State the number of possible triangles that can be formed using the given measurements.
Answers
Answer: 39) 1 40) 2
41) 1 42) 0
Step-by-step explanation:
39) ∠A = ? ∠B = ? ∠C = 129°
a = ? b = 15 c = 45
Use Law of Sines to find ∠B:
[tex]\dfrac{\sin B}{b}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin B}{15}=\dfrac{\sin 129}{45}\rightarrow \quad \angle B=15^o\quad or \quad \angle B=165^o[/tex]
If ∠B = 15°, then ∠A = 180° - (15° + 129°) = 36°
If ∠B = 165°, then ∠A = 180° - (165° + 129°) = -114°
Since ∠A cannot be negative then ∠B ≠ 165°
∠A = 36° ∠B = 15° ∠C = 129° is the only valid solution.
40) ∠A = 16° ∠B = ? ∠C = ?
a = 15 b = ? c = 19
Use Law of Sines to find ∠C:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin 16}{15}=\dfrac{\sin C}{19}\rightarrow \quad \angle C=20^o\quad or \quad \angle C=160^o[/tex]
If ∠C = 20°, then ∠B = 180° - (16° + 20°) = 144°
If ∠C = 160°, then ∠B = 180° - (16° + 160°) = 4°
Both result with ∠B as a positive number so both are valid solutions.
Solution 1: ∠A = 16° ∠B = 144° ∠C = 20°
Solution 2: ∠A = 16° ∠B = 4° ∠C = 160°
41) ∠A = ? ∠B = 75° ∠C = ?
a = 7 b = 30 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{7}=\dfrac{\sin 75}{30}\rightarrow \quad \angle A=13^o\quad or \quad \angle A=167^o[/tex]
If ∠A = 13°, then ∠C = 180° - (13° + 75°) = 92°
If ∠A = 167°, then ∠C = 180° - (167° + 75°) = -62°
Since ∠C cannot be negative then ∠A ≠ 167°
∠A = 13° ∠B = 75° ∠C = 92° is the only valid solution.
42) ∠A = ? ∠B = 119° ∠C = ?
a = 34 b = 34 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{34}=\dfrac{\sin 119}{34}\rightarrow \quad \angle A=61^o\quad or \quad \angle A=119^o[/tex]
If ∠A = 61°, then ∠C = 180° - (61° + 119°) = 0°
If ∠A = 119°, then ∠C = 180° - (119° + 119°) = -58°
Since ∠C cannot be zero or negative then ∠A ≠ 61° and ∠A ≠ 119°
There are no valid solutions.
Related Questions
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answers
Answer:
Volume of the cylinder is 1521π in³
Step-by-step explanation:
Hello,
To find the volume of a cylinder, we need the know the formula used for calculating it.
Volume of cylinder = πr²h
r = radius
h = height
Data,
Radius = 13in
Height = 9in
Volume of a cylinder = πr²h
Now we need to substitute the values into the formula
Volume of a cylinder = π × 13² × 9
Volume of a cylinder = 169 × 9π
Volume of a cylinder = 1521π in³
Therefore the volume of the cylinder is 1521π in³
Answer:
1521
Step-by-step explanation:
a car was bought for 5500 and sold at 6500 find the percentage
Answers
Answer:
18.18%
Step-by-step explanation:
Percent change formula:
(new amount - old amount)/(old amount) * 100%
new amount: 6500
old amount: 5500
percent change:
(6500 - 5500)/5500 * 100% = 18.18%
Answer:
18.18%
Step-by-step explanation:
1000/5500 x (100) =(1000/5500)(100/1) =(2/11)(100/1)=(2)(100) (11)(1)= 200/11
=18.18%
For which system of equations would you need to estimate the solution?
On a coordinate plane, 2 lines intersect at (3, 0).
On a coordinate plane, 2 lines intersect around (negative 2.1, negative 3.5).
On a coordinate plane, 2 lines intersect at (negative 2, 3).
On a coordinate plane, 2 lines intersect at (2, 2).
Answers
Answer: It is option 2 or B
Step-by-step explanation: Simple and easy, the test said it was right too.
what is 0.6n = $2.10
Answers
Answer: 3.5
Step-by-step explanation:
2.10/0.6=3.5
3.5x0.6=2.10
What is the result of adding these two equations?
