The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. B = 137°, c = 6, b = 11
Answers
a ≈ 5.82
A ≈ 21.2°
C ≈ 21.8°
Since the longest side (b) is opposite the given angle (B), the triangle has one solution.
.. C = arcsin(6/11*sin(137°))
.. A = 180° -137° -C
.. a = sin(A)*11/sin(137°)
The measurements given can form a triangle, and to solve it, we would use the Law of Sines. After confirming the possibility of a triangle, we solve for the unknown angle C using the known values and compute the remaining angle and side.
Explanation:To determine if a triangle is formed by the given measurements and solve it using the Law of Sines, we need to check if the given angle and sides satisfy the triangle inequality. The measurements given are angle B = 137°, side c = 6, and side b = 11. A triangle is possible if the sum of the two smallest sides is greater than the length of the longest side. Here the angle is very large, suggesting that the opposite side (b) must be the longest; however, since side b is indeed longer than side c, this condition is satisfied, so a triangle can be formed.
To solve the triangle using the Law of Sines, we set up the following ratio:
b/sin(B) = c/sin(C)
After substituting the known values into the equation, we get:
11/sin(137°) = 6/sin(C)
Now, we solve for sin(C) to find the angle C, and subsequently use the sum of angles in a triangle (180°) to find the remaining angle A. Once angle A is known, we can use the Law of Sines again to find the remaining side a. If at any point we find that the calculation results in an invalid sine value (greater than 1 or less than -1), we must then state that no real solution exists.
It is important to note that if we find angle C to be obtuse (greater than 90°), the triangle will not have a unique solution because it would contradict our initial assumption that angle B, being the largest given angle, is opposite the longest side.
Related Questions
The distance between city A and city B is 22 miles. The distance between city B and city C is 54 miles. The distance betweeb city A and city C is 51 miles.
What type of trianglr is created by the three cities?
A. An acute triangle, beacuse 22^2+54^2>51^2
B. An acute triangle, beacuse 22^2+51^2>54^2
C. An obtuse triangle, beacuse 22^2+54^2>51^2
D. An obtuse triangle, beacuse 22^2+51^2>54^2,
Answers
The answer is B. It is an acute triangle because of 22^2 + 51^2 > 54^2. To identify the type of triangle referred to the problem, we use the Pythagorean Theorem which involves squaring the lengths of all sides of the triangle. If the hypotenuse’s square is less than the two smallest sides' squares added together, than it is an acute triangle. However, if the hypotenuse’s square is larger, then it is an obtuse triangle.
54 is the hypotenuse since it is the longest side.
Following the Pythagorean Theorem, a^2 + b^2 = c^2:
54^2=2916
51^2=2601
22^2=484
It becomes 2601+484 = 2916.
When the two shorter sides are added, the sum is greater than the square of the hypotenuse which is 2916. Thus, the formed triangle is acute.
Answer:
B
Step-by-step explanation:
Find the perimeter of the figure. Round your answer to the nearest tenth.
a) 41 Units b) 34.2 Units c) 23 Units d) 11.2 Units
Answers
(12 + 5) + 32 × (10 − 5) =
Answers
177 hope this helps
[tex]17 + 32 \times 5 = [/tex]
[tex]17 + 160 = [/tex]
[tex]177[/tex]
So the answer is 177.
Carlos ran 3/8 of the race course. Lori ran 3/6 of the same race. Who ran further? Explain.
Answers
what is the scale factor of ABC to UVW
Answers
It's a scale factor of 5 because,
5*5=25
5*3=15
5*4=20
Hope this helps!
Answer:
C. 5
Step-by-step explanation:
We have been given an image of two triangles. We are asked to find the scale factor of ABC to UVW.
To find the scale factor of our given triangles, we will divide one side of triangle UVW by its corresponding side of triangle ABC.
[tex]\text{Original side}\times\text{Scale factor}=\text{New side}[/tex]
[tex]5\times\text{Scale factor}=25[/tex]
Upon dividing both sides of equation by 5, we will get:
[tex]\frac{5\times\text{Scale factor}}{5}=\frac{25}{5}[/tex]
[tex]\text{Scale factor}=5[/tex]
Therefore, the scale factor of triangle ABC to triangle UVW is 5 and option C is the correct choice.
You are finding the product of two square roots. Each radicand is the same variable raised to an odd power. Explain why you would want to multiply the radicands together first and then simplify the product.
