Answer: 8.26 m
Step-by-step explanation:
[tex]$$Let s be the length of the wire used for the square. \\Let $t$ be the length of the wire used for the triangle. \\Let $A_{S}$ be the area of the square. \\Let ${A}_{T}}$ be the area of the triangle. \\One side of the square is $\frac{s}{4}$ \\Therefore,we know that,$$A_{S}=\left(\frac{s}{4}\right)^{2}=\frac{s^{2}}{16}$$[/tex]
[tex]$$The formula for the area of an equilateral triangle is, $A=\frac{\sqrt{3}}{4} a^{2}$ where $a$ is the length of one side,And one side of our triangle is $\frac{t}{3}$So,We know that,$$A_{T}=\frac{\sqrt{3}}{4}\left(\frac{t}{3}\right)^{2}$$We have to find the value of "s" such that,$\mathrm{s}+\mathrm{t}=19$ hence, $\mathrm{t}=19-\mathrm{s}$And$$A_{S}+A_{T}=A_{S+T}$$[/tex]
[tex]$$Therefore,$$\begin{aligned}&A_{T}=\frac{\sqrt{3}}{4}\left(\frac{(19-s)}{3}\right)^{2}=\frac{\sqrt{3}(19-s)^{2}}{36} \\&A_{T+S}=\frac{s^{2}}{16}+\frac{\sqrt{3}(19-s)^{2}}{36}\end{aligned}[/tex]
[tex]$$Differentiating the above equation with respect to s we get,$$A^{\prime}{ }_{T+S}=\frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}$$Now we solve $A_{S+T}^{\prime}=0$$$\begin{aligned}&\Rightarrow \frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}=0 \\&\Rightarrow \frac{s}{8}=\frac{\sqrt{3}(19-s)}{18}\end{aligned}$$Cross multiply,$$\begin{aligned}&18 s=8 \sqrt{3}(19-s) \\&18 s=152 \sqrt{3}-8 \sqrt{3} s \\&(18+8 \sqrt{3}) s=152 \sqrt{3} \\&s=\frac{152 \sqrt{3}}{(18+8 \sqrt{3})} \approx 8.26\end{aligned}$$[/tex]
[tex]$$The domain of $s$ is $[0,19]$.So the endpoints are 0 and 19$$\begin{aligned}&A_{T+S}(0)=\frac{0^{2}}{16}+\frac{\sqrt{3}(19-0)^{2}}{36} \approx 17.36 \\&A_{T+S}(8.26)=\frac{8.26^{2}}{16}+\frac{\sqrt{3}(19-8.26)^{2}}{36} \approx 9.81 \\&A_{T+S}(19)=\frac{19^{2}}{16}+\frac{\sqrt{3}(19-19)^{2}}{36}=22.56\end{aligned}$$[/tex]
[tex]$$Therefore, for the minimum area, $8.26 \mathrm{~m}$ should be used for the square[/tex]
6. Annie has a cube that has a side length of 9 cm. What is the surface area of the cube?
Answer:
486
Step-by-step explanation:
Surface area means the area of each side added upIn a cube, every side is the samethe area of one side = 9 * 9 = 81, since it is a square (width*height) and width and height are the same. in a cube there are 6 sidesso there are 6 sides with area 8181 * 6 = 486Which of the following is equivalent to
?
60 ^1/2
Answer:
60^1/2 = 60^0.5 = sqrt 60 = 7.75
good luck :))) <3
Find the area of the triangle.
Height = 4 ft
Base = 12 1/2 ft
Area = ? square feet
If two lines intersect, their intersection is___________
O many points
O one plane
O many planes
O one point
Answer:
one point and one plane
Step-by-step explanation:
Any two line if they intersects... they will intersects in one point..
And to have an intersection they always need to be on one plan..
What is the factorization of the polynomial graphed below? Assume it has no
constant factor. Write each factor as a polynomial in descending order.
Evaluate and simplify
Answer:
[tex]\frac{-3}{-26}[/tex]
Step-by-step explanation:
[tex]\frac{-x-8}{x^{2}-4x-21}[/tex] is what you are looking for.
So with x = -5, it would look like this
[tex]\frac{-(-5)-8}{-5^{2}-(-5)4-21}[/tex]
Simple math now.
-(-5) is 5
[tex]-5^{2} = -25[/tex]
-5 * -4 = 20.
So it should be [tex]\frac{5-8}{-25+20-21}[/tex]
5-8=-3
-25+20-21 = -26
So the answer is[tex]\frac{-3}{-26}[/tex]
Can someone help me find the volume of this?
Answer:
97.2 m³
Step-by-step explanation:
The volume of a triangular prism is half the volume of a rectangular prism with the same length, width, and height.
V = 1/2LWH
V = 1/2(9 m)(7.2 m)(3 m) = 97.2 m³
_____
Additional comment
The relation we used above comes from the more general formula for the volume of a prism:
V = Bh
where B is the area of the base.
