Answers
Angles are said to be produced whenever two or more straight lines intersect. Some types of angles are right angle, obtuse angle, acute angle, etc. Thus, the required proof is stated below:
Prove: <A > <C
<B > <D
An obtuse angle is a given angle that is greater than [tex]90^{o}[/tex] but less than [tex]180^{o}[/tex]. While an acute angle is a given angle that is less than [tex]90^{o}[/tex].
Thus extend AB to F, such that BF = CD.
Draw a perpendicular from a to intersect CD at point E.
So that;
<BAD = <BAE + <DAE (addition property of an angle)
Such that;
<A is an obtuse angle, while <C is an acute angle. Thu,
<A > <C (different types of angles)
Also,
<ADC = <CDF - <ADF (subtraction property of angles)
But both angles B and D are acute angles.
So that;
<B > <C (comparison of measures of two angles)
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Related Questions
Assume that each circle shown below represent one unit express the shaded amount as a single fraction and as a mixed number
Answers
One fraction: 5/2.
Mixed-fraction: 2 1/2.
In the question, we are asked to assume that each circle shown below represents one unit, and are asked to express the shaded amount as a single fraction and a mixed fraction.
The given circle is divided into 8 equal parts.
In the first circle, all 8 parts are shaded, shown by the fraction, 8/8.
In the second circle, all 8 parts are shaded, shown by the fraction, 8/8.
In the third circle, 4 parts are shaded, shown by the fraction, 4/8.
Thus, the total shaded part can be calculated by adding:
8/8 + 8/8 + 4/8,
= (8 + 8 + 4)/8
= 20/8
= 5/2 {Cancelling off by 4}.
Thus, one fraction is 5/2.
To convert this to a mixed fraction, we divide 5 by 2, write the quotient as the whole part, the remainder as the numerator, and 2 as the denominator.
5÷2 gives quotient 2, and remainder 1.
Thus, the mixed-fraction is 2 1/2.
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A gardener wants to design a rectangular garden and has 100 feet of fencing available. A house is on one side of the garden, so no fencing will be needed there. What dimensions will give the maximum area?
Answers
Answer:
50 ft and 25 ft give the maximum area
Step-by-step explanation:
Let l and w be the dimensions of rectangle.
The length of fencing is 100 ft:
l + 2w = 100Then:
l = 100 - 2wThe area is:
A = lw = w(100 - 2w) = 100w - 2w²In order to have the maximum area we need to find the vertex of the quadratic function:
y = - 2w² + 100wThe vertex has x-coordinate:
w = - b/(2a) It comes from quadratic function y = ax² + bx + cor
w = - 100/(2*(-2)) = 25So the width is 25 ft.
Find the length:
l = 100 - 2*25 = 50 ftThe area is:
A = 50*25 = 1250 ft²See the attached graph.
Question 3 of 10
Which of the following must be true for an expression to be a difference of
two squares?
a. all variables are raised to an even power
b. there are only two terms
c. both terms have negative coefficients
OA. a, b, and c
B. a and b
OC. a and c
D. b and c
Answers
B is true: you cannot have a trinomial, only binomial or two terms
C is FALSE: you cannot take a square root of a negative and get a real number
B. a and b
write a solution system for the inequality 3x-2>10
Answers
Answer:
x>4
Step-by-step explanation:
3x - 2 >10 add 2 to both sides
3x > 12 Divide both sides by 3
x >4
Answer:
[tex]x > \bf 4[/tex]
Step-by-step explanation:
To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:
[tex]3x - 2 > 10[/tex]
⇒ [tex]3x - 2 + 2 > 10 + 2[/tex] [Add 2 to both sides]
⇒ [tex]3x > 12[/tex]
⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex] [Divide both sides by 3]
⇒ [tex]x > \bf 4[/tex]
Given the function f(x) = -5x²-x+ 20, find f(3).
O-28
O-13
O62
O64
Answers
Answer: [tex]\Large\boxed{First~Choice.~-28}[/tex]
Step-by-step explanation:
Given function expression
f(x) = -5x² - x + 20
Requirement of the question
Find the value of f(3)
Substitute the values into the function
f(x) = -5x² - x + 20
f(3) = -5(3)² - (3) + 20
Simplify the exponents
f(3) = -5(9) - 3 + 20
Simplify by multiplication
f(3) = -45 - 3 + 20
Simplify by subtraction and addition
f(3) = -48 + 20
[tex]\Large\boxed{f(3)=-28}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The prices for different lengths of ribbon sold at a fabric store are shown in the table.
Which statement best justifies whether or not the relationship between the length and price represents a function?
Answers
the correct option is the last option, the table represents a function because no length of ribbon has more than one price.
What is a function?
A function is a relationship that maps elements from a set, the domain (set of the inputs), into elements from another set, the range (set of the outputs).
Such that each element of the domain can be mapped into only one element of the range.
