Answer:
B) The maximum y-value of f(x) approaches 2
C) g(x) has the largest possible y-value
Step-by-step explanation:
f(x)=-5^x+2
f(x) is an exponential function.
Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞
Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→
Lim x→ -∞ f(x) = 2
Then the maximun y-value of f(x) approaches 2
g(x)=-5x^2+2
g(x) is a quadratic function. The graph is a parabola
g(x)=ax^2+bx+c
a=-5<0, the parabola opens downward and has a maximum value at
x=-b/(2a)
b=0
c=2
x=-0/2(-5)
x=0/10
x=0
The maximum value is at x=0:
g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2
The maximum value of g(x) is 2
answer quickly please il give brainliest
Answer:
Second Option is the correct answer 3/2
Step-by-step explanation:
Tangent of an angle in a triangle is given by Perpendicular of that triangle / Base of that triangle , with resoect to angle in consideration.
Tangent Ratio for angle B = Perpendicular / Base
Tangent Ratio for angle B = AC / BC
Tangent Ratio for angle B = 3/2
Hope it helps.
Thank you.
The formula Q=MCT where Q=heat flow M=mass, C specfic heat, and T change of temperature is used to calculate heat flow Solve this formula for t
Answer:
q/mc=t
Step-by-step explanation:
q=mct
q/mc=t
Answer:
The formula for t is [tex]T=\frac{Q}{MC}[/tex]
Step-by-step explanation:
Consider the provide formula.
[tex]Q=MCT[/tex]
Where Q=heat flow M=mass, C specific heat, and T is the change of temperature is used to calculate heat flow.
We need to solve the above formula for T.
Divide both the sides by MC.
[tex]\frac{Q}{MC}=\frac{MCT}{MC}[/tex]
[tex]\frac{Q}{MC}=T[/tex]
[tex]T=\frac{Q}{MC}[/tex]
Hence, the formula for t is [tex]T=\frac{Q}{MC}[/tex]
can someone help wil mark brainest if u can help and show work please help if u can
Answer:
-24>Step-by-step explanation:
1. You can use a calculator if your knowledge of arithmetic fails you.
... 98 +17 +37 -176 = 152 -176 = -24
___
2. -37/8 = -(32 +5)/8 = -4 5/8 = -4.625
This number is on the left side of zero on the number line, but is slightly closer to zero than -4.63, so is "greater than" -4.63.
In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈CM and a line AP intersecting BC at point Q. Find the lengths of segments CQ and BQ, if P divides CM into CP:PM=1:2.
Answer:
CQ = 2.4 cmBQ = 9.6 cmStep-by-step explanation:
This development is ugly, but it works.
Let area ΔABC = 6a. Then area ΔAMC = 3a, and area ΔAPC = a. Similarly, area ΔBMC = 3a, and area ΔBPC = a.
Let area ΔCPQ = x. Then ...
... area ΔACQ = area ΔAPC + area ΔCPQ
... area ΔACQ = a + x
Define k such that BQ : CQ = k : 1. Then ...
... area ΔBPQ + area ΔCPQ = area ΔBPC
... kx + x = a = (k +1)x
The division of BC into parts of ratio k : 1 means ...
... area ΔABQ = k × area ΔACQ
... area ΔABQ + area ΔACQ = area ΔABC
... k × area ΔACQ + area ΔACQ = area ΔABC
... (k +1)(x +a) = 6a . . . . . . . area ΔACQ = x+a
... (k +1)x +(k +1)a = 6a . . . . . distributive property
... a + (k +1)a = 6a
... k +2 = 6 . . . . . . . . . . . . . . . divide by a, simplify
... k = 4
Now, we know BQ : CQ = 4 : 1, so ...
... BQ = 4/5 × 12 cm = 9.6 cm
... CQ = 1/5 × 12 cm = 2.4 cm
The function y = –16t2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.
Question 7 options:
0.25 seconds
5.51 seconds
11.02 seconds
7.79 seconds
5.51 seconds
Step-by-step explanation:y = 0 when the stone hits the ground. At that point, t can be found from ...
... 0 = -16t^2 +486
... 0 = t^2 -30.375 . . . . divide by -16
... 30.375 = t^2 . . . . . . add the opposite of the constant
Take the square root to get ...
