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Draw any two convex pentagons. For each of them measure the sum of its interior angles using a protractor. Explain the result of the measuring.
Answers
In a convex polygon, all interior angles are less than or equal to 180. So pentagons are polygons of five sides. We need to draw two different pentagons with the previous characteristics and measures of the internal angles. Therefore, we will choose to type of pentagons.
Every pentagon can be divided up into three triangles, either a regular or irregular one and each triangle adds up to 180 degrees. Therefore, the angles in every pentagon must add up to 540 degrees.
1. Drawing of the first convex pentagon (Regular Pentagon).
A polygon is regular when all angles are equal and all sides are equal. The regular pentagon is a 5-sided polygon. This is shown in Figure 1. Note that all angles are equal to 108°.
1.1. Sum of the interior angles of the first convex pentagon.
According to Figure 1, the sum of its interior angles is as follows:
[tex]\alpha=5 \times 108^{\circ}=540^{\circ}[/tex]
As we said, the angles in every pentagon must add up to 540 degrees. If the pentagon is regular each internal angle measures 108°. In fact, in a Regular Polygon with N sides, each angle is:
[tex]\frac{(N-2)180{^\circ}}{N} \\ \\ Since \ N=5 \\ \\ \\ \frac{(5-2)180{^\circ}}{5}= 108^{\circ}[/tex]
2. Drawing of the second convex pentagon (Irregular Pentagon)
This is a type of polygon that does not have all sides equal and all angles equal. In Figure 2 is shown this pentagon. Note that there are five sides and all angles are not equal.
2.1 Sum of the interior angles of the second convex pentagon.
According to Figure 2, the sum of its interior angles is given by:
[tex]\beta=81^{\circ}+139^{\circ}+139^{\circ}+94^{\circ}+87^{\circ}=540^{\circ}[/tex]
As we said, no matter if the pentagon is irregular, the angles in every pentagon must add up to 540 degrees.
Answer with explanation:
A Polygon is said to be convex, if all the diagonals of the polygon lies in the interior of the polygon.
→Sum of interior angle of polygon =(n-2)×180°, where n is the number of sides of the polygon.-----(1)
→A pentagon is said to be convex, if it has 5 sides and all the Diagonals of pentagon lies in the interior.
Sum of interior Angles of Triangle =(3-2)×180°=180°
Sum of interior angles of Quadrilateral = (4-2)×180°=2×180°=360°
Sum of Interior angles of Polygon =(5-2)×180°=3×180°=540°
Used the formula (1) in all the three cases.
Related Questions
a car travels 450 miles in the same time that a motorcycle travels 390 miles. if the car’s speed is 10 miles per hour more than the motorcycle’s, find the speed of the car and the speed of the motorcycle.
the speed of the motorcycle is ___ mph.
the speed of the car is ___ mph
Answers
Henry lives in Mississippi, which has a sales tax of 7%. He just bought a bed whose full price was $1600, but he got 30% off, because the store was having a sale. What was the total amount that Henry paid?
A.) $1120.00
B.) $1198.40
C.) $1934.40
D.) $1712.00
Answers
Answer:
B.) $1198.40
Step-by-step explanation:
Given,
The original price of the bed = $ 1600,
Since, in sale, he got 30 % off,
The price of bed in sale = The original price of the bed - 30 % of the original price of the bed
[tex]= 1600 - 30\% \text{ of } 1600[/tex]
[tex]=1600-\frac{30\times 1600}{100}[/tex]
[tex]=1600-\frac{48000}{100}[/tex]
[tex]=1600-480=\$ 1120[/tex]
Also, there is a sales tax of 7 % ,
Thus, the final price of the bed = The price of bed in sale + 7 % of the price of bed in sale
[tex]=1120+\frac{7\times 1120}{100}[/tex]
[tex]=1120+\frac{7840}{100}[/tex]
[tex]=1120+78.40=\$1198.40[/tex]
Hence, he paid $ 1198.40.
