Answers
Given:
A figure of a right angle triangle.
To find:
The length of the shorter leg.
Solution:
In a right angle triangle,
[tex]\tan\theta =\dfrac{Opposite}{Adjacent}[/tex]
In the given triangle,
[tex]\tan (60^\circ) =\dfrac{18}{x}[/tex]
[tex]\sqrt{3}=\dfrac{18}{x}[/tex]
[tex]x=\dfrac{18}{\sqrt{3}}[/tex]
[tex]x=\dfrac{18}{\sqrt{3}}\times \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]
On further simplification, we get
[tex]x=\dfrac{18\sqrt{3}}{3}[/tex]
[tex]x=6\sqrt{3}[/tex]
[tex]x=10.3923[/tex]
[tex]x\approx 10.4[/tex]
Therefore, the length of the shortest leg is 10.4 and the correct option is B.
Related Questions
The temperature outside changed from 64°F to 43°F over a period of seven days. If the temperature changed by the same amount each day, what was the daily temperature change?
Answers
Answer: -3°F
Step-by-step explanation:
From the question, we are informed that the temperature outside changed from 64°F to 43°F over a period of seven days. The total change will be:
= 43°F - 64°F
= -21°F
If the temperature changed by the same amount each day, the daily temperature change will now be:
= -21°F / 7
= -3°F
The temperature decreased by 3°F daily
El largo de una sala es 2 metros más grande que su ancho. El área es de 80 m?. ¿Cuánto mide de largo? Cuánto mide de ancho?
Answers
Answer: Translation:
The length of a room is 2 meters greater than its width. The area is 80 m ?. How long is it? How wide is it?
Step-by-step explanation:
The first triangle is dilated to form the second triangle.
Select True or False for each statement.
Statement True False
The scale factor is 0.25.
True – The scale factor is 0.25.
False – The scale factor is 0.25.
The scale factor is 4.
True – The scale factor is 4.
False – The scale factor is 4.
A right triangle with a hypotenuse of 4.4. An arrow points to a smaller right triangle with a hypotenuse of 1.1
Answers
Answer:
Both true
Lelelelellele
I need help ASAP pleaseeeeee
Answers
Answer: area of smaller is 18 and larger is 45 so the answer is 27
Step-by-step explanation:
A triangular prism where the base is a right traingle with lengths of the edge are given 3cm,4cm,5cm,3cm what are the total surface
Answers
Answer:
Total surface area is 48 square Centimeter
Step-by-step explanation:
Total surface area is equal to the product of triangular base area and the height of the prism
Area calculation of triangular base
[tex]S = \frac{3+4+5}{2} = 6\\[/tex]
Area =
[tex]\sqrt{S(S-a)(S-b)(S-c)}[/tex]
Substituting the given values in above equation we get
[tex]\sqrt{6 *3*2*1} = 6[/tex] square centimeter
Total surface area
= [tex]2 * 6 + (3*3)+(3*4)+(3*5)\\= 12 + 9 + 12+ 15\\= 48[/tex] square Centimeter
HELP PLEASE!! WILL GIVE BRAINLIEST!!!
Answers
The slope is 5/7
Step-by-step explanation:
When you find slope you need to find both points and use the ordered pairs and subtract y1 - y2 and x2 - x1 and then you get your slope which is 5/7
sorry im bad at explaining
10.
8. "Orta Asya'da kurulan ilk Müslüman Türk Devleti
Haniyim. Müslümanlığı kabul ederek Abdülkerim
Satuk Buğra Han adını aldım. Devletin resmi dinini
Islamiyet olarak kabul ettim. Bu durum kısa sürede
Türk boylarının islamlaşmasını sağladı."
Satuk Buğra Han'ın bu açıklamalarına göre, Türk-
lerin Müslüman olmasının aşağıdakilerden han-
gisine etki ettiği söylenebilir?
A) Kültürel değerlerini kaybetmelerine
B) Siyasal alanda değişimlere
C) Topraklarini genişletmelerine
D) Yerleşik hayata geçmelerine
Answers
A square has an area of 64 square units. If its sides were only half as long, what would its area be?
Answers
Answer:
16
Step-by-step explanation:
the sides now are 8x8
1/2 of that is 4x4 and 4x4=16
What is the slope of a line perpendicular to the line whose equation is 4x−y=9. Fully reduce your answer.
