Answer:
Each interior angle of a regular polygon is 174°
To find The number of sides of the polygon.
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)
Now, the sum of an interior angle and an exterior angle of a regular polygon is always equal to 180°.
So, the exterior angle of the given regular polygon :
= (Sum of an interior angle and an exterior angle) - (An interior angle)
= 180° - 174°
= 6°
Let, the number of sides of the regular polygon = n
Now, the value of an exterior angle of a regular polygon = (360° / Number of sides)
So, the exterior angle of the given regular polygon :
= (360°/n)
By, comparing the two values of an exterior angle of the given regular polygon, we get :
360/n = 6
n × 6 = 360
n = 360/6
n = 60
Number of sides of the regular polygon = n = 60
(This will be considered the final result.)
Hence, the number of sides of the regular polygon is 60.
What is the location of the image of P(-8, 1) after a counterclockwise rotation of 90° about the origin?
O (1, -8)
O (-8,-1)
O (-1,8)
O (8, -1)
Answer:
(-1, -8)
Step-by-step explanation:
You want the image of P(-8, 1) after rotation 90° counterclockwise about the origin.
RotationThe transformation for 90° CCW is ...
(x, y) ⇒ (-y, x)
Then
P(-8, 1) ⇒ P'(-1, -8)
__
Additional comment
We observe that this answer is not among the choices listed in this problem statement. We suspect a typo somewhere. The transformations represented by the given choices are ...
A: reflection across the x-axis and rotation 90° CCW
B: reflection across the x-axis
C: reflection across the x-axis and rotation 90° CW
D: reflection across the origin
These are shown in the second attachment.
find the measure of each angle indicated
Answer:127 degrees
Step-by-step explanation: 180-74 = 106 106+21 = 127 180-127 = 53 180-53 =127
I need help please please
Value of angle T is 60°, angle U is 60°, TS is 13 cm and SU is 22.49 cm.
Given in question,
Triangle STU,
TU = 13 cm
∠S = 60°
ST = TU
= 13 cm
∠U = ∠S (Their sides are equal)
= 60°
∠S + ∠T + ∠U = 180°
60 + ∠T + 60 = 180
∠T + 120 = 180
∠T = 180 - 120
= 60
Hence, ∠T is 60°.
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the radius of a sphere is increasing at a rate of 5 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 80 mm? (round your answer to two decimal places.)
The rate of change of the volume of the sphere is 100,530.96 mm^3/s
How to calculate rate of change of the volume of the sphere?
Given,
radius = r = 80 / 2 = 40 mm
rate of change radius = [tex]\frac{dr}{dt}[/tex] = 5 mm/s
Formula to calculate volume of the sphere is
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
Differentiating the volume formula and we get new formula to calculate rate of change of the volume.
[tex]\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}[/tex]
Simplify to
[tex]\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}[/tex]
Now, we put the given value to formula and calculate it
[tex]\frac{dV}{dt} = 4\pi (40)^{2}(5)[/tex]
[tex]\frac{dV}{dt} = 100,530.96[/tex] mm^3/s
Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s
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Question 13-19, fill in all unknown values.
given m<6 = 131 find all other measures
13. m<1 =
14. m<2=
15. m<3=
16. m<4=
17. m<5=
18. m<7=
19. m<8=
The values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.
Given the measure of angle 6 is 131.
We can see that from the figure, angle 6 and angle 2 are corresponding angles and angle 6 and angle 4 are alternative angles.
So, angle 2 = angle 6 = 131
angle 4 = angle 6 = 131
Since angle 1 and angle 4; angle 2 and angle 3 are Linear pairs. So.
angle 3 = 180 - angle 2 = 180-131 = 49
angle 1 = 180 - angle 4 = 180-131 = 49
Since, angle 1 and angle 5; angle 4 and angle 8; angle 3 and angle 7 are corresponding angles to each other.
angle 5 = angle 1 = 49
angle 7 = angle 3 = 49
angle 8 = angle 4 = 131
Hence the values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.
