Answer:
y = -0.2x + 4.6
Step-by-step explanation:
We can set up a point-slope form to calculate for the equation:
y - y1 = m (x - x1)
Before we plug the coordinate into the formula, we need m, the slope of L, we know that L is perpendicular to the straight line, and the slope of the straight line is 5:
Perpendicular slope form is: opposite reciprocal of m, which is:
-1/5 or -0.2
Now we plug all the numbers into the previous equation:
y - 5 = -0.2 (x + 2)
y = -0.2 (x + 2) + 5
y = -0.2x + -0.4 + 5
y = -0.2x + 4.6
Now this is a slope-intercept form.
Apply the skills you've learned in the tutorial in
a short project or investigation.
The tutorial feature such as begin thinking about the lesson’s main topic is important part.
What are the multi-step project in tutorial features?The multi-step project is one that can be utilized in leading different kinds of examination and they help in an examination as a lab project.
The student on the creatures and assists us with really taking a look at about the information by giving us similar warm-up questions and furthermore comprise of sorts of the illustration movement.
In this way the response to a short multi-project is a warm-up question.
Therefore, the undertaking incorporates different kinds of exercises and these should be visible in the inquiry, glossary joins, ace tests, and information checks.
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Correct question:
Drag each tutorial feature to its learning purpose.
Tiles
Warm-Up question
Glossary link
Knowledge check
Lesson Activity
Mastery test
Pairs
Begin thinking about the lesson’s
main topic.
arrowBoth
Make sure you’ve met the lesson’s
overall learning objective.
arrowBoth
View the definition of an important
lesson word.
arrowBoth
Do a short, multistep project or
investigation.
arrowBoth
See if you’re getting the main idea
or developing an important skill in
the lesson.
arrowBoth
Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial.
4a-3b+2c and -6a+4b-2c-2
RIGHT SOLUTION GETS BRAINLIST!!!!
Answer:
see below
Step-by-step explanation:
1st polynomial = 4q + 3b + 2c
2nd polynomial= -6a +4b -2c -2
Subtracting 2nd from 1st ,
= 4a -3b +2c - (-6a +4b -2c -2)
= 4a - 3b + 2c +6a -4b +2c +2
group like terms ,
=(6a +4a)-(4b +3b) +(2c+2c)+2
= 10a -7b +4c +2
since the highest degree of any variable is 1 so its degree is 1.
And we are done!
-Rishabh
For a frequency polygon to display the distribution of data accurately, intervals of equal width must be used.
a) Explain why, using examples.
b) Can some of the data be left out of the frequency polygon? Justify your answer.
Answer:
[tex] x 2 + 4x + 4[/tex]
Step-by-step explanation:
yes
The table identifies how many thousands of units of corn and diamonds the united states and congo can produce in one week. Use this data to answer the question that follows. Corn diamonds united states 60 10 congo 20 5 how many thousands of units of corn can congo produce in one week? 5 10 20 60.
the answer to the question of how many thousands of units of corn can Congo produce in one week is 20. In conclusion, Congo can produce number - 20 thousands of units of corn in one week.
The table identifies how many thousands of units of corn and diamonds the united states and congo can produce in one week. The table shows that Congo can produce 20 thousands of units of corn in one week. Therefore, the answer is 20.
The given table provides information on how many thousands of units of corn and diamonds the United States and Congo can produce in one week. According to the table, the United States can produce 60 thousands of units of corn and 10 thousands of units of diamonds. On the other hand, Congo can produce 20 thousands of units of corn and 5 thousands of units of diamonds. Thus,The table identifies how many thousands of units of corn and diamonds the united states and congo can produce in one week. The table shows that Congo can produce number - 20 thousands of units of corn in one week. Therefore, the answer is 20.
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Answer:
C) 20
Step-by-step explanation:
I got it right on the test
Ron has several solar panels on the roof of his garage and plans to add more solar panels to the roof of his house. The total amount of energy his solar panels will produce on a sunny day depends on how many new solar panels Ron adds.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation?
