Jeremy is given the choice between two chocoletes,chocolates, and Y. Which..........
Answers
To determine which option is correct, we first need to find the volume of both chocolate.
The volume of X:
The shape is a square-based pyramid. The volume is given by
[tex]\begin{gathered} V_x=\frac{1}{3}\times base\text{ area }\times height \\ V_x=\frac{1}{3}\times l\times b\times h \end{gathered}[/tex]From the diagram,
l = 5 cm
b = 6 cm
h = 10 cm
Substituting,
[tex]\begin{gathered} V_x=\frac{1}{3}\times5\times6\times10 \\ V_x=100\operatorname{cm}^3 \end{gathered}[/tex]The volume of Y:
The shape is a triangular-based pyramid. The volume is given by
[tex]\begin{gathered} V_y=\frac{1}{3}\times base\text{ area }\times height \\ V_y=\frac{1}{3}\times\frac{1}{2}\times b\times l\times h \end{gathered}[/tex]From the diagram,
l = 8 cm
b = 7.5 cm
h = 10 cm
[tex]\begin{gathered} V_y=\frac{1}{3}\times\frac{1}{2}\times7.5\times8\times10 \\ V_y=100\operatorname{cm}^3 \end{gathered}[/tex]From here, the volumes of both chocolates are the same.
Therefore, the chocolate he picks does not matter as both volumes are equivalent.
The SECOND OPTION is correct.
Related Questions
Instructions: Find the missing side of the triangle. tion 24 x 7 2 =
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We are given a right-angled triangle.
Two of the side lengths are given and the third is missing.
We can us the Pythagorean theorem to find the missing side of the triangle.
[tex]c^2=a^2+b^2[/tex]Where c is the longest side, a and b are the shorter sides of the triangle.
[tex]\begin{gathered} c^2=a^2+b^2 \\ x^2=7^2+24^2 \\ x^2=49^{}+576 \\ x^2=625 \\ x^{}=\sqrt[]{625} \\ x^{}=25 \end{gathered}[/tex]Therefore, the missing side of the triangle is 25
Solve the system of equation graphed on the coordinate axed below y=-4/3x-1
Y=4/3x+7
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Answer:
[tex]x=-3, y=3[/tex]
Step-by-step explanation:
The solution to a system is where the graphs intersect.
Which expression is undefined? -8÷(-8) -8÷80÷88÷0
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The expressions where a number is divided by 0 are undefined, as the result would became indefinitely big (infinity).
The expression -8÷80÷88÷0 has a division by 0, so it is undefined.
which ordered pair below would prevent this table from being a function?
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We have the following:
A relation is a correspondence of elements between two sets.
A function is a relation where each element of a set (A) corresponds to one and only one element of another set (B).
Therefore, the only value in x that is repeated is -2, therefore the answer (-2, 0)
Find the surface area of the isosceles trapezoid prism , Do not round answer
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From the question;
The Area formula for a trapezoid is;
[tex]\begin{gathered} B=\frac{1}{2}h(b_1+b_2) \\ Where\text{ B=Area} \\ h=\text{height of the trapezoid} \\ b_1,b_2=bases_{} \end{gathered}[/tex][tex]\begin{gathered} B=\frac{1}{2}(3)(4+8) \\ B=18\operatorname{cm} \end{gathered}[/tex]So, we have the surface area as;
[tex]\begin{gathered} SA=ph+2B \\ \text{Where SA= surface area} \\ p=\text{perimeter of the trapezoid} \\ h=\text{height of the prism} \end{gathered}[/tex]But the perimeter p of the trapezoid is;
[tex]\begin{gathered} p=3.7\operatorname{cm}+4\operatorname{cm}+8\operatorname{cm}+3.7\operatorname{cm} \\ p=19.4\operatorname{cm} \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} SA=19.4(9)+2(18) \\ SA=174.6+36 \\ SA=210.6\operatorname{cm} \end{gathered}[/tex]50. What is the intersection of plane STUV and plane UYXT?SуUWZA. SVB.YZC. STD. TX
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The intersection of plane STUV and plane UYXT will be the line segment TU.
The task is to determine the intersection of the planes UYXT and STUV.
We are aware of;
When two planes overlap, their intersection is a straight line.
The points 'T' and 'U' are shown in the picture to be on both planes UYXT and STUV.
As a result, the line connecting these two points, that is, the line TU likewise lies on both planes.
As a result, the line 'TU' is formed by the intersection of both planes.
Thus, the intersection of plane STUV and plane UYXT will be the line segment TU.