Answers
Answer:
slope of given line is 4.
so slope of line perpendicular to it will be -1/4
When the stress on a rock in the mantle is greater than the rock is strong ________.
the rock breaks and energy is released in the form of s-waves and p-waves
a volcano erupts
a tsunami builds under the ocean
sedimentary rock is formed
Answers
Answer:
sedimentary rock is formed
Step-by-step explanation:
Cos^4x csc^2x = csc^2 x sin^2 -2
Answers
Answer:
0
Step-by-step explanation:
i think im not sure the way this question is written doesn't make a lot of sense
Hello immediately please
Sandy's aunt lives 250 miles away. If Sandy drives 55
ph, how long will it take her to get to her aunt's house?
A3 hours
B. 5 hours
C. 4.5 hours
D 6 hours
Answers
Solve by elimination:
9x + 4y = 97
9x + 6y = 123
14
15'
B (5, 13)
(13,5)
D (1, 22)
Answers
Answer:
B (5, 13)
Step-by-step explanation:
9x + 4y = 97
9x + 6y = 123
To solve by elimination, we want to eliminate a variable. To do this, we must make one variable cancel out.
First, we can see that both equations have 9x. To cancel out x, we must make one of the 9x's negative. To do this, multiply each term in the equation by -1.
-1(9x + 6y = 123)
-9x - 6y = -123
This is one of your equations. Set it up with your other given equation.
9x + 4y = 97
-9x - 6y = -123
Imagine this is one equation. Since every term is negative, you will be subtracting each term.
9x + 4y = 97
-9x - 6y = -123
___________
0x -2y = -26
-2y = -26
To isolate y further, divide both sides by -2.
y = 13
Now, to find x, plug y back into one of the original equations.
9x + 4(13) = 97
Multiply.
9x + 52 = 97
Subtract.
9x = 45
Divide.
x = 5
Check your answer by plugging both variables into the equation you have not used yet.
-9(5) - 6(13) = -123
-45 - 78 = -123
-123 = -123
Your answer is correct!
(5, 13)
Hope this helps!
what is the surface area of a cylinder in 9in,7in, and 5in ?
Answers
A wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake. She paddles across the lake for one hour longer than she paddled up the river. Find the speed of the boat as she paddles the lake if the river current is 2 km/h.
Answers
Answer:
5 or 6
Step-by-step explanation:
So I did it in a different way than shown in rsm classes. I said that the speed was x-2 and x.
then I said the distance was 6 and 15. If the time taken was 1 hour more, then we can come up with this equation:
Since the time is 6/x-2 or 15/x
15/x-6/x-2=1
multiply everything to get a common denominator then cancel it out to get
(15x-30)-6x=x^2-2x
11x-30=x^2
x^2-11x+30=0
(x-5)(x-6) is factored form.
so x=5 or x=6. this means that the speed of the boat is either 5km/h or 6 km/h
[tex]\frac{1}{4} ^{0}[/tex]
how do I solve this equation?
Answers
Answer:
The solution is 1.
Step-by-step explanation:
Any number raised to the 0th power will always be 1.
Which pair of angles is congruent?
Answers
Answer:
Option 2
Step-by-step explanation:
Corresponding Angles Theorem
A triangle has side lengths of (6a-3b)(6a−3b) centimeters, (5a+5c)(5a+5c) centimeters, and (8c-b)(8c−b) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answers
Answer:
P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringGeometry
Perimeter Formula [Triangle]: P = L₁ + L₂ + L₃
L₁ is one sideL₂ is another sideL₃ is the 3rd sideStep-by-step explanation:
Step 1: Define
L₁ = (6a - 3b)(6a - 3b)
L₂ = (5a + 5c)(5a + 5c)
L₃ = (8c - b)(8c - b)
Step 2: Find Perimeter
Substitute in variables [Perimeter - Triangle]: P = (6a - 3b)² + (5a + 5c)² + (8c - b)²Expand [FOIL]: P = (36a² - 36ab + 9b²) + (25a² + 50ac + 25c²) + (b² - 16bc + 64c²)Combine like terms (a²): P = 61a² - 36ab + 9b² + 50ac + 25c² + b² - 16bc + 64c²Combine like terms (b²): P = 61a² + 10b² - 36ab + 50ac + 25c² - 16bc + 64c²Combine like terms (c²): P = 61a² + 10b² + 89c² - 36ab + 50ac - 16bcRearrange variables: P = 61a² - 36ab + 50ac + 10b² + 89c² - 16bcFactor: P = a(61a - 36b + 50c) + 10b² + 89c² - 16bctwo cube numbers from 3,6,8,14,16,28,41,64
Answers
Answer:
67
70
73
76
79
82
85
Answer:
The answer are 8 and 64
Step-by-step explanation:
[tex] \sqrt[3]{8} = 2 \\ \sqrt[3]{64} = 4[/tex]
Please hurry
Select all the points that are on the graph of the line
3x + 5y = 20 ?