A. ron plans to add 10 new solar panels.
B. each new solar panel will produce 150 watts of energy.
C. each new solar panel will produce 600 watts of energy
D. the solar panels already on the garage produce 600 watts of energy
Answer: the answer is D. The panels already on the garage produce 600 watts of energy
Step-by-step explanation:
any starting energy would be above zero with there already being solar panels! So that leads to a y-intercept! Whatever the line starts at will tell you the amount of energy you get from the starting panels:) I hope this is helpful!
You can rent a car via two options. Option A charges $30 per day plus $0.07 per mile. Option B charges $0 per day, but $0.75 per mile. How many miles must you drive in one day for option A to be cheaper?
For 44.1 miles, the option {A} is cheaper than option {B}.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that you can rent a car via two options. Option A charges $30 per day plus $0.07 per mile. Option B charges $0 per day, but $0.75 per mile
We can write the equations for each case as -
{A} -A(x) = 30 + 0.07x
{B} -B(x) = 0.75x
Now, for option {A} to be cheaper, we can write -
A(x) < B(x)
30 + 0.07x < 0.75x
30 < 0.75x - 0.07x
30 < 0.68x
x > (30/0.68)
x > 44.1 miles
Therefore, for 44.1 miles, the option {A} is cheaper than option {B}.
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each table has 8 seats how many are needed to seat 349 people
Answer:
Step-by-step explanation:
when you divide you get 43. something but you can't have half of a chair so you should get another one making it 44 chairs
if wrong i'm sorry.
Zoey is playing an arcade
game. She needs to earn more
than 850 points to beat its
high score. So far, she has 75
points. She earns 25 points
each time she finishes a level.
Write an inequality to find
the number of levels, L, that
Zoey still needs
to beat to break
the record.
Answer:
31 levels
Step-by-step explanation:
Zoey already has 25 points
So she needs at least 850-25 more points to beat the high score
850-25 = 775
So Zoey needs at least 775 points more
Since she earns 25 points for each level, if she has to play L levels to beat the high score, she will need at least 25L points and that should be greater than or equal to 775
Therefore the inequality is
25L ≥ 775
Dividing by 25 on both sides of the inequality gives:
L ≥ 775/25
which simplifies to L ≥ 31
So Zoey needs at least 31 levels before she can break the record
The point of intersection of all the three altitudes of a triangle is called the? A
A.orthocenter
B.incenter
C.centroid
The point where the triangle's three altitudes connect is known as the orthocentre.
The circumcentre is the center of a triangle's circumcircle. It can be found as the point of intersection of the perpendicular bisectors of the triangle.
The letter H is frequently used to denote the orthocentre.
The kind of triangle determines where the orthocentre is.
The orthocentre will be located inside an acute triangle.
The orthocentre will be outside of an acute triangle.
Finally, the orthocentre will be the vertex at the correct angle if the triangle is right.
Thus, The point where the triangle's three altitudes connect is known as the orthocentre.
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the inequality 4/5 - 1/2 p greater than or equal to 9/5 is given
Which of the following is not a polynomial a) x²+√2x+3 b)x²+√2x+6 c)x³+3x²-3. d)6x+4
x²+√2x+3 and x²+√2x+6 are expressions that are not polynomial. (Option a and Option b)
What is polynomial expression?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.
For the algebraic expression to be called a polynomial, the exponents in the algebraic expression should be non-negative integers. Also if an algebraic expression has a radical in it then it can not be called a polynomial.
a) x²+√2x+3. This expression is not a polynomial as the polynomial expression does not contain any radicals. √2 here is a radical root.
⇒ Hence, option a is not a polynomial expression.
b) x²+√2x+6.This expression is also not a polynomial expression as it has a radical √2 present in the expression.
⇒ Hence, option b is not a polynomial expression.
c) x³+3x²-3. This expression can be termed as a polynomial expression since all of the variables have positive integer exponents.
⇒ Hence, option c is a polynomial expression.
d) 6x+4. This expression is also a polynomial expression as all of the variables have positive integer exponents.
⇒ Hence option d is a polynomial expression.