To learn more about the intersection of the planes visit:
https://brainly.com/question/1646172
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7 thirds x 3 eighths
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Answer: 0.875
Step-by-step explanation:
7/3 x 3/8 -> 21/24 -> 7/8
7/8 converted to decimal: 0.875
264 milligrams is how many grams
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SOLUTION
Milligrams is a unit of measurement for mass in which a unit is a thousandth gram.
Hence
[tex]1000mg=1g[/tex]Then
[tex]264mg=xg[/tex]Therefore
[tex]x=\frac{264}{1000}=0.264g[/tex]Hence
[tex]264mg=0.264g[/tex]Therefore we conclude that
264 milligrams is 0.264g
can you help with this one its has 11 part to it
Answers
Recall that the limit of a function exists if
[tex]\lim_{x\to n^+}f(x)=\lim_{x^\to n^-}f(x).[/tex]Now, from the graph, we get that:
[tex]\begin{gathered} \lim_{x\to0^-}f(x)=0, \\ \lim_{x\to0^+}f(x)=0, \end{gathered}[/tex]therefore:
[tex]\lim_{x\to0}f(x)=0.[/tex]Answer: [tex]True.[/tex]How do you solve literal equation:u=x-k, solve for x12am=4, solve for aa-c=d-r, solve for a
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In order to solve a literal equation, we just need to isolate the chosen variable in one side of the equation. So we have:
[tex]\begin{gathered} u=x-k \\ u+k=x \\ x=u+k \\ \\ 12am=4 \\ a=\frac{4}{12m} \\ a=\frac{1}{3m} \\ \\ a-c=d-r \\ a=d-r+c \end{gathered}[/tex]-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10 Which of the following inequalities is represented by the number line?
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Here, we want to select the inequality that is represented by the plot
The first thing we will do here is to get the type of circle given, whether shaded or unshaded
As we can see, the circle on the number -3 is unshaded
What this mean is that the type of inequality we shall be considering is the one without equal to
Hence, option A and C is out of it
To get the correct one between B and D, we have to look at the direction of the black line beside the circle
The direction of the black line as we can see is towards the right hand side
What this mean is that the inequality in question is greater than the value on which we have the circle
Conclusively, this mean that our answer is the second option
what is the answer to the equation-2n+3=8
Answers
-2n + 3 = 8
-2n = 8 - 3
-2n = 5
n = -5/2
Ashton, Anywhere had a population of 294876 in 2007. The population is inci upon this data, predict the population for in 9 years.
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Answer:
378,075
Explanation:
The population of Ashton in 2007 = 294876
The population increases at a constant rate of 2.8%.
Therefore, the population at any time, t after 2007 is:
[tex]\begin{gathered} P(t)=294876(1+2.8\%)^t \\ P(t)=294876(1+0.028)^t \\ P(t)=294876(1.028)^t \end{gathered}[/tex]Therefore, the population in 9 years time will be:
[tex]\begin{gathered} P(9)=294876(1.028)^9 \\ =378074.6 \\ \approx378,075 \end{gathered}[/tex]The predicted population in 9 years will be 378,075.
A hummingbird can travel up to 15 meters per second.What is the hummingbird's speed in miles per hour?1 mile ≈ 1609 meters Enter your answer, as a decimal to the nearest tenth, in the box. mph
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SOLUTION
The speed of the hummingbird is giving as
[tex]\text{ 15meter/seconds }[/tex]Recall that
[tex]1\text{mile}\approx1609\text{ meters }[/tex]Hence
[tex]\begin{gathered} 15\text{meters will be }\frac{15}{1609}miles\text{ } \\ \\ \end{gathered}[/tex]Recall that
[tex]3600\text{ seconds =1hour }[/tex]Hence
the speed of the hummingbird in miles per hour will be
[tex]\begin{gathered} \frac{15}{1609}\times\frac{3600}{1}=\frac{54000}{1609}=33.56\text{miles per hour } \\ \\ \end{gathered}[/tex]Therefore the speed in miles per hour to the nearest tenth is 33.6mph
Brad expects that he will need $12,000 in 6 years to start an engineering consulting business. He has been offered an investment at 5%, compounded monthly. How much must he invest today to have enough money in 6 years? How much interest will he have earned?
Answers
Answer:
Invest today: $8895.36
Interest earned: $3104.64
Explanation:
The amount after t years can be calculated as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the initial amount invested, r is the interest rate and t is the number of years and n is the number of times the interest rate is compound. Solving the equation for P, we get:
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Now, we can replace A by $12,000, r by 5% = 0.05, n by 12 because it is compounded monthly and t by 6
[tex]P=\frac{12000}{(1+\frac{0.05}{12})^{12(6)}}=8895.36[/tex]Therefore, he should invest $8895.36 today to have enough money in 6 years.