... √30.375 = t ≈ 5.51 . . . . seconds
How many no real complex roots does the polynomial f (x) = x^4 - x^2- 12 have?
A. 0
B. 1
C. 2
D. 3
E. 4
f(x) factors as ...
... f(x) = (x² -4)(x² +3) = (x -2)(x +2)(x² +3)
The real roots are x = ±2.
The complex roots are x = ±i√3.
___
We don't know what "no real complex roots" means. We suspect your answer may be C. 2.
The Shop and Save is starting their annual clearance and the store has sent out to all their customers a coupon book offering a variety of savings on their products. The LCD television that you have wanted was reduced by 35% prior to the annual clearance. In addition, the coupon book has a 10% off coupon for the LCD television. Determine what you would pay after applying the discounts given that the price of the LCD television was $1,325. Round your answer to the nearest cent.
a. $728.75
c. $596.25
b. $775.13
d. $46.38
Answer:
A
Step-by-step explanation:
First discount is the original price reduced by 35% prior to the annual clearance.
So, 35% of 1325 = 0.35 × 1325 = 463.75.
After the discount of $463.75, the price that remains = 1,325 - 463.75 = $861.25.
Then, additional disount of 10%.
10% of $1,325. = 0.10 × 1,325. = 132.50
The final price after discount of 10% = 861.25 - 132.50. = 728.75.
Round to the nearest cent, we get 728.75.
Therefore, you would pay $ 728.75 after applying the discounts.
Answer:
B. 775.13
Step-by-step explanation:
Edge says A was wrong.
What is the perimeter, in feet, of the polygon?
You are given the length of every side, except for two, that can be easily derived from the others:
The long horizontal side on top is the sum of the three beneath it, so it is [tex] 22+18+14=54 [/tex]The vertical one on the right is, similarly, the sum of the opposite side to the far left, and the two small sides near it: [tex] 15+5+5=25 [/tex]The sum of all sides, including these two, will give you the perimeter of the polygon.
The perimeter of the polygon is determined as P = 210 feet.
Given data:
The polygon of the perimeter is the total side length of all the sides of the polygon.
Let the perimeter be represented as P.
From the attached figure of the polygon:
P = ( 15 + 22 + 10 + 18 + 10 + 14 + 5 + 16 + ( 15 + 5 + 5 ) + 16 + 5 + ( 14 + 18 + 22 )
On simplifying the equation:
P = 210 feet
So, the value of P is 210 feet.
Hence, the perimeter is 210 feet.
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Parker and Company pays Selma Stokes on a variable commission scale. In a month when Selma had net sales of $155,000, what was her Gross Pay based on the following scale?
Net Sales Commission Rate
Up to $40,000 5%
Excess of $40,000 to $75,000 5.5%
Excess of $75,000 to $100,000 6%
More than $100,000 7%
Answer:
$9275
Step-by-step explanation:
Selma earns 5% on the first $40,000, which is $2000.
She earns 5.5% on the next $35,000, which is $1925.
She earns 6% on the next $25,000, which is $1500.
And she earns 7% on the last $55,000 (the amount over 100,000), which is $3850.
Altogether, Selma's commission is ...
... $2000 +1925 +1500 +3850 = $9275.
_____
Comment on the sliding scale
Each of the segments of this sliding scale could be rewritten to simplify its computation. For example, for amounts above $100,000, the formula could be either of ...
7% of the amount over $22,5007% of sales, less $1575.A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below.
Plan A: 27 text, 21 Internet
Plan B: 13 text, 10 Internet
Answer the questions to determine a conditional probability.
How many customers are on payment plan B?
____ customers
How many of the customers on plan B text?
____ customers
What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
_____
Answer:
23 are on plan B13 on plan B text13/23 is the probability a customer on plan B will textStep-by-step explanation:
Assuming the categorization is mutually exclusive (customers either text or internet, but not both), the total number of Plan B customers in the sample is the sum of those in each category:
.... 13 + 10 = 23 . . . . plan B customers
The problem statement tells you
... 23 plan B customers text
Since 13 out of 23 customers surveyed use the phone for text, the empirical probability that a plan B customer will use the phone for texting is ...
... 13/23 . . . . probability that text is used most
There are 23 customers are on payment plan B.
