For each triangle shown below, determine whether you would use the Law of Sines or Law of Cosines to find angle x, and explain how you know which Law to use. Then find angle x to the nearest tenth.
NOTE: The perimeter of ABC-31
Given:
The figure of a triangle.
The perimeter of the triangle ABC is 31.
To find:
The value of x in the given triangle.
Solution:
Three sides of the triangle ABC are AB, BC, AC are their measures are [tex]3b-4,2b+1,b+10[/tex] respectively.
The perimeter of the triangle ABC is 31.
[tex]AB+BC+AC=31[/tex]
[tex](3b-4)+(2b+1)+(b+10)=31[/tex]
[tex]6b+7=31[/tex]
Subtract 7 from both sides.
[tex]6b=31-7[/tex]
[tex]6b=24[/tex]
[tex]b=\dfrac{24}{6}[/tex]
[tex]b=4[/tex]
Now, the measures of the sides are:
[tex]AB=3b-4[/tex]
[tex]AB=3(4)-4[/tex]
[tex]AB=12-4[/tex]
[tex]AB=8[/tex]
[tex]BC=2b+1[/tex]
[tex]BC=2(4)+1[/tex]
[tex]BC=8+1[/tex]
[tex]BC=9[/tex]
And,
[tex]AC=b+10[/tex]
[tex]AC=4+10[/tex]
[tex]AC=14[/tex]
Using the law of cosines, we get
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
[tex]\cos A=\dfrac{(AC)^2+(AB)^2-(BC)^2}{2(AC)(AB)}[/tex]
[tex]\cos A=\dfrac{(14)^2+(8)^2-(9)^2}{2(14)(8)}[/tex]
[tex]\cos A=\dfrac{179}{224}[/tex]
Using calculator, we get
[tex]\cos A=0.7991[/tex]
[tex]A=\cos ^{-1}(0.7991)[/tex]
[tex]x=36.9558^\circ[/tex]
[tex]x\approx 37.0^\circ[/tex]
Therefore, the value of x is 37.0 degrees.
Help please guys if you don’t mind
Step-by-step explanation:
Step 2:
[tex] ({15x}^{2} - 9x) + (5x - 3)[/tex]
Stepc3:
[tex]3x(5x - 3)[/tex]
What kind of statement does the shorthand below represent?
Answer:
it's a transitive statement.
Similar to "If a is equal to b and b is equal to c, then a is equal to c."
a = b and b = c, then a = c
Step-by-step explanation:
The ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5 . Find their present ages.
Answer:
Age of Raju = 12
Age of Ravi = 16
Step-by-step explanation:
Let the Ages of Raju and Ravi be 3x and 4x years
According to question, [tex]\frac{3x+4}{4x+4}[/tex] = [tex]\frac{4}{5}[/tex]
⇒ 5(3x+4)=4(4x+4)
⇒ 15x+20 = 16x+16
⇒ 15x−16x=16 - 20
⇒ −x = −4
⇒ x = 4
Age of Raju = 3 × 4 = 12
Age of Ravi = 4 × 4 = 16
HOPE IT HELPS!!
Answer:
raju=16 years
Ravi=20 years
Step-by-step explanation:
raju =4×4=16
Ravi=5×4=20
please help!
factor f(x)=6x^2-x-2
Hi there!
[tex]\large\boxed{(3x - 2)(2x + 1) }[/tex]
6x² - x - 2
To solve, we must factor into the following format:
(ax - b)(cx - d)
The following conditions must be met:
a · c = 6
da + bd = -1
b · d = -2
By guessing and checking, we get:
(3x - 2)(2x + 1)
Answer for Acellus:
(2 x + 1) (3 x - 2)
Step-by-step explanation:
i checked the equation on an online calculator, and it came up with it switched (compared to the other answer that is posted) like so...
I put the answer in and it said it was right for Acellus.
Hope this helps :))
Please help i need to find X.
Answer:
(11√42)/2
Step-by-step explanation:
Thanks to the given information we can say that the smaller leg of the left triangle is
(11√7)/2
while the other leg is
11/2 √7 * √3 = 11/2 √21
the triangle on the right has two congruent legs. For the Pythagorean theorem
x^2 = 2 (11/2 √21)^2
x^2 = 2 * 121/4 * 21
x^2 = 2541 / 2
x = √11^2 * 3 * 7/√2
x = 11√21/√2
x = (11√42)/2
If you know the answer to any of these please Ill mark brainliest.
Answer:
Step-by-step explanation:
1) 2/9 = 185/x
2x = 1665
x = 832.5 or 8.325 meters
2) unit rate is the cost of one unit
i.e a dozen eggs cost $1.20 that
would be 10 cents each
3) 300 tissues for $3.75 vs. 250 for $2.99
one is 1.24 cents per tissue
the other 1.19 ... the 250 package is a better buy
4 Two number cubes are rolled. The faces have the numbers 1-6 on them. The number that shows on top is recorded. What is the probability that
the same number shows on both number cubes?