Finally, the interest earned is calculated as
$12000 - $8895.36 = $3104.64
So, the answers are:
Invest today: $8895.36
Interest earned: $3104.64
Bailey wants to buy a house, paying approximately $1000 per month. The bank estimates a 4.5% annual interest rate for 15 years. Which formula approximates the total value of a house Bailey can afford?
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Data:
Amount per month: $1000
Interest rate: 4.5% annual for 15 years
As Bailey wants to pay approx. $1000 per month, in a year he wants to pay approx.: $12000
[tex]1000\cdot12=12000[/tex]>>Хx = [?](Enter the number that belongs in the green box.
Answers
Answer: x = 90 degrees
Explanation:
In the given figure, the opposite sides are parallel. This means that the vertices are right angles. A right angle is 90 degrees. Thus,
x = 90 degrees
I have a practice question that I need explained and answered. Thank you - Rose
Answers
To determine the x - coordinate of the distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The distance between the two points is estimated using the above formular
[tex]\begin{gathered} x_2=4 \\ x_1=?_{} \\ y_1=-1 \\ y_2=9 \\ d=6\sqrt[]{6} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ 6\sqrt[]{6}=\sqrt[]{(x-4)^2+(9--1)^2} \\ \text{square both side } \\ (6\sqrt[]{6)^2}=(\sqrt[]{(x-4)^2+10^2})^2 \\ 216=(x-4)^2+100 \\ 216-100=(x-4)^2 \end{gathered}[/tex][tex]\begin{gathered} 116=(x-4)(x-4) \\ 116=x^2-8x+16 \\ 100=x^2-8x \\ x^2-8x-100=0 \end{gathered}[/tex]Solve using quadratic formular
[tex]\frac{-b\pm\sqrt[]{b^2}-4ac}{2a}[/tex][tex]\begin{gathered} \frac{-b\pm\sqrt[]{b^2}-4ac}{2a}\ldots..\text{ a= 1 , b = -8 , c = -100} \\ \frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-100)}}{2(1)} \\ \frac{8\pm\sqrt[]{64+400}}{2} \\ \frac{8\pm\sqrt[]{464}}{2}=\frac{8\pm4\sqrt[]{29}}{2} \\ \frac{2(4\pm2\sqrt[]{29)}}{2}=4\pm2\sqrt[]{29} \end{gathered}[/tex]Therefore the correct answer for the x - coordinates are:
[tex]\begin{gathered} x=4+2\sqrt[]{29}\text{ and } \\ x_{}=4-2\sqrt[]{29} \end{gathered}[/tex]Justin’s shop sells 6 1/2 quarts of ice cream each day. How much is this in pints? Write your answer as a whole number or a mixed number in simplest form.Include the correct unit in your answer.
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1) In this question we need to remind ourselves that there is one equivalence between quarts and pints, namely:
[tex]1\:quart--->2\:pint[/tex]2) Based on that, we can write out the following set of ratios:
[tex]\begin{gathered} \frac{1}{6\frac{1}{2}}=\frac{2}{x} \\ \\ x=2\times6\frac{1}{2} \\ \\ x=13 \end{gathered}[/tex]Note that there is a proportional relationship between them.
3) Thus, this is the answer.
What is the slope of the points (3,64) and (9,79).
m=
m =
= 15
6
m =
Un Hồ
2-#1
m=2.5
6
15
Answers
Answer:
[tex]\boxed{\bf Slope(m)=2.5}[/tex]
Step-by-step explanation:
We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,64) and (9,79).
The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.
[tex]\boxed{\bf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf \left(x_1,\:y_1\right)=\left(3,\:64\right)[/tex]
[tex]\sf \:\left(x_2,\:y_2\right)=\left(9,\:79\right)[/tex]
[tex]\sf m=\cfrac{79-64}{9-3}[/tex]
[tex]\sf m=\cfrac{5}{2}[/tex]
[tex]\sf m=2.5[/tex]
Therefore, the slope of (3,64) and (9,79) is D) 2.5!!
___________________
Hope this helps!
Have a great day!