There are 13 customers who are on plan B text.
The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
Given
A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet.
They sort the data by payment plans, as shown below.
Plan A: 27 texts, 21 Internet
Plan B: 13 texts, 10 Internet
What is probability?The probability is defined as the ratio of the sum of all observations and the total number of observations.
The total number of observation is;
= 13 +10 = 23
1. How many customers are on payment plan B?
There are 23 customers are on payment plan B.
2. How many of the customers are on plan B text?
There are 13 customers who are on plan B text.
3. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text?
[tex]\rm Probability = \dfrac{Customer \ plan \ B}{Total \ number \ of \ customers}\\\\Probability = \dfrac{13}{23}[/tex]
The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
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Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side BC at point M. What is the length of MC?
16 mm
24 mm
32 mm
48 mm
Answer:
16 mm
Step-by-step explanation:
Since ABC is an equilateral triangle, all three sides are the same length. The perimeter is found by adding together all of these equal sides; letting x represent the length of a side of the triangle, this gives us
x + x + x = 96
Combining like terms,
3x = 96
Dividing both sides by 3,
3x/3 = 96/3
x = 32
Since AM is a perpendicular bisector, it splits BC into two congruent sections. This means the length of MC, half of BC, will be 32/2 = 16.
Option (B) is correct which is 24 mm
Step 1:
Find the length of each side.
Let the side be a,
3×a = 96mm
⇒ a = 96/3
⇒ a = 32 mm
Step 2:
Length of MC = length of BC/2 (As AM is a perpendicular bisector)
⇒ MC = 32/2 = 16 mm
Step 3:
Now, in the triangle, AMC, using Pythagoras theorem,
AC² = MC² + AM²
⇒ (32)² = MC² + (16)²
After solving,
⇒ MC = 16√3 = 27.77 mm
This is closest to option (B) which is 24 mm
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please help i will give brainliest
For this case, we have that by definition:
Let "x" be an angle of any vertex of a right triangle.
[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]
So, if we want to find the tangent of angle A:
[tex]tangent (A) = \frac {6} {8}[/tex]
Thus, the tangent of angle "A" is [tex]\frac {6} {8}[/tex]
Answer:
[tex]\frac {6} {8}[/tex]
Option b
I need help on this. The portrait studio can buy photographs on canvas. The small canvas photograph print is $20 and the large canvas photograph is $45. The studio wants to sell twice as many small prints as large prints. The studio also has to make at least $510 total to cover the costs of printing. How many of each type does the studio need to sell?
Numerical Reasoning
Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...
... 2×$20 +45 = $85
To have revenue of at least $510, the studio must sell ...
... $510/$85 = 6
sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.
_____
With an equation
Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...
... 20·2x +45·x ≥ 510
... 85x ≥ 510
... x ≥ 510/85
... x ≥ 6
The studio needs to sell at least 6 large prints and 12 small prints.
find the value of both missing side ( not just y)
y = 10(√3)/3
unnamed side = 5(√3)/3
Step-by-step explanation:Side ratios in a 30°-60°-90° triangle are 1 : √3 : 2.
Multiplying these by 5/√3 gives ...
... unnamed side : 5 : y = 5/√3 : 5 : 10/√3
Then ...
... unnamed side = 5/√3 = 5(√3)/3
... y = 10/√3 = 10(√3)/3
Which transformation maps the strip pattern onto itself pdpd
half-turn
Step-by-step explanation:There is a point of rotational symmetry at the center of the pattern. Thus, turning it 180° (a half-turn) will map it to itself.
_____
Comment on other choices
Any sort of reflection will change it to bqbqbqbqbq. Translation puts its somewhere else, not on top of itself.
Answer:
A half turn reversal of direction (as in a staircase) either by one 180-degree turn or two right-angle turns
Step-by-step explanation:
Hope this helps :) -Mark Brainiest Please :)
In the 9th and 10th grades at Jefferson High School, there are 236 students. Of thoes students, 121 are in 9th grade, Of the 214 students who are right- handed, 103 of them are in 10th grade.
Total -
Right-handed: 214! Left-handed: 22!
Total of students: 236 students
I hope this helped! :D
Step-by-step explanation:
9th Grade: Right Handed: 111! Left Handed: 10!