OF
OS
Which number line model represents the expression 5/2 + 3
The line graph (A) represents the expression 5/2 + 3 the first term is 2 and-a-half units, and the second term is 3 units option (A) is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have an expression:
= 5/2 + 3
Here 5/2 = 2.5 = 2 and half
= 2.5 + 3
The first arrow should indicate the 2 and-a-half unit
And the second arrow should represent the 3 unit
The line graph(A) represents the above situation or expression.
Thus, the line graph (A) represents the expression 5/2 + 3 the first term is 2 and-a-half units, and the second term is 3 units option (A) is correct.
Learn more about the number line here:
brainly.com/question/13189025
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The sum of a father's and his son's age is 60. Eight years ago, the father's age was 3 times that of his son. How old is each of them?
Answer:
Father=41
Son=19
Step-by-step explanation:
Father=f
Son=s
f+s=60
Eight years ago would mean that 16 is subtracted from 60 since there is both of them
3s+s=4s
4s=44
s=11
11+8=19
33+8=41
Find the measure of the missing angle using the exterior angle sum theorm.
Answer:
28°
Step-by-step explanation:
Theorem: the exterior angle of a triangle is equal tobthe sum of opposite interior angles of the triangle
therefore,
55 = unknown angle + 27
let the unknown angle be x
55 = x + 27
isolating x
x = 55 - 27
x = 28
thus, the missing angle is 28°
Come get your 11 points :)
Find x in the kite below
Answer:
5
Step-by-step explanation:
The given is 3-4-5 special triangle so the missing side represented with x is 5
The line y = 2x + 6 cuts the x-axis at A and the y-axis at B. Find
(a) the length of AB,
(b) the shortest distance of O to AB, where O is the origin (0,0)
Answer:
(a)
[tex]3 \sqrt{5} [/tex]
(b)
[tex] \frac{6}{ \sqrt{5} } [/tex]
Step-by-step explanation:
A(-3,0)
B(0,6)
[tex]d = \sqrt{{( - 3 - 0)}^{2} + {(0 - 6)}^{2} } = \sqrt{9 + 36} = 3 \sqrt{5} [/tex]
[tex]d = \frac{ax0 + by0 + c}{ \sqrt{ {a}^{2} + {b}^{2} } } [/tex]
2x-y+6=0
a=2, b=-1, c=6
x0=0, y0=0
[tex]d = \frac{6}{ \sqrt{4 + 1} } = \frac{6}{ \sqrt{5} } [/tex]
proportional linear relationships can be represented in how many different forms
Proportional Linear Relationships can be expressed in the following ways:
a graphan equation, or a list of points.What is a proportional linear relationship?From a graphical point of view, a relationship is proportional and linear if the line representing the equation goes via the origin. It is to be noted that a relationship must be linear for it to be proportional and vice versa.
Thus, it is correct to state that Proportional Linear Relationships can be expressed in the following ways:
a graphan equation, or a list of points.An example of an equation that is proportional and linear is:
y = 6x + 8. Note that this linear equation is proportional because it has a constant component.
Learn more about the proportional linear relationships at;
https://brainly.com/question/2143065
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Which expression is equivalent to 5g+9+8g+4?
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5g + 9 + 8g + 4}\\\\\huge\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{5g + 8g + 9 + 4}\\\\\large\textsf{5g + 8g = \bf 13g}\\\\\large\textsf{9 + 4 = \bf 13}\\\\\boxed{\huge\textsf{= 13g + 13}}\large\checkmark\\\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: \bf 13g + 13}}}\huge\checkmark\\\\\\\\\\\\\\\\\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
HELP ASAP PLEASEEE !!!!
WILL GIVE BRAINLIEST
which equation represents the general form of a circle with a center at (-2 -3) and a diameter of 8 units ?
• x²+y²+4x+6y-51=0
•x²+y²-4x-6y-51=0
•x²+y²+4x+6y-3=0
•x²+y²-4x-6y-3=0
Answer:
it’s the 3rd one:)
Step-by-step explanation:
Answer:
In this situation, (h, k) = (-2, -3)Radius = 8/2 = 4 unitsSubstitute them into the circle equation: (x - h)² + (y - k)² = r²
(x - (-2))² + (y - (-3))² = 4²
(x + 2)² + (y + 3)² = 4²
Now expand the equation:
(x + 2)² + (y + 3)² = 4²
(x + 2)(x + 2) + (y + 3)(y + 3) = 16
(x² + 2x + 2x + 4) + (y² + 3y + 3y + 9) = 16
x² + 4x + 4 + y² + 6y + 9 = 16
x² + y² + 4x + 6y + 13 - 16 = 0
x² + y² + 4x + 6y - 3 = 0
The graph of y=x^3+x^2-6x is shown....
hello,
" a turning point is defined as the point where a graph changes from either increasing to decreasing, or decreasing to increasing"
a)
[tex]y=x^3+x^2-6x\\\\y'=3x^2+2x-6=0\\x=\dfrac{-2-\sqrt{76} }{6} \approx{-1.786299647...}\\or\\x=\dfrac{-2+\sqrt{76} }{6} \approx{1.1196329...}\\[/tex]
b)
Zeros are -3,0,2.
Sol={-3,0,2}
The solution of the graph function y=x³+x²-6x are -3 , 0 and 2
What is graph?The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of certain points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.
We have the function
y=x³+x²-6x
now, equating it to 0
x³+x²-6x = 0
x² + x - 6= 0
x² - 3x + 2x -6 =0
x(x -3) + 2(x -3)
x= 3 and -2
Now, ew can see from the that the equation is touching the x-axis at three points and it will represent three zeroes of the equation.
So, the solution of the graph are -3 , 0 and 2
Learn more about graph here:
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Which of the following is an arithmetic sequence?
Find the length of CZ
A. 32
B. 45
C. 9
D. 1
Answer:
c
Step-by-step explanation:
just took it
Answer:
D. 1
Step-by-step explanation:
CA = 17
ZA = 16
CZ + ZA = CA
CZ + 16 = 17
CZ = 1
D. 1
HELP ASAP PLEASE NOWWWW!!!!!!!!!!!!!!!
(x - [3])² + (y- [2])² = 16
Arlene is a clothing store manager and she set the price for a pair of jeans at $40 and is selling 120 pairs each week. She estimates that if she changes the price by x dollars, where x can be positive or negative. she will sell 120 - 3x pairs of jeans a week, for a total of (40 + x)(120 - 5x) dollars in sales. According to her estimate, what will result in the greatest value of sales?
A) Decreasing the price by $2.50
B) Decreasing the price by 51.50
C) Leaving the price unchanged.
D) Increasing the price by $2.00.
Answer:
B
Step-by-step explanation:
This is literlly the same question I had 2 minutes ago
click the image below to find out the question.
Seo-Yun organizó una fiesta. Comprar 50 recuerditos para regalar y les dio 3 recuerditos a cada uno de sus invitados conforme llegaban a la fiesta.
Escribe una fórmula explícita para la sucesión.
g(n)=
Answer: nose
Step-by-step explanation:
Please answer the question that is attached below
Refer to the picture in the question for reference.
A statement-reason format is used to solve this problem. Statements are in normal print, reasons are bolded.
Statement Reason
1. AD = AE Given
<B = <C
2. <A = <A Reflexive Property
3. ΔABE = ΔACD Angle - Angle - Side
The given information refers to the information that is given with the problem.
The reflexive property states that if two polygons share a part (a side or an angle), then this part called in one of the polygons is congruent to itself in the other polygon.
Finally, the (angle-angle-side) congruence theorem states that if two triangles have two congruent angles and a congruent side between them, then the triangles as a whole are congruent to each other.
Triangle ABC is congruent to LMN. Find the value of x. Please and thank you!
Warning: if you give an answer that is NOT related to the question at all then I will report you - FIND THE VALUE OF X
Answer:
x = 9
Step-by-step explanation:
The ratios of corresponding sides are equal, that is
[tex]\frac{BC}{MN}[/tex] = [tex]\frac{AB}{LM}[/tex] , substitute values
[tex]\frac{x}{15}[/tex] = [tex]\frac{6}{10}[/tex] ( cross- multiply )
10x = 90 ( divide both sides by 10 )
x = 9
Circle the equation of a straight line that does not intersect the curve y = x2
(1 m
y = 5
X=-3
y = 2x - 5
y= -3x + 1
Answer:
[tex] \boxed{y = 2x\: – \: 5} [/tex]
Nadia is mountain climbing. She started at an altitude of 19.26 feet below sea level and then changed her altitude by climbing a total of 5,437.8 feet up from her initial position. What was Nadia’s altitude at the end of her climb?
Answer:
5418.54 ft
Step-by-step explanation:
So sea level is 0, okay? So Nadia (her name is more than 3 letters and I'm lazy so from now on she'll be reffered to as "N") is at -19. 26 ft. N goes up 5,437.8 ft, so we add this value on.
-19. 26+ 5437.8= 5418.54
Now just add on the units!
Hope this helps!
Answer:
Answer:
5418.54 ft
Step-by-step explanation:
Answer:
5418.54 ft
Step-by-step explanation:
So sea level is 0, okay? So Nadia (her name is more than 3 letters and I'm lazy so from now on she'll be reffered to as "N") is at -19. 26 ft. N goes up 5,437.8 ft, so we add this value on.
-19. 26+ 5437.8= 5418.54
8,X,20 are in arithmetic progression,find the value of "x".
Answer:
x = 14
Step-by-step explanation:
Since the terns form an arithmetic progression then they have a common difference d , that is
a₂ - a₁ = a₃ - a₂
x - 8 = 20 - x ( add x to both sides )
2x - 8 = 20 ( add 8 to both sides )
2x = 28 ( divide both sides by 2 )
x = 14
Question 4 Multiple Choice Worth 4 points)
(01.02 LC)
What is the solution for the equation 6x - 8 = 4x?
Answer:
Algebra
Step-by-step explanation:
(+) it's the same thing btw6x -8 = 4x
(collect like terms) meaning the numbers with x go over the " = " sign
making it = -8 = 4x -6x
the signs change when it crosses over so it becomes that
-8 = -2x
-8 ÷ -2 = 4 (cause - ÷ by - is + )