When given a quadratic function and a line, the points of intersection can be found by solving for x using the Quadratic Formula.
The Quadratic Formula states that:
x² + ax+ b = 0
where the constants are a, b, and c. We utilise this equation to solve for x in order to determine the places of intersection. In order to accomplish this, we must be aware of both the line's slope and the quadratic function's y-intercept.
The slope of the line can be found by dividing the y-intercept by the distance between the points of intersection (x1 and x2), and then multiplying that number by the slope of the line (y/x).
The y-intercept can be found by simply plugging in x1 into the equation above. Once we have these two pieces of information, we can solve for x using algebraic equations.
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3. The circle is circumscribed by the pentagon as shown (not drawn to scale). If QZ = 10, IX = 9, XT = 9, UW = 17, and SU = 10, find the perimeter of the pentagon and show work.
The perimeter of the pentagon is 76 units. The solution is obtained using tangent to circle.
What is tangent to a circle?
A line that touches a circle only once is said to be tangent to it. A point to circle can only have one tangent.
In the figure, the circle is circumscribed by the pentagon.
We are given QZ = 10, YX = 9, WX = 9, UW = 17, and US = 10
VW = WX = 9 (tangent of circle)
So, VU = UW - VW
VU = 17-9= 8
Since, VU and UT are tangents of circle, therefore
UT = 8
US = UT + TS
⇒10 = 8 + TS
⇒TS = 2
Now, TS and SR being tangents, therefore
TS = SR = 2
Also, RQ and QZ are tangents, therefore
RQ = QZ = 10
Similarly, ZY and YX are tangents, therefore
ZY = YX= 9
Thus, Perimeter = SQ + QY + YW + WU + US
⇒Perimeter = SR+ RQ+ QZ+ ZY+ YX+ XW+ UW+ US
⇒Perimeter = 2+ 10+ 10+ 9+ 9+ 9+ 17+ 10
⇒Perimeter = 76 units
Hence, the perimeter of the pentagon is 76 units.
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In triangle ABC, AC = 21, BC = 28, and ∠ACB = 90◦
. The bisector of ∠ACB meets AB at D.
Find the length BD and CD
Sorry don't have image
The length of BD and CD are 15 units and 20 units respectively
How to find the length BD and CD?By the Angle Bisector Theorem, we have:
BD/DC = AC/BC = 21/28
We can use the Pythagorean Theorem to find AC:
AC² + BC² = AB²
21² + 28² = AB²
AB = 35 units
Now we can use the Angle Bisector Theorem to find BD:
BD/DC = 21/28
BD + DC = AB
BD = (21/49) × AB
BD = (21/49) × 35
BD = 15 units
To find CD, we can use the fact that BD + DC = AB:
CD = AB - BD
CD = 35 - 15
CD = 20 units
Therefore, the length are BD = 15 and CD = 20 units.
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What is the square of negative 4?.
Answer:
16
Step-by-step explanation:
Simplify the following:
(-4)^2
(-4)^2 = 16:
Answer: 16
someone help solve this pls
Using SAS, property of triangle congruency, ΔRTV ≅ ΔRTS.
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.
The five congruent triangle theorems are therefore SSS, SAS, AAS, HL, and ASA.
Given,
Two triangles,
ΔRTV and ΔRTS,
RT = RT (Side) [Common side]
∠RTV = ∠RTS (Angle) [Both are 90°]
VT = TS (Side) [As T is the mid - point of VS ]
Using SAS, property of triangle congruency,
ΔRTV ≅ ΔRTS
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A question on a quiz asked students to factor the expression 32m - 24. Ryan and jane's answers are given below. Explain who is correct and why
Answer:
Ryan's answer: 8m - 6
Jane's answer: 4m - 3
Ryan is correct. By factoring out the greatest common factor from the expression, we get:
32m - 24 = (8m - 6) (4m - 2)
Jane's answer 4m-3 is not factor of the given expression.
The expression 32m - 24 can be written as (8m-6)(4m-2) but not as (4m-3)
So Ryan is correct.
Step-by-step explanation:
Alex ran 4 1/2 kilometers in 3/4 of an hour. How many kilometers he ran per hour?
How many kilometers he ran per hour?
Alex ran 6 kilometers per hour.
