If the sum of the interior angle measures of a polygon with n sides is 2280 degrees, find n.
Please Help Me!!
Answers
Final answer:
Using the sum of the interior angles formula for a polygon, S = (n - 2) x 180 degrees, and substituting the provided sum of 2280 degrees, it is calculated that the polygon has 14 sides.
Explanation:
To solve for the number of sides n in a polygon given the sum of the interior angles, we use the formula:
S = (n - 2) × 180°
where S is the sum of the interior angles in degrees. Given that the sum of the interior angles S is 2280 degrees, we can set up the equation:
2280 = (n - 2) × 180
Divide both sides of the equation by 180:
2280 ÷ 180 = n - 2
12 = n - 2
Now, add 2 to both sides of the equation to find n:
n = 12 + 2
n = 14
So, the polygon has 14 sides.
Related Questions
a triangle has two sides of lenghts 7 and 12 what value could the length of the third side be check all that apply
Answers
12-7 = 5
12+7 = 19
Third length can be only in this range
5Means the third length must be greater than 5 and less than 19.
Hope this helps!
Answer:
Third length =
12-7 = 5
12+7 = 19
Third length can be only in this range
5Means the third length must be greater than 5 and less than 19.
Step-by-step explanation:
What is the greatest common factor of 8m, 36m3, and 12
Answers
ANSWER
GCF=4
EXPLANATION
The given monomials are:
[tex]8m = {2}^{3} m[/tex]
[tex]36 {m}^{3} = {2}^{2} \times {3}^{2} {m}^{3} [/tex]
[tex]12 = {2}^{2} \times 3[/tex]
The greatest common factor is the product of all the least powers of the common factors.
We can see that:
[tex] {2}^{2} [/tex]
is the common to all the factors.
Therefore the greatest common factor is
[tex] {2}^{2} = 4[/tex]
Answer: [tex]GCF=4[/tex]
Step-by-step explanation:
To find the Greatest Common Factor (GCF) of 8m, 36m³, and 12, you need to descompose them into their prime factors. Then:
[tex]8m=2*2*2*m=2^3*m\\\\36m^3=2*2*3*3*m^3=2^2*3^2*m^3\\\\12=2*2*3=2^2*3[/tex]
You can observe that the common factor with the lowest exponent is the following:
[tex]2^2[/tex]
Therefore, the Greatest Common Factor (GCF) of 8m, 36m³, and 12 is:
[tex]GCF=2^2\\GCF=4[/tex]
After you rewrite subtraction as addition of the
additive inverse, how can the like terms be
grouped?
[3a2 + (-3a2)] + (-5ab + 8ab) + [b2 + (-2b2)]
[3a2 + (-3a2)] + (-5ab + 8ab) + (b2 + 262)
© (3a2 + 3a2) + (-5ab + (-8ab)] + [b2 + (-262)]
(3a2 + 3a2) + (-5ab + (-262)] + [b2 + (-8ab)]
Answers
Answer:
(3a2 + 3a2) + [–5ab + (–8ab)] + [b2 + (–2b2)]
Step-by-step explanation:
Answer: c. (3a^2+3a^2)+[-5ab+(-8ab)]+[b^2+(-2b^2)]
for the second part: =a. 6a^2-13ab-b^2
Step-by-step explanation:
i did it
What is an equation bof the line that is perpendicular to y-4=2(x-6);and passes through the point (-3,-5)
Answers
Answer:
y+5=-1/2(x+3)
Step-by-step explanation:
as perpendicular,
compare that given eqn with y-y1=m(x-x1),
m1=2
then,
perpendicular case,
m1×m2=-1
m2=-1/2
now,
as the eqn passes through point (-3,-5),
we know,
y-y1=m(x-x1)
then putting value,
y+5=-1/2(x+3)
Answer:
y + 5 = - [tex]\frac{1}{2}[/tex](x + 3)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line.
