The measure of each angle of a regular 22-gon is 163.6 degrees.
How to find the sum of angles of a polygon?In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.
Polygon can be named base on the number of sides they possess. For example pentagon has 5 sides, hexagon has 6 sides, heptagon has 7 sides, octagon has 8 sides, nonagon has 9 sides and decagon has 10 sides.
Therefore, a regular polygon is one which sides and angles are congruent.
A regular 22-gon has 22 sides.
The measure of each angle of 22-gon can be found as follows;
angle= 180(n - 2) / n
where
n = number of sides
angle = 180 (22 - 2) / 22
each angle = 180(20) / 22
each angle = 3600 / 22
Therefore,
each angle = 163.636363636
each angle = 163.6 degrees.
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16. Doug's family buys 7 postcards while on vacation. Each
postcard costs $0.25 including tax.
Part A
How can Doug use place-value blocks to
find the total cost of the postcards? What is
the total cost?
The total cost is $1.75
What is Place value?The foundation of our entire number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number. The digits in the numbers 42,316 and 61,432 are distinct from one another.Given that we've done it:
7 postcards were purchased by Doug's family.Each postcard costs $0.25 after tax.The total price is shown by:
7 x 0.25 = $1.75Now, let's display the following in a number line:
Put all the numbers with a difference of 0.25 on the number line, run it seven times, and the result will appear.There are 7 hops between each step of 0.25 duration to get to the needed answer.So, after seven hops, we arrive at 1.75, which is the correct response.
Hence, the total cost is $1.75
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Which equation is the inverse of y = 100-x²?
Oy=± √100-x
O y=10± √√x
Oy=100+√x
Oy=+√x-100
Answer:
y = ±√100-x
Step-by-step explanation:
To work out the inverse of this function :
We solve for x then swap x and y :
Solving for x :
y = 100 - x²
Add x² to both sides :
x² + y = 100
Subtract y from both sides :
x² = 100-y
Square root both sides :
x = ±√100-y
Now we have solved for x. Now swap x and y :
y = ±√100-x
This is our final answer and is the first option.
Hope this helped and have a good day
Please help me with the attached question
The expression equivalent to [tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex] is m - 2.
How to find equivalent expression?Equivalent expressions are expressions that work the same even though they look different.
In other words, equivalent expressions are expressions that have the same value.
Therefore, the expression that is equivalent can be calculated as follows:
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex]
Hence, let's simplify the expression to find it's equivalent,
open the bracket
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m[/tex]
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m = -\frac{21}{2}+\frac{17}{2}+2m-m[/tex]
[tex]-\frac{21}{2}+\frac{17}{2}+2m-m=-\frac{4}{2} + m[/tex] = m - 2
Therefore,
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = m-2[/tex]
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Gavin deposited money into his savings account that is compounded annually at an interest rate of 9% Gavin thought the equivalent quarterly interest rate would be 2.25% is Gavin correct?
The quarterly interest rate is equal to 2.25%. This implies that Gavin is correct.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this formula:A(t) = P(1 + r/n)^{nt}
Where:A represents the future value.
r represents the interest rate.
n represents the number of times compounded.
P represents the principal.
T represents the time measured in years.
In this scenario, Gavin's savings account is compounded annually at an interest rate of 9%. This ultimately implies that, the equivalent quarterly interest rate would be calculated by dividing the annual interest rate of 9% by 4 as follows:
Quarterly interest rate = 9/4
Quarterly interest rate = 2.25%
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a football team travels to an away game in cars that seat five players and vans that can hold nine players. If there are 47 players on the team find the equation for this situation
The equation to illustrate the information when the football team travels to an away game is 5c + 9v = 47.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let cars = c
Let van = v
The equation will be 5c + 9v = 47.
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What pattern do you see?