Select the quadratic that has roots x=8 and x=-5
Answers
[tex]\bf \begin{cases} x=8\implies &x-8=0\\ x=-5\implies &x+5=0 \end{cases} \\\\\\ (x-8)(x+5)=\stackrel{original~polynomial}{y}\implies x^2-3x-40=y[/tex]
Answer:
Quadratic equation: [tex]x^2-3x-40=0[/tex]
Step-by-step explanation:
We are given two roots of the quadratic equation and we need to find the quadratic equation.
If roots are a and b then equation
[tex]x^2-(\text{sum of roots})x+\text{Product of root}=0[/tex]
Roots are x=8 and x=-5
Sum of roots = 8 + (- 5) = 3
Product of roots = 8 x -5 = -40
Substitute the value into formula
Quadratic equation:
[tex]x^2-3x-40=0[/tex]
In factor form:
[tex](x-8)(x+5)=0[/tex]
Hence, The equation is [tex]x^2-3x-40=0[/tex]
Let f(x)=√x find g(x), the function that is f(x) shifted up 1 units and left 5 units.
Answers
f(x)=√x shifted up 1 units is √x -1
f(x)=√x shifted left 5 units is √(x +5)
So g(x)= √(x +5) -1
What is the degree of the polynomial a4 + b3 - 2ab + c?
Answers
The variables of the polynomial are:
variable 1: a
variable 2: b
The degree of the polynomial, in this case, is given by the term of the polynomial that has the highest exponent.
We then have the following polynomial:
[tex]a ^ 4 + b ^ 3 - 2ab + c [/tex]
The term with the greatest exponent is:
[tex]a ^ 4 [/tex]
Therefore, the polynomial is of degree 4.
Answer:
The polynomial is of degree 4.
The degree of any given polynomial is said to be the highest power in the exponent of variables given in the polynomial.
For example, quadratic equations like (4x² + 4x + 1) have degree 2.
Here given polynomial is (a⁴ + b³ - 2a·b + c), this polynomial is a multivariable expression.
It is clearly visible that the highest power in the exponent of its variables is 4.
So, the degree of the given polynomial is 4.
Suppose f and g are continuous functions such that g(3) = 6 and lim x → 3 [3f(x) + f(x)g(x)] = 54. find f(3).
Answers
When f and g are continuous functions such that g(3) = 6 and lim x → 3 [3f(x) + f(x)g(x)] = 54 the value of f(3) is 6.
Rewrite the given limit as: lim x→3 [3f(x) + f(x)g(x)] = lim x→3 [3f(x)] + lim x→3 [f(x)g(x)]
Substitute the limits using continuity: 54 = 3 lim x→3 f(x) + lim x→3 f(x) ⋅ lim x→3 g(x) 54 = 3f(3) + f(3) ⋅ 6 (since lim x→3 f(x) = f(3) and lim x→3 g(x) = 6)
Combine like terms: 54 = 9f(3)
Divide both sides by 9: f(3) = 6
Therefore, f(3) = 6.
Which graph correctly solves the system of equations below? y = x2 + 2x + 3 y = −x2 + 3
Answers
Answer:
Graphs are attached for both solutions.
Step-by-step explanation:
Using a graphing calculator, we can graph both equations and then find the solutions.
The solutions to the system of equations will be the points of intersection of the graphs. There are two points of intersection, so there are two solutions. One of them is at (0, 3); the other is at (-1, 2).
how many triangles have the following measurements? A=38, a=432, b=382
Answers
_____
You know this because the given angle is opposite the longest given side. You only have ambiguous cases if the given angle is opposite the shorter of two given sides.
Using the Law of Sines, we determined that it is possible to form one triangle with the given measurements A=38°, a=432, and b=382. The calculation includes finding angle B and angle C, ensuring all triangle conditions are met.