The ratio can be calculated as follows:
The first is to convert mixed fractions to improper fraction
4 [tex]\frac{1}{2}[/tex] km = [tex]\frac{(4x2)+1}{2}[/tex] km
= [tex]\frac{8+1}{2}[/tex] km
= [tex]\frac{9}{2}[/tex] km
The next step is to compare worth comparison
[tex]\frac{a1}{b1}[/tex] = [tex]\frac{a2}{b2}[/tex]
[tex]a_{1}[/tex] = 4 [tex]\frac{1}{2}[/tex] km = [tex]\frac{9}{2}[/tex] km
[tex]a_{2}[/tex] = X
[tex]b_{1}[/tex] = [tex]\frac{3}{4}[/tex] hour
[tex]b_{2}[/tex] = 1 hour
So,
[tex]\frac{9/2}{3/4}[/tex] = [tex]\frac{X}{1}[/tex]
X = [tex]\frac{(9/2)x1}{3/4}[/tex]
X = [tex]\frac{9/2}{3/4}[/tex]
X = [tex]\frac{9}{2}[/tex] × [tex]\frac{4}{3}[/tex]
X = [tex]\frac{36}{6}[/tex] kilometers
X = 6 kilometers
Alex ran 6 kilometers per hour.
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What is the Y − intercept?.
The equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.
The equation y = 2x - 4 can be written in slope-intercept form as y = 2x + b, where b is the y-intercept. To find the slope and y-intercept of the equation, we need to solve for b.
The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we can set x equal to 0 in the equation to get y = 2(0) - 4. This simplifies to y = -4, so the y-intercept is -4.
The slope is the rate at which the line rises. To find the slope, we can take the coefficient of x, which is 2. So the slope of the equation y = 2x - 4 is 2.
In summary, the slope of the equation y = 2x - 4 is 2 and the y-intercept is -4. We can write the equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.
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complete question : what is the slope and y-intercept of the equation
y = 2x - 4 ?
What is the value of k if the system of equations kx 5y 2 6x 2y 7 has no solution?.
So, the value of k that makes the system of equations kx - 5y = 2, 6x + 2y = 7 has no solution is -1.
A system of linear equations has no solution when the equations are inconsistent, which means that there is no set of values for the variables that would make both equations true at the same time.
In the case of the system of equations kx - 5y = 2, 6x + 2y = 7, we can check for consistency by trying to find a unique solution for the system. We can use different methods such as elimination, substitution or Gaussian elimination.
If we use elimination method, we try to eliminate one of the variable from one equation and substitute it in another equation. By adding the two equations, we get: (k + 6)x = 9, which implies that the value of x is x = 9/(k+6).
Now by substituting this value into the first equation we get k*9/(k+6) - 5y = 2
And we can find the value of y by dividing both sides by -5/1: y = (2*(k+6))/(5*k)
Now if we substitute this value of x and y into the second equation:
6x + 2y = 7
We get: 6*(9/(k+6)) + 2*((2*(k+6))/(5*k)) = 7
And if we simplify this equation we get: 9 + 4/(5*k) = 7(k+6)/(k+6)
And that gives us k = -1, which means the system has no solution.
Therefore, the value of k that makes the system of equations kx - 5y = 2, 6x + 2y = 7 has no solution is -1.
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Hanon opened a aving account and depoited $800. 00 a principal. The account earn 4% interet, compounded annually. What i the balance after 9 year?
Ue the formula A=P1
r
n
nt, where A i the balance (final amount), P i the principal (tarting amount), r i the interet rate expreed a a decimal, n i the number of time per year that the interet i compounded, and t i the time in year. Round your anwer to the nearet cent
The balance after 9 years is $1139.94 rounded to the nearest cent.
The formula to use in this case is A = P(1 + r)^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Given the information in the problem, we know that:
P = $800.00 (the principal or starting amount)
r = 0.04 (the interest rate as a decimal)
n = 1 (the interest is compounded annually)
t = 9 (the number of years)
Plugging these values into the formula, we get:
A = $800.00(1 + 0.04)^9
To solve for A, we need to calculate (1 + 0.04)^9
=1.04^9
=1.041.041.041.041.041.041.041.041.04
=1.424928
A = $800.00*1.424928
A = $1139.94
So the balance after 9 years is $1139.94 rounded to the nearest cent.
Therefore, The balance after 9 years is $1139.94 rounded to the nearest cent.
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A = $800.00(1 + 0.04)^9
To solve for A, we need to calculate (1 + 0.04)^9
=1.04^9
=1.041.041.041.041.041.041.041.041.04
=1.424928
A = $800.00*1.424928
A = $1139.94
Shade the portion of the diagram that illustrates the set. A ∪ B ∩ C
The portion of the diagram that illustrated the set A ∪ B ∩ C is given on the image presented at the end of the answer.
