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The regular pentagon can divide into 5 congruent isosceles triangles
The equal sides of each triangle have length r and vertex angle of measure 72 degrees
Then we will use the sine rule of the area to find the area of each triangle, then multiply it by 5 to get the area of the pentagon
Since the radius is 7mm, then
r = 7
[tex]A=5\times\frac{1}{2}\times r\times r\times sin72[/tex]Substitute r by 7
[tex]\begin{gathered} A=5\times\frac{1}{2}\times7\times7\times sin72 \\ \\ A=116.5044232\text{ mm}^2 \end{gathered}[/tex]Round it to the nearest whole number
A = 117 mm^2
The area of the pentagon is 117 mm^2
Related Questions
How many ones are between 1 and 1,000,000 (inclusive)?
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There are 600,001 ones are between 1 and 1,000,000.
By using the below process we can find the number of ones between 1 and 1,000,000.
The number of times a digit 2 to 9 digit appears in numbers 1 to [tex]10^n = n(10^(^n^-^1^))[/tex].
The number of times the digit 1 appears in numbers in numbers 1 to [tex]10^n = n(10^(^n^-^1^)) + 1[/tex]
Therefore, the number of times a digit 1 appears in numbers 1 to 1,000,000 [tex]= 6(10^(^6^-^1^)) + 1\\= 6(10^5) + 1\\= 600,000 + 1\\= 600,001[/tex]
Therefore, there are 600,001 ones are between 1 and 1,000,000.
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On a particular college campus, 22% of the students belong to a fraternity or sorority. If 56 college students are randomly chosen:a. What is the probability that 16 are members of a fraternity or sorority?Round to at least three decimal places.Incorrectb. What is the mean of this distribution? Round to at least one decimal.Incorrectc. What is the standard deviation of this distribution? Round to at least one decimal
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Explanation
Part A
From the question,
[tex]\begin{gathered} p=\frac{22}{100};q=1-\frac{22}{100} \\ p=0.22;q=0.78 \\ Also,n\text{ =56} \end{gathered}[/tex]Using the binomial probability distribution formula;
[tex]undefined[/tex]Ex) The function f(x) is shown on the graph. Plot two points on this grid to create the graph of the line that would represent f(x) - 2.
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ANSWER and EXPLANATION
We have the graph of the function f(x) given.
We want to find 2 points that will represent f(x) - 2.
This (f(x) - 2) is a transformation of the function f(x).
It is called a vertical translation. It means that the function moves on the y axis.
It is generally represented as:
f(x) + b
Comparing the required translation with the general form, we can conclude that there is a -2 shift on the y axis.
Therefore, to find two points for the new function, we have to simply pick two points from the given graph and subtract 2 from their y coordinates.
Let the two points be:
(0, 1) and (-4, 4)
Therefore, the two points will be:
(0, 1) => (0, 1 - 2) = (0, -1)
(-4, 4) => (-4, 4 - 2) = (-4, 2)
Plotting them:
The green line is the line of the new function.
Hi I need help with this
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Graphed the dilated image of quadrilateral MNOP using a scale factor of 3 and the origin as the center of dilation
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To dilated the figure by a scale factor 3 and center origin
Multiply the coordinates of each point by 3
The image of the point (x, y) is (3x, 3y)
PLS HELP WILL ASAP WILL GIVE BRAINLIST
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Answer:
if the bottom side is 4n + 15, then n=8
n times 5 is 40
40+7=47
Step by step
The parallelogram rule says the opposite sides are equal length so our equation is
4n + 15 = 5n + 7
Subtract 5n from both sides to combine variable
4n - 5n + 15 = 5n - 5n + 7
Combine
-n + 15 = 7
Subtract 15 from both sides to solve
-n + 15 -15 = 7 -15
-n = -8
n = 8
Now substitute 8 for n in the KL expression
5n + 7
5(8) + 7
40 + 7 = 47
Side KL is 47 units
(A) The lines have different slopes and intersect at one point?(B) The lines have the same slope and y intercept.?(C) The lines are parallel and do not intersect.?(D) The lines have the same slope and y-intercept.?(E) Infinitely many solutions.?(F) They are the same line.? (G) No Solution ? (H) One solution.?
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Recall that if two lines have the same slop then these two lines are parallel to each other.
the y-intercept is an x-coordinate of the point where the line intersects at the y-axis.
Consider graph 1.
The line intersects at one point and has different slopes, hence this has one solution.
(A) and (H) is true for graph 1.