To determine how many triangles can have the given measurements (A=38°, a=432, b=382), we need to check if these values satisfy the triangle inequalities and if they can form a possible triangle using the Law of Sines.
First, let's use the Law of Sines which states that:
sin(A)/a = sin(B)/b = sin(C)/c
Given:
A = 38° (angle)a = 432 (side opposite to angle A)b = 382 (side opposite to angle B)We can calculate angle B using:
sin(B) = (b × sin(A)) / a
sin(B) = (382 × sin(38°)) / 432 ≈ 0.556
Finding the arc sine of 0.556, we get:
B ≈ 33.8°
Now, we find angle C:
C = 180° - A - B ≈ 180° - 38° - 33.8° = 108.2°
Using the Law of Sines again to find side c:
c = (a × sin(C)) / sin(A)
c = (432 × sin(108.2°)) / sin(38°) ≈ 676.85
Thus, it's possible to form one such triangle with the given conditions.
What is the approximate area of the circle shown below 3.5cm
Answers
Answer:
D. 38.5 cm²
Step-by-step explanation:
The area of a circle is given by:
A = πr²
where r is the radius of the circle.
From the given figure,
Radius of the circle is r = 3.5 cm.
Therefore, the area of the circle is:
⇒A = 3.14 × (3.5 cm)² = 38.5 cm²
Thus, the correct option is D.
What is the area of a sector with a central angle of 4pi/3 radians and a radius of 11cm
Use 3.14 for pi and round to the nearest hundredth
Answers
Hannah has $1000 in her savings account. During 1 month , she withdraws $25. Each successive month, she withdraws $10 more than the previous month . How much remains in her savings account after 10 months ?
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The total she withdrawn after ten months was $700.00. So $1000 - $700 = $300. That is how much that is left after ten months
Answer: A-$300 is correct
Please help! The question is attached. And also I know the numbers on the triangle are blurry. The number on the long bottom of the triangle is 24, the one in the corner of the bottom of the triangle is 90 degrees, the side length is 18, and the diagonal angle is 26.
Answers
glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
Answers
Answer:
The correct option is 1.
Step-by-step explanation:
It is given that the glacier is moving at a rate of 0.3 inches every hour. It means the average rate of change is 0.3.
Let d is the total moved distance of glacier and t is number of hours. Then the total moved distance of glacier after t hours is defined as
[tex]d=0.3t[/tex]
At t=1,
[tex]d=0.3(1)=0.3[/tex]
At t=2,
[tex]d=0.3(2)=0.6[/tex]
At t=3,
[tex]d=0.3(3)=0.9[/tex]
At t=4,
[tex]d=0.3(4)=1.2[/tex]
Total moved distance of glacier after 4 hours is 1.2 inches.
The value of x is 1.2. Therefore the correct option is 1.
What is the x-coordinate for the minimum point in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?
Answers
[tex]cos(2x- \pi )=-1[/tex]
[tex]2x- \pi=\pi[/tex]
[tex]2x=2\pi[/tex]
[tex]x=\pi[/tex]
The x-coordinate for the minimum point of the function f(x) must be π.
f(x) = 4 cos(2x − π)
using a graph tool
see the attached graph
the x-coordinate for the minimum point from x = 0 to x = 2π
if the interval is [0,2π]
there are 3 minimal points
(0,-4) (π,-4) (2π, -4)
if the interval is (0,2π)
there is 1 minimal point
(π,-4)
I'M OFFERING 10 POINTS (More Than What It's Worth) AND BRAINLIEST ANSWER PLEASE SHOW ALL OF YOUR WORK. Thanks In Advance Guys
Answers
can anyone give an explanation and answer to this question,my sister needed help on this also :) Thank you again for taking your time to answer and read this <3
what is the circumference of a circular pond with a radius of 14 meters?
Answers
The circumference of a circle is calculated by 2πr
2π14 2*14=28
So it can be either 28π or you can take the first digits of π which are 3.1415 and multiply that by 28
28*3.1415= 87.96
Therefore you end up with 2 different answers...