y - 4 = 2(x - 6) is in this form with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
Hence the equation passing through (- 3, - 5) is
y - (- 5) = - [tex]\frac{1}2}[/tex] (x - (- 3)), that is
y + 5 = - [tex]\frac{1}{2}[/tex](x + 3) ← equation of perpendicular line
For f(x)=x-14 and g(x)=x^2+14 find (fog)(x). A. x^2+x B. x^2-28x+210 C. x^2 D. x^3-14x^2+14x
Answers
Answer:
C
Step-by-step explanation:
To evaluate (f ￮ g)(x)
Substitute x = g(x) into f(x)
f(x² + 14) = x² + 14 - 14 = x² → C
The value of (fog)(x) = x^2. So, option C is correct.
How to solve a composite function?The functions f(x) and g(x) are composite functions then,
(fog)(x) = f(g(x)).
Substitute g(x) in place of x in the function f(x).Simplify the equation.Calculation:Given that,
f(x) = x - 14
g(x) = [tex]x^2+14[/tex]
Then,
(fog)(x) = f(g(x))
= ([tex]x^2+14[/tex]) - 14
= x² + 14 - 14
= x²
Therefore, the value of (fog)(x) = x².
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Find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9).Find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9).
Answers
The midpoint of the line segment with endpoints (-2, 5) and (4, -9) is found using the midpoint formula and is (1, -2).
Explanation:To find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9), you use the midpoint formula, which is derived from finding the average of the x-coordinates and the y-coordinates of the endpoints respectively.
The midpoint formula is:
( (x1 + x2) / 2, (y1 + y2) / 2 )
Plugging in our given endpoints (-2, 5) and (4, -9) into the formula, it becomes:
( (-2 + 4) / 2, (5 + (-9)) / 2 )
This simplifies to:
( 2 / 2, -4 / 2 )
And finally:
( 1, -2 )
Therefore, the midpoint of the line segment is at coordinates (1, -2).
Could you guys help me answer these two questions
Answers
Answer:
1. C. Jana
2. I. Matthew and Jake
Maggie needs to spend at least six hours each week practicing the piano. She has already practiced 3
hours this week. She wants to split the remaining
practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours she needs to practice on each of
the two days
Answers
Final answer:
Maggie needs to practice at least 1.5 hours on each of the two remaining days.
Explanation:
To determine the minimum number of hours Maggie needs to practice on each of the two remaining days, we can set up an inequality based on the given information. Maggie needs to spend at least six hours each week practicing the piano, and she has already practiced three hours. Let's let x represent the number of hours she needs to practice on each of the remaining two days. The inequality can be written as:
3 + 2x ≥ 6
Solving for x, we subtract 3 from both sides of the inequality:
2x ≥ 3
Then, we divide both sides by 2 to solve for x:
x ≥ 1.5
Therefore, Maggie needs to practice at least 1.5 hours on each of the two remaining days.
Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.
Let x equal the number of hours Maggie practices each of the last two days. Since she Needs to practice at least 6 hours per week, and she already practiced 3 hours this week, she must practice for at least 6 - 3 = 3 more hours.
Splitting this time evenly between the two days means she practices x hours each day.
This can be expressed in the following inequality: [tex]$x + x \geq 3$[/tex] which combines the information about the minimum number of hours needed and the fact that she splits the remaining time evenly.
Simplifying the left side of the inequality gives [tex]$2x \geq 3$[/tex]. Dividing both sides by 2 gives [tex]$x \geq \dfrac{3}{2}$[/tex].
Thus, Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.
Suppose the first equation in a system of two linear equations is 12x + 7y = 25. The second equation being which of these will cause the system to have no solution?
A.
12x + 7y = 20
B.
12x + 7y = 25
C.
12x + 9y = 20
D.
12x + 9y = 25
Answers
Answer:
A. 12x + 7y = 20
Step-by-step explanation:
Obviously, 12x + 7y cannot both be equivalent to unique [different] quantities.