Answers
Then the square root (even root/radicand) can be taken eliminating the radicand.
Here's an example to show you what I mean, so you can put it in your own words if you want.
[tex] \sqrt{ x^{3} } * \sqrt{ x^{7} } = \sqrt{ x^{10} } = x^{5} [/tex]
A 16 foot ladder is leaning against a 10 foot wall. How far away from the building should the bottom of the ladder be placed
Answers
Use the quadratic formula to solve x^2+8x+9=0
What are the solutions to the equation?
Round irrational solutions to the nearest tenth.
x=−1 and x=−8
x = 1 and x=−9
x=−6.6 and x=−1.4
x=−1.2 and x=−6.8
Please explain the answer!
Answers
Solve for x over the real numbers:
x^2 + 8 x + 9 = 0
x = (-8 ± sqrt(8^2 - 4×9))/2 = (-8 ± sqrt(64 - 36))/2 = (-8 ± sqrt(28))/2:
x = (-8 + sqrt(28))/2 or x = (-8 - sqrt(28))/2
sqrt(28) = sqrt(4×7) = sqrt(2^2×7) = 2sqrt(7):
x = (2 sqrt(7) - 8)/2 or x = (-2 sqrt(7) - 8)/2
Factor 2 from -8 + 2 sqrt(7) giving 2 (sqrt(7) - 4):
x = 1/22 (sqrt(7) - 4) or x = (-2 sqrt(7) - 8)/2
(2 (sqrt(7) - 4))/2 = sqrt(7) - 4:
x = sqrt(7) - 4 or x = (-2 sqrt(7) - 8)/2
Factor 2 from -8 - 2 sqrt(7) giving 2 (-sqrt(7) - 4):
x = sqrt(7) - 4 or x = 1/22 (-sqrt(7) - 4)
(2 (-sqrt(7) - 4))/2 = -sqrt(7) - 4:
Answer: x = sqrt(7) - 4 or x = -sqrt(7) - 4_____________________________________________________
Solve for x:
x^2 + 8 x + 9 = 0
Subtract 9 from both sides:
x^2 + 8 x = -9
Add 16 to both sides:
x^2 + 8 x + 16 = 7
Write the left hand side as a square:
(x + 4)^2 = 7
Take the square root of both sides:
x + 4 = sqrt(7) or x + 4 = -sqrt(7)
Subtract 4 from both sides:
x = sqrt(7) - 4 or x + 4 = -sqrt(7)
Subtract 4 from both sides:
Answer: x = sqrt(7) - 4 or x = -4 - sqrt(7)
Can someone help me with this word problem?
Answers
for part B the angle of depression can be found using the trigonometric function of tangent.
tan x = 40/130
tan^-1 (tan x) = tan^-1 (40/30)
x = 17 degrees
I hope i am right
When constructing a regular hexagon inscribed in a circle, what is the measure of an angle formed by any two adjacent vertices of the hexagon and the center of the circle?
Answers
Answer:
Measure of angle is 60°
Step-by-step explanation:
Given when constructing a regular hexagon inscribed in a circle, we have to measure an angle formed by any two adjacent vertices of the hexagon and the center of the circle.
we have to find the measure of central angle of hexagon
Total measure of angle at centre is 360°
As polygon is given regular hexagon therefore central angle divides into six equal angles.
Hence, measure of an angle formed by any two adjacent vertices of the hexagon and the center of the circle is
[tex]\frac{\text{Total angle at centre}}{\text{number of sides}}=\frac{360}{6}=60^{\circ}[/tex]
A restaurant offers three vegetable side dishes, two fruit side dishes, and five grain-based side dishes. Each entree comes with two side dishes.
What is the approximate probability of randomly choosing one vegetable and one grain-based side dish?