If we look at the table, we can see that each input (length of ribbon) is mapped into only one output (price). Then we conclude that this table represents a function.
Then the correct option is the last option, the table represents a function because no length of ribbon has more than one price.
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please please please
Answers
The amount of water in each mug is 2 / 5 litres
How to find the litres of water in each mug?The water bottle has 4/5 litres of water.
The litre of water is poured equally in 2 mugs.
Therefore, the amount of water in each mug can be calculated as follows;
amount of water in each mug = 4 / 5 ÷ 2
amount of water in each mug = 4 / 5 × 1 / 2
amount of water in each mug = 4 / 10
amount of water in each mug = 2 / 5 litres
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Solve the equation. Write the smaller value of x. x^2-4x-5=0
Answers
(x-5)(x+1) = 0
x = 5
x = -1
x = 5 OR x = -1
since it says write the smaller value, then i think the answer is -1.
of
Given the triangle ABC at points A=(1,6) B=(-3,5) C=(7,1), and if the triangle is first reflected over the
y axis, and then over the x axis, find the new point A".
Select one:
O a. (1,-6)
Ob. (3,5)
Oc. (-1,-6)
O d. (1,6)
Answers
After reflected over the triangle the point a become A = (-1,-6). The option c is correct.
According to the statement
we have given that the a triangle ABC at the points A=(1,6) B=(-3,5) C=(7,1), and we have to find the points of a when the triangle is first reflected over the y axis.
So, For this purpose
we know that the when the triangle is at the x axis then the point A is A=(1,6).
But when the triangles reflected over the y - axis then the point A goes to the negative side of the graph. In other words whole of the triangle shift to the negative side of the graph. That's why the point become negative.
So, The option c is correct. After reflected over the triangle the point a become A = (-1,-6)
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Find the value of x.
OA. 66
OB. 122
OC. 98
O D. 76
SUBMIT
Answers
Answer:
C) 98
Step-by-step explanation:
Hope this helps! sry if I'm wrong
The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.
An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.
The given equation is
15x + 120 = 5x + 1100
Take the like terms together,
15x - 5x = 1100 - 120
10x = 980
x = [tex]\frac{980}{10}[/tex]
x = 98.
Thus, the option C is correct stating that the value of x in the given equation is 98.
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The complete question is as follows:
Find the value of x in the equation:
15x + 120 = 5x + 1100.
A. 66
B. 122
C. 98
D. 76
SUBMIT.
A Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. Which Equations Can Be Used To Find The Numbers Of Miles Driven For A Truck That Cost A Total Of $42.50 To Rent For One Day?
A)$25m + 0.35m = $42.50
B)$0.35 + $25m = $42.50
C)$42.50 + $0.35m = $25
D)$0.35 = $42.50
Answers
The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
According to the statement
we have given that the Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.
And we have to find the equation for this.
So, for given purpose,
we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
And from the given values the equation formed that the
In the equation the charges per mile is added to the original charges is equal to the total charges per day.
So, The equation become
$25m + 0.35m = $42.50
And by this equation we represent the all given conditions related charges.
So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
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A vase in the shape of an oblique cylinder has the dimensions shown. What is the volume in the vase in liters?round nearest tenth
Answers
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Cylinder is solid geometrical figure with straight parallel sides and a circular or oval cross section
Let us assume that the vase has a base with radius of 1 m and height of 7 m, hence:
Volume of vase = π * radius² * height
Volume of vase = π * (1)² * 7 = 22 m³ = 22000 L
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
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please help i dont understand
Answers
The box and whisker plot is a 71 and 53 and 89 which represent the
median, upper value and lower value.
According to the statement
we have given that the some data of the marks of 18 students and we have to make the plot of that data.
So, For this purpose, we have given that the
A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.
And it is used to find the median and the lower value and the maximum value.
So, The median become:
median = n /2
median = 18/2
median = 9th term and
median value is 71.
And then the lower value of the data is a 53.
And the upper value of the data is a 89.
So, overall we can say that the combination of median, upper value and lower value is called the box and whisker plot.
So, The box and whisker plot is a 71 and 53 and 89 which represent the
median, upper value and lower value.
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Based on these segment lengths, which group of segments cannot form a triangle? a. 12, 7, 8 b. 8, 7, 13 c. 1, 2, 3 d. 80, 140, 70
Answers
(D) 80°, 140°, and 70° group of segments cannot form a triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC represents a triangle with vertices A, B, and C.In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. In other words, the triangle is contained in just one plane, and every triangle is contained in some plane. There is just one plane and all triangles are enclosed in it if the entire geometry is merely the Euclidean plane; but, in higher-dimensional Euclidean spaces, this is no longer true.To find which group of segments cannot form a triangle:
80°, 140°, and 70° cannot form a triangle because the sum of the three angles is 290°, whereas the sum of the angles in a triangle is 180°.Therefore, (D) 80°, 140°, and 70° group of segments cannot form a triangle.