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sson 1.1)
x³ = 1,728
Ms. Gallo buys a 64-ounce of peanut butter for $6.33. What is the cost per ounce
(2.3*10^2)(3*10^5)
in scientific notation 
Answer:
(2.3*10^2)(3*10^5)
in scientific notation 
Step-by-step explanation:
6.9 × 10^7
Please help 50 points
Step-by-step explanation:
look at where the dotted line is : it is vertical at x = -3.
that is automatically is equation : x = -3.
now, look at where the shaded side of that line is - to the left or to the right of the line ?
it is to the left of the line. and that message all values smaller than x = -3. but not equal indicated by the dotted line (that means the line itself is not included).
so, this is described by x < -3.
therefore, the first answer option is out.
now, look at the solid line.
what is the y-intercept (the y- value when x = 0) ?
when x = 0, the y-value is -1.
and everything to the left and below of the line is included (incl. the line itself, hence the solid line), so, the line inequality is then (just given by the available choices)
y <= -x - 1
and the 3rd answer option is therefore correct.
Answer:
[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]
Step-by-step explanation:
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.From inspection of the given graph, there is a dashed line at x = -3 with shading under the line (to the left).
Therefore, the inequality that represents this is:
[tex]x < -3[/tex]The solid line has a negative slope. For each decrease of 1 unit in the y-direction, the x-values increase by 1 unit. Therefore, the slope of this line is -1.
From inspection of the given graph, the y-intercept of the solid line is -1.
Therefore, the equation of this line is y = -x - 1.
As the shading is under the line, the inequality that represents this is:
[tex]y \leq -x - 1[/tex].Therefore, the system of linear inequalities that represents the graph is:
[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]
Work out
a) 5 - 21
b) 7/3/3 + 2/1/20
import the dataset states.csv , from your data folder, into rstudio. make a scatter plot of high (x-axis) vs pctdemocrat (y-axis) with points colored by region. using stat smooth , determine which region has the strongest negative correlation. o west n. east midwest o south states state region alabama south west alaska arizona war d
The region which have strongest negative correlation is Midwest.
Given that,
From your data folder, import the states.csv dataset into rstudio. create a scatter plot with high (x-axis) and pctdemocrat (y-axis) data points that are colored according to region. Stat smooth is used
To find : Which region has the strongest negative correlation
What Is Negative Correlation?
A link between two variables known as "negative correlation" occurs when one variable rises as the other falls, and vice versa. In statistics, -1.0 denotes a perfect negative correlation, 0 denotes no connection, and +1.0 denotes a perfect positive correlation. The relationship between two variables is always absolutely opposite when there is a perfect negative correlation.
Therefore, the region which have strongest negative correlation is Midwest.
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Emma is x years old
Kate is 12 years younger than Emma. The sum of their ages is 24
Work out the age of Emma
Answer:
Step-by-step explanation:
Emma's age= x
Kate's age= x-12
sum of their ages=24
so Emma's age= 24-12
x=24-12
x=12
Emma's age=12
when it is 8:00, the hour hand on an analog clock is 240$^\circ$ ahead of the minute hand. how many minutes elapse (to three significant digits) before the minute hand next points in the same direction as the hour hand?
506.433 minutes elapse before the minute hand next points in the same direction as the hour hand.
Conversion of hours to minute:
As we all know, an hour is made up of sixty minutes, therefore
1 hour=60minutes
Thus, all you need to do to convert time from hours to minutes is to multiply the time in hours by 60 to get the time in minutes.
If you want to convert minute to hours divide the given time in minutes by 60.
The hands line up 11 times every 12 hours, or roughly every 1:05.5 hours; the precise number is 1:05.4545 repeating.
The repetition time is 8:43.6363. When expressed in seconds, the result is 8:43:38.1818 repeating, or 8:43:38 and 2/11.
This is 261 and [tex]\frac{9}{11}[/tex] degrees, or 261.818 repeated.
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Mary leaves her house at noon , traveling in her car at 45mi / h . Later , Mary's brother Joe leaves their house and travels in the same direction at 60mi / h . If Joe leaves at 2:00 PM., at what time will he catch up with Mary ?
The time that it will take Joe to catch up with Mary is; 8 hours
How to solve Algebra Word Problems?We are told that;
Time Mary leaves the house = 12 pm
Time that Joe leaves the house = 2 pm
Speed of Mary = 45 mi/hr
Speed of Joe = 60 mi/hr
This means that Mary had a 2 hour time lead over Joe.
Thus;
Distance is calculated from the formula;
Distance = Speed * time
Thus;
Distance covered by Mary in the 2 hours lead is;
Distance = 45 * 2 = 90 miles
Thus, time that it will take Joe to catch up with mary is;
t = 2 + (90/(60 - 45))
t = 2 + 6
t = 8 hours
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h(t)=( 1)/(3) t-10, find h(t) when t =27 and when t= -15
The sum of the squares of two numbers is 32. the product of the two numbers is 16. find the numbers.