a.0.08889
b.0.17778
c.0.16667
d.0.33333
Answers
The approximate probability of randomly choosing one vegetable and one grain-based side dish is: d. 0.33333
Explanation
Vegetable side dishes = 3, Fruit side dishes = 2 and Grain-based side dishes = 5
So, total number of side dishes [tex]= 3+2+5= 10[/tex]
Number of ways for choosing two side dishes from total 10 dishes will be : [tex]^1^0C_{2}[/tex]
We need to randomly choose one vegetable and one grain-based side dish, so the number of ways [tex]= ^3C_{1} * ^5C_{1}[/tex]
Thus, the probability [tex]= \frac{^3C_{1} * ^5C_{1}}{^1^0C_{2}} = \frac{3*5}{45}= \frac{15}{45}= \frac{1}{3}= 0.3333...[/tex]
Answer:
D. 0.33333
Step-by-step explanation:
describe the graph of y={1/(2x-10)}-3 compared to the graph of y=1/x
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
with that template in mind, let's check these two
[tex]\bf \stackrel{parent}{y=\cfrac{1}{x}}\qquad \qquad\qquad \qquad \stackrel{transformed}{y=\cfrac{1}{\stackrel{B}{2}x\stackrel{C}{-10}}\stackrel{D}{-3}}\\\\ -------------------------------\\\\ B=2\qquad \textit{shrinks horizontally by }\frac{1}{2} \\\\\\ C=-10\qquad \cfrac{C}{B}=\cfrac{-10}{2}\implies -5\qquad \textit{horizontally right-shifted by }5 \\\\\\ D=-3\qquad \textit{vertically down-shifted by }3[/tex]
A store carries two different sizes of a certain brand of potato chips. bag 1 contains 8 ounces and costs $3.49. bag 2 contains 12 ounces, and costs $4.59. which bag has the lowest price per volume
Answers
P = (cost) / (volume of the bag)
For bag 1:
P1 = (cost) / (volume of the bag)
P1 = (3.49) / (8) = 0.43625 $
For bag 2:
P2 = (4.59) / (12) = 0.3825 $
We know that
P1> P2
Answer:
bag 2 has the lowest price per volume 0.3825 $
Bag 2, with a price of $0.3825 per ounce, has a lower price per volume compared to Bag 1, which has a price of $0.43625 per ounce.
To determine which bag of potato chips has the lowest price per volume, we need to calculate the price per ounce for each bag.
For Bag 1, it contains 8 ounces and costs $3.49, so the price per ounce is $3.49 / 8 ounces = $0.43625 per ounce.For Bag 2, it contains 12 ounces and costs $4.59, so the price per ounce is $4.59 / 12 ounces = $0.3825 per ounce.Comparing these values, we see that Bag 2 has the lower price per ounce at $0.3825 per ounce, making it the more economical choice per unit of volume.
A railroad crew can lay 7 miles of track each day. they need to lay 189 miles of track. 17 day how many miles. How many day to lay all the track
Answers
Given that a crew can lay 7 miles of railroad track a day, it would take them a total of 27 days to lay 189 miles of railroad track.
Explanation:The subject of this question is the calculation of the number of days it would take for a railroad crew to lay a specified number of miles of track. Given that the crew can lay 7 miles of track each day, and they need to lay a total of 189 miles of track.
To determine the total number of days required, we would divide the total miles by the miles the crew can lay each day.
So, 189 miles ÷ 7 miles/day = 27 days. Therefore, it would take the railroad crew a total of 27 days to lay all the track.
Learn more about Calculating Time here:https://brainly.com/question/20416068
#SPJ11
in the second picture, i have included a picture of the theorem that this question is based upon.
Answers
Kite ABCD has a longer diagonal AC with a length of 14 in. and a shorter diagonal BD with a length of 8 in. The diagonals intersect at point E. What is the length of BE?
4 in
7 in
8 in
14 in
Answers
The longer diagonal is an axis of symmetry of the Kite.
So E is the middle of BD and BE=8/2=4
Answer A: 4in.
A hybrid car averages 600 miles on a 12.9 gallon tank of gas. Manuel is planning a 1240-mile vacation in his hybrid car. Find how many gallons of gas he can expect to burn.