10 Grade: Right Handed: 103! Left Handed: 22!
Add left handed for both grades. Add right handed for both grades. And add total numbers.
I hope this helped :D
There are 121 students in 9th grade and 115 students in 10th grade at Jefferson High School.
Explanation:This question involves counting and analyzing data about grade levels and handedness of students at Jefferson High School. To answer the question, we need to use the given information:
- There are 236 students in 9th and 10th grades combined.
- Out of these, 121 students are in 9th grade.
- Among the 214 right-handed students, 103 are in 10th grade.
We can use these numbers to find out how many students are in each grade level.
Let's denote the number of 9th-grade students as 'x' and 10th-grade students as 'y'.
From the given information:
x + y = 236 (total number of students)
x = 121 (number of 9th-grade students)
y = 103 (number of 10th-grade students)
To find the value of 'y', we can substitute the given value of 'x' into the first equation:
121 + y = 236
y = 236 - 121
y = 115
Therefore, there are 121 students in 9th grade and 115 students in 10th grade.
What is the measure of angle N to the nearest whole degree?
Answer:
9°
Step-by-step explanation:
You can make use of any of the trigonometric ratios to determine N, or you can let your calculator tell you what it is by solving the triangle.
SOH CAH TOA reminds you that
... sin(N) = 13/85 . . . . N = arcsin(13/85)
... cos(N) = 84/85 . . . N = arccos(84/85)
... tan(N) = 13/84 . . . . N = arctan(13/84)
all will tell you N ≈ 8.79741° ≈ 9°
_____
If you use inverse functions on your calculator, be sure it is in degrees mode.
The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of y when x = 5?
The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of x when y = 21?
Which equation represents a proportional relationship?
y=−x
y=−5(x+1)
y = 5x + 1
y=15x
Answer:
y= 35/2 when x=5
x=6 when y =21
Proportinal relatiionships: y=−x , y=15x
Step-by-step explanation:
The formula for direct variation is
y= kx
If y=7 and x=2, we can solve for k
7 =k*2
Divide by 2
7/2 =k
y =7/2 x
Now if x=5
y =7/2 * 5
y =35/2
Now if y=21
21 =7/2 * x
Multiply by 2/7
21 * 2/7 = 7/2 * 2/7 x
6 =x
Which equation represents a proportional relationship?
y=−x
YES k = -1 Some people debate about having a negative constant, but everything I have read and taught says you can have a negative constant.
y=−5(x+1)
This does not go through the origin so no
if x=0 y = -5
y = 5x + 1
if x = 0 y =1 so no
y=15x
YES k = 15
Answer:
17.5
i just did it on my quiz and it was wrong(the other guy is wrong)
The angle measure of a triangle are 2x + 5 degrees, 6x - 5 degrees, and 7x degrees. What is each angle measure
DAY 15: The measures of the angles in a certain triangle are in the ratio 1: 5: 6. Find the measure of the smallest angle.
x +5x +6x=180
12x =180
x=15º
DAY 16: In triangle ABC, the measure of angle A = 7x - 32, the measure of angle B = 3x + 4, and the exterior angle at C has measure 12 (x - 5). Find the value of x.
exterior angle = sum of two remote (other) interiors
7x -32 +3x+4 =12(x-5)
10x -28 =12x -60
32-2x
x=16
DAY 17: Find the slope of the line perpendicular to the line through the points (21, 11) and (-4, -12).
11 - -12 / 21 - -4 =23/25
slope of perpendicular line is negative reciprocal =
-25/23 ( no 17!)
DAY 18: In a certain triangle, the largest angle is 6 times the smallest. The third angle is 18 less than 4 times the smallest. What is the measure of the smallest angle?
x= smallest
6x =largest
third angle =4x-18
x+6x +4x-18 =180
11x =198
x=18º
Just number 9 not the other one please help
Answer:
I do believe the answer is C
Step-by-step explanation:
.004 / .0004 =
Answer:
c 10
Step-by-step explanation:
If we want to know how much bigger object A is than object B is we take object A and divide it by object B
object A 4 * 10^-3
----------- = -------------
Object B 4 * 10 ^-4
When dividing exponents with the same base
We can subtract them. The numbers out front get divided
4/4 * 10 ^ (-3- -4)
1 * 10 ^(-3+4)
1 * 10 ^1
10
Which of the following is defined by distinct lines which intersect at right angles and at exactly one point
What type of function is this ? 15 points
Answer:
quadratic polynomialminimum at (1, -9)decreasing on (-1, 1)Step-by-step explanation:
1. First differences in the y-values are ...
... -5-0 = -5; -8-(-5) = -3; -9-(-8) = -1; -8-(-9) = 1; -5-(-8) = 3; 0-(-5) = 5
Second differences are ...