You know a rectangular base will have an area of ...
A = bh
and a triangle with the same base and height will have an area of ...
A = 1/2bh
That is, the base area of a triangle is half that of a rectangle with the same dimensions. When we use this fact in the volume formula, we find the volume of a triangular prism is 1/2 that of a rectangular prism with the same length, width, and height.
Solve the equation. Write your answer as an integer or simplified fraction.
5n−6 n−2 =19
n = _____
Explaination :
The given equation,
[tex] \boxed{\sf{5n \: - 6(n - 2) \: = \: 19}} \: \bigstar[/tex]Lets start solving it..!!
★ Multiplying -6 by (n -2),
[tex] \implies \: \sf{5n \: - 6 \times (n - 2) \: = \: 19} [/tex]
[tex] \implies \: \sf{5n \: - 6n + 12 \: = \: 19} [/tex]
★ Subtracting 5n from 6n,
[tex]\implies \: \sf{ - n + 12 \: = \: 19} [/tex]
★ Transposing 12 from L.H.S. to R.H.S. it would be in negative,
[tex]\implies \: \sf{ - n \: = \: 19 - 12} [/tex]
★ On subtracting 12 from 19 we gets,
[tex] \implies \: \sf{ - n \: = \: 7} [/tex]
★ Now,
[tex] \implies \: \red{\bf{ n \: = \: - 7} }[/tex]
Therefore,
Value of n is -7What is the solution to the inequality |2x + 3| < 7? 4 < x < 10 –5 < x < 2 x < 4 or x > 10 x < –5 or x > 2
Answer:
4(−10−9x)
Step-by-step explanation:
You mix the letters S,E,M,I,T,R,O,P,I,C,A, and L throughly.Without looking,you draw one letter.Find the probability that you select a vowel.Write your answer in simplest form.
A. 12/5
B. 5/12
C. 1/3
D. 7/12
I need this answer in 5 MINUTES!
Answer:
B. 5/12
Explanation:
Total Letters mixed: {S, E, M, I, T, R, O, P, I, C, A, L} = 12 Letters
There are 5 vowels and they are: 'a', 'e', 'i', ' o', and 'u'
In here the vowels are: E, I, O, I, A = 5 vowels here
So,
probability: number of favourable outcomes/total number of outcomes
probability: 5/12
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Step-by-step explanation:
z = 180° - 113° = 67°
sum of angles of quadrilateral shape = 360°
y = 360° - ( 67° + 81° + 106° ) = 106°
On a long hike, Austin drank 5 pints of water. How much did he drink in quarts?
Answer:
Austin drank 2.5 quarts.
Step-by-step explanation:
There are 2 pints in a quart.
To get from pints to quarts, divide by 2
5/2 = 10
2.5 quarts
mark brainliest please!
What is the answer to this?…
[tex]~~~~~\dfrac 34n = 9\\\\\\\implies n = \dfrac{9 \times 4} 3\\\\\\\implies n = \dfrac{36}3\\\\\\\implies n = 12[/tex]
Please help me GENIUS Rank
Directions: Complete the following frequency distribution table, then compute the mean, median, and mode of the distribution. Show your complete solutions. (25 points)
Class interval] frequency (f)] fxm
99-101 ] 17 ].
102-104 ] 25 ]
105-107 ] 13 ]
108-110 ]. 16 ]
111-113 ]. 29 ]
total ]N= ]. Efxm=
less than cumutalti frequency (<cf)
[. ]
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suppose the integers from 1 to 25 are arranged in consecutive order. How many different pairs of integers may be selected if there are at least four integers between the selected integers?
Solve for x in the given equation: ax - b = c
An equation is formed of two equal expressions. The value of x is the equation ax-b=c is (c+b)/(a).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of x in the given equation can be written as,
[tex]ax - b = c\\\\ax = c+b\\\\x = \dfrac{c+b}{a}[/tex]
Hence, the value of x is the equation ax-b=c is (c+b)/(a).
Learn more about Equation:
https://brainly.com/question/2263981
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The bacteria in a petri dish doubles every hour. If there are 3 present, how many will there be in 15 hours?
Answer:
98304 bacteria
Step-by-step explanation:
3x2^1 = 6
3x2^2 = 12
3x2^3 = 24
3x2^15 = 98304
The number of bats in a colony is growing exponentially. After 1 year, there were 70 bats. After 4 years, there were 560 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 7 years?
Answer:
23040 bats
Step-by-step explanation:
Let N(t) be the number of bats at time
We know that exponential function
[tex]y = ab[/tex]
According to question
[tex]N(t) = ab^{2}[/tex]
Where t (in years)
Substitute t=2 and N(2)=180
[tex]180 = ab^{2}[/tex]
Substitute t=5 and N(5)=1440
[tex]1440 = ab^{5}[/tex]
Equation (1) divided by equation (2)
[tex]\frac{180}{1440} = \frac{ab^{2} }{ab^{5}} = \frac{1}{b\frac{5-2}{}}[/tex]
By using the property
Substitute the values of b in equation (1)
Substitute t=9
Hence, after 9 years the expected bats in the colony=23040 bats
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest hundredth.
its a tringale
Step-by-step explanation:
The track is 9.76 m wide all the way around. What is the distance around the outside of the track? Explain or show your reasoning.
