If a regular polygon has interior angles each measuring 165 degrees, the polygon has 24 sides. This is calculated by using the formula to find the number of sides in a regular polygon, given the angle size.
Explanation:To find out how many sides a regular polygon has, based on the size of its interior angles, you can use the formula to calculate the sum of the interior angles of a polygon:
n
= 180(
n
- 2), where
n
is the number of sides.
However, this formula gives the sum of the interior angles as a whole. Since, in a regular polygon, all angles are equal, you can then divide this sum by the known size of each angle.
So the specific formula to calculate the number of sides of a regular polygon, given the angle size, is:
n
= 360 / (180 -
angle size
).
In this case, you can substitute the angle size of 165 degrees into this formula:
n
= 360 / (180 - 165) = 360 / 15 = 24.
So a regular polygon with interior angles each measuring 165 degrees has 24 sides.
Learn more about Regular Polygon here:https://brainly.com/question/18179471
#SPJ2
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
13.4 units
17.9 units
26.8 units
40.0 units
see the attached figure to better understand the problem
Let
x------> the length side of a rectangle
y-------> the width side of a rectangle
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
in this problem
[tex]AB=DC=x[/tex]
[tex]AD=BC=y[/tex]
Step 1
Find the distance AB
[tex]A(-6,4)\\B(2,8)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(8-4)^{2} +(2+6)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2} +(8)^{2}}[/tex]
[tex]dAB=\sqrt{80}\ units[/tex]
Step 2
Find the distance BC
tex]B(2,8)\\C(4,4)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(4-8)^{2} +(4-2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2} +(2)^{2}}[/tex]
[tex]dBC=\sqrt{20}\ units[/tex]
Step 3
Find the perimeter
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
[tex]P=2AB+2BC[/tex]
we have
[tex]dAB=\sqrt{80}\ units=8.9\ units[/tex]
[tex]dBC=\sqrt{20}\ units=4.5\ units[/tex]
substitute the values of the distance in the formula
[tex]P=2*8.9+2*4.5=26.8\ units[/tex]
therefore
the answer is
The perimeter of the rectangle is equal to [tex]26.8\ units[/tex]
How many possible outcomes exist when four fair coins are flipped
Answer: 16
Step-by-step explanation:
The number of outcomes exist , when a coin is flipped (tails , head) = 2
The number of possible outcomes , when 'n' number of coins are flipped :_
[tex]2^n[/tex]
For n= 4, the number of possible outcomes , when four coins are flipped :_
[tex]2^4=2\times2\times2\times2=16[/tex]
Hence, the possible outcomes exist when four fair coins are flipped = 16
Only four countries have not officially adopted the metric system
True or false?
Answer:
true
Step-by-step explanation:
Please Help!!!
In isosceles triangle ∆ABC with base
BC
draw the median
AM
. Find AM, if the perimeter of ∆ABC is 32 cm and perimeter of ∆ABM is 24 cm.
A pizza shop makes a profit of $1.50 for each small pizza and $2.15 for each large pizza. On a typical Friday, it sells between 70 and 90 small pizzas and between 100 and 140 large pizzas. The shop can make no more than 210 pizzas in a day. How many of each size pizza must be sold in order to maximize profit?
The pizza shop should sell 70 small pizzas and 140 large pizzas to maximize profit.
What is a linear equation in two variables?A linear equation in two variables is an algebraic equation of degree one in two variables generally in x and y.
As there is no condition for how much time is required to make one small and one large pizza and by making large pizza the shop makes more profit.
∴ Pizza shops should make the least amount of small pizzas in the given range which is 70 and the most amount of large pizzas in the given range which is 140.
So, the profit of the pizza shop will be = 1.50(70) + 2.15(140) dollars.
= (105 + 301) dollars.