Answer:
m = (y2 - y1)/(x2 - x1) m = 15/6 m = 2.5Step-by-step explanation:
Formula we use,
→ m = (y2 - y1)/(x2 - x1)
Then the required slope is,
→ m = (y2 - y1)/(x2 - x1)
→ m = (79 - 64)/(9 - 3)
→ m = 15/6
→ [ m = 2.5 ]
Hence, the slope is 2.5.
find the area of a regular 18-gon with radius of 14 mmA≈ __ mm squared do not found until the final answer, then round to the nearest tenth as needed.
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ANSWER
EXPLANATION:
Given that;
The radius of the 18-gon is 14mm
Follow the steps below
Step 1; Calculate the interior angle by using the below formula
[tex]\text{ }\theta\text{ = }\frac{\text{ 180 \lparen n - 2\rparen}}{n}[/tex]Since the polygon has 18 sides, then n = 8
[tex]\begin{gathered} \text{ }\theta\text{ }=\text{ }\frac{180\text{ \lparen18 - 2\rparen}}{18} \\ \\ \theta\text{ }=\text{ }\frac{180\text{ }\times\text{ 16}}{18} \\ \\ \theta\text{ }=\text{ }\frac{2880}{18} \\ \theta\text{ }=\text{ 160}\degree \end{gathered}[/tex]Step 2; Find the base angle of the triangle
Recall, that all regular polygon can be divided into isosceles triangle by joining the vertices to the center. Hence, the base angle can be calculated below as
[tex]\begin{gathered} \text{ Base angle = }\frac{160}{2} \\ \text{ Base angle = 80}\degree \end{gathered}[/tex]Step 3; Find the height of triangle using trigonometric
[tex]\begin{gathered} \text{ tan }\theta\text{ }=\text{ }\frac{\text{ opposite}}{\text{ adjacent}} \\ \text{ } \end{gathered}[/tex]Since the radius of the polygon is 14mm, therefore, the base length is
[tex]\begin{gathered} \text{ Base length = }\frac{14}{2} \\ \text{ Base length = 7mm} \end{gathered}[/tex][tex]\begin{gathered} \text{ Tan 80 = }\frac{h}{7} \\ \text{ cross multiply} \\ \text{ h = tan 80 }\times\text{ 7} \\ \text{ h = 7tan 80} \\ \text{ tan 80 = 5.671} \\ \text{ h = 7 }\times\text{ 5.671} \\ \text{ h = 39.697 mm} \end{gathered}[/tex]Step 4; Find the area of the triangle
[tex]\begin{gathered} \text{ Area of a triangle = }\frac{1}{2}bh \\ \text{ Area of a trianlge = }\frac{1}{2}\times7\times39.697 \\ \text{ Area of a triangle = }\frac{277.879}{2} \\ \text{ Area of a triangle = 138.94 mm}^2 \end{gathered}[/tex]Step 5; Find the area of the polygon
Since there are 18 triangles in the polygon, then calculate the area of the 18-gon
Area of 18-gon = 18 x 138.94
Area of 18-gon = 2500.9 mm^2
Therefore, the area of the 18-gon is 2500.
help me out please thanks
Answers
Answer:
1/10
Step-by-step explanation:
=a+4/5=3/2
=a=4/5-3/2
=a=1/10
Answer: a = 7/10
Step-by-step explanation:
Convert and mix 1 and 1/2 to get 3/2
Next move 4/5 to the right side
Then multiply 4/5 by 3/2 to get the answer 7/10
Can you please show me how to do this so I can teach it to my boys? They need to Express percents as fractions or mixed numbers, and to express each percent as a decimal.
Answers
A. Let's convert the following percents into a fraction or a mixed number in the simplest form.
1.) 24%
4.) 150%
To be able to convert percentage into a fraction, we just apply the following formula:
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex]We get,
1.) 24%
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex][tex]\text{ = }\frac{24}{100}[/tex][tex]\text{ = }\frac{\frac{24}{4}}{\frac{100}{4}}\text{ = }\frac{6}{25}[/tex]Therefore, the fractional form of 24% is 6/25.
4.) 150%
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex][tex]\text{ = }\frac{150}{100}[/tex][tex]\text{ = 1 }\frac{50}{100}\text{ = 1}\frac{1}{2}[/tex]Therefore, the fractional form of 150% is 1 1/2.
B. Express each percent as a decimal.
9.) 8%
14.) 568%
To be able to convert a percentage to a decimal, we just divide all percentages by 100.
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex]9.) 8%
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex][tex]\text{ = 8 }\div\text{ 100}[/tex][tex]\text{ Decimal Equivalent = 0.08}[/tex]14.) 568%
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex][tex]\text{ = 568 }\div\text{ 100}[/tex][tex]\text{ Decimal Equivalent = 5.68}[/tex]Therefore, the decimal equivalent of 568% is 5.68.