Answer:
The distance around the outside of the track is 4183.58m².
Step-by-step explanation:
The area of running track that goes around the field is 9.76m
To proof :
Formula -
(Area of rectangle = length × breadth)
(Area of running track = outside area - inside area)
First case (outside),
length = 73 +2× 9.76
= 92.52m
Breadth = 84.39 m
radius of outside semi circle,
= 46.26m
outside area = area of rectangle + 2 × area of the semi-circle
= 92.52 x 84.39 + 3.14 x 46.26 × 46 × 26
= 7807.76+6719.56
Second case,
radius of the semi-circle,
=36.5m
inside area = area of rectangle + 2x area of the semi-circle
=73x 84.39+ 3.14x 36.5×36.5
= 6160.47 +4183.27
= 10343.74m²
Now,
Area of running track = 14527.32 m²- 10343.74m²
= 4183.58m²
The distance around the outside of track is 4183.58m².
Evaluate 27+ x when x = 3.
What is the value of the expression
Answer:
30
Step-by-step explanation:
Evaluating an expression when given a value of an unknown means to substitute the unknown value with a certain value given and simplify fully:
27 + (3)
Simplify by doing simple addition :
27 + 3 = 30
Therefore our answer is 30.
Hope this helped and brainliest please.
Replace the variable x with 3 in the expression.
27 + 3
Remove parentheses.
27 + 3
Add 27 and 3.
30
8x = 2/3 ; x =
1 1/2 = 2x; x =
5x = 2/7; x =
1/4x = 5; x =
1/5 = 2/3x; x =
We can simply solve the equations by just dividing by the coefficient value of x. For example, we would divide both sides of the first equation by 8 to make the equation into x = 2/24 = 1/12
8x=2/3 --> x=1/12
1.5=2x --> x=0.75
5x=2/7 --> x= 2/35
1/4x=5 --> x=20
1/5=2/3x --> 3/5=2x --> x=3/10
a 23 ө C С B 2
help me??
i need help with this math
please help me!!
a bag contains 18 marbles. there are 6 red marbles, 6 yellow marbles, and 6 green marbles. a marble is drawn at random and returned. then another marble is drawn at random
which statements are true?
A. the expected probability of drawing a green marble first is the same as the expected probability of drawing a green marble second.
B. there are six possible outcomes
C. the probability of drawing a red marble first is the same as not drawing a red marble second
D. the expected probability of drawing a red marble and then a yellow marble is 1/9
E. there are three possible outcomes from drawing the same color twice
F. the probability of drawing a yellow marble and then a yellow marble is 1/6
Answer:
Step-by-step explanation:
A. False. The probability of drawing a green marble twice is even smaller (It may be true though depending on what the question is asking, if it is asking the chance of drawing a green marble second is the same as the 1st chance, then yes it is True.
B.False
C. False
D.True, 1/3*1/3 (Simplified version of 6/18*6/18) is 1/9
E. False (Although this may be true, again depending on the type of question)
F. False
Please Help!!!!
Find the slope of the line.
Answer:
-1/2
Step-by-step explanation:
Use the two points shown.
slope = rise/run
Start at teh left point.
Go down 2 units. That is a rise of -2.
Now go right 4 units. That is a run of 4.
slope = rise/run = -2/4 = -1/2
Resuelve el siguiente problema aplicando las estrategias de solución de problemas:
• La suma de dos números es 20 y su diferencia es de 4. Halla los números.
Una persona camina desde su casa hasta el parque la distancia de 100 M y el tiempo recorrido fue de 10 minutos cuál fue su velocidad
Usando la relación entre la velocidad, la distancia y el tiempo, se encuentra que su velocidad fue de 10 m/min.
¿Cuál es la relación entre la velocidad, la distancia y el tiempo?Velocidad es distancia dividida por el tiempo, o sea:
[tex]v = \frac{d}{t}[/tex]
En este problema, hay que:
La distancia es de d = 100 m.El tiempo es de t = 10 min.Por eso:
v = 100 m/10 min = 10 m/min.
Su velocidad fue de 10 m/min.
Puede-se aprender más a cerca de la relación entre la velocidad, la distancia y el tiempo en https://brainly.com/question/24558377
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Pls help giving 20 points
Answer:
220.5 ft
Step-by-step explanation:
Zearnn help... I've been stuck working hard
Calculate the area of the room and then subtract the area of the tiled floor.
area of room = 11 3/4 x 5 = 58 3/4
Area of tiled floor = 7 1/2 x 3 1/4 = 24 3/8
area of carpet = 58 3/4 - 24 3/8 = 34 3/8
answer: 34 3/8