How to shade the set?The union operation, symbolized by U, is composed by the elements that belong to at least one of the sets.
The intersection operation, symbolized by ∩, is composed by the elements that belong to all the sets.
Hence, for the set A ∪ B ∩ C, the requirements are given as follows:
Element belongs to either set A or set B.Element belongs to set C.The shaded region corresponding to the operation is given at the end of the answer.
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Direction:Solve for the meaning term to form equivalent
1)2:3=N:21
2)5:2=20:N
3)2:7=12:N
4)6:7=30:N
5)N:10=15:55
The equation states the ratio of two numbers, where the numerator and denominator can be changed to obtain an equivalent equation. To solve for the meaning term, the numbers in the numerator and denominator must be manipulated to get the same ratio and the value of the meaning term can be found.
1)2:3=N:21
N=21*2/3
N=14
2)5:2=20:N
N=20*5/2
N=50
3)2:7=12:N
N=12*2/7
N=4.57
4)6:7=30:N
N=30*7/6
N=35
5)N:10=15:55
N=15*10/55
N=2.73
The equation states the ratio of two numbers, where the numerator and denominator can be changed to obtain an equivalent equation. To solve for the meaning term, the numbers in the numerator and denominator must be manipulated to get the same ratio. To do this, the numerator and denominator of the first equation can be multiplied or divided by the same number to get the same ratio as the second equation. When the ratio is the same, the meaning term can be found by dividing the numerator of the second equation by the denominator of the first equation. For example, the equation 2:3 = N:21 can be solved by multiplying 3 and 21 by 2, giving 6:42 = N:42, which has the same ratio. The meaning term is then found by dividing 42 by 3, giving N = 14. This process can be applied to all equations to find the meaning term.
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how many words can be formed with pati regardless of the meaning
The number of words that can be formed with PATI is a total of 24 words.
Step by step explanation:Expressed mathematically, we can use the Permutations method.
The Permutation allows us to symbolically express the number of words that we can form and order with just one.
A permutation is defined as the variation of the position of the elements belonging to a given set.
The PATI permutation:
We see how many elements are in the word: 4 elements.
[tex] \: \: \: \: \: \: \: \: \: \: \begin{gathered} \bold{4 ! = 4 \times 3 \times 2 \times 1} \\ \bold{ 4! = 12 \times 2 \times 1 }\\ \bold{4! = 24 \times 1 }\\ \bold{4! = 24}\end{gathered}[/tex]
[tex]\therefore[/tex] The number of words that can be formed with PATI is a total of 24 words.
Bruna i comparing the pay for advertied job. Which 2 way could Bruna find the bet paying job? ( choo 2 anwr)
1. She can look at similar job postings online to compare the salary range offered.
2. She can contact the average employer and ask directly what salary range they offer for the job.
There are two ways Bruna can compare the pay for advertised jobs. First, she can research the salary range of similar job postings. This can be done through job search websites, social networks, and other online resources. She can look at the salary range offered for similar jobs to get an idea of the pay she can expect from an employer.
The second way she can find out the best paying job for her is to ask the employer directly about the salary range. She can contact the employer and ask directly what salary range they offer for the job. This will give her an accurate picture of the salary range that the employer is offering, so she can make an informed decision on which job to apply for. By using these two methods, Bruna can compare the pay for advertised jobs and find the one that offers the best salary.
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What are the 4 conditions of a binomial distribution?.
The four conditions of a binomial distribution are: independence, normality, symmetry, and rarity.
Independence: Each trial in a binomial distribution is independent of the other trials, meaning that the outcome of one trial does not affect the outcome of any other trial.
Normality: The distribution of the data follows a normal distribution, meaning that it is bell-shaped and symmetrical.
Symmetry: The binomial distribution is symmetrical around the mean, meaning that the probability of the outcome being above the mean is the same as the probability of the outcome being below the mean.
Rarity: The binomial distribution is characterized by rare events, meaning that the probability of an event occurring is relatively low. This is because the outcomes of each trial are determined by a random process.
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*URGENT*
I’ve been doing this problem over and over but i have a feeling i’m wrong, please help!!
[tex]\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m[/tex]
Is this function linear, quadratic, or exponential?
X 2 3 4 5 6 Y 40 90 160 250 360
Answer:
Step-by-step explanation:
It is Linear
Trigonometric Ratios
Answer:Hi there the answer is in quizlet is another page :) flashcards TRIGONOMETRIC RATIOS
What is one more then 12?.