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What is an equation of the line that passes through the point (-4, 5) and is
perpendicular to the line 4x +y = 72
Submit Answer
attempt 1 out of
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Answer:4(-4)+5=72
Step-by-step explanation:
A cylinder has a radius of 9 inches and a height of 14 inches what is the volume
Answer:
Volume= πr^2h
Step-by-step explanation:
if you plot the values in above given formula
V≈0.058m³
V≈3562.57in³
The sum of the speeds of two trains is 720.4 miles per hour. If the speed of the first train is 9.6 mph faster than that of the second train, find the speeds of each.
The speeds of each train are 355.4 miles per hour and 365 miles per hour
How to find the speeds of each trainFrom the question, we have the following parameters that can be used in our computation:
The sum of the speeds of two trains = 720.4 miles per hour. The speed of the first train = 9.6 mph faster than the second trainThis means that
Train 1 + Train 2 = 720.4
Train 2 = 9.6 + Train 1
Substitute Train 2 = 9.6 + Train 1 in Train 1 + Train 2 = 720.4
Train 1 + 9.6 + Train 1 = 720.4
So, we have
2Train 1 = 710.8
Divide both sides by 2
Train 1 = 355.4
Recall that
Train 2 = 9.6 + Train 1
So, we have
Train 2 = 9.6 + 355.4
Evaluate
Train 2 = 365
Hence, the speeds are 355.4 and 365
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the function of f(x)= x^2 is transformed to obtain function g. the graphs of both functions are shown. determine which transformations took place to produce function g use complete sentences to explain your reasoning
The graph of function g is a reflection of the graph of function f in the x-axis. This means that the transformation that took place to produce function g was a reflection in the x-axis.
What is transformation?Transformation is the process of changing something into a different state or form. It can refer to physical, emotional, spiritual, or psychological changes. It can involve transformation of an object, person, or situation. Transformation is often associated with growth and development and can require significant effort and dedication. Transformation can be used to make positive changes in our lives and ultimately lead to a better future. It is a process of self-discovery and can be a powerful tool for personal growth and development.
This means that for each x-value in function f, the corresponding y-value in function g is the negative of the y-value in function f.
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Given rhombus with diagonal , it follows from the definition of a rhombus that. By the reflexive property of congruence,. So, by the. Since corresponding parts of congruent triangles are congruent, and. So, by the definition of segment bisector bisects and.
The diagonal of a rhombus is a line lump that joins any two non-adjacent apexes of a rhombus.
A rhombus has two diagonals that cut each other at right angles, thus, they form 4 right-angled congruent triangles.
When the opposing vertices of a rhombus are joined, they form the diagonals of a rhombus. A rhombus has two diagonals that oppose each other at 90 degrees. Observe this rhombus to identify its diagonals and their properties listed in the following section.
The diagonals of a rhombus are line segments that are unavoidable between the opposite vertices of the rhombus. The quality of the diagonals of the rhombus are listed below.
The diagonals of a rhombus cut each other at right angles.
The diagonals of a rhombus may not be fundamentally equal.
The two diagonals cleave the rhombus into four congruous right-angled triangles.
The length of the diagonals can be calculated by different methods like using the Pythagoras theorem or by using the area of the rhombus.
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(-7,13); slope=-2 in slope intercept form with given point and slope
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{13})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-7)}) \implies y -13= -2 (x +7) \\\\\\ y-13=-2x-14\implies {\Large \begin{array}{llll} y=-2x-1 \end{array}}[/tex]
Let A and B be nxn matrices. Show that if AB is invertible, then B is invertible. (Note that IMT stands for Invertible Matrix Theorem.) a. Let W be the inverse of AB. Then WAB=B. Therefore we can write B as the product of two invertible matrices Wand AB, and this makes B invertible. The product of two invertible matrices is invertible by Theorem 6 in Section 2.2. b. Since AB is invertible, then (AB)T is invertible by the IMT. Therefore the matrix Bis invertible by part (1) of the IMT. c. Since AB is invertible, this means that A= B-1 and B = A-1 by the IMT. Therefore B is invertible. d. Let W be the inverse of AB. Then WAB=I and (WA)B=l. Therefore, the matrix Bis invertible by part (j) of the IMT by letting C=WA.