= 406 dollars.
learn more about linear equations here :
https://brainly.com/question/24085666
#SPJ2
PLEASE HELP
Write the linear inequality shown in the graph. The gray area represents the shaded region.
y ≤ –3x + 5
y ≥ –3x + 5
y ≥ –3x – 5
y ≤ –3x – 5
Answer:
[tex]y\leq-3x+5[/tex]
Step-by-step explanation:
we know that
The solution of the inequality is the shaded area below the solid line (the gray area)
The slope of the solid line is negative
The y-intercept of the solid line is positive
The equation of the solid line is equal to [tex]y=-3x+5[/tex]
therefore
the equation of the inequality is equal to
[tex]y\leq-3x+5[/tex]
Identify the polynomial written in ascending order. (1 point) 8x3+ 2x2− 6x − 11 2x2− 11 + 8x3− 6x −6x + 8x3− 11 + 2x2 −11 − 6x + 2x2+ 8x3
The polynomial which is written in ascending order is:
[tex]-11-6x+2x^2+8x^3[/tex]
Step-by-step explanation:To write the polynomial in ascending order means to write it in the increasing powers of x.
Here the polynomial which is written in ascending order is:
[tex]-11-6x+2x^2+8x^3[/tex]
because the first term i.e. -11 is a term with power 0 of x.The second term i.e. -6x is a term with power 1 of x.The third term i.e. 2x² is a term with power 2 of x.The last term i.e. 8x³ is a term with power 3 of x.What are the zeros of f left parenthesis x right parenthesis equals x cubed minus 57 x plus 56 ?
Which of the following is important in a two-column proof?
A.) a list of all theorems
B.) staircase Logic
C.) order
D.) detailed explanations for each step
Identify the property demonstrated.
4(3 + 5) = 4 • 3 + 4 • 5
The distributive property demonstrated.
4(3 + 5) = 4 • 3 + 4 • 5
What is distributive property?This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.
Given:
Expression,
4(3 + 5) = 4 • 3 + 4 • 5
Here,
we take LHS,
4(3 + 5)
= 4 x 3 + 4 x 5
= 12 + 20
= 32
We take RHS,
4 • 3 + 4 • 5
= 12 + 20
32.
So, this property is distributive property.
To learn more about the distributive property;
https://brainly.com/question/6276874;
#SPJ2
What is the solution to 2x^2+x+2=0 ??
Answer:
[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]
Step-by-step explanation:
[tex]2x^2+x+2=0[/tex]
Apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=2, b= 1, c=2
Plug in the value in the quadratic formula
[tex]x=\frac{-1+-\sqrt{1^2-4(2)(2)}}{2(2)}[/tex]
[tex]x=\frac{-1+-\sqrt{-15}}{4}[/tex]
Square root of -1 is 'i'
[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]
The solution of the given quadratic equation is,
x = [-1±i√15]/4
Hence option 3rd is correct.
The given quadratic equation is,
2x²+x+2=0
Here we can see that it is of the form of ax² + bx + c = 0.
Since we know that
The quadrature formula for ax² + bx + c = 0 is
⇒ x = [-b±√(b²- 4ac)]/2a
Here we have,
a = 2
b = 1
c = 2
Put these value in quadrature formula we get,
⇒ x = [-1±√(1²- 4x2x1)]/2x2
= [-1±√(1- 16)]/4
= [-1±√(-15)]/4
Since we know that, i = √-1
Therefore,
⇒ x = [-1±i√15]/4
To learn more about quadratic equation visit:
https://brainly.com/question/30098550
#SPJ6
What is the value of g?
−5+7g=3g+9 Please, i need this answer ASAP, Thanks.
the answer to your question is g=3 1/2
For women at hartford college, times to run 400 meters are normally distributed with a mean of 84 seconds and a standard deviation of 7 seconds. what percentage of the times are more than 91 seconds? more than 63 seconds?
Approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.
To find the percentage of times that are more than 91 seconds and more than 63 seconds, we can use the properties of a normal distribution and the standard normal distribution table (also known as the z-table).
Given:
Mean (μ) = 84 seconds
Standard deviation (σ) = 7 seconds
1. Probability of times more than 91 seconds:
First, we need to find the z-score for the value 91 seconds:
[tex]\(z = \frac{X - \mu}{\sigma} = \frac{91 - 84}{7} = \frac{7}{7} = 1\)[/tex]
Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = 1\)[/tex]. The z-table provides the percentage of values below a given z-score, so we need to find the complement (1 - percentage) to get the percentage of values above [tex]\(z = 1\).[/tex]
From the z-table, the area to the right of [tex]\(z = 1\)[/tex] is approximately 0.1587.