Option A (12x + 7y = 20) would make the system of linear equations with 12x + 7y = 25 have no solution because the lines would be parallel and never intersect.
Second equation would make a system of linear equations with 12x + 7y = 25 have no solution. A system of linear equations will have no solution if the two lines represented by the equations are parallel, which means they have the same slope but different y-intercepts. Since the first equation is 12x + 7y = 25, we need a second equation with the same coefficients for x and y but a different constant term in order to represent parallel lines.
Option A (12x + 7y = 20) meets the criteria for causing the system to have no solution because it has the same coefficients for x and y as the first equation but a different constant term. This indicates that the lines are parallel and will never intersect, hence no solution exists for this pair of equations.
What is the y-intercept of a line that has a slope of –3 and passes through point (–5, 4)?
–17
–11
7
19
Answers
The y-intercept of a line that has a slope of –3 and passes through point (–5, 4) is -11.
What is the slope-intercept form of a line?The slope-intercept of a line is
[tex](y-y_{1})=m(x-x_{1})[/tex]
Here, [tex](x_{1},y_{1})[/tex] is the point through which the line passes and 'm' is the slope of the line.
Given, the line has a slope of –3 and passes through point (–5, 4).
Therefore, [tex](y-4)=-3[x-(-5)][/tex]
⇒ [tex](y-4)= -3(x+5)[/tex]
⇒ [tex](y-4)= -3x-15[/tex]
⇒ [tex]3x+y = -11[/tex]
⇒ [tex]y = -3x-11[/tex]
Comparing it with the standard form of equation, we get:
the y-intercept of the required line is -11.
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If $190 is invested at an interest rate of 11% per year and is compounded continuously, how much will the investment be worth in 4 years? Use the continuous compound interest formula: A = Pert.
Answers
Answer:
295.01
Step-by-step explanation:
Use A = Pe^(rt)
$294.88 is the worth of the investment after 4 years.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that $190 is invested at an interest rate of 11% per year and compounded continuously.
We need to find the worth of the investment after 4 years.
[tex]A=Pe^{rt}[/tex]
A is the final amount
p is the principal amount
r is the rate of interest
t is the time.
[tex]A=190e^{0.11(4)}[/tex]
[tex]A=190e^{0.44}[/tex]
A=190×1.552
A=294.88
Hence, $294.88 is the worth of the investment after 4 years.
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how much would it be worth in 5, 10, 20 years
Answers
Answer:
$675
$850
$1200
Step-by-step explanation:
Use formula for simple interest:
A = P (1+rt)
where
A = accrued amount (principal + interest) = what we want to find
P = Principal (initial) amount = Given as $500
r = rate of interest = Given as 7% = 0.07
t = time
For 5 years, t = 5
A = 500 [ 1 + 0.07(5) ] = $675
For 10 years, t = 10
A = 500 [ 1 + 0.07(10) ] = $850
For 20 years, t = 20
A = 500 [ 1 + 0.07(20) ] = $1200
Match the vocabulary word with the correct definition.
1. trapezoid
A trapezoid with legs of the same length.
2. bases of a trapezoid
A quadrilateral with at least one pair of parallel sides.
3. legs of a trapezoid
The parallel sides.
4. median of a trapezoid
The segment connecting the midpoints of the legs.
5. isosceles trapezoid
The nonparallel sides
Answers
Answer:
1. trapezoid
A quadrilateral with at least one pair of parallel sides.
2. bases of a trapezoid
The parallel sides
3. legs of a trapezoid
The nonparallel sides.
4. median of a trapezoid
The segment connecting the midpoints of the legs.
5. isosceles trapezoid
A trapezoid with legs of the same length.
Answer:
Trapezoid:A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, when the trapezoid as equal legs, it's called an isosceles trapezoid.
Bases of a trapezoid:The bases of a trapezoid are the pair of parallel sides, both of them are called base, the longer one is the major base, and the shorter one is the minor base.