Answers
amount of gas used up - 12.9 gallons
therefore when he travels 600 miles he uses up 12.9 gallons
for every mile the amount of gas used up - 12.9 gallons / 600 miles = 0.0215 gallons / mile
therefore 0.0215 gallons used up per mile
so when he's going for 1240 miles - gas used up is 0.0215 gallons/ mile x 1240 miles = 26.66 gallons
amount of gas needed is 26.66 gallons
Answer:
26.66 gallon of gas
Step-by-step explanation:
A car uses 12.9 gallons of gas for travelling 600 miles
For travelling one mile , the car will use gas = 12.9 gallon of gas/600 miles
= 0.0215 gallon of gas /mile
For travelling 1240 miles, gallon of gas required =
= 0.0215 gallon of gas /mile x 1240 miles
= 26.66 gallon of gas
PLEASE HELP ASSSAAAAPPPP
Answers
[tex]f(x) = 5^x \\ f(2) = 5^2 = 25[/tex]
helpppppppppppppppppppppppppppppppppppppppppppp
Answers
they want 20 characters n stuff but if you want me to show work or whatever i can
----------------
Multiply each side by 4
4 * x/4 ≥ -8 * 4
x ≥ -32
HELP please :)
A patient requires an IV of 0.9% saline solution, also known as normal saline solution. How much distilled water, to the nearest milliliter, must be added to 100 milliliters of a 6 % saline solution to produce normal saline?,
Answers
2/(100+x)=9/(1000)
2000=900+9x
1100=9x
122.22=x
x= 122
The answer is 122 milliliters of distilled water must be added
A coach bought some shirts and 5 pairs of shorts. each shirt cost $12 and each pair of shorts cost $10. let t represent the number of shirts. write an expression that can be used to find the total cost of the shirts and shorts. answer
Answers
T=total cost (shirts + shorts)
12t+5(10)=T
12t+50=T
Answer: 12t + 50=T
t=number of shirts
T=total cost.
can someone help me? im not sure if my answers are right
Answers
What is the measure of angle 1?
Answers
80o + 60o = <1
140 = <1 <<<<<<< ==== answer.
At the snack bar, a hot dog costs $1.50 and a slice of pizza costs $2. What percent of the cost of a slice of pizza is a cost of a hot dog? Which equation can be written to represent this scenario?
A. 1.5p=2
B. 1.5=2p
C. 2(1.5)=p
D. 2/1.5=p
How would you determine this answer?
Answers
There are several answers for this
A and D
Simplify -|-5 + 2|.
I'm not good with Math, can someone please help me how to Simplify, I have no clue to solving these questions that ask me to simplify, On my Online Schooling I wish to get better. Thanks for the time :)
Answers
The answer will be "-5+2".
Reason:
I These lines turn negative numbers into positive:
Therefore the answer will be -5+2 (since how the first - sign was outside of the I).
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
The equation x2+y2−4x+2y=b describes a circle. Complete the square to find the center of the circle. The center of the circle is ( , ) The radius of the circle is 7 units. What is the value of b in the equation? b=
Answers
divide each coefficient by 2 and square to determine what to add.
(-4/2)^2 = 4 needs to be added to complete the square for x.
(2/2)^2 = 1 needs to be added to complete the square for y.
add to both sides of the equal sign to keep the equation balanced.
x^2 - 4x + 4 + y^2 + 2y + 1 = b + 4 + 1
factor
(x - 2)^2 + (y + 1)^2 = b + 5
The general equation for a circle is:
(x - h)^2 + (y - k)^2 = r^2
with center (h,k) and radius r
compare this to the equation. you see that the center is: (2, -1)
we can write
r^2 = b + 5
given that r = 7
49 = b + 5
49 - 5 = b
44 = b
The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.
Answers
Please note that odd numbers differs by 2...1,3,5,7,9etc....
If the first odd integer Is x
The next(consecutive one) = x+2
The third = (x+2)+2 = x+4
The fourth one = (x+4)+2 = x+6..
The sum of all this equals to - 72 that is......
x+x+2+x+4+x+6 =-72
4x+12 = - 72
4x=-72-12
4x=-84
x=-84/4
x= -21...
x+2 = - 21+2 = -19
x+4 = -21+4 = -17
x+6 = -21+6 = -15
Those number have been highlighted above..
Hope this helped....
Answer: n + n+2 + n+4 + n +6 = 4n + 12 = -72 4n = -84 n = -21 -21,-19,-17 and -15
What’s the correct answer
Answers
[tex]total = 11 + 3x[/tex]
For 10 weeks:
[tex]14 + 17 + 20 + 23 + 26 + 29 + 32 + 35 + 38 + 41 = 275[/tex]
Total:
Andrew will have earned $275 after 10 weeks
What is the solution to the equation 5x = 40?
7
8
45
200
Answers
40 divided by 5 = 8.
To check we can do 5 x 8 = 40.
X = 8
5x/5=40/5
next, simply dived 40 by 5 which is 8, x=8
Please help does anyone know the answer Giving 20pts I need ASAP
Answers
That is because x, 67, and 52 make a straight line, hence, they will equal to 180.
So if you subtract the sum of 67 and 52 from 180 you'll get the value of x.