Gallons
0.1
10
Miles
118
Step-by-step explanation:
why ? the same pattern your saw yourself, as the handwritten numbers indicate.
it is 1:118.
event on the left is multiplied by 118 to create the numbers on the right.
please help me i never learned divison im sorry87,628÷931=
Answer:
94.1224489796
this is the answer
write each system of equations as a matrix
Answer:
Step-by-step explanation:
Write the quadratic equation whose roots are -5 and 4, and whose leading coefficient is 5.
(Use the letter x to represent the variable.)
3
x
2
−
3
x
−
60
=
0
Explanation:
A quadratic equation whose roots are
α
and
β
and leading coefficient is
a
is
a
(
x
−
α
)
(
x
−
β
)
=
0
Hence, the quadratic equation whose roots are
5
and
−
4
and leading coefficient is
3
is
3
(
x
−
5
)
(
x
−
(
−
4
)
)
=
0
or
3
(
x
−
5
)
(
x
+
4
)
=
0
or
3
(
x
2
−
5
x
+
4
x
−
20
)
=
0
or
3
(
x
2
−
x
−
20
)
=
0
or
3
x
2
−
3
x
−
60
=
0
Answer:
5x^2+5x-100=0
Step-by-step explanation:
5(x+5)(x-4)=0
(x+5)(x-4)= 0
x= -5
x= 4
one positive number is 8 more than twice another. if their product is 1242, find the numbers?
Answer:
Step-by-step explanation:
is the ordered pair (2, 4) a solution to the following equation
5x + 2y = 23?
Answer: Can't Say for sure but probably it is so I would Say Yes.
i need help answering this question
Answer:
Step-by-step explanation:
there is no question?
Complete the chart to show similarities and differences between multiplying by 0.1, 0.01, 10, 100. Tell how many places the decimal point appears to move and in which direction when you multiply by each
Answer:
they all are being multiplied by 10
Step-by-step explanation:
0.01 x 10 = 0.1
0.1 x 10 = 1
1 x 10 = 10
10 x 10 = 100
Solve the absolute value equation: |6z-3|=5
The required solution of the given absolute value equation is z = 4/3 and z = 1/3.
Given that,
To solve the absolute value equation |6z-3|=5
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given the absolute value equation,
|6z-3|=5
Simplify,
6z - 3 = ± 5
Taking (+)
6z - 3 = 5
6z = 8
z = 4/3
Taking (-)
6z -3 = -5
z = -1/3
Thus, the required solution of the given absolute value equation is
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Mr. Pinello has 80 colored pencils and 64 markers to divide into containers for his class. He wants each container to have the same number of items. What is the greatest number of containers Mr. Pinello can make if he wants each container to have the same number of colored pencils and the same number of markers? Show your work.
Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.
What is the Greatest Common Factor?
The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.
We have,
The number of coloured pencils Mr. Pinello has = 80.
The number of markers and pencils Mr. Pinello has = 60.
The most containers Mr. Pinello can create to ensure that each one contains an identical amount of coloured pencils and markers.
The GCD of the number of coloured pencils and markers will be the largest number of containers to have the same number of items when the same number of items must be preserved.
Calculating the gcd of and 80 and 64 is:
The greatest common divisor (GCD) of both 80 and 64 is 16.
∴ GCD = 16
Therefore, If Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.
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How would I solve this? i know how to solve easier variations but not like this the question is:
Write a linear function f with the values f (-1) = 8 and ƒ (5) = 6.
The linear function with values of f(-1)=8 and f(5)=6 is f(x) = [tex]\frac{-x+23}{3}[/tex].
What is linear function?
A straight line on the graph has the equation or formula y = f(x) = px + q is linear function .One independent and one dependent variables are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable. A straight line on the coordinate plane is represented by a linear function.
Here the given values are f(-1)=8 and f(5)=6.
We know that f(x)=y , Then the points are (-1,8) and (5,6).