87.96 or 28π
Tara and julia run a race. Julia takes 42 seconds to run the race. She is 7 seconds faster than Tara. How many seconds does Tara take?
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A rectangular room is 14 feet by 20 feet. The ceiling is 8 feet high. How do you find the length and width of the smaller and larger wall?
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We need to visualize the box by using a diagram attached with this problem.
[tex] Length = 14 \; feet [/tex]
[tex] Width = 20 \; feet [/tex]
[tex] Height = 8 \; feet [/tex]
The blue is smaller rectangle and brown is the larger rectangle
Conclusion:
Length of smaller wall (in blue color) is 14 feet
Width of smaller wall (in blue color) is 8 feet
Length of Larger wall (in brown color) is 20 feet
Width of the Larger wall (in brown color) is 8 feet
To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expression 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit? The inequality that will determine the number of items that need to be sold to make a profit is ? The solution to the inequality is ? The company must sell at least? items to make a profit.
Answers
Operation Costs = 5.8x + 79.86
To break even, operation cost = Revenue
⇒ 7.5x - 100 = 5.8x + 79.86
7.5x = 5.8x + 179.86 (Add 100 to both sides)
7.5x - 5.8x = 179.86
1.7x = 179.86
x = 105.8
This implies that the company will need to sell at least 106 items to make a profit.
The inequality that will determine the number of items at need to be sold to make a profit is x ≥ 106
The solution to the inequality is as follows
Revenue = 7.5x - 100
if x =106
Revenue = 7.5(106) - 100
Revenue = 695
Operational Cost = 5.8x + 79.86
if x = 106
Operational Cost = 5.8(106) + 79.86
Operational Cost = 694.66
Profit ≥ (695 - 694.66)
Profit ≥ 0.34
The company must sell at least 106 items to make a profit.
Using the profit concept, it is found that:
The inequality is: [tex]1.7x - 179.6 > 0[/tex]The solution is [tex]x > 105.6[/tex]The company must sell at least 106 items to make a profit.Profit is revenue subtracted by operations costs, that is:
[tex]P(x) = R(x) - C(x)[/tex]
In this problem, the functions are:
[tex]R(x) = 7.5x - 100[/tex]
[tex]C(s) = 79.6 + 5.8x[/tex]
Thus, the profit function is:
[tex]P(x) = R(x) - C(x)[/tex]
[tex]P(x) = 7.5x - 100 - 79.6 - 5.8x[/tex]
[tex]P(x) = 1.7x - 179.6[/tex]
It makes a profit if:
[tex]P(x) > 0[/tex]
Thus, the inequality is:
[tex]1.7x - 179.6 > 0[/tex]
The solution is:
[tex]1.7x > 179.6[/tex]
[tex]x > \frac{179.6}{1.7}[/tex]
[tex]x > 105.6[/tex]
Thus, the company must sell at least 106 items to make a profit.
A similar problem is given at https://brainly.com/question/24373628
Can you solve the measure of an angle is twenty-nine times the measure of a supplementary angle. what is the measure of each angle
Answers
Let's assume A the measure of the angle,
180-A the supplementary angle
A=29*(180-A)
A=29*180 -29A
30A=29*180
A=29*180/30
A=29*6
A=174
Proof: 174=29*(180-174)
in y=16500-1500x what is the rate of change
Answers
Final answer:
The rate of change in the linear equation y=16500-1500x is -1500, indicating that y decreases by 1500 for each increase in x by one unit. This represents the slope of the line and shows a direct relationship between x and y in a regression line context.
Explanation:
In the equation y=16500-1500x, the rate of change is represented by the coefficient of x, which is -1500. This means that for each unit increase in x, the value of y decreases by 1500. Contrary to the provided reference which mistakenly lists the slope as -105,000/1, the actual rate of change in this linear equation is -1500. Such linear equations are often used to describe a regression line, which showcases the average relationship between the variables x and y in a scatter diagram.