Let W be the inverse of AB. Then WAB = I and (WA)B = l. Therefore, matrix B is invertible by part (j) of the IMT by letting C = WA.
We have A and B are two n × n matrices and AB is invertible. We have to prove that B is invertible by showing a valid reason given by one of the four options:
Option (a) False:
The first option is not valid proof. since W is the inverse of A B would imply WAB = I, as multiplying a matrix by its inverse will produce the identity matrix of the corresponding order. Here stated that WAB = B, which is invalid.
Option (b) False:
It is true that AB invertible implies [tex]$(A B)^{\top}$[/tex] is invertible but this does not imply B is invertible (not a valid statement).
Option (c) False:
A B is invertible does not mean [tex]$A=B^{-1}$[/tex]. Since [tex]$A=B^{-1}$[/tex] implies AB = I, but AB need not be only the identity matrix. So these statements are invalid.
Option (d) True:
W being inverse of AB, this gives WAB = I
(WA) B = I since matrix multiplication is associative.
WA is the inverse of B, as multiplying WA by B produces the identity matrix I. Hence, this is valid proof to show that B is invertible.
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How many solutions are there for the trigonometric equation 2cos(x/3) - 1 = 0 between 0 and 2π ?
Answer:
..................................
Which numbers could be solutions to the inequality? −2(−3x+4)−5>−3(x+7)−19
The solution of the inequality −2(−3x+4) − 5 > −3(x+7) − 19 is x > -3.
How to solve inequality?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Therefore, let's solve the inequality as follows:
−2(−3x+4) − 5 > −3(x+7) − 19
let's open the brackets on both sides
−2(−3x+4) − 5 > −3(x+7) − 19
6x - 8 - 5 > -3x - 21 - 19
6x - 13 > -3x - 40
add 13 to both sides of the inequality
6x - 13 > -3x - 40
6x - 13 + 13 > -3x - 40 + 13
6x > -3x - 27
add 3x to both sides of the inequality
6x + 3x > -3x + 3x - 27
9x > -27
divide both sides by 9
x > -27 / 9
Hence,
x > -3
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Given 1 tanx/1 cotx=2, find a numerical value of one trigonometric function of x.
Hence, if one trigonometric function of x is tangent, the value of x is arctan [tex]\frac{1}{\sqrt{5} }[/tex]. We can start solving this equation by isolating one of the trigonometric functions.
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is a fundamental part of geometry, and is also used in other areas such as physics, engineering, and navigation.
Trigonometry functions such as sine, cosine and tangent are used to describe the ratios between the sides of a right angled triangle, These functions are periodic and defined for all real numbers.
Since the tangent and cotangent functions are reciprocals of each other, we can multiply both sides of the equation by the reciprocal of the tangent function:
[tex]\frac{1}{tan(x)}[/tex] = [tex]\frac{1}{2} * \frac{1}{cot(x)}[/tex]
Now we can use the fact that the cotangent function is the reciprocal of the tangent function to write:
[tex]\frac{1}{tan(x)}[/tex] =[tex]\frac{1}{2} * \frac{1}{\frac{1}{tan(x))} }[/tex]
Solving for tan(x) we get:
tan(x) = [tex]\frac{1}{\sqrt{5} }[/tex]
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PLEASE HELP HURRY IM IN A BIG RUSH RN HELPPP
The expression that can be used to calculate the rate per second in which the machine launches the balls is given as follows:
A. 32/4.
What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
As the graph of the function has a constant slope and an intercept of zero, it represents a proportional relationship.
The rate per second is equivalent to the constant of proportionality of the function.
From the graph, when x = 4, y = 32, meaning that the rate can be calculated as follows:
4k = 32
k = 32/4
k = 8.
Meaning that option A is correct.
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Estimate the sum or difference. use the benchmarks, 0 1/2, and 1. 1. 23/40 - 11/30estimate the sum or difference. use the benchmarks, 0 1/2, and 1. 1. 23/40 - 11/30estimate the sum or difference. use the benchmarks, 0 1/2, and 1. 1. 23/40 - 11/30
The Estimated answer is 0.
