The solution of the equation b² = 48 is b = 4√3
How to solve equation?The equation can be solved as follows;
b² = 48
Therefore, we are to find the value of b in the equation.
The value of b comes with a square sign, so we have to remove the square to make b stand alone in the equation.
By removing the square sign we have to square root both sides.
Hence,
b² = 48
square root both sides of the equation
b² = 48
√b² = √48
Therefore,
b = √16 × 3
b = 4√3
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This question is not from a test. This is an extra credit MATHS assignment. Please help me if you can. If you do, thank you! :)
we have the equation
[tex]y=31sin5x+32[/tex]Find out the first derivative
[tex]\begin{gathered} y^{\prime}=(5)(31)c0s5x \\ y^{\prime}=155cos5x \end{gathered}[/tex]equate to zero the derivative, to find out the critical points
[tex]\begin{gathered} 155cos5x=0 \\ cos5x=0 \end{gathered}[/tex]The value of cosine is zero when the angle is 90, 270 degrees (pi/2 and 3pi/2)
so
[tex]\begin{gathered} 5x=\frac{\pi}{2} \\ \\ x=\frac{\pi}{10} \end{gathered}[/tex][tex]\begin{gathered} 5x=\frac{3\pi}{2} \\ \\ x=\frac{3\pi}{10} \end{gathered}[/tex]For x=pi/10
Find out the y-coordinate
[tex]\begin{gathered} y=31s\imaginaryI n\frac{5\pi}{10}+32 \\ \\ y=31sin\frac{\pi}{2}+32 \\ \\ y=31+32=63\text{ ft} \end{gathered}[/tex]Verify for x=3pi/10
[tex]\begin{gathered} y=31s\imaginaryI n5(\frac{3\pi}{10})+32 \\ \\ y=31s\imaginaryI n(\frac{3\pi}{2})+32 \\ y=-31+32=1\text{ ft} \end{gathered}[/tex]The maximum height is 63 ftIf QR = 6x, RS = 10, and QS = 5x + 13, what is QS?
If QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units.
The length of the line QR = 6x
The length of the line RS = 10
The length of the line QS = 5x+13
We know
The length of the line QS = The length of the line QR + The length of the line RS
Substitute the values in the equation
5x+13 = 6x + 10
Move the 6x to the left hand side of the equation and move 13 to the right hand side of the equation
5x-6x = 10-13
Subtract the terms
(5-6)x = 10-13
-1x = -3
x = 3
Then the length of the QS = 5x+13
Substitute the value of x in the equation
The length of the line QS = 5×3+13
= 15+13
= 28 units
Hence, if QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units
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Can anyone tell me if what i put is correct? Thank you!
service call has just come in, but the type of malfunction is unknown. it is p.m. and service technicians usually get off at p.m. what is the probability the service technician will have to work overtime to fix the machine today?
(a) The probability distribution table is provided in the attachment.
(b) The probability distribution of X is discrete.
Let X = number of hours a service calls take.
(a)The probability of an event E is:
P(E)=n(E)/N
Here,
n (E) = number of favorable outcomes
N = total number of outcomes.
The probability distribution table is provided in the attachment.
(b)For a discrete probability distribution:
f(x) >= 0
summation f(x)= 1
Check that the probability distribution of X is discrete as follows:
The value of f (x) for all values of x is greater than 0.
The sum of all f (x) is 1.
Thus, the probability distribution of X is discrete.
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A credit card bill for $559 was due on September 14. Purchases of $286 were made on September 19, and $15 was charged on September 28. A payment of $250 was made on
September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year.
Round your answer to the nearest cent.)
With 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.
What is interest?In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed). It is not the same as a fee that the borrower might pay to the lender or another party. It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve but not at a set rate predetermined in advance, but rather on a pro-rata basis as a share of the reward received by risk-taking businesspeople when revenue is earned that exceeds all costs.So, the finance charge due:
(+) $ 559 due on sep 14, $ 559 * (19.5*31) / (100 * 365) = $ 9.20(+) purchase $ 289 on Sep 19, $ 289 * (19.5*26 ) / (100 * 365) = $ 2.42(+) finance charge on sep 28, $ 18 *(19.5*17 ) / (100 * 365) = $ 0.17(-) Repayment on 25 sep , $ 250 * (19.5*20 ) / (100 * 365) = (2.745)Finance charges from 14 sep to 14 oct = $ 9.7= appr. 10Amount due on 14 October = $559+$289+$15+$11.855- $250= $ 623Therefore, with 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.