Consider graph 2.
The lines have the same slope, therefore parallel but there is no y-intercept point.
This have infinitely many solutions.
They are also the same line.
(E) and (F) is true for this graph 2.
Consider graph 3.
The lines have the same slope and they are parallel.
It gives B) is correct
They do not intersect since parallel does not intersect each other.
It gives C) is correct
There is no solution since they do not intersect.
It gives G) is correct.
These lines have intercepted at -1 and -4.
It gives D) is correct
B), D), C), G), D) are correct for graph 3.
Results:
Options Graph
A) 1
B) 3
C) 3
D) 3
E) 2
F) 2
G) 3
H) 1
I need help with this practice problem solving. It is trigonometry It asks to graph the function, if you can.. use Desmos to do so..
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Notice that f(x) is
[tex]h(x)=\cos (x)[/tex]translated π/6 to the left.
Now, recall that the period of the cotangent is
[tex]\pi\text{.}[/tex]Since f(x) is just a translation, both functions have the same period.
Answer:
POSSIBLE POINTS: 1One-half of a number increased by 16 is 4 less than two-thirds of the number. What is the number?
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Let the number be x.
[tex]\begin{gathered} \frac{1}{2}x+16=\frac{2}{3}x-4 \\ \\ \frac{2}{3}x-\frac{1}{2}x=20 \\ \frac{4-3}{6}x=20 \\ \frac{1}{6}x=20 \\ x=120 \end{gathered}[/tex]The number is 120
there are 3 members on a hockey team (including all goalie) at the end of a hockey game each member if the team shakes hands with each member of the opposing team. how many handshakes occur?
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help me pleaseeeeeeeee
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Answer:
x = -2
Step-by-step explanation:
f(x) = y
f(x) represents the y-axis
f(x) = -3 or y = -3 or y = (0, -3)
When y = -3, x = -2
x = -2
I hope this helps!
what is its base of the parallelogram is72 meters²
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The area of a parallelogram is computed using the formula base x height.
Here we have a parallelogram with an area of 72 square meters and a height of 9 meters. Using the formula, we can solve for the base.
[tex]\begin{gathered} A=bh \\ 72=b(9) \\ \\ \frac{72}{9}=\frac{b(9)}{9} \\ \\ 8=b \end{gathered}[/tex]The base is 8 meters long.
Which region labeled in the graph below would represent the solution (the final shaded area) to the system of linear inequalities:≤12−3<−23+1
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Since both inequalities include the less than symbol, <, the shaded region must be below the two lines.
The intersection (common) of the shaded regions, which are both below the two lines, is region D.
9. In 1621, the remaining settlers from the Mayflower and Native Americans gathered for a
harvest feast. There were 140 people at the feast and 40 more Native Americans than settlers.
How many people were from each group?
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In order to solve this, we have to formulate some equations describing the number of people. The total number of people can be calculated by adding the number of natives to the number of settlers, like this:
Total = N + S
Where N is the number of natives and S is the number of settlers. We already know that there were 140 people in total, then we can rewrite the above expression to get:
140 = N + S
We are also told that there were 40 more native Americans than settlers, then the number of natives can be calculated by adding 40 to the number of settlers like this:
N = S + 40
By replacing S + 40 for N into 140 = N + S, we get:
140 = N + S
140 = (S + 40) + S
140 = S + 40 + S
140 = S + S + 40
140 = 2S + 40
140 - 40 = 2S + 40 - 40
100 = 2S
100/2 = 2S/2
50 = S
S = 50
By replacing 50 for S into N = S + 40, we get:
N = S + 40
N = 50 + 40 = 90
N = 90
Then, there were a total of 90 natives and 50 settlers
Explain why m<1>m<3.which statement below can be made, according to the corollary to the Triangle Exterior Angle Theorem?
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In the given image you have that m∠1 is lower than angle m∠3 becasue it is clear that angle ∠1 is an angle greater than 90° and angle ∠3 is lower than 90°. Then m∠1 > m∠3.
Now, in order to determine which of the given statements is true for the given figure, you take into account that the exterioir angle theorem stablishes that the measure of an exterior angle of the triangle is greater that any of the measure of the remote interioir angles of the triangle.
Thus, you can notice that the measure of the external angle ∠1 is greater than the measure either angle ∠4 or angle ∠2.