Legs of a trapezoid:The legs of a trapezoid are the nonparallel sides, because if they were parallel, that wouldn't be a trapezoid, it would be another quadrilateral.
Median of a trapezoid:The median of a trapezoid is a segment that connects the midpoints of the legs. Remember that medians are always line that intercept midpoints.
Isosceles trapezoid:As we said before, an isosceles trapezoid are those which have legs with equal legs. The name isosceles refers to equality.
Therefore, the right matches are
1. Trapezoid: A quadrilateral with at least one pair of parallel sides.
2. Bases of a trapezoid: The parallel sides.
3. Legs of a trapezoid: The nonparallel sides.
4. Median of a trapezoid: The segment connecting the midpoints of the legs.
5. Isosceles trapezoid: A trapezoid with legs of the same length.
Write an expression for the missing value in
the table.
Tom’s Age Kim’s Age
10 13
11 14
12 15
a ?
A a + 1 C a + 3
B a + 15 D a + 10
Answers
10 + 3 = 13
11 + 3 = 14
12 + 3 = 15
a + 3 = ?
Answer:
C) a+3
Step-by-step explanation:
We are given the following data:
Tom's Age: 10 11 12 a
Kim's Age: 13 14 15
We have to evaluate Kim's age when Tom's age is a.
We have to build a relationship between Tim's age and Kim's age. If we look at their ages carefully we can see a pattern and their relation can be described as:
[tex]\text{Kim's age = Tim's age + 3}[/tex]
Thus, when Tim's age is a, we can compute Kim's age as:
[tex]\text{Kim's age = a + 3}[/tex]
Highly appreciated if someone help me with this question
Answers
Answer:
C
Step-by-step explanation:
B and D are equal. You could call their sum = 2x
a = 25 degrees (Vertically Opposite Angles)
C = 95 degrees. (Vertically Opposite Angles)
The total is 360 degrees. So let's add everything up and see what we get.
a+b+c + 25 + d + 95 = 360 degrees. Substitute for the known letters.
25 + x + 95 + 25 + x + 95 = 360 Combine like terms on the left
50 + 2x + 95 + 95 = 360 Combine numbers on the left
240 + 2x = 360 Subtract 240 on both sides
240 - 240 + 2x = 360 - 240 Combine
2x = 120 Divide by 2
x = 60
b = 60
a = 25
a + b =60 + 25 = 85
which congruency theorem can be used to prove that triangle abd is congruent to triangle dca
Answers
Answer:
SAS
Step-by-step explanation:
we know that
Triangles are congruent by SAS, if any pair of corresponding sides and their included angles are equal in both triangles
so
In this problem
we have that
the pair of corresponding sides AB with DC and AD with DA and their included angles ∠ BAD with ∠CDA are equal
therefore
Triangle ABD is congruent with triangle DCA by SAS congruency theorem
Answer:
sas
Step-by-step explanation:
i just did the assignment. please mark me brainliest!!!!!
What is the slope of a line is parallel to y = (1/2)x+ 3?
Answer here
Answers
Answer:1/2
Step-by-step explanation:
the slope of a line in an equation comes before x
since we know parallel lines have the same slope it is 1/2
Which calculator correctly shows the quotient of
6.47 x 10-15
3.36 * 10-29
Answers
Answer:
the second one
Step-by-step explanation:
Answer:
the second one
Step-by-step explanation:
the one that says +14
Find the LCM of each pair of numbers 6 and 10
Answers
Answer:
LCM = 30
Step-by-step explanation:
Please mark brainliest and have a great day!
SHORT ANSWER Use the Distributive
Property to write a numerical
expression that is equivalent to
25 + 10.
Answers
Answer:
5(5 + 2)
Step-by-step explanation:
The distributive property states that If 2 numbers have a common factor you can divide the common factor out. Similarily, if they share a common factor, you can distribute the common factor into each number in the parenthesis.