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Solve the absolute value by re writing it as an equaulant compound in
| 3x - 1 > 11
The solution of the inequality will be;
⇒ x > 4 or x < -10/3
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is;
|3x - 1| > 11
Now, The inequality is solved as;
|3x - 1| > 11
⇒ 3x - 1 > 11 or 3x - 1 < -11
Solve the inequality as;
⇒ 3x - 1 > 11
Add 1 we get;
⇒ 3x - 1 + 1 > 11 + 1
⇒ 3x > 12
Divide by 3;
⇒ x > 4
And, Solve the inequality as;
⇒ 3x - 1 < - 11
Add 1 we get;
⇒ 3x - 1 + 1 < - 11 + 1
⇒ 3x < -10
Divide by 3;
⇒ x < -10/3
Thus, Solution of the inequality will be;
⇒ x > 4 or x < -10/3
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The Distributive Property Use the Distributive Property to rewrite each expression without parenthesis. 1. 6(x + 3) 2. 5( y - 4 ) 3. -7( m - 1 )
Answer:
1. 6x+18 2. 5y-20 3. -7m+7
Step-by-step explanation:
1. 6(x+3) 2. 5(y-4) 3. -7(m-1)
6x+24. 5y-20. -7m+7 <--- - times - = +
Dentro de 65 años tendré 6 veces la edad que tenía hace 10 años ¿qué edad tengo?
Based on the calculations, the age of this person is equal to 25 years.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to solve this word problem, we would assign a variable to the age of this person and then translate the word problem into algebraic equation as follows:
Let x represent the age.
Translating the word problem into an algebraic equation, we have;
x + 65 = 6(x - 10)
Opening the bracket, we have:
x + 65 = 6x - 60
Re-arranging the equation, we have:
6x - x = 60 + 65
5x = 125
Dividing both sides by 5, we have:
x = 125/5
x = 25 years.
In conclusion, we can reasonably infer and logically state that this person's age was 25 years ten (10) years ago.
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Complete Question:
In 65 years I will be 6 times as old as I was 10 years ago. How old am I?
-8n-4+n+7 where like terms need to be simplified
Answer:
- 8n -4 +n+7
like terms (-8n, n) and (-4, 7)
so; -8n+n-4+7
= -7n+3
Answer:
-7n + 3
Step-by-step explanation:
Simplify:Like terms are terms that have same variable with same power.
-8n and n are like terms. subtract or add the coefficient of the like terms.
(-8) and 1. So, subtract and it is -7n
(-4) and 7 are like terms(constants).
-8n - 4 + n + 7 = -8n + n - 4 + 7
= -7n + 3
In the given figure, AD is adjacent to BC.
if AB = 13 cm, BD = 5 cm and DC = 16 cm,
find the values of :
(I) sin B
(II) sec B
(III) cot B
(iv) cos C
(v) cosec C
(vi) tan C
By using the method of trigonometry,
(1)sin B=P/H=AD/AB=12/13
(2)sec B=H/B=AB/BD=13/5
(3)cot B=B/P=BD/AD=5/12
(4)cos C=B/H=CD/AC=16/20=4/5
(5)cosec C=H/P=AC/AD=20/12=5/3
(6)tan C =P/B=AD/DC=12/16=3/4
What is trigonometry?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry. The unit circle is the most straight forward way to define the trigonometric functions. Let theta represent an angle that is calculated along a circle's arc counterclockwise from the x-axis.
Given that,
[tex]AD^{2}= AB^{2}- BD^{2}= 13^{2}- 5^{2}= 169-25= 144[/tex]
=>AD=12cm
(1)sin B=P/H=AD/AB=12/13
(2)sec B=H/B=AB/BD=13/5
(3)cot B=B/P=BD/AD=5/12
[tex]AC^{2}= AD^{2}+ DC^{2}= 12^{2}+ 16^{2}= 144+ 256= 400[/tex]
=>AC=20cm
(4)cos C=B/H=CD/AC=16/20=4/5
(5)cosec C=H/P=AC/AD=20/12=5/3
(6)tan C =P/B=AD/DC=12/16=3/4
note: P=perpendicular
B=base
H=hypotenuse
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A magazine subscription has a cover price of $35. Amanda received an offer for 67% off the cover price. What is the sale price of the magazine subscription?