So, the percentage of times more than 91 seconds is [tex]\(1 - 0.1587 = 0.8413\)[/tex] or 84.13%.
2. Probability of times more than 63 seconds:
Similarly, we need to find the z-score for the value 63 seconds:
[tex]\(z = \frac{X - \mu}{\sigma} = \frac{63 - 84}{7} = \frac{-21}{7} = -3\)[/tex]
Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = -3\)[/tex]. Again, we need to find the complement to get the percentage of values above [tex]\(z = -3\).[/tex]
From the z-table, the area to the right of [tex]\(z = -3\)[/tex] is approximately 0.9987.
So, the percentage of times more than 63 seconds is [tex]\(1 - 0.9987 = 0.0013\)[/tex] or 0.13%.
Therefore, approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.
To know more about time:
https://brainly.com/question/13932039
#SPJ2
Find the Least Common Multiple of of these two monomials:
15x^2y^8z^5 and 6x^4y^3z^9
30x^4y^8z^9
3x^2y^3z^5
3x^4y^8z^9
30x^6y^11z^14
LCM of 15 & 6 = 30
then take the highest exponent for each variable
answer is:
30x^4y^8z^9
EXPERTS ONLY!! Ill mark as brainlist!
Write the equation of a vertical line that passes through the point (–4, 4).
A. y = 4
B. x = 4
C. y = -4
D. x = -4
IT COST 859.32 TO HAVE A SCHOOL DANCE A. HOW MANY TICKETS MUST BE SOLD TO COVER THE COST. B HOW MANY TICKETS MUST BE SOLD TO MAKE A 980.68 PROFIT
a. At least 108 tickets must be sold to cover the cost.
b. To make a $980.68 profit, 230 tickets must be sold.
To solve this problem, let's break it down step by step:
a. To cover the cost of $859.32, we need to find out how many tickets need to be sold at $8 each.
Let's denote:
C = total cost of the dance
T = number of tickets sold
P = price per ticket
Given:
C = $859.32
P = $8
We can use the formula: Cost = Number of tickets * Price per ticket
So, we have:
859.32 = T * 8
To find T, divide both sides by 8:
T = 859.32 / 8
T = 107.415
Since we can't sell a fraction of a ticket, we round up to the nearest whole number.
T = 108
Therefore, at least 108 tickets must be sold to cover the cost.
b. To make a $980.68 profit, we need to find out how many tickets must be sold.
Profit = Total Revenue - Total Cost
Profit = (Price per ticket * Number of tickets) - Total Cost
Given:
Profit = $980.68
Total Cost = $859.32
Price per ticket = $8
Let T represent the number of tickets to be sold.
So, we have:
Profit = (8 * T) - 859.32
We want to solve for T:
Profit + Total Cost = Price per ticket * Number of tickets
Profit + Total Cost = 8T
(Profit + Total Cost) / Price per ticket = T
(980.68 + 859.32) / 8 = T
1840 / 8 = T
T = 230
Therefore, to make a $980.68 profit, 230 tickets must be sold.
Complete Question:
It costs $859.32 to have a school dance. The dance is $8 per ticket.
a. How many tickets must sold to cover the cost?
b. How many tickets must be sold to make a $980.68 profit?
Imran and Aubrey were asked to find an explicit formula for the sequence 14,5,-4,-13...
Imran said the formula is g(n)=14-9(n-1)
Aubrey said the formula is g(n)=14-9n
Which one of them is right?
Just Irman
Just Aubrey
Both
Neither
PLEASE HELP ASAP!!!
Answer with Step-by-step explanation:
An explicit formula for the sequence
14,5,-4,-13...
given by Imran is g(n)=14-9(n-1)
and by Aubrey is g(n)=14-9n
We have to determine who is right
g(n)= 14-9n
g(1)=14-9
= 5
Hence, formula given by Aubrey is wrong
g(n)=14-9(n-1)
g(1)=14-9(0)=14
g(2)=14-9(1)=5
g(3)=14-9(2)= -4
g(4)=14-9(3)= -13
Hence, formula given by Imran is correct
Hence, correct option is:
Just Imran
Answer:
Only Imran
Step-by-step explanation:
Find the difference.