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Answer:
80, 140, 70
Step-by-step explanation:
please help if u cannot skip
Answers
The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
How to determine which statement is true?To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.
Conditions for continuity and differentiablity of a function.For a function f(x) to be continuous at a point x = a, then both the left hand limit of f(x) and the right hand limit of f(x) as x → a must be equal. That is [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x)[/tex]. So, [tex]\lim_{x \to a^{} } f(x)[/tex] must exist since [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x) = \lim_{x \to a^{} } f(x)[/tex]Also, for a function to be differentiable at a point x = a, it must also exist at x = a
So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}
From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.
That is [tex]\lim_{x \to 3^{-} } f(x) \neq \lim_{x \to 3^{+} } f(x)[/tex] . Thus, the function is discontinuous at x = 3.
For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.
So, the function is discontinuous and non-differentiable at x = 3.
So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
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solve for x
2^x,2^4=2^3x
Answers
Answer:
x=2
Step-by-step explanation:
2^x *2^4=2^3x
using law of indices
2^x+4=2^3x
x+4=3x
4=3x-x
4=2x
2=x
Select the correct answer from each drop-down menu.
Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.
Prove: WXYZis a square.
Using the distance formula, I found that
…
A. all four sides have a length of 5
B. all four sides have different lengths
C. only 2 sides have the same length
D. all four sides have a length of 10
Answers
Answer: A
Step-by-step explanation:
[tex]WX=\sqrt{(-1-3)^2 +(1-4)^2}=5[/tex]
Since WXYZ must be a square, all the sides must have a length of 5.
d. If you double a certain number and subtrack 7 you get the same answer as when you add 5 to the number, Determine the number
Answers
Answer:
12
Step-by-step explanation:
Let n = the number.
2n - 7 = n + 5
n = 12
Let’s check if we got the right answer by substituting 12 for n into the original equation.
2*12 - 7 = 12 + 5
24 - 7 = 17
17 = 17
uh help please dont know whats wrong step by step will help a lot
Answers
let's keep in mind that i² = -1, and let's use the conjugate of the denominator.
[tex]\cfrac{2+5i}{3-2i}\cdot \cfrac{3+2i}{3+2i}\implies \cfrac{(2+5i)(3+2i)}{\underset{\textit{difference of squares}}{(3-2i)(3+2i)}}\implies \cfrac{6+4i+15i+10i^2}{(3)^2~~ - ~~(2i)^2} \\\\\\ \cfrac{6+19i+10(\stackrel{i^2}{-1})}{9~~ - ~~(2^2 i^2)}\implies \cfrac{6+19i-10}{9~~ - ~~4(\underset{i^2}{-1})}\implies \cfrac{-4+19i}{9+4}\implies -\cfrac{4}{13}+\cfrac{19i}{13}[/tex]
6. If x is the largest of three consecutive integers, represent the sum of the three integers.
a) If x is the largest of three consecutive integers, how do we represent the three integers?
b) How do we convert this information into a solvable equation?
c) Find the sum
Answers
Answer:
See below
Step-by-step explanation:
x = largest
x-1 previous
x -2 smallest
sum = x + x-1 + x-2
sum = 3x -3
The graph of the function f(x)= 5/4 sin(x)+1 is shown. What are the key features of this function?
- The maximum value of the function is....(2pi,2.25,1)
- The minimum value of the function is...(pi/2,-0.25,-1)
- On the interval (0,pi/2), the function is...(increasing, decreasing)
-the range of the function is...([-0.25,2.24],all real numbers, [-1,1])
Answers
The answers to this question can be given as
The maximum value of the function is 2.25- The minimum value of the function is -0.25- On the interval (0,pi/2), the function is increasing-the range of the function is ([-0.25,2.25]What is the maximum value of a function?This is the point of the function while is it shown on the graph where it is said to be at its highest point or it is at its highest vertex.
When you trace the graph, the highest point is at 2.25.
What is the minimum value of a function?This is the point or the part of the function where it is at the vertex that is the lowest in the graph.
This is at -0.25
This is a function that can be said to be increasing from the behavior of this graph.
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Two equations are shown Y equals four over X +3 and Y equals negative 2X subtract four which statement best describes the graph of the two equations
Answers
The graph for the given system of equations is shown below
Graph of System of Linear equationsFrom the question, we are to determine the graph that describes the given system equations
First, we will graph the given system of linear equations.
The given equations are
Y equals four over X +3
and
Y equals negative 2X subtract four
That is,
y = 4/(x+3)
y = -2x -4
The graph for the given system of equations is shown below
The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below
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Find the m of
Find the m of
Can someone help I’m so very confused on how I even start this??
Answers
Both of these problems will be solved in a similar way, but with different numbers. First, we set up an equation with the values given. Then, we solve. Lastly, we plug into the original expressions to