The sale price of the magazine subscription is $11.55
How to calculate the sale price of the magazine subscription?From the question, the given parameters are:
Subscription = $35
Discount = 67% off
The sale price of the magazine subscription is then calculated as
Sales price = Subscription x (1 - Discount)
Substitute the known values in the above equation
So, we have the following equation
Sales price = 35 x (1 - 67%)
Evaluate the product
Sales price = 11.55
Hence, the sales price is $11.55
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what fraction of one minute is 7 seconds
express the mix number as the sum of an integer and a fraction.
-1 2/3 = + (2/3)
We will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.
What is integer?
An integer, often known as a "round number" or "whole number," is any positive or negative number that does not contain fractional or decimal parts. Examples are 3, -10, and 1,025 which are all integers, but 2.76 (decimal), 1.5 (decimal), and 3 12 (fraction) which are not.Three categories of integers exist: Negative integers with a value of 0 (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers).What is fraction?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.- [tex]1\frac{2}{3}[/tex] = _ + (2/3)
we will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.
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twice the sum of -17 and a number is -14
After thoroughly calculating we have come to find that, a number twice the sum of -17 and -14 is −62
How to find sum of two numbers?To sum and complete mathematical operations, numerical values are needed. Numbers are used to represent numerical values, and they can also be used to represent them alphabetically. For instance, the number 22 can be expressed in writing or by using the alphabet 22. One more example is the number 3, which can be written as 3.
Numbers can take many different forms. Examples of opposites include odd and even, fraction and integer, rational and irrational, natural and whole, and many more. A few of the operations include arithmetic, algebra, and trigonometry.
Twice the sum of -17 and -14 is
2((-17) + (-14))
⇒ 2(-17 -14)
⇒ 2 × (-31)
⇒ −62
So, a number twice the sum of -17 and -14 is −62.
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I WILL GIVE BRAINLIEST TO THE ONE WITH THE CORRECT ANSWER.
Solve for x. Assume that lines which appear to be diameters are actual diameters.
The value of x is 4 , the correct option is (C)4 .
In the question ,
it is given that AD and BE are diameters , hence they are straight lines .
From the figure shown below , we can see that
∠AOE and ∠BOD are vertically opposite angles ,
the property of vertically opposite angle states that " the vertically opposite angles are equal in measure ."
So,
substituting the values of ∠AOE and ∠BOD from the figure , we get
36x-4 = 92+(11x+4)
36x-11x = 92+4+4
25x = 100
x=4
Therefore , the value of x = 4, the correct option is (C)4 .
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Translate the triangle 4 units right and 3 units down
Answer:
L'(0,-2)
K' (3, -2)
J' (0,3)
Step-by-step explanation:
how many non-empty subsets of consist entirely of prime numbers? (we form a subset of the group of numbers by choosing some number of them, without regard to order. so, is the same as .)
The question is testing knowledge on subsets. The application of combinations is used to sum up. Consider prime factors between 1 and 11. They are{1,2,3,4,5,6,7,8,9,10,11}.
The prime factors in the set are {2,3,5,7,11}. This set has 5 elements.
Apply combinations to obtain the total subsets.
The subsets with 1 element is 5C1 = 5 subsets
The subsets with 2 elements is 5C2= 10 subsets
The subsets with 3 elements is 5C3= 10 subsets
The subsets with 4 elements is 5C4= 5 subsets
The subsets with 5 elements is 5C5= 1 subset
The total non-empty subsets are 5+10+10+5+1 = 31 subsets.
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A
(3x+8)°
B=
(6x-2)
C =
69°
x=?
CAB=?
ACB=
ABC=
The value of x is 11.7.
The angles CAB, ACB, and ABC are 43.1°, 69°, and 68.2° respectively.
What is the Angle Sum Property?According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180°, regardless of whether it is acute, obtuse, or right.Given angles are:
A = (3x+8)°
B= (6x-2)°
C = 69°
Using the Angle sum property we get,
(3x+8)° + (6x-2)° + 69° = 180°
9x + 75° = 180°
9x = 180°- 75°
x = 11.7
CAB = (3 × 11.7 + 8)° = 43.1°
ACB = 69°
ABC = (6 ×11.7 - 2) = 68.2°
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Write an algebraic equation for the following problem and then solve it.