The answer of 1 more than 12 is 13.
The answer of 1 more than 12 is 13 which can be derived using simple mathematical calculations.
To find 1 more than 12, you can add 1 to the original number 12.
1 + 12 = 13
It's a simple arithmetic operation where you add a specific number, in this case 1, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 1 more than 12 is 13.
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What is the equation of the linear relationship in slope-intercept form?
Answer:
y = 10x + 20.
Step-by-step explanation:
Slope of the line = (60-30) / (4 - 1)
= 30/3
= 10
y-intercept = 20
Formula is y = mx + c where m = slope and c = y-intercept
So, the answer is y = 10x + 20.
a popsicle tray has 6 cone-shaped popsicle molds. each popsicle mold has a diameter of 5.4 cm and a height of 12.9 cm. how many cubic centimeters will one tray hold
One tray will hold 590.877 cubic centimeters.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
We have to find the volume of a cone-shaped popsicle mold and then multiply it with 6 to find the required answer.
Volume of a cone = [tex]\frac{1}{3}[/tex] π r² h
Given,
Diameter = 5.4 cm
Radius = Diameter / 2 = 5.4 / 2 = 2.7 cm
Height = 12.9 cm
Volume of the cone = [tex]\frac{1}{3}[/tex] π × (2.7)² × 12.9
= [tex]\frac{1}{3}[/tex] π × 94.041
= 98.4795
Total volume of 6 molds in the tray = 98.4795 × 6
= 590.877 cubic centimeters
Hence the volume of the molds that the tray hold is 590.877 cubic centimeters.
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What percent of the 8th graders estimated they spend less than an hour a day on social media? Round your answer to the nearest whole number percent.
43% of eighth graders claim to spend more than an hour every day on social media.
What is the percentage?A ratio written as a fraction of 100 is what is referred to as a percentage.
Students were asked in a survey if they thought they used social media more or less than an hour every day.
Added to Less
7th 12 14
8th 20 26
The number of students who responded "more" must be divided by the total number of 8th-grade students polled, and the result must then be multiplied by 100 to get the percentage of students who said they spend more than an hour a day on social media.
20 out of 46 students (20+26) responded "more," or roughly 43.48%.
As a result, 43% of eighth graders believe they spend more than an hour every day on social media.
The Complete Question.
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What is the mirror image of (- 2 3 on Y axis?.
As per the given coordinates (-2, 3), the mirror image is (2,3)
In math the term coordinate is defined as a set of values which helps to show the exact position of a point in the coordinate plane.
Here we have given the coordinates as (-2,3) and we need to find the mirror image on y axis.
The general term for the mirror image on y axis is written as,
=> (x, y) = (-x, y)
Which the rule defines that the sign of x coordinate is changed when we calculate the mirror image on y axis.
Therefore here we have to change the sign of x coordinate that is -2, then we get the mirror image as,
=> (-2,3) = (2,3)
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45% of 1 hour expressed in minutes
Answer:
27 minutes
Step-by-step explanation:
Convert 45% to a fraction
45% = 45/100 = 9/20 (divide numerator and denominator by 5)
1 hour = 60 minutes
45% of 1 hour = 9/20 x 60 = 27 minutes
Do parallel equations have no solution?.
The equation pair cannot be solved if the lines are parallel.
Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). When the graphs cross at a particular point, a system of linear equations has a single solution.
When the graphs are parallel, an equation system with linear components cannot be solved. The graphs of a system of linear equations have an infinite number of solutions. The lines must connect since the slopes differ. The system of equations that the lines represent has just one solution since the lines intersect at a specific place.
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Alyson deposits $500 in the bank for 12 years. The bank offers her a 4% interest rate compounded annually. How much money will be in her account at the
end of the 12 years? (Remember to round your answer to the nearest cent.)
Answer:
$800.516
Step-by-step explanation:
We use the equation
A = P(1 + [tex]\frac{r}{n}[/tex])^nt
P = principal
r = rate of interest
t = times
Now let's solve
P = $500
r = 4% = 0.04
t = 12 years
A = $500(1 + [tex]\frac{0.04}{12}[/tex] ) ^12 = $800.516
PLEASE TELL ME WHAT ONES TO PUT INSIDE THE BOXES
Eric is adding water to a 60
-gallons pool.