... -3-(-5) = 2; -1-(-3) = 2; 1-(-1) = 2; 3-1 = 2; 5-3 = 2
These 2nd differences are constant, so the points can be described by a 2nd-degree polynomial.
2. Values on the graph range from 0 to a low of -9 and back up to 0. There is a minimum at (1, -9).
3. The value at x=-1 is -5; at x=1, it is -9, which is less than -5. The function is decreasing on the interval -1 to 1.
In the figure below, TRS = RTU and SR = UT. Which of the following triangle congruence criteria proves that TRS = RTU
HELLP MMMEEE PLZ
Answer:
B. side-angle-side
Step-by-step explanation:
You are given that side SR matches its counterpart; angle SRT matches its counterpart; and you know side ST matches its counterpart, because they are the same segment.
Hence, you have two matching sides and the angle between them. This set of side-angle-side lets you invoke the theorem that matches that name.
What is a quartic polynomial function in standard form with zeros -2,4,4,and 3
We can simply multiply the roots together to find the original function.
(x + 2)(x - 4)(x - 4)(x - 3)
FOIL.
x^2 - 4x + 2x - 8(x - 4)(x - 3)
Combine like terms.
x^2 - 2x - 8(x - 4)(x - 3)
FOIL.
x^3 - 2x^2 - 8x - 4x^2 + 8x + 32(x - 3)
Combine like terms.
x^3 - 6x^2 + 32(x - 3)
FOIL.
x^4 - 6x^3 + 32x - 3x^3 + 18x^2 - 96
Combine like terms.
x^4 - 9x^3 + 18x^2 + 32x - 96 is the original function with the given roots.A quartic polynomial function with roots at -2,4,4,and 3 can be written in standard form as f(x) = (x + 2) * (x - 4)^2 * (x - 3)
Explanation:A quartic polynomial function is a function of the fourth degree. Its general form is f (x) = ax^4 + bx^3 + cx^2 + dx+ e, where a, b, c, d, and e are constants, and a ≠ 0. Given the roots or zeros of the function (-2,4,4,3), we can construct the quartic polynomial function.
The quartic polynomial with roots r1, r2, r3, r4 is represented by: f(x) = a(x - r1)(x - r2)(x - r3)(x - r4). The roots of your polynomial function are -2, 4, 4, and 3. So, we substitute those roots into the equation:
f(x) = a(x - (-2)) * (x - 4) * (x - 4) * (x - 3). We may choose the leading coefficient a to be 1 (a ≠ 0) for simplicity's sake. Thus, the quartic polynomial function in standard form with zeros -2,4,4, and 3 is:
f(x) = (x + 2) * (x - 4)^2 * (x - 3)
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If f(x) is a third degree polynomial function and g(x) = f(2x) + 2, which of the following must be true?
f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(x) and g(x) have the same number of zeros.
f(0) = g(0) – 2
Answer:
Choice D) which is f(0) = g(0) - 2
Step-by-step explanation:
Plug x = 0 into the g(x) function to find that....
g(x) = f(2*x) + 2
g(0) = f(2*0) + 2 .... replace every x with 0
g(0) = f(0) + 2
g(0) - 2 = f(0) + 2 - 2 .... subtract 2 from both sides
g(0) - 2 = f(0)
f(0) = g(0) - 2
Can someone please answer this for me.
Answer:
See picture
Step-by-step explanation:
The rule is ...
[tex]x^{m/n}=\sqrt[n]{x^m}[/tex]
The index of the surd becomes the denominator of the exponents inside.