If a set of grades for a class has a large range and a small standard deviation,what can you say about the class? Include an interpretation that is specific togrades in a class.
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A large ranges indicates that there is a large difference between the highest and lowest grade scores. A smaller deviation indicates that the grades scores are less varied amom themselves.
An example is when the highest grade is 100 and the lowest grade is 5. In this case the range is larger than the case when the highest is 100 and the lowest 60.
A smaller standard deviation means that the data set of grades are close to the mean of the data set. The behavior is the following
Chase rode a Ferris wheel 93 timesaround, one lap after the other. If eachlap of the Ferris wheel took 20 seconds,how long was Chase's ride?minute
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If Chase rode 93 times around, and each lap takes 20 seconds, to find out how long was Chase's ride we must multiply the time for each lap, and how many laps she did, then, the calculus will be
[tex]time=93\cdot20[/tex]The result will be in seconds!
[tex]\begin{gathered} time=93\cdot20 \\ \\ \text{time}=1860\text{ seconds} \end{gathered}[/tex]Then Chase's ride was 1860 seconds long! We can covert it in minutes by doing the division by 60
The time in minutes will be
[tex]\begin{gathered} \text{time}=\frac{1860}{60}\text{ minutes} \\ \\ \text{time}=31\text{ minutes} \\ \end{gathered}[/tex]Therefore, Chase's ride took 31 minutes
how much higher is 1,774 than -118(adding and subtracting integers)
Answers
To find the difference between two numbers, we substract the smaller one from the bigger one. In this case, the smaller one is -118 and the bigger one is 1,774. Then:
[tex]1774-(-118)=1774+118=1892[/tex]Then 1774 is higher than -118 by 1892
Find the area bounded by the given curves. y=x², y=4 Options:32/3 31/3 34/3 37/3
Answers
We have to find the area within the given curves.
We have to integrate the difference between the two functions.
First, we have to find the intersections between the curves to know the interval for which we will integrate.
We then write:
[tex]\begin{gathered} y_1=y_2 \\ x^2=4\Rightarrow x_i=-2,x_f=2 \end{gathered}[/tex]We will integrate in the interval [-2, 2]. In this interval, the function y=4 is greater than y=x^2, so we will integrate the difference of the functions as:
[tex]\begin{gathered} A=\int ^2_{-2}\lbrack y_2(x)-y_1(x)\rbrack dx \\ A=\int ^2_{-2}(4-x^2)dx \\ A=4x-\frac{x^3}{3}+C \\ A=(4\cdot(2)-\frac{(2)^3}{3})-(4\cdot(-2)-\frac{(-2)^3}{3}) \\ A=(8-\frac{8}{3})-(-8+\frac{8}{3}) \\ A=8-\frac{8}{3}+8-\frac{8}{3} \\ A=16-\frac{16}{3} \\ A=\frac{48-16}{3} \\ A=\frac{32}{3} \end{gathered}[/tex]The area bounded by the curves y=x^2 and y=4 is A = 32/3.
slove two-step liner equations 19=s/2+15
Answers
s = 8
Explanation:
19=s/2+15
collect like terms:
19 - 15 = s/2
4 = s/2
[tex]\begin{gathered} 4\text{ =}\frac{s}{2} \\ \text{cross multiply} \\ s\text{ = 4}\times2 \\ s\text{ = 8} \end{gathered}[/tex]Use the drop-down menus to identify the values of theparabola.Vertex=Domain=Range=
Answers
Given:
We get the point (0,4) from the graph.
Recall that the vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.
[tex]\text{Vertax =(0,4)}[/tex]Every single number on the x-axis results in a valid output for the function.
The domain of the parabola is real values.
[tex]\text{Domain}=(-\infty,\infty)[/tex]
The maximum value of y is 4 and the parabola is open down.
[tex]Range=(-\infty,4\rbrack[/tex]Final answer:
[tex]\text{Vertax =(0,4)}[/tex][tex]\text{Domain}=(-\infty,\infty)[/tex][tex]Range=(-\infty,4\rbrack[/tex]need help- don’t mind the writing in pencil I forgot to erase it
Answers
We will deteremine the length of segment TV as follows:
[tex]A=\frac{WU\cdot TV}{2}\Rightarrow200=\frac{16\cdot TV}{2}[/tex][tex]\Rightarrow400=16\cdot TV\Rightarrow TV=25[/tex]So, the lenght of segment TV is 25 centimeters.