A benchmark is a whole number or fraction that is easy to use when you estimate. The benchmarks 0, 1/2, and 1 are particularly useful when estimating sums and differences of fractions.
When Numerator value is close to 0 and Denominator value is not close to 0 then the benchmark is 0.
For Examples : 1/2 , 3/16 , 2/25 , 9/100
When Numerator value is about 1 half of denominator value then the benchmark is 1/2.
For Examples : 3/8 , 9/16 , 11/25 , 52/100
When Numerator value and Denominator value are close to each other then the benchmark is 1.
For Examples : 7/8 , 14/16 , 23/25 , 95/100
1/4 ≤ 23/40 ≤ 3/4 so round it to 1/2.
1/4 ≤ 11/30 ≤ 3/4 so round it to 1/2.
Estimating:
1/2 - 1/2 = 0
Therefore, the estimated answer is 0.
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The estimation will be 0
Now, According to the question:
What is estimating in math?
Estimating in math is a way of approximately calculating an answer (getting a ‘rough answer’) to check its accuracy (the ‘right answer’). You shouldn’t need to use a calculator or any written methods when estimating, even with large numbers or decimal numbers.
When Numerator value is close to 0 and Denominator value is not close to 0 then the benchmark is 0.
For Examples : [tex]\frac{1}{2} ,\frac{3}{16},\frac{2}{25},\frac{9}{100}[/tex]
When Numerator value is about 1 half of denominator value then the benchmark is 1/2.
For Examples : [tex]\frac{3}{8} ,\frac{9}{16} , \frac{11}{25} , \frac{52}{100}[/tex]
When Numerator value and Denominator value are close to each other then the benchmark is 1.
For Examples : [tex]\frac{7}{8} , \frac{14}{16} , \frac{23}{25} , \frac{95}{100}[/tex]
1/4 ≤ 23/40 ≤ 3/4 so round it to 1/2.
1/4 ≤ 11/30 ≤ 3/4 so round it to 1/2.
Then, the Estimating:
[tex]\frac{1}{2}-\frac{1}{2}[/tex] = 0
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What is HL congruence example?
HL congruence is the principle that states that two triangles are congruent if they have two sides and the included angle equal. An example of HL congruence is shown below:
Triangle ABC is congruent to triangle DEF because they have two sides, AB and BC, and the included angle, ∠B, equal.
AB = DE
BC = EF
∠B = ∠D
Using HL Congruence to Determine Triangle CongruenceHL congruence is an important concept in geometry that states that two triangles are congruent if they have two sides and the included angle equal. This means that if two triangles have the same lengths for two of their sides, and the angle between those two sides is the same, then the triangles are congruent. This principle is useful in geometry because it allows us to determine whether two triangles are congruent without needing to calculate any other lengths or angles.
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A school ordered 3 large boxes of markers. After giving 15 markers to each of 3 teachers, there were 90 markers left in the box. Draw a diagram and write an equation to represent this situation.
A possible equation to represent the situation described is x (total of markers)= 90 + (15 x 3) and the diagram is attached below.
What is an equation?An equation can be defined as a mathematical expression that shows equality of two mathematical expressions. Due to this, equations include the symbol =.
What is a possible equation in this case?A possible equation to represent this situation is:
x = 90 + (15 x 3)
In this equation:
X = Number of total markers
90 = Number of markers left after the first markers were given to the teachers
15 = Number of markers given to the teachers
3 = Number of teachers
In this way, we know that the total of markers is equivalent to ninety markers plus forty-five markers as fifteen markerts were given to three different teachers.
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d. Explain how the graph would change if the unit
rate was $1.75 per scoop.
e. How would the coordinates of the point in part (a)
change if the unit rate was $1.75 per scoop?
a) The point (4, 6) represent the cost for 4 scoops will be $6.
b) The unit cost will be $1.5.
c) The cost of 12 scoops will be $18.
d) If the unit rate was $1.75 per scoop then the graph will be change.
e) if the unit rate was $1.75 per scoop for the point (4, 6), then the point become (4, 7).
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The graph shows the cost of buying scoops of gelato.
Now,
By the graph we get;
The point (4, 6) represent the cost for 4 scoops will be $6.