Answer:
4
Step-by-step explanation:
The answer really just popped into my head.
4^2 + 4^2 = 32
4x4=16
Of all the closed right circular cylindrical cans of volume 128πcm
3, find the dimensions of the can which has minimum surface area.
The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.
Given:
The volume of closed right circular cylindrical cans = 128π cm³
As we know the volume of a cylinder = πr²h
By equating;
πr²h = 128π
h = 128/r²
To get the dimensions of a can with minimum surface area;
S = 2πrh + 2πr
Put h = 128/r²;
Therefore, S(r) = 256π/r + 2πr²
S'(r) = -256π/r² + 4πr
S''(r) = -(2*256π)/r³ + 4π
Now, for S(r) = 0;
r = 4cm
for S''(4) > 0 at r = 4 is minimum point.
Hence,
h = 128π/(π*4*4)
h = 8cm
Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.
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2f-3.7<2.3 inequality?
f < -5
> -1.3
≤ 5
≥ 1.3 pick one one each side
The solution to the inequality expression is f >-3
How to determine the solution to the inequality expression?From the question, we have the following parameter that can be used in our computation:
-2f - 3.7 < 2.3
Add 3.7 to both sides of the expression
This gives
-2f < 6
Divide both sides of the expression by -2
So, we have the following representation
f >-3
Hence, the solution is f >-3
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Let h(x) = x² + 1 and g(x) = 2x.
FIND (h-g)(2).
A.)3
B.)10
C.)1
D.)9
Answer:
C
Step-by-step explanation:
(h - g)(2)
= h(2) - g(2)
= 2² + 1 - 2(2) = 4 + 1 - 4 = 1
[tex](8x^{6} )^{\frac{2}{3} }[/tex] someone explain?
Answer:
Step-by-step explanation:
so use the properties of powers, recall that powers like [tex]x^{2^{2} }[/tex] is the same as [tex]x^{2} *x^{2}[/tex] which can also be written as [tex]x^{2*2}[/tex] = [tex]x^{4}[/tex].
I want to make this clearer.
[tex]x^{3^{3} }[/tex] = [tex]x^{3}[/tex] * [tex]x^{3}[/tex] * [tex]x^{3}[/tex] = [tex]x^{3*3*3}[/tex] =[tex]x^{27}[/tex]
I'm not sure if that's making it clearer or not.
so for your question of [tex](8x^{6}) ^{2/3}[/tex] we can rewrite it to look like the above multiplication of powers
[tex]8x^{6*(2/3)}[/tex]
[tex]\frac{6}{1}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{12}{3}[/tex] = 4
[tex]8x^{4}[/tex]
The first step in simplifying is to apply that outer exponent of [tex]\frac{2}{3}[/tex] to each factor inside the parentheses.
[tex]\left(8\cdot x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3}[/tex]
Now using the concept that [tex](a)^{m/n} = \sqrt[m]{a^n}[/tex] for positive real numbers a and integers m and n, we can evaluate the first part:
[tex](8)^{2/3} = \sqrt[3]{8^2} = \sqrt[3]{64} =4[/tex]
For the second part, we use the power-to-a-power rule, that says [tex](a^m)^n = a^{m\cdot n}[/tex]:
[tex]\left(x^6\right)^{2/3} = x^{6\cdot \frac{2}{3}} = x^4[/tex]
Putting that all together, we have
[tex]\left(8 x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3} = 4x^4[/tex]
PLEASE HELP !!!!
Mia and her family went to dinner, and the bill, including tax, came to $54.65. Mia suggested giving the server a gratuity of about 20 percent of the bill.
If they give a gratuity of 20 percent, what would be the tip rounded to the nearest dollar?
If they give a gratuity of 20 percent, rounded to the nearest dollar, what is the total cost of the dinner, including the tip?
The amounts, using proportions, are given as follows:
Tip: $10.93.Total cost of the meal: $65.58.What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem from which the fraction was built.
The tip is of 20% of the total bill of $54.65, hence it's value is given as follows:
Tip = 0.2 x 54.65 = $10.93.
(because 0.2 is the decimal equivalent to the percentage of 20%, then it is multiplied by the total amount to find the desired amount).
The total cost of the meal is given by the sum of the bill of the meal plus the tip, hence:
Total Cost = 54.65 + 10.93 = $65.58.