Using slope formula ,
=> slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = -2/6=-1/3
Now using slope formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=>y-8=-1/3(x+1)
=>3y-24=-x-1
=> 3y=-x+23
=> y = [tex]\frac{-x+23}{3}[/tex]
Hence the linear function is f(x) = [tex]\frac{-x+23}{3}[/tex].
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Rationalize the denominator 1/ square root of 2
Answer:
Multiply and divide by √2 . You'll get √22
Step-by-step explanation:
HELP PLEASE HELP I NEED HELP PLEASEEEEEEEEEEE
The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.
What is a linear relation?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
The first and the second differences are:
x y first differences second differences
4 18 ----
5 28 10 ------
6 35 7 -3
7 39 4 -3
8 40 1 -3
9 38 -2 -3
The values of second differences are constant, therefore, the relation is linear.
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Solve for X in the equation;
2x+5=7
Answer:
x=1
Step-by-step explanation:
Answer: x=1
Step-by-step explanation:
2x + 5 = 7
2x + 5 - 5 = 7 - 5
2x = 2
2x/2 = 2/2
x=1
Point M (5,-7) is the midpoint of the line segment CD. If C is (2, "-3)," which of these are the coordinates of D?
Answer:
D(8, -11)
Step-by-step explanation:
You want the coordinates of end point D if C is (2, -3) and the midpoint of CD is M(5, -7).
MidpointThe midpoint is the average of the endpoint coordinates:
M = (C +D)/2
Solving for D, we find ...
D = 2M -C
End pointThen point D is ...
D = 2(5, -7) -(2, -3) = (2·5-2, 2(-7)+3)
D = (8, -11)
I need help with solving problem.
Answer:
x=-1,x=3/5
Step-by-step explanation:
Those are the two values of x
Car A is travelling east at a steady speed .......
Answer:
for 20 miles per hour
Step-by-step explanation:
.
Paul inherited a stamp collection. Since receiving the
collection, Paul has gone to the store and bought the
same number of new stamps each week to add to his
collection. The equation shown below can be used to
determine the number of stamps (y) in Paul's stamp
collection x weeks after he inherited the stamps.
y = 3x + 40
Based on the equation, which statement is true?
A) The stamp collection had 3 stamps in it when Paul inherited it.
B) So far, Paul has purchased 40 additional stamps for the collection.
C) Since inheriting the collection, Paul has bought 3 new stamps each week.
D) Six weeks after he inherited the collection, Paul's stamp collection contains 18 stamps
Based on the equation y = 3x+40 where y is the number of stamps and x is number of weeks after Paul inherited the stamps, the correct statement is since inheriting the collection, Paul has bought 3 new stamps each week.
According to the question,
We have the following information:
y = 3x+40 where y is the number of stamps and x is number of weeks after Paul inherited the stamps
Now, when we observe this equation carefully, we notice that 3x is added to 40. So, it means that 40 is constant. Then, the number of stamps increasing per week is in the multiplication of 3. Or, in other words, 3 new stamps are bought each week.
For 1st week:
y = 3*1+40
y = 43
For 2nd week:
y = 3*2+40
y = 6+40
y =46
Hence, the correct option is C.
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Confused please help.
The image of the corresponding to each slope is attached
What is slope?A line's steepness can be determined by looking at its slope.
Slope is determined mathematically as "rise over run" (change in y divided change in x).