And, The cost of 4 scoops = $6
Hence, The unit cost = 6/4
= $1.5
So, The cost of 12 scoops = 12 × $1.5
= $18
Now if the unit rate was $1.75 per scoop then the graph will be change by the unit cost of scoop.
And, if the unit rate was $1.75 per scoop for the point (4, 6).
Then , The cost of 4 scoops = 4 x $1.75
= $7
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The complete question is shown in image.
How do you solve a complex fraction with a whole number?
To solve a complex fraction with a whole number, you will need to first simplify the fraction by dividing the numerator and denominator by the same number.
A complex fraction is a fraction that contains another fraction within its numerator or denominator. To solve a complex fraction with a whole number, you will need to first simplify the fraction. This can be done by dividing the numerator and denominator of the fraction by the same number. Once the fraction has been simplified, you can further reduce the fraction as much as possible by cancelling out common factors. Finally, you can divide the numerator by the denominator of the fraction to find the answer as a whole number. It is important to note that the answer can also be in the form of a mixed number, depending on the result of the division.
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You must first simplify the fraction by dividing the numerator and denominator by the same amount in order to solve a complex fraction with a whole number.
A fraction that includes another fraction in either the numerator or denominator is referred to as a complicated fraction. You must first simplify the complex fraction in order to solve it with a whole number.
To achieve this, divide the fraction's numerator and denominator by the same number. After the fraction has been made simpler, it can be further decreased as much as feasible by removing frequent elements.
To find the solution as a whole number, divide the fraction's numerator by its denominator. It is significant to remember that, depending on how the division turned out, the solution could possibly take the shape of a mixed number.
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Solve using identities
ii. (5x – 6) (5x – 4)
iii. (8m – 3n) (8m + 6n)
iv. (4a – 6) (4a + 6)
v. 98 × 102
vi. 104 × 103
pls give correct answer FOR ALL
Answer:
ii. (5x – 6) (5x – 4)
= 5x(5x - 4) - 6(5x - 4)
= 25x^2 - 20x - 30x + 24
= 25x^2 - 50x + 24
iii. (8m – 3n) (8m + 6n)
= 8m(8m + 6n) - 3n(8m + 6n)
= 64m^2 + 48mn - 24mn - 18n^2
= 64m^2 - 18n^2
iv. (4a – 6) (4a + 6)
= 4a(4a + 6) - 6(4a + 6)
= 16a^2 + 24a - 24a - 36
= 16a^2 - 36
v. 98 × 102
= (100 - 2)(100 + 2)
= 10000 - 400
= 9600
vi. 104 × 103
= (100 + 4)(100 + 3)
= 10000 + 300 + 400 + 12
= 10,712
Step-by-step explanation:
2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles. the top angle of the triangle is (2 x 10) degrees. the bottom right angle of the triangle is 79 degrees. the exterior angle to the bottom left angle is (6 x 1) degrees. what is the value of x?
Where the properties of the triangle are given, by angle sum property the value of x in the expression (2 x + 10) + (6 x + 1) +79 =180 is 11.25
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 °.
2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles.
The top angle of the triangle is (2 x + 10) °. The bottom right angle of the triangle is 79°.
The exterior angle to the bottom left angle is (6 x + 1) °.
By angle sum property
(2 x + 10) + (6 x + 1) +79 =180
8x+11 + 79 =180
8x+11=180-79
8x+11 =101
8x = 90
x = 11.25
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Find the measures of an exterior angle and an interior angle given a regular polygon with 7 sides. Round to the nearest tenth, if necessary.
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=7 \end{cases}\implies 7\theta =180(7-2) \\\\\\ 7\theta =900\implies \theta =\cfrac{900}{7}\implies \theta =128\frac{4}{7}\implies \theta \approx 128.57^o \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underset{in~degrees}{\textit{sum of all exterior angles}}\\\\ n\beta = 360 ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \beta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=7 \end{cases}\implies 7\beta=360 \\\\\\ \beta=\cfrac{360}{7}\implies \beta=51\frac{3}{7}\implies \beta\approx 51.43^o[/tex]