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Please solve both blanks and round to the nearest tenth please
The inequality is x ≤ 39.2. The actual number of items that can be bought is 39.
There is a set budget of $145 to buy some items. The price of each item is $3.70. We need to form an inequality for the given information and solve it.
Let the number of items be denoted by the variable "x". Then we can say that :
3.70*x ≤ 145
x ≤ 145/3.70
x ≤ 39.2
The actual number of items that can be bought must be a whole number. We will take the greatest integer less than or equal to the solution.
The actual number of items that can be bought is 39.
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Joseph removes 5/8 gallon of white paint from a can. Then he adds 5/8 gallon of blue paint to the can.
Write and then evaluate a subtraction expression to find the overall increase or decrease in the amount of paint in the can.
Enter the correct answers in the boxes.
Expression:
gallon(s)
Joseph removes 5/8 gallon of white paint from a can.The amount of paint in the can = - 2.8 gallons
Step-by-step explanation:
Let X be the starting amount of paint in the can, in gallons.
"Removes 5/8 gallon" can be written -(5/8)gal
"Adds 3/8 gallon" becomes +(3/8)gal
The result is : X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)
Consolidating: Remaining (gallons) = X - (2/8)gal
If we want the overall increase/decrease, subtract the initial volume:
Initial - Remaining = Change in amount of paint in can
Change = (X-(2/8)gal) - X = - (2/8) gallons
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The bookstore sold 40 biographies and
100 mysteries. Find the ratio of biographies
to mysteries sold.
Answer:
40;100
step by step explanation:
I know a) is 100
Confused about b) I got 81 but its wrong
Need an explanation along with answer
Step-by-step explanation:
a) 100
b)45
trust me it will helps you
3x^2+12x=7 Complete the square to solve
Answer:
Step-by-step explanation:
Answer:
x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]
Step-by-step explanation:
3x² + 12x = 7 ← factor out 3 from each term on the left side
3(x² + 4x) = 7
to complete the square
add/ subtract ( half the coefficient of the x- term)² to x² + 4x
3(x² + 2(2)x + 4 - 4) = 7
3(x + 2)² - 12 = 7 ( add 12 to both sides )
3(x + 2)² = 19 ( divide both sides by 3 )
(x + 2)² = [tex]\frac{19}{3}[/tex] ( take square root of both sides )
x + 2 = ± [tex]\sqrt{\frac{19}{3} }[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]
Which of the following numbers are irrational?
-8.2183,ñ /3,√25, 9+ √4
-8.2183 and 9+√4
-8.2183 and ñ/3
ñ/3 and 3√25
3√25 and 9+√4
Answer:
ñ/3 and 3√25
Step-by-step explanation:
pi is irrational and the cube root of 25 is irrational :)
y+8= -7(x-2) in slope intercept form
Answer:
[tex]y=-7x+6[/tex]
Step-by-step explanation:
1 ) Our given equation is [tex]Y\left(x\right)+8=-7\left(x-2\right)[/tex]
2 ) We can now graph this equation ( desmos is a good online graphing calculator ). The graph is shown in the attachment...
3 ) Now that the equation has been graphed we can see that the slope intercept form is [tex]y=-7x+6[/tex]
Hope this helps! :)
you get a loan from the loan star bank to help pay for your home. find the interest on the loan if you borrowed $12,000 at 10% for one year.
The interest on the loan is $1200.
Given,
In the question:
You get a loan from the loan star bank to help pay for your home.
and, if you borrowed $12,000 at 10% for one year.
To find the interest on the loan.
Now, According to the question;
Based on the given conditions:
Formulate:
Borrowed= $12,000
At 10% for one year
12000 x 10%
Convert percentage into decimal
12000 x 0.1
calculate the product or quotient:
= 1200
Hence, The interest on the loan is $1200.
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What is the simplified form of each expression? 2b^-1.5b^10
By using some exponent properties we will get:
2*(1/b)^15
How to simplify the expression?Remember that the product of exponents can be written as:
(a^x)*(a^y) = a^(x*y)
In this case, we have the expression:
2*b^(-1.5)*b^10
Using the above property we can rewrite:
2*b^(-1.5)*b^10 = 2*b^(-1.5*10) = 2*b^(-15)
And a negative exponent means that we need to take the inverse of the base, then:
2*b^(-15) = 2*(1/b)^15
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