assuming slope is m
m = (y₂ - y₁) / (x₂ - x₁) = change in y / change in x
considering the formula
slope is between 0 and 1 when rise (change in y) is so smaller than run (change in x) hence the line is closer to horizontal
slope is greater than 1 then the rise is more than run, in this case the line is approaching vertical line
numbers less than zero are negative hence slope has a negative value
A horizontal line is a line that has a slope of of zero while vertical lines has its slope as infinity
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please help I need to find X
Answer:
x = 12
Step-by-step explanation:
if l and m are parallel that means that since the two angles are consecutive interior they add to 180
so add them both and set that to 180
9x - 4 + 5x + 16 = 180
now combine like terms
14x + 12 = 180
subtract 12 from both sides
14x = 168
divide everything by 14
x = 12
that is the answer
Answer:
[tex]\sf x=12^o[/tex]Step-by-step explanation:
Let's find x:-
[tex]\sf 9x-4+5x+16=180^o[/tex]
Combine like terms:-
[tex]\sf 9x+5x-4+16=180[/tex]
[tex]\sf 14x-4+16=180[/tex]
[tex]\sf 14x+12=180[/tex]
Add/Subtract numbers:-
[tex]\sf 14x+12-12=180-12[/tex]
[tex]\sf 14x=168[/tex]
Divide both sides by 14:-
[tex]\sf \cfrac{14x}{14}=\cfrac{168}{14}[/tex]
[tex]\sf x=12^o[/tex]
__________________
Hope this helps!
Have a great day!
Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
The exponential function that can model the county population, y, x decades after Tiana was born, is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 when y = 600000, hence:
[tex]y = 641000(0.99)^x[/tex]
[tex]600000 = 641000(0.99)^x[/tex]
[tex](0.99)^x = \frac{600000}{641000}[/tex]
[tex]\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}[/tex]
x = 6.6 decades.
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answer as a decimal with 3 significant digits
Answer:
0.08330.75Step-by-step explanation:
There are four different color marbles.
Probability of blue:
P(B) = 1/4,Next, there are 3 marbles left in the bag since no replacement.
Probability of red after blue:
P(R) = 1/3The probability of these two steps in order:
P(Blue then Red) = 1/4*1/3 = 1/12 = 0.0833Complement of R is:
P(Rc) = 1 - P(R) = 1 - 1/4 = 3/4 = 0.75Find the average rate of change of the given function on the interval [1,6]. g(x)=2x2−x
Answer:13
Step-by-step explanation:
g(1)=2(1)^2-1= 1
g(6)=2(6)^2-6=66
66-1/6-1=13
Describe the transformers of the parent function, f(x)=x, performed to create g(x).
g(x)= -3 • f(x) + 1
The function g(x) is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit of the parent function f(x).
What is a function?A capability is a declaration, idea, or rule that lays out a relationship between two factors. Capabilities might be found all through science and are fundamental for the advancement of huge connections.
The functions are given below.
f(x) = x
g(x) = -3f(x) + 1
g(x) = -3x + 1
The parent function is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit.
The functions g(x) and f(x) are shown below.
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The birth weights of the 908 babies born at Valley Hospital in 2019 were normally
distributed with a mean of 7.2 pounds with a standard deviation of 1.5. Use the Z-
Score Table from the book to determine the number of babies that weighed more
than 10 pounds.
Round your answer to the nearest whole number, but do not include the word
"babies" in your response.
PLEASE HELP I POSTED THIS QUESTION LIKE TWICE AND NO ONE IS HELPING ME
Using the z-score tables, the number of babies that weighed more than 10 pounds is; 43
How to find the p-value from z-score?A probability distribution that can be considered to be symmetric about the mean is the normal distribution, which can often be referred to as the Gaussian distribution. This depicts to us the concept of data being close to the mean occurring more often than data that are considered far from the mean. The normal distribution usually has a bell curve graph.
We are given that;
The total number of babies is 908.
Mean of the normal distribution is 7.2 pounds.
Standard deviation of the normal distribution is 1.5 pounds.
The formula of z score is given by;
z = (x - μ)/σ
where;
x is sample mean
μ is population mean
σ is standard deviation
We are given that;
x = 10
μ = 1.5
σ = 7.2
Thus;
z = (10 - 7.2)/1.5
z = 1.86667
The P-value from Z-Table gives us:
P(x > 10) = 1 - P(x < 10) = 0.030974
The number of babies that weighed more than 10 pounds is;
(0.030974 × 908) ≈ 43
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