Find the factors of 25 & 10:
25: 1, 5, 25
10: 1, 2, 5, 10
Note that the largest common factor is 5. Divide 5 from both number:
(25 + 10)/5 = 5(5 + 2)
5(5 + 2) is your answer.
~
PLEASE HURRY. 55P WRONG ANSWERS GET REMOVED!!!!!!!
Answers
1172. 08 in²
Step-by-step explanation:Hi there !
A(prism) = 2(lw + lh + wh) - Ab(cylinder)
= 2(16*11 + 16*11 + 11*11) - πr²
= 2(176 + 176 + 121) - 3.14*16
= 2*473 - 50.4
= 946 - 50.24
= 895.76 in²
A(cylinder) = πr² + 2πr*h
= 3.14*16 + 2*3.14*4*9
= 50.24 + 226.08
= 276.32 in²
A(total) = 895.76in² + 276.32in² = 1172.08 in²
Good luck !
At the end of the year, a library reported 32 books lost or stolen and 24 books were sent out for repair. If the library originally had 1,219 books, how many were left on the shelves or in circulation?
A. 1,219
B. 1,187
C. 1,163
D. 1,275
Answers
there were D. 1163 books left on the shelves or in circulation.
///////////////////////////////////////////////////////////////////////////
let us count the number of books that are NOT on the shelves now.
1st step: 32 + 24 = 56
2nd step: the total number of books minus the amount of books that are damaged or out: 1,219 - 56 = 1163
Answer:
C. 1,163
Step-by-step explanation:
Total books = books on shelves + books lost + books out for repair
What do we know
1219 = books on shelves + 32 + 24
1219 = books on selves + 56
Subtract 56 from each side
1219-56 = books on shelves - 56
1163 = books on shelves
A circle is centered at the point (5, -4) and passes through the point (-3, 2).
The equation of this circle is
Answers
Answer:
[tex](x-5)^{2} +(y+4)^{2} =10^{2}[/tex]
Step-by-step explanation:
To calculate the formula of a circle that is not in the center fo the graph, you need two things, the point where the cirlce is centered and any point in the circumference, and with this you can calculate the radius, to calculate the first part you just need the next formula:
[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]
Where [tex]x^{c}y^{c}[/tex] are the x and y where the center of the circle is, so you just evaluate with the values you are given:
[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]
[tex](x-(5))+(y-(-4))=r^{2}[/tex]
[tex](x-5)+(y+4)=r^{2}[/tex]
Now that you have the first part, we can calculate the radius, remember taht the radius of any given circumference in the graph is the hypotenuse of the X´s and Y´s that are part of those two points given, so we just calculate it like any hypotenuse:
[tex]c=\sqrt{x^{2}+ y^{2} }[/tex]
To calculate this we would rest to the point in the circumference, the center of the circumference, like this:
[tex]c=\sqrt{(x^{2}-x^{1})^{2}+ (y^{2}-y^{1})^{2} }[/tex]
[tex]c=\sqrt{(-3-5)^{2}+ (2-(-4))^{2} }[/tex]
[tex]c=\sqrt{(-8)^{2}+ (6)^{2} }[/tex]
[tex]c=\sqrt{64+ 36 }[/tex]
[tex]c=\sqrt{100 }[/tex]
[tex]c=10[/tex]
So your radius would be 10, now we just put that into our previous formula:
[tex](x-5)+(y+4)=r^{2}[/tex]
[tex](x-5)+(y+4)=10^{2}[/tex]
So the formula for the circle that is centered at (5,-4) and passes through the point (-3,2) would be:
[tex](x-5)+(y+4)=10^{2}[/tex]
HELP PLEASE RIGHT AWAY! WILL GIVE BRAINLIEST AND BECOME FRIENDS :)
Answers
Answer:
iii) P=65h
iv) P=70h
Step-by-step explanation:
Payment of First day = $300
Number of hours = 5
Payment per hour = $60
Payment of First day = $240
Number of hours = 4
Payment per hour = $60
Payment of First day = $360
Number of hours = 6
Payment per hour = $60
Hence the rate of Payment for an hour is $60
Hence the rates
P=65h
and
P=70h
are more than the rate of payment made to labor.