Answers
Answer:
x=5
y=1
Step-by-step explanation:
3*5=15
5*1=5
15+5=20
Will mark brainliest for whoever answers
Answers
Answer:
i think g(x) is not the inverse function of f(x). HOPE THIS HELPS!
Step-by-step explanation:
Help me please :)....
Answers
Answer:
a = 6, b = 12, c = 18, d = 12
Step-by-step explanation:
Maria rents a bicycle while on vacation. It costs a flat fee of $19.95 plus $5.50 an hour. Maria rents it for 4 hours. What is the total cost?
Answers
Answer:
36.45
Step-by-step explanation:
5.50 × 3 = 16.5
16.5 + 19.95 = 36.45
sorry if wrong.
hope it helps.
Find the slope when given (2,3) (3,5) plz
Answers
=(5-3)/(3-2)
=2/1
=2
so the slope is 2
hope this helps !
The slope is 2.
Just need answer for both
Answers
Answer:
First one: 12 ft
Second one: 50ft^2
Step-by-step explanation:
Because both triangles are congruent, any value on one triangle is the same one on the other triangle so CBD= 12ft for the perimeter
Second one:
because both triangles are congruent like I stated above, both triangle are congruent.
But in this case we have to find the area of the whole rectangle.
What we do here is multiply 25 by 2
or
add 25+25
our answer is 50ft^2
Suppose 65% of jurors come to a just decision. In a jury of ten people, what is the probability more than half come to a just decision? 0.7515 0.2485 0.0949 0.8374 0.9051
Answers
Answer: 0.7515
Step-by-step explanation:
Binomial probability formula:
[tex]P(X=x)=\ ^nC_xp^x(1-p)^{n-x}[/tex] , where
n = total number of trials.
p= probability of success in each trial.
x= Number of successes.
Let x be a binomial variable that represents the number of jurors come to just decision.
p= 0.65
n= 10
Required probability= [tex]P(x>5)=P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)\\\\ =\ ^{10}C_6(0.65)^6(0.35)^4+ ^{10}C_7(0.65)^7(0.35)^3+ ^{10}C_8(0.65)^8(0.35)^2+ ^{10}C_9(0.65)^9(0.35)^1+^{10}C_{10}(0.65)^{10}(0.35)^0\\\\=0.75149550912\approx0.7515[/tex]
Hence, the probability more than half come to a just decision = 0.7515
please Help me i'm timed
Answers
Answer:
X=28
Step-by-step explanation:
4x+248=360
112=4x
x=28
Answer:
28
Step-by-step explanation:
On sports day at Lakewood middle school, gold, silver, and bronze medals were awarded to the top three finishers in each event Miniature replicas of the medals were sold as souvenirs in booths around the field. For $26, attendees could purchase a package containing 5 gold, 4 silver, and 2 bronze replicas, or one containing 4 gold, 4 silver, and 4 bronze replicas, or one that had 3 gold, 4 silver, and 6 bronze replicas. Which system of equations may be used to find the price, in dollars, of each type of replica?
Answers
Answer:
[tex]5G + 4S + 2B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
[tex]3G + 4S + 6B = 26[/tex]
Step-by-step explanation:
Given
Represent Gold with G, Silver with S and Bronze with B
Required
Determine the system of equations
The packages are represented as:
The first: 5G + 4S + 2B
The second: 4G + 4S + 4B
The third: 3G + 4S + 6B
Each of the package costs $26.
So, we have:
[tex]5G + 4S + 2B = 26[/tex] -- (1)
[tex]4G + 4S + 4B = 26[/tex] -- (2)
[tex]3G + 4S + 6B = 26[/tex] -- (3)
Divide both sides of (2) by 2
[tex]4G + 4S + 4B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
So, the system of equations are:
[tex]5G + 4S + 2B = 26[/tex]
[tex]2G + 2S + 2B = 13[/tex]
[tex]3G + 4S + 6B = 26[/tex]
Juan tiene 15 años más que Antonio. Dentro 10 años, la edad de Juan será el doble que la de Antonio¿ Cuantos años tienen los dos?
Answers
Solve the equation y – 5x = –7 for y.
A. y = 5x – 7
B. y = –5x – 7
C. y = 5x + 7
D. y = –5x + 7
Answers
Answer:
the answer is B
Step-by-step explanation:
Answer: A. y = 5x -7
Step-by-step explanation:
Y - 5x = -7
+ 5x + 5x
Y = 5x - 7
**you can’t subtract -5x to -5x because it’s already a negative. It should be a positive 5x so you can move it to the other side.