The slope of a line in a linear equation like this one is crucial for understanding how changes in one variable affect another. This linear model is straightforward and does not change across different values of x, unlike in nonlinear models where the rate of change can vary.
10 POINTS AND BRAINLIEST FOR CORRECT ANSWER!
A rectangle is inscribed in a square so that each vertex of the rectangle is located on one side of the square, and the sides of the rectangle are parallel to the diagonals of the square. Suppose that one side of the rectangle is twice the length of the other and that the diagonal of the square is 12 meters long. Find the sides of the rectangle.
Answers
9514 1404 393
Answer:
The sides of the rectangle are 4 and 8 meters long.
Explanation:
Please consider the attached figure. Both the rectangle and the square are symmetrical about the x- and y-axes, so we only need to consider the corner of the rectangle in one quadrant.
If the rectangle is twice as long as wide, then the distance of the corner to one axis (we chose y) will be twice the distance to the other axis. The locus of points for which that is true is the line with slope 1/2. The corner of the rectangle will be on that line.
If the corner of the rectangle is also on the square, then it will be located at the point of intersection of the line with slope 1/2 and the line representing the edge of the square. That point of intersection is the point (4, 2) on this graph. That is, half the length of the rectangle is 4 m, and half the width is 2 m. This indicates the sides of the rectangle are 8 m and 4 m in length.
__
The diagonals of the square are 12 m long, so orienting the square the way we have makes the x- and y-intercepts 6 units from the origin in each quadrant.
Answer:
Step-by-step explanation:
four and eight, use soh cah toa
675,360.41 in expanded notation
Answers
The expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
How to rewrite the number?The number is given as:
Number = 675,360.41
Express the numbers using their place values
Number = 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
The above expression represents the expanded notation
Hence, the expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
Read more about expanded notation at:
https://brainly.com/question/567952
What is the solution of the system?
{ 2x+y=15
{x−y=3
Enter your answer in the boxes.
(__ ,__ )
Answers
+ x -y= 3
-------------
3x = 18
x= 6
2(6)+y=15
12+y=15
y=15-12
y= 3
(6,3)
Help I can't find anyone who knows the answer to this! I will fan and medal to the first person who can answer it!
A scientist sets up an experiment to see how colored lights affect the height of plant growth. He grows one group of plants in full sunlight, one group under red lights, one group under blue lights, and one group under green lights. All the plants are exactly that same type and all receive an equal intensity of life. At the end of the experiment he measures all the plants.
What is the independent and dependent variable in this equation?
(A) the color of the light
(B) the height of the plant
(C) sunlight
(D) The intensity of the light
Answers
Dependent variable-the variable that is observed or measured.
Answer:
Independent variable is the color of the light Dependent variable is the height of the plant
Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
How mach is deducted from her paycheck for retirement plan?
A) $26.11
B) $52.22
C) $104.44
D) $522.24
Answers
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
So the deduction will be given as
[tex]\rm Deduction = \dfrac{4}{100} *1305.6\\\\Deduction = 0.04 * 1305.6\\\\Deduction = 52.224 \approx 52.22[/tex]
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
More about the percentage link is given below.
https://brainly.com/question/8011401
m ∠ U = (2x−5)° and m ∠W = (x+38)°What is m ∠W?
Question 1 options:
49°
180°
87°
90°
Answers
(2x -5) +(x +38) = 180
3x = 147
x = 49
m∠W = (49 +38)° = 87° . . . . . . . . . . corresponds to the 3rd selection
What is the value of x in the quadrilateral shown below?
A. 80°
B. 70°
C. 60°
Answers
85+150+55=290
360-290= 70
X= 70 degrees
a taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. the rule c=0.20m + 2.00 describe the relationship between the number of miles m and the total cost of the ride c.
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What is the written form of the decimal number .954?
Answers
your answer is Nine hundred fifty-four thousandths.