The population of a country in 2015 was estimated to be 321.4 million people. This was an increase of 17% from the population in 1990. What was the population of the country in 1990?
The algebraic equation is _=321.4
The population of the country in 1990 will be 274.7 million.
How to illustrate the information?From the information given, the population of a country in 2015 was estimated to be 321.4 million people and this was an increase of 17% from the population in 1990.
Therefore,since let the population on 1990 be x. Therefore, this will be illustrated as:
x + (17% × x) = 321.4
x + 0.17x = 321.4
1.17x = 321.4
Divide
x = 321.4 / 1.17
x = 274.7
The population is 274.7 million.
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Factor 63a–35. Write your answer as a product with a whole number greater than 1.
The expression 63a–35 factored as a product with a whole number greater than 1 is 7(9a - 5)
What are algebraic expressions?Algebraic expressions are defined as expressions made up of variables, terms, coefficient, constants, and factors.
The are also made up of arithmetic or mathematical operations which includes;
SubtractionMultiplicationParenthesesAdditionBracketDivision, etcWhat is factorization?Factorization can be defined as the mathematical method of breaking a number down into similar and smaller numbers which are the products of the original number.
Given the expression;
63a–35
To factor expression, we need to find a common product of the values
We have;
7(9a - 5)
This cannot be further factorized
Hence, the factored form is 7(9a - 5)
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Last night, Bruce completed all 5 levels of his favorite video game, Extreme Treasure Hunter. In the game, you can earn points by collecting gemstones or finding pieces of the treasure map. Bruce collected 10 gemstones in each level, earning x points per gemstone. He also earned 30 points in each level by finding pieces of the treasure map! Pick all the expressions that represent Bruce's score at the end of the game.
The expressions that represent Bruce's score at the end of the game will be 5(10x) + 30(5) = 150 + 50x.
How to illustrate the expression?From the information, Bruce completed all 5 levels of his favorite video game, Extreme Treasure Hunter and in the game, you can earn points by collecting gemstones or finding pieces of the treasure map.
The expression to illustrate the number of points will be:
= 5(10x) + 30(5)
where c = number of points per gemstone
= 50x + 150
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It took a plane 2 hours to fly from Dallas to New York with the head wind and 1.5 hours to return with the tailwind. If the speed of the wind was 30 mph, how far apart are the 2 cities? Giving brainliest to correct answer
Answer:
The distance between the two cities is 360 miles.
Step-by-step explanation:
Let value "a" equal the airspeed of the plane in still air, and let value "d" be the distance between the two cities. Then:
d/a+30=1.5
d=1.5a+45
and
d/a-30=2
d=2a-60
So
2a-60=1.5a+45
.5a=105
a=210
d/210-30=2
d=360
The distance between the two cities is 360 miles.
Find the equation of the line that contains the point P(−4, 6) and has slope 4. (Let y be the dependent variable and let x be the independent variable.)
The equation of the line that contains the point P(-4,6) and has slope 4 is y=4x+22 .
The equation of line passing through the point (x₁,y₁) with slope (m) is given by the formula
(y-y₁)=m(x-x₁)
In the question ,
it is given that
the required line passes through the point P(-4,6) and has slope 4
So, x₁= -4 , y₁=6 and m = 4
Substituting the values of x₁, y₁ and m in the equation of line formula , we get
y-6=4(x-(-4))
y-6=4(x+4)
y-6=4x+16
y=4x+16+6
y=4x+22
Therefore , the equation of the line that contains the point P(-4,6) and has slope 4 is y=4x+22 .
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Write an equation that represents the line.
Use exact numbers.
Answer:
y=4/3-5
Step-by-step explanation:
Y=mx+c
mx=gradient which is 4/3
c is y intercept which is -5
uh?????????????????????????
Answer:
I'm sure it's 1.2506407mm
Step-by-step explanation:
if A = 32 degrees, a = 17, and b =11 find the measure of angle B
round to the nearest tenth
The 32° measure of A and the length of side a which is 17, and side B with length 11, using the law of sines, gives;
The value of angle B is approximately 20.1°What is the law of sines?The law of sines can be stated as follows;
The ratio of the sine of an interior angle in an oblique triangle to the length of the side opposite the given angle, is a constant for the angles and their opposite sides of the triangle.