(8 - 6i) ( -1 -3i )
a) 7 - 9i
b) 9 - 9i
c) 7 - 3i
d) 9 - 3i
Thank you!
He ratio of black socks to white socks in the sock drawer is 1:4. there are 8 black socks. how many white socks are there? white socks
Final answer:
Based on the ratio of 1:4 for black socks to white socks, and knowing there are 8 black socks, we calculate the number of white socks to be 32.
Explanation:
The question asks us to find the number of white socks when given the ratio of black socks to white socks in a drawer and the number of black socks. The ratio is 1:4, which implies for every black sock, there are 4 white socks. Since there are 8 black socks, to find the number of white socks, we multiply the number of black socks by the ratio of white socks to black socks, which would be 8 * 4 = 32. Therefore, there are 32 white socks in the drawer.
Darryl has $5 left in his pocket. He spent $16 on a book, $20 on a compact disc, and $2 on a magazine. How much money did he have at the beginning of the day?
Answer:
He had a total of $43 at the beginning of the day
Step-by-step explanation:
Step 1
Express the amount of money Darryl had in the beginning as follows;
A=E+R
where;
A=initial amount he had at the beginning
E=total expenditure
R=total remainder after spending
In our case;
A=unknown
E=Amount spent on book+amount spent on compact disc+amount spent on magazine
E=(16+20+2)=$38
R=$5
Step 2
Substitute the values in the expression and solve for A;
A=(38+5)=43
He had a total of $43 at the beginning of the day
Which point on the graph represents the y-intercept?
V
W
Y
Z
The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 =1/2 (x – 1). What is the slope-intercept form of the equation for this line?
y = 1/2x + 2
y = 1/2x – 4
y = 1/2x + 5/2
y =1/2x – 7/2
A cyclist rides her bike at a rate of 10 meters per second. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 3 hours? Do not round your answers.
The product of (-8+2i) and its conjugate is equal to
The conjugate of the complex number -8 + 2i is -8 -2i. By multiplying the complex number by its conjugate we get the answer 68, which corresponds to option C.
Explanation:To solve this question, we first need to know what a conjugate is. In complex numbers, if a number is represented as a + bi, its conjugate will be a - bi. The provided complex number in the question is -8 + 2i, so its conjugate would be -8 - 2i.
Next, we multiply the complex number by its conjugate. This would give us (-8 + 2i) × (-8 - 2i). Executing this multiplication based on the rule of multiplication of brackets (a+b)(a-b) = a2 - b2, we have (-8)2 - (2i)2, which results in 64 - (-4) = 68.
Therefore, the product of (-8 + 2i) and its conjugate is equal to 68, which is option C.
https://brainly.com/question/20566728
#SPJ3
How do you simplify 2√5+3√5-√5
Lines that form the outer edge of a three-dimensional shape and suggest its volume are called
Express the area a of an equilateral triangle as a function of the length of its side s
Help finding angles 4, 3 ,2 ,5... Picture attached this time
Nadia cuts 3 pieces of equal length from a 8 yards of ribbon. how long is each piece?
Each piece is approximately (2.67) yards long.
To find the length of each piece, we divide the total length of the ribbon (8 yards) by the number of pieces (3).
First, we set up the division:
[tex]\[ \frac{8 \text{ yards}}{3} \][/tex]
Now, let's perform the division:
[tex]\[ 8 \div 3 = 2 \, \text{with a remainder of } 2 \][/tex]
So, each piece is [tex]\(2 \frac{2}{3}\)[/tex] yards long.
To express the length in a mixed number (a whole number plus a fraction), we rewrite [tex]\(2 \frac{2}{3}\)[/tex] as:
[tex]\[ 2 + \frac{2}{3} \][/tex]
To convert the fraction into yards, we multiply the numerator (2) by the unit fraction [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ 2 \times \frac{1}{3} = \frac{2}{3} \][/tex]
So, each piece is [tex]\(2 \frac{2}{3}\)[/tex] yards long, or [tex]\(2\frac{2}{3}\)[/tex] yards.
Alternatively, in decimal form:
[tex]\[ 2 \frac{2}{3} \text{ yards} = 2.666... \text{ yards} \][/tex]
So, each piece is approximately (2.67) yards long.