The pool already has 12
gallons of water, and he wants to fill it to at least 27
gallons. The water flows at a rate of 6
gallons per minute.
How many minutes, x
, will it take for Eric to fill the pool with at least 27
gallons of water?
Inequality that represents this situation:
27≤12+6x
To solve the inequality, you can begin by solving the equation as shown.
Drag a diagram to each row of the table to show which number line represents all of the solutions for the inequality and which number line represents all of the solutions for the problem situation.
All possible solutions for the inequalities are from 2.5 to infinity.
Option F is the correct answer.
All possible solutions for the problem situation are 2.5 to 8.
Option D is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
27 ≤ 12 + 6x
Solve for x.
27 - 12 ≤ 6x
15 ≤ 6x
x ≥ 15/6
x ≥ 5/2
x ≥ 2.5
This means,
x values can be 2.5 and more.
Now,
For x = 8,
12 + 6 x 8
= 12 + 48
= 60 gallons (possible)
For x = 9,
12 + 6 x 9
= 12 + 54
= 66 gallons (not possible)
Since the maximum gallon the pool can contain is 60 gallons.
Thus,
All possible solutions for the inequalities are from 2.5 to infinity.
All possible solutions for the problem situation are 2.5 to 8.
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\sqrt{8}\cdot\sqrt{6}
The value of the expression is 4√3
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, [tex]\sqrt{8}\cdot\sqrt{6}[/tex]
On solving we get
[tex]\sqrt{8}\cdot \sqrt{6}= \sqrt{48\\} \\=\sqrt{48} \\\\= \sqrt{16.3} \\\\=4 \sqrt{3}[/tex]
Hence, the value of the expression is 4√3
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What is the type of polynomial 2x2 3x 9 expressing area of the garden?.
The expression 2x2 3x 9 area of the garden is a quadratic polynomial.
2x2 contains a power value and 3x contains the constant x and 9 is the integer so this is the Quadratic Polynomial. When a variable term in the polynomial expression has a highest power of 2, the polynomial is said to be quadratic.
Only the exponent of the variable is taken into account when determining a polynomial's degree. It is not taken into account how strong a coefficient or constant term is.
A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0. The roots or zeros of the quadratic equation are the name given to the solutions of such an equation.
The capability to derive a number of significant inferences from the analysis of the discriminant is an additional advantage of this approach.
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Full Question: What is the type of polynomial 2x^2-3x-9 expressing area of the garden?
(a) linear polynomial
(b)Quadratic polynomial
(c) cubic polynomial
(d) constant polynomial
Evaluate 0.5^3 and 0.5^-3 as fraction
Answer:
To evaluate 0.5^3 and 0.5^-3 as fractions, you can use the Decimal to Fraction Calculator. 0.5^3 is equal to 1/8 and 0.5^-3 is equal to 8/1. your welcome
Answer:
1/8 and 8.
Step-by-step explanation:
0.5^3
= (1/2)^3
= 1/ 2^3
= 1/8.
0.5^-3
= 1 /0.5^3
= 1 / 1/8
= 8.
Find m/G.
F
150°
H
G
The measure of angle G is 121 degrees and this can be determined by using the sum of interior angle properties.
What is sum of interior angles?
Sum of interior angles is calculated using the formula (n 2) 180, where is the total number of sides. In a regular polygon, each inside angle is the same. Interior angle of a polygon is equal to the sum of interior angles divided by the number of sides, according to the following formula. One of the first things we all learned about triangles was that the sum of the internal angles is 180 degrees.
Given :
Triangle FHG
Angle F = (x - 5) degreesAngle G = (3x + 25) degreesAngle H = (x) degreesApplying the sum of interior angles property on the triangle FHG. According to the sum of interior angles property:
[tex]$$\angle \mathrm{F}+\angle \mathrm{H}+\angle \mathrm{G}=180^{\circ}$$[/tex]
Now, substitute the values of the known terms in the above equation.
[tex]$$(x-5)+(x)+(3 x+25)=180$$[/tex]
Simplify the above equation In order to determine the value of ' $x$ '.
[tex]& 5 x+20=180 \\[/tex]
[tex]& 5 x=160 \\[/tex]
[tex]& \mathbf{x}=\mathbf{3 2} \text { degrees }[/tex]
So the angle[tex]$\mathbf{G}$[/tex] is given by:
[tex]& \angle \mathrm{G}=3(32)+25 \\[/tex]
[tex]& \angle \mathrm{G}=121^{\circ}[/tex]
The complete question is,
What is m∠G ?
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