An athletic coach conducted an experiment to test whether a four week strength training program will reduce the number of muscular injuries that occur during athletic events. The coach randomly selected 30 athletes from several sports and assigned 15 athletes to a four week strength training program. The remaining 15 athletes did not participate in any type of strength training program during the four weeks of the program. After the program was completed, the coach monitored each of the 30 athletes for five athletic events. At the end of this process, he reported that the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program. What can be concluded from the coach's report? A. There is not enough information to make any conclusions regarding the coach's report. B. It can be concluded that the strength training program does not reduce the number of muscular injuries that occur during an athletic event. C. It can be concluded that the strength training program increases the number of muscular injuries that occur during an athletic event. D. It can be concluded that the strength training program reduces the number of muscular injuries that occur during an athletic event.
Answers
Answer: B. It can be concluded that the strength training program does not reduce the number of muscular injuries that occur during an athletic event.
Step-by-step explanation: In the question it states the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program.
From the coach's report, it can be concluded that the strength training program does not reduce the number of muscular injuries that occur during athletic events. This conclusion is drawn from the experiment's finding that both participants in the training program and those who did not participated had the same average number of injuries.
Explanation:The student's question concerns the effectiveness of a strength training program in reducing the number of muscular injuries during athletic events. The coach conducted an experiment with 30 athletes, where half participated in a strength training program and the other half did not. After both groups were monitored for five athletic events, it was found that the average number of muscular injuries was the same for both groups. Hence, from the given information, the correct conclusion would be:
B. It can be concluded that the strength training program does not reduce the number of muscular injuries that occur during an athletic event.It's important to note that this conclusion does not necessarily imply that strength training is ineffective in all contexts, just that in this specific experiment, it did not lead to a reduction in injuries. Further, the conclusion does not indicate that the strength training program increases injuries, which eliminates option C. Meanwhile, option D is also incorrect because the data indicates no reduction in injuries.
Use the converse of the side-splitter theorem to determine
if TU || Rs. Which statement is true?
Answers
Answer:
Line segment TU is parallel to line segment RS because 32/36 = 40/45.
Step-by-step explanation:
The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The converse theorem states that if TU || RS, then the ratio of the corresponding sides will be constant.
32 / 36 = 40 / 45 = 8 / 9 = constant
The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.
Then the correct option is A.
The graph is given below.
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Help !!! Thank you guys !
Answers
Answer:
d
Step-by-step explanation:
what is the slope of the line that passing through point (2,3) and (-2,5)?
Answers
Answer:
[tex]\displaystyle \boxed{-\frac{1}{2}}[/tex]
Step-by-step explanation:
Slope formula:
↓
[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}[/tex]
[tex]\displaystyle Y_2=5\\\displaystyle Y_1=3\\\displaystyle X_2=(-2)\\\displaystyle X_1=2\\[/tex]
[tex]\displaystyle \frac{5-3}{(-2)-2}=\frac{2}{-4}=\frac{2\div2}{-4\div2}=\frac{1}{-2}=-\frac{1}{2}[/tex]
Therefore the slope is -1/2.
-1/2 is the correct answer.
Hope this helps!
29. A circle has a diameter of 16 inches.
What is the circumference of the
circle rounded to the nearest
hundredth? Use 3.14 for pi
A 50.24 inches
B 100.48 inches
C 200.96 inches
D 803.84 inches
Answers
Answer:
answer is A
Step-by-step explanation:
The formula for circumference of a circle using diameter is pi times "d". "d" means diameter. 3.14 x 16= 50.24
C = pi•d
C = 3.14(16)
C = 50.24 inches
What is the largest fraction in each group?
5/6 29/36
Answers
Answer:
5/6 is larger
Step-by-step explanation:
5/6 * (6/6) = 30/36
30/36 > 29/36
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