Answer:
x^(5/3)*y^(1/3)
Step-by-step explanation:
note (a*b)^c = a^c*b^c
the given expression can be rewritten as (x^5*y)^1/3
=x^(5/3)*y^(1/3)
ans is the 2nd choice
Find the value of the variable for which the value of the expression –3(2x+1) is 20 greater than the value of the expression 8x+5
-2
Step-by-step explanation:20 greater than 8x +5 is ...
... 8x +5 +20 = 8x +25
We want this value to be -3(2x +1), so we want to solve the equation ...
... 8x +25 = -3(2x +1)
... 8x +25 = -6x -3 . . . . . . eliminate parentheses
... 14x = -28 . . . . . . . . . . . add 6x-25
... x = -2 . . . . . . . . . . . . . . divide by the coefficient of x
The desired value of the variable is -2.
_____
Check
-3(2x+1) = -3(2(-2)+1) = -3(-3) = 9
8x+5 = 8(-2) +5 = -11
9 is 20 greater than -11, so the answer checks OK.
Answer:
X = -2
Step-by-step explanation:
There are 650 visitors to an art gallery on Friday. There are 10% more visitors on Saturday than on Friday. How many visitors are there on Saturday?
Answer:
10% of 650 visitors is:
650 visitors* (10/100)= 65 visitors.
650 visitors+ 65 visitors= 715 visitors.
There are 715 visitors on Saturday
Step-by-step explanation:
Ans7wer:
715 people
Step-by-step explanation:
650÷100=6.5
6.5X10=65
650+65=715
find an equation with vertical asymptotes 1 and 4 and horizontal asymptote 1 please help
Answer:
y = 1 + 1/((x -1)(x -4))
Step-by-step explanation:
To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.
To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.
Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.
... y = 1 + 1/((x -1)(x -4))
If you like, this can be "simplified" to ...
... y = (x² -5x +5)/(x² -5x +4)
_____
In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).
Could someone help me with these please!?
Answer:
7. The sum of the measures of the interior angles of this polygon is 900°.
8. The sum of the measures of the interior angles of this polygon is 540°.
9. The polygon has 10 sides.
10. The polygon has 5 sides.
Step-by-step explanation:
7. Vertices: A, B, C, D, E, F and G
Number of vertices: n=7
Sum of the measures of the interior angles of the polygon: S=?
S=180°(n-2)
Substituting n by 7 in the formula above:
S=180°(7-2)
S=180°(5)
S=900°
8. Vertices: A, B, C, D and E
Number of vertices: n=5
Sum of the measures of the interior angles of the polygon: S=?
S=180°(n-2)
Substituting n by 5 in the formula above:
S=180°(5-2)
S=180°(3)
S=540°
9. Each interior angle of a regular polygon (i) measures 144°:
i=144°
How many sides does the polygon have?
n=?
i=180°(n-2)/n
Substituting i by 144° in the formula above:
144°=180°(n-2)/n
Solving for n: Cross multiplication:
144°n=180°(n-2)
Eliminating the parentheses on the right side of the equation applying the distributive property:
144°n=180°(n)-180°(2)
Multiplying
144°n=180°n-360°
Grouping n's on the right side of the equation: Subtracting 144°n both sides of the equation:
144°n-144°n=180°n-360°-144°n
Subtracting:
0=36°n-360°
Adding 360° both sides of the equation:
0+360°=36°n-360°+360°
Adding:
360°=36°n
Dividing both sides of the equation by 36°:
360°/36°=36°n/36°
10=n
n=10
The polygon has 10 sides.
10. Each interior angle of a regular polygon (i) measures 108°:
i=108°
How many sides does the polygon have?
n=?
i=180°(n-2)/n
Substituting i by 108° in the formula above:
108°=180°(n-2)/n
Solving for n: Cross multiplication:
108°n=180°(n-2)
Eliminating the parentheses on the right side of the equation applying the distributive property:
108°n=180°(n)-180°(2)
Multiplying
108°n=180°n-360°
Grouping n's on the right side of the equation: Subtracting 108°n both sides of the equation:
108°n-108°n=180°n-360°-108°n
Subtracting:
0=72°n-360°
Adding 360° both sides of the equation:
0+360°=72°n-360°+360°
Adding:
360°=72°n
Dividing both sides of the equation by 72°:
360°/72°=36°n/72°
5=n
n=5
The polygon has 5 sides.