62 + 2y = -2
3x - 2y = -5
Answers
Answer:
x = -7/9; y = 4/3.
Step-by-step explanation:
I will assume that the top equation is 6x + 2y = -2, and the bottom one is 3x - 2y = -5.
If you add the two...
(6x + 3x) + (2y + (-2y)) = (-2 + (-5))
9x + 0 = -7
9x = -7
x = -7/9
6(-7/9) + 2y = -2
-42/9 + 2y = -18/9
2y = 24/9
y = 24/18
y = 12/9
y = 4/3
Hope this helps!
please help me answer this question Solve: y − x = 12 y + x = -26 (19, -7). (-7, 1). (7, 19). (-19, -7).
Answers
Answer:
(-19 , -7)
Step-by-step explanation:
y - x = 12
y + x = -25 we sum them to get
2y = -14 , y = -7
then we put -7 instead of y in any of the equations:
-7 - x = 12
-x = 19
x = -19,
finally (x , y) is (-19 , -7)
An oblique cylinder has a radius of 10 units and slant length of 26 units. An oblique cylinder has a radius of 10 units and a slant length of 26 units. What is the volume of the cylinder? 2,400π cubic units 2,500π cubic units 2,600π cubic units 2,700π cubic units
Answers
The volume of the oblique cylinder with the given parameters is: 2,400π
What is the Volume of an Oblique Cylinder?Volume of an oblique cylinder = πr²h
r is the radius, h is the height of the cylinder.
Given the following:
r = 10 unitsSlant height (l) = 26 unitsh = √(26² - 10²) = 24 units [Pythagorean Theorem]Volume of oblique cylinder = π(10²)(24)
Volume of oblique cylinder = 2,400π
Learn more about the volume of oblique cylinder on:
https://brainly.com/question/15940389
Answer: a
Step-by-step explanation:
Find the zeros of y=x^2+4x-9 by completing the square.
Answers
Answer:
[tex]\boxed{x =-2 \±\sqrt{13} }[/tex]
Step-by-step explanation:
Let y = 0
0 = x^2+4x-9
x² + 4x -9 = 0
Add 9 on both sides.
x² + 4x = 9
(b/2)² = (4/2)² = 2² = 4
Add 4 on both sides.
x² + 4x + 4 = 13
Facror left side.
(x+2)² = 13
Take the square root on both sides.
x + 2 = ±√13
Subtract 2 on both sides.
x = ±√13 - 2
En la ecuación x2 + 2x −p = 0 una de las soluciones es -5, ¿cuál es el valor de p?
Answers
Answer:
p = 15
Step-by-step explanation:
Si
x₁ = -5
entonces:
x² + 2x - p = 0
-5² + 2*-5 - p = 0
25 - 10 - p = 0
15 - p = 0
15 = p
im confused how many solutions are parellel lines and how many solutions are intersecting lines
Answers
Answer:
There are no solutions to paralell lines and there is exactly one solution to intersecting(perpendicular) lines.
Step-by-step explanation:The solutions would be the point of intersection and paralell lines never meet at any points. Interesecting lines intersect at exactly one point, which proves my answer above. Hope this helped
find the value of x and explain
Answers
Answer:
D
Step-by-step explanation:
The chord- chord angle 105° is half the sum of the arcs intercepted by the angle and its vertical angle, thus
[tex]\frac{1}{2}[/tex](120 + x) = 105 ( multiply both sides by 2 )
120 + x = 210 ( subtract 120 from both sides )
x = 90 → D
A polygon with 9 sides is shown. An exterior angle has a measure of x degrees. In the regular nonagon shown, what is the measure of angle x? 36° 40° 45° 60°
Answers
Answer:
40°Step-by-step explanation:
First we must know that the sum of all the exterior angle of all polygons is 360°.
Measure of each angle of a polygon = 360°/total sides of the polygon
Since a regular nonagon has 9 sides, the measure of each angle of a polygon is expressed as thus;
Measure of each angle of a polygon = 360°/9
Measure of each angle of a polygon = 40°
Hence the measure of an exterior angle x of a nonagon is 40°
Answer:
B in Edg
Step-by-step explanation:
Bruhhh I need help dude !!!