Mathematically, we have;
[tex] \frac{sin( A) }{a} = \frac{sin( B )}{b} =\frac{sin( C )}{c} [/tex]
Where;
Angle A is the angle opposite to side a
Angle B is the angle opposite to side b
Angle C is the angle opposite to side c
The given measure of angle A = 32°
The length of segment, a = 17
The length of segment, b = 11
Taking the given dimensions as the measurements of parts of a triangle, using sine rule, we have;
[tex] \frac{sin( A)}{s } = \frac{sin( B )}{b} [/tex]From the question, we have;
A = 32°
a = 17
b = 11
Which gives;
[tex] \frac{17}{sin( 32^{ \circ} ) } = \frac{11}{sin( B )} [/tex]
Therefore;
[tex] sin( B ) = \frac{11 \times sin( 32^{ \circ} ) }{17} [/tex]
Which gives;
[tex] \displaystyle{ B = arcsin \left( \frac{11 \times sin( 32^{ \circ} ) }{17} \right) \approx 20.1 ^{ \circ} }[/tex]
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Please help for 100 points.
By using matrix operations, the resulting matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].
How to simplify a combination of matrices
In this problem we must simplify a combination of two matrices, this can be done by using properly the fundamental operations for matrices. Matrices are algebraic constructions characterized by a number of row and a number of columns. For instance, there is a matrix with two rows and three columns:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex]
There are two fundamental operations for matrices:
Sum - The respective elements of the same row and the same column of the matrix are summed:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]
Where C(i, j) = A(i, j) + B(i, j), i is the row index and j is the column index.
Scalar mutiplication - Every element of the matrix is multiplied by a scalar:
[tex]2 \cdot \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]
Where B(i, j) = k · A(i, j), k is the scalar.
Now we show the complete procedure to find the simplified expression:
[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] Given
[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] + (- 1) \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] Definition of subtraction
[tex]\left[\begin{array}{cc}4&8\\16&20\end{array}\right] + \left[\begin{array}{cc}- 1&- 2\\- 4&- 5\end{array}\right][/tex] Scalar multiplication
[tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex] Sum of matrices / Result
The simplifed form of the matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].
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Choose the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed.
The expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]
Nine raised to the negative third power = [tex]9^{-3}[/tex]
Three raised to the negative second power times nine squared = [tex](3x^{-2})(9^{2} )[/tex]
The expression is [tex](\frac{9^{-3} }{(3^{-2})(9^{2} ) } )^{3}[/tex]
=[tex]\frac{9^{(-3)(3)} }{(3^{(-2)(3)})(9^{(2)(3)} }[/tex]
=[tex]\frac{9^{-9} }{(3^{-6})(9^{6}) }[/tex]
= [tex]\frac{3^{6} }{(9^{9})(9^{6}) }[/tex]
= [tex]\frac{3^{6} }{9^{15} }[/tex]
Hence, the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]
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Which expressions are equivalent to 25? Choose ALL that apply.
6-6-6-6-6-6
2-6
12-12
2-2-2-2-2-2
4-16
8-8
None of the given expressions are equivalent to 25.
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (operands), variable, operations, units, brackets, punctuation, and groups can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features.
Many writers make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.
The expressions are solved as follows
6-6-6-6-6-6 = -24
2-6 = -4
12-12 = 0
2-2-2-2-2-2 = -8
4-16 = -12
8-8 = 0
Hence, none of the expressions are equivalent to 25.
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anyone have a clue on how to do this?
If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD. If m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°, then the value of m ∠ BGF exists 80°.
What is meant by angles?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The two rays are called the sides of an angle, and the common endpoint is called the vertex.
If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD.
Given: m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°,
m ∠ BGC = m ∠ CGF
7x - 8 = 8x - 8
substracting 2 from both sides of the equation, we get
7x - 8 = 8x - 8 - 8
7x - 8 = 8x
simplifying the above equation, we get
x = 6
Therefore, the value of x = 6.
⇒ m ∠ BGC = m ∠ C G F = 40°
Therefore, the value of m ∠ BGF = 2(40)° = 80°
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