Hence, following statement is true:
m∠1 > m∠4 and m∠1 > m∠2
solve on a map. 1 inch equals 14.7 miles. if two cities are 3.5 inches apart on the map, how far are they actually apart? (round to a decimal)
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On a map. 1 inch equals 14.7 miles
1 inch = 14.7 miles
Two cities are 3.5 inches apart on the map
Distance between two cities = 3.5 inches
[tex]\begin{gathered} \text{ 1 inch = 14.7 miles} \\ \text{ Then for 3.5 inches in miles : Multiply 3.5}\times14.7\text{ } \\ 3.5\text{ inches=3.5}\times14.7\text{ miles} \\ 3.5\text{ inches=}51.45\text{ miles} \end{gathered}[/tex]So, the distance between two cities is 51.45 miles
Answer : 51.45 miles
A manufacturer pays its assembly line workers $11.06 per hour. In addition, workers receive a piece of work rate of $0.34 per unit produced. Write a linear equation for the hourly wages W in terms of the number of units x produced per hour. Linear equation: W = _______ What is the hourly wage for Mike, who produces 17 units in one hour? Mike’s wage = _________
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Let's assume the following variables.
x = number of units produced
It is stated in the problem that for every unit produced, there is an additional wage of $0.34. Hence, on top of $11.06 per hour wage, there will be an additional of $0.34x per hour. In equation, we have wage per hour:
[tex]W=11.06+0.34x[/tex]If Mike was able to produce 17 units, our x here is 17. Let's plug this value to the formula.
[tex]W=11.06+0.34(17)[/tex]Then, solve.
[tex]\begin{gathered} W=11.06+5.78 \\ W=16.84 \end{gathered}[/tex]Therefore, Mike's hourly wage is $16.84.
From the origin of the coordinate plane, how many units does one travel along the y-axis to find the point with the coordinates (1,8)?
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Solution:
Let's recall that in a coordinate plane, we consider (0, 0) as the origin because this is the point where the x and y-axes intersect.
Therefore, the unit you travel along the y-axis from the origin is:
8 - 0 = 8 (Value of y given - Value of y at the origin)
The answer is 8 units
Student unresponsive. No interaction at all. Session ended by tutor.
Rhombus EfGH is shown in the diagram the measure of angle HEF =64 degrees. What is the measure of angle EJF.
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Diagonals of a rhombus bisect each other at right angles, This means that
[tex]m\measuredangle EJF=90\text{ degre}es[/tex]I need some help. Could someone explain it to me?
Answers
Problem
We have the following table given:
x y
0 2
1 6
4 -9
8 8
Solution
We know that the domain correspond to the value of x in the relationship and then the correct answer for this case would be:
2
0
Jusrt 2,9 are the values in the domain of the function
A convention center is in the shape of the rectangular pyramid with a height of 444 yd. Its base measures 348 yd by 418 yd. Find the volume of the convention center. If necessary, round your answer to the nearest tenth.
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Given:
Length of the base = 418 yd
Width of the base = 348 yd
Height of the pyramid = 444 yd
Find: Volume of the rectangular pyramid
Solution:
The formula to get the volume of the rectangular pyramid is:
[tex]V=\frac{1}{3}\text{Area of the base}\times height[/tex]Since the base is rectangular, we can replace the "area of the base" into "length x width" since that is the formula for the area of a rectangle.
[tex]V=\frac{1}{3}l\times w\times h[/tex]Let's plug in the given data to the formula above.
[tex]V=\frac{1}{3}418yd\times348yd\times444yd[/tex]Then, solve for V or volume.
[tex]\begin{gathered} V=\frac{1}{3}\times64,586,016yd^3 \\ V=21,528,672yd^3 \end{gathered}[/tex]Answer: The volume of the convention is 21, 528, 672 yd³.
g(x)= x^2+3h(x)= 4x-3Find (g-h) (1)
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Given:-
[tex]g(x)=x^2+3,h(x)=4x-3[/tex]To find:-
[tex](g-h)(1)[/tex]At first we find the value of (g-h)(x), so we get,
[tex]\begin{gathered} (g-h)(x)=g(x)-h(x) \\ =x^2+3-(4x-3) \\ =x^2+3-4x+3 \\ =x^2-4x+6 \end{gathered}[/tex]So the value of,
[tex](g-h)(x)=x^2-4x+6[/tex]So the value of (g-h)(1) is,
[tex]\begin{gathered} (g-h)(x)=x^2-4x+6 \\ (g-h)(1)=1^2-4\times1+6 \\ (g-h)(1)=1-4+6 \\ (g-h)(1)=7-4 \\ (g-h)(1)=3 \end{gathered}[/tex]So the required value is,
[tex](g-h)(1)=3[/tex]Write the sentence as an equation. 136 is equal to 194 times b Type a slash (/) if you want to use a division sign.