Answers
Answer:
(B), in which the first two values are 2 and 10.
Step-by-step explanation:
We can tell that this is a proportional relationship because we can examine the numbers in there.
(2,10)
(4,20)
and (6,30).
If you notice, the x value times 5 gets us the y value for every single point there.
Therefore, B is proportional and it's equation is y = 5x.
Hope this helped!
Answer:
B.
Step-by-step explanation:
B. Is the only one that proportional because,
(2,10)
(4,20)
(6,30)
All these x values multiply by 5 to get the y value.
So the equation is y = 5x meaning it is linear and it goes through the origin which makes it proportional.
Thus,
answer choice B is correct.
Hope this helps :)
hi :) how to do the last part?
Answers
Answer: 1200
Step-by-step explanation:
as t → ∞, the e-value will get very very very small and be considered insignificant. In other words, as t → ∞, e → 0.
600(2 + 0) = 1200
Furthermore, if you graph this equation, you will see that the asymptote is: y = 1200. So, the y-value will get really close to 1200 but will never actually reach this value.
WILL MARK BRAINLIEST!!! EASY QUESTION!!(✿◡‿◡) Can someone please give me an example of a FIFTH DEGREE POLYNOMIAL WITH THREE TERMS IN STANDORD FORM? I just need to know what it looks like, please.
Answers
Answer:
f(x) = x⁵ + 3x³ - 2 I think, if its incorrect I apologize
Step-by-step explanation:
1 to the tenth power
Answers
Explanation:
1 to any power will always be 1
Answer:
1
Step-by-step explanation:
1 to the tenth power is also 1 multiplied by 1 10 times.
1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 = 1
1 to any power will always have the answer of 1.
A pair of dice is rolled. What is the probability that the sum of the two dice will less than 4 given that the first die rolled is a 2?
Answers
The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
Answers
Answer:
A square.
Step-by-step explanation:
Using the two-way table, what percentage of the students that do not like camping like traveling out of state? Round to the
nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping
52
38
90
Does Not Like Camping 36
74
110
Column totals
88
112
200
30%
33%
36%
41%
Answers
Answer:
In Grade 8, 17% of students like running.
Step-by-step explanation:
Let's do process of elimination.
For the first choice, we have that In Grade 8, 14 students liked swimming. This is wrong because based on the two-way frequency table, we are dealing with decimals, which can written as percentages. Also, you can't have 0.14 of a person.
Therefore, the first choice is incorrect.
Now for the third choice. The statement is that in Grade 9, 31 percent of students liked volleyball. Okay, so we have a percentage this time. That is a good thing, but we have to know what this percentage means. This answer is incorrect because 31 percent goes with the column of running, not volleyball. It would also be a marginal frequency as well. The 31 percent actually means that 31 percent of all students in both grades liked running. In other words, a total of 31 percent of students in both 8th and 9th grade liked running.
Therefore, the third choice is incorrect.
For the last choice. The statement is 22 students like volleyball. Just like the first choice, we are dealing with percentages, not people.
Therefore, the last choice is incorrect.
Now for the second choice. We are given that in Grade 8, 17 percent of students liked running. We have a percentage, so that is good. This choice is correct because if you were to go to Grade 8 and running. Draw some lines down. You do get to 17 percent. This 17 percent means that 17 percent of students did actually like running. It also means that out of all 8th graders, 17 percent enjoyed running.
Therefore, the second choice is correct.
Hope this helps! I hope you enjoy the rest of your day.
what is the quotient of 1 and 2/3 divided by 4/5
Answers
Answer:
2 and 1/12
Step-by-step explanation:
1 and 2/3 = 5/3.
when dividing fractions, invert and multiply.
5/3x5/4=25/12
=2 and 1/12
Answer:
The quotient is:
2 and 1/12
Step-by-step explanation:
1 and 2/3 = 1 + 2/3
1 = 3/3
1 + 2/3 = 3/3 + 2/3 = (3+2)/3 = 5/3
1 and 2/3 divided by 4/5 is:
(5/3) / (4/5) = (5*5) / (3*4) = 25/12
25/12 = 24/12 + 1/12 = 2 + 1/12 = 2 1/12 = 2 and 1/12
Answer the following question. (need to show work) 20/2-10+3*15=
Answers
Answer:
45.
Step-by-step explanation:
To solve this equation, we must use PEMDAS...
The operations listed first must be solved first before we can continue.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Using this, we find that we must complete the multiplication and division before we add or subtract.
20 / 2 - 10 + 3 * 15
= (20 / 2) - 10 + (3 * 15)
= 10 - 10 + 45
= 0 + 45
= 45
Hope this helps!
A restaurant catered a party for 45 people. A child’s dinner (c) cost $15 and an adult’s dinner (a) cost $25. The total cost of the dinner was $1,015. How many children and adults were at the party? Use the table to guess and check.
Number of People
a
c
c + a = 45
15 c + 25 a = 1,015 dollars
9 adults and 36 children
10 adults and 35 children
34 adults and 11 children
36 adults and 9 children
Answers
Answer:
34 adults and 11 children
Step-by-step explanation:
15 times 11 is 165dollars for kids
25 times 34 adults equals 850 dollars
add it and its 1015
Answer:
34 and 11
Step-by-step explanation:
21.(03.02)
If f(x) = 7x – 1, what does f(12) represent?
Answers
Answer:
83
Step-by-step explanation:
f(x) = 7x - 1
Put x as 12.
f(12) = 7(12) - 1
f(12) = 84 - 1
f(12) = 83
Consider the equations:
y=15x-45
y=12x+18
How many solutions do they have?
Answers
Explanation:
Because the two equation has a different slope and different y intercept
Answer:
1
Step-by-step explanation:
Both equations are linear, and they do not have an equivalent slope, therefore they MUST intercept each other once and only once.
Please answer it now in two minutes
Answers
Answer:
4.5
Step-by-step explanation:
Use sin64=x/5 and simplify to
5sin64 and plug it into a calculator to get 4.49 which is 4.5
Please answer this question now
Answers
Answer:
If it's not too late by now, the answer is 19.9 [tex]mm^{2}[/tex]
how many digits are in the decimal expansion of 2^34
Answers
Answer:
2^34 = 17179869184
I hope this helps :)
Please answer this question now
Answers
Answer:
397.7 m²
Step-by-step Explanation:
The are of ∆UVW can be found ones we know the measure of 1 angle that is in between known lengths of two sides. Then, we would apply the formula, ½*a*b*sin(θ)
Where, a and b, are the lengths having an included angle (θ), in between them.
To find area of ∆UVW, we need m < V, side lengths of UV and VW.
m < V = 113°
VW = 29 m
UV = ?
Step 1: find UV using the Law of sines
[tex] \frac{UV}{sin(W)} = \frac{VW}{sin(U)} [/tex]
W = 34° [180 - (113+33)]
U = 33°
VW = 29 m
UV = ?
[tex] \frac{UV}{sin(34)} = \frac{29}{sin(33)} [/tex]
Multiply both sides by sin(34)
[tex] \frac{UV*sin(34)}{sin(34)} = \frac{29*sin(34)}{sin(33)} [/tex]
[tex] UV = \frac{29*sin(34)}{sin(33)} [/tex]
[tex] UV = 29.8 m [/tex]
Step 2: find the area of the triangle
Area = ½*a*b*sin(θ)
a = 29.8 m
b = 29 m
θ = 113°
Area = ½*29.8*29*sin(113)
Area = 397.7 m² (nearest tenth)
Help please.... what is the solution of sqrt -4x=100? A- x=-2500 B-x=-50 C-x=-2.5 D-no solutions
Answers
Answer:
A. x = -2,500.
Step-by-step explanation:
sqrt(-4x) = 100
(sqrt(-4x)^2 = (100)^2
-4x = 10,000
4x = -10,000
x = -2,500
Check your work...
sqrt(-4(-2,500))
= sqrt(4 * 2,500)
= sqrt(10,000)
= plus or minus 100
A. x = -2,500 is your answer.
Hope this helps!
Answer:
The answer would be A, x=-2500
Explanation:
To remove the radical on the left side of the equation, square both sides of the equation.
√ − 4 x^ 2 = 100^ 2
Simplify each side of the equation.
− 4 x = 10000
Divide each term by
−4
and simplify.
x = -2500
Look at picture to see question