radius of the dough is increasing at a rate of 2 mm per minute.
Part A: At time t, at what rate is the area of the circular surface of the cookie dough increasing with respect to time? (5 points)
Part B: At time t, at what rate is the height of the dough decreasing with respect to time?
Answers
Answer:
a) dA/dt = 125,42 mm/min
b) dh/dt = - 1,78 mm/min
Step-by-step explanation:
The volume of the cylinder is:
V(c) = π*r²*h ( r and h radius of the base and heigh respectively )
Then the surface area is: Area of the base : π*r²
Plus lateral area : h*2*π*r
A(c) = π*r² + 2*π*r*h
With the help of differentials we obtain:
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt (1)
In this equation and at time t we know:
r = 18 mm dr/dt = 2 mm/min h = 8 mm dh/dt = ??
dA/dt = increasing rate of the surface area ( with respect to time)
To find dh/dt we know:
V(c) is constant, then
V(c) = π*r²*h then h = V(c) / π*r²
dh/dt = - [V(c)*2*π*r*dr/dt ] / π²*r⁴
By subtitution of V(c)
dh/dt = - [ π*r²*h *2*π*r*dr/dt ] / π²*r⁴
dh/dt = - [2*π²h*r³*dr/dt ] /π²*r⁴
dh/dt = - [2*h* dr/dt ] / r
dh/dt = - 2*8*2 / 18 mm/min
dh/dt = - 1,78 mm/min
By subtitution in equation (1)
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt
dA/dt = 2*π*18*2 + 2*π*8*2 + (- 2*π*18*1,78 )
dA/dt = 226,20 + 100,53 - 201,31
dA/dt = 125,42 mm/min
Following are solutions to the given points:
Formula:
Cylinder volume [tex]v = \pi r^2 h...............(i)[/tex]
[tex]\to \frac{dr}{dt} = 2 \frac{mm}{min}\\\\ \to \frac{dh}{dt} = -2 \frac{mm}{min}\\\\ \to h=8\\\\ \to r=18 \\\\[/tex]
Part A:
Calculating the circular area of the surface:
[tex]\to A=\pi r^2\\\\[/tex]
So, [tex]\frac{dA}{dt}=2 \pi r \frac{dr}{dt}.........(ii)[/tex]
Therefore
[tex]\to \frac{dA}{dt}= 2\pi \times 18 \times 2= 72 \pi \ \frac{mm^2}{min}\\\\[/tex]
Part B:
[tex]\to \frac{dh}{dt}= - 2 \frac{mm}{min}[/tex]
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Answer:
(3,1)
Step-by-step explanation:
Solve the following system of equations.
5x+4y = 10
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Answer:
(-2, 5), x = -2, y = 5
Step-by-step explanation:
When x = -2 and y = 5 on both equations, the equations become true.
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Answer:
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Step-by-step explanation:
what is 1/4(8+x+4) simplified using the distributive property
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Answer:
x4+3
Step-by-step explanation:
i think this is the answer i aint sure tho
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Answer:
Javier. (5.6 × x) + y = 26.96
Ellema. (13.2 × x) + y = 48.62
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Answer:
18%, 34%, 9/25, 0.25
Step-by-step explanation:
36% = 18%
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13.8 is the answer ...............
How to you Simplify x+4-5x-2?
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Combine the like terms
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simplify 4 - 3(-2a + 2) please!
Answers
Answer:
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4 - 3(-2a + 2)
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Determine whether the mapping diagram shown below represents a
function
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Answers
Answer:
Not a Function
Step-by-step explanation:
Each y-value has 2 x-values. It is supposed to only have one. hope this helped you!! Give brainliest
What is the equation of this line?
Please Help
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y=-2x -2
y=2x -2
y=-1/2x -2
Answers
Answer:
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Step-by-step explanation:
the slope is the rise over run (up over across) and the line meets the y axis at -2 so that is your intercept
It’s not b!!!! Help me please
Answers
Answer:
D maybe? im not sure
Step-by-step explanation:
Lae bought grapes for $1.50 per pound. A 2-column table has 4 rows. Column 1 is labeled Pounds x with entries 1, 2, 3, 4. Column 2 is labeled Dollars y with entries 1.50, 3.00, 4.50, 6.00. Create a graph of the relationship between the two quantities. Complete the statements. Use the numbers in the table to create . are graphed on the x-axis. are graphed on the y-axis. Plot the on the graph. Draw a that starts at the origin and connects all the points.
Answers
The graph of dollar and pound table of Lae is graphed below in which pounds are graphed on the x-axis and dollars are graphed on the y-axis.
How to plot a graph from table?To plot a graph from a table, make the ordered pair of values of coulom 1 and 2 of the table. Plot a line or curve with these ordered pair on the graph.
Lae bought grapes for $1.50 per pound. A 2-column table has 4 rows.
Column 1 is labeled Pounds x with entries 1, 2, 3, 4. Column 2 is labeled Dollars y with entries 1.50, 3.00, 4.50, 6.00.The created graph of the relationship between the two quantities is attached below. Now lets complete the statements.
Use the numbers in the table to create ordered pair. Pounds are graphed on the x-axis. Dollars are graphed on the y-axis. Plot the ordered pair on the graph. Draw a straight line that starts at the origin and connects all the points.Hence, the graph of dollar and pound table of Lae is graphed below in which pounds are graphed on the x-axis and dollars are graphed on the y-axis.
Learn more about plot a graph here;
https://brainly.com/question/26403321
Answer:
1. ordered pairs
2. pounds
3. dollars
4. ordered pairs
5. straight line
I apologize if im late!
The first line of the passage includes a
to introduce a
section and help readers locate it easily,
that
CELL PHONE POLICY
Devices Supplied by the Company
The use of company supplied devices must be limited to
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Personal Cell Phones and Devices
Employees are encouraged to limit their use of personal
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The passage also includes
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The passage is organized according to a
y sequence
Answers
Answer:
Step-by-step explanation:
Answer: 1. heading and subheading
2. subheading
3. point-by-point
Step-by-step explanation:
Which size bottle of ketchup is the best deal with the lowest unit price?
Prices for Different Sizes of Bottles of Ketchup
Size Bottle
Price
10 oz.
$2.50
14 oz.
$2.80
16 oz.
$4.00
18 oz.
$5.40
Answers
Answer:
14oz for $2.80
Step-by-step explanation:
Well to determine the unit prices you must divide the price by whatever the weight is. As so:
10oz: 2.5/10=0.25
14oz: 2.8/14=0.20
16oz: 4/16=0.25
18oz: 5.4/18=0.30
So your answer is 14oz for $2.80
Answer: I’m pretty sure ur answer would be 14 oz. :)
Step-by-step explanation: good luck !<3
23) Which graph shows a proportional relationship between x and y?
Answers
Answer:
B
Step-by-step explanation:
For something to be directly proportional it has to go through the origin (0,0) of the graph.
Answer:
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Step-by-step explanation:
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Answer:
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a flour company in minneapolis wants to know what percent of local households bake at least twice a week. A company representative calls 500 randomly selected local households from 8am to 5pm during the week and finds that 56% of them bake at least twice a week
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Answer:
Step-by-step explanation:
The response of this would be to say that those people without daytime jobs that are outside the home, are more likely to be home and thus, have more time on their hands to attempt to bake. So basically, the quoted 56% is definitely going to be higher than the population percentage.
Is there another way to extend the plane of complex numbers other than by the Riemann sphere?
No answer needed! Just take the points.
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Step-by-step explanation:
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No I never lied hahahah
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Answer:
liar
Step-by-step explanation:
+1112
12
2
−
4
(
6
)
+
1
11
2
.
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Answer:
1113210
Step-by-step explanation:
Answer:
I think its 7844
Step-by-step explanation:
bc 4(6) means 4x6
Item 2
Find the area of the trapezoid.
b1=4,b2=8,h=2
ASAP TIMED WILL GIVE 35 POINTS>
Answers
Answer:
12 units squared.
Step-by-step explanation:
The formula for the area of a trapezoid is 1/2(base1+base2)*height. First, add the two bases together. 4+8=12. Then multiply that number by both 1/2 and the height, 2. 1/2*2*12 equals 12 units squared.
Timed!! Answer hurry!
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Which of these isn't a proportional relationship? 15:30 & 1:2 3:9 & 9:27 05.10 & 10:20 2:4 & 4:2
Answers
Answer:
4:2
Step-by-step explanation:
How much is 3/5 of 31/8 ?
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Answer:
2.325
Step-by-step explanation:
i used a calculator ,i think i did it right lol
You hear that tuition is going to increase by 3% next year. If tuition
this
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Answers
Answer: $7416
Step-by-step explanation:
You look up 3% of $7200 ($216) and add that to the original price to get $7416 :)
Which of the following ratios are equivalent to 34:21?
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Answer:
https://brainly.com/question/19692618
Step-by-step explanation:
https://brainly.com/question/19692618https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618 https://brainly.com/question/19692618
I have 8 Twix bar that I want to share with 6 students how much of the Twix bar will each student get
Answers
Answer:
1.3
Step-by-step explanation:
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BRAINLIEST PLEASE
Answer:
1.3
Step-by-step explanation:
Hope this helped have an amazing day!
what is -3 exponent 2 in expanded form?
Answers
Answer:
-3 times -3 that is -4 exponent two in expanded form
Step-by-step explanation:
-3²
= -3 • -3
eg. Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression. 5,325 in expanded notation form is 5,000 + 300 + 20 + 5 = 5,325.