Answers
Given the sentence 136 is equal to 194 times b, we are to write this statement as an equation.
Let us take it one after the other.
For 194 times b, this can be written as;
= 194 * b
= 194b .
Since 136 is equal to the exxpression, the final equation will be gotten by simply equationf 136 to 194b as shown;
136 = 194b
You can then re-arrange
194b = 136
Hence the reuired equation is 194b = 136
Knowledge CheckUse the distributive property to remove the parentheses.--7(-5w+x-3)X 5
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The distributive property states that:
[tex]k\cdot\left(a+b+c\right?=k\cdot a+k\cdot b+k\cdot c.[/tex]In this problem, we have the expression:
[tex]-7\cdot(-5w+x-3)=(-7)\cdot(-5w+x-3).[/tex]Comparing this expression with the general expression of the distributive property, we identify:
• k = (-7),
,• a = -5w,
,• b = x,
,• c = -3.
Using the general expression for the distributive property with these values, we have:
[tex]\left(-7\right)\cdot(-5w)+\left(-7\right)\cdot x+\left(-7\right)\cdot(-3).[/tex]Simplifying the last expression, we get:
[tex]35w-7x+21.[/tex]AnswerApplying the distributive property to eliminate the parenthesis we get:
[tex]35w-7x+21[/tex]the marketing department of a company has determined that the profit for selling x units of a product is appropriated by function f(x)= 15× -600
Answers
You have the following function for the profit for selling x units of a product:
f(x) = 15x - 600
in order to determine the profit for 15,600 units, replace x = 15,600 into the previous function and simplify:
f(15,600) = 15(15,600) - 600 = 233,400
Hence, the profit for 15,600 units is $233,400
Steel bars shrink 8% when cooled from furnace temperature to room temperature. If a cooled steel bar is 46 in. long, how long was it when it was formed?The steel bar was __ in. long when it was formed.(Round to the nearest whole number as needed.)
Answers
Answer:
50 inches
Explanation:
Let the length of the steel bar when it was formed = y
Steel bars shrink 8% when cooled from furnace temperature to room temperature.
[tex]\begin{gathered} \text{Room Temperature Length}=(100-8)\%\text{ of y} \\ =92\%y \\ =0.92y \end{gathered}[/tex]Given that a cooled steel bar is 46 in. long, then:
[tex]0.92y=46[/tex]Divide both sides by 0.92.
[tex]\begin{gathered} \frac{0.92y}{0.92}=\frac{46}{0.92} \\ y=50\;in. \end{gathered}[/tex]The steel bar was 50 in. long when it was formed.
Translate this phrase into an algebraic expression.Six less than the product of 13 and Mai's heightUse the variable m to represent Mai's height.
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If m is the Mai's height you can write for the given description:
13m - 6
The previous expression means six less than the product of 13 and Mai's height.
Find g(x), where g(x) is the translation 4 units left of f(x)=|x|.
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The equation for the translated function is:
g(x) = |x + 4|
How to find g(x)?
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.if N < 0, the translation is to the right.Here we have:
f(x) = |x|
And the translation is of 4 units to the left, so the translated function is:
g(x) = f(x + 4) = |x + 4|
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The zookeeper records how many scoops of peanuts she feeds the elephant for several days . Tuesday 21 Wednesday 19 5/8.
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Explanation:
We want to know the difference between the amount of scoops she fed the elephant on Wednesday and on Tuesday:
[tex]21-19\frac{5}{8}[/tex]We can write the second number as an improper fraction:
[tex]21-(19\cdot\frac{8}{8}+\frac{5}{8})=21-(\frac{152}{8}+\frac{5}{8})=21-\frac{157}{8}[/tex]And now substract the two numbers:
[tex]\begin{gathered} 21-\frac{157}{8}=\frac{21\cdot8}{8}-\frac{157}{8} \\ 21-\frac{157}{8}=\frac{168}{8}-\frac{157}{8} \\ 21-\frac{157}{8}=\frac{168-157}{8}=\frac{11}{8} \end{gathered}[/tex]Answer:
She fed the elephant 11/8 scoops of peanuts more on Tuesday than on Wednesday
what is the density of a 10g box measuring 10 cm by 5 cm by 5 cm
Answers
Answer:1 g/cm^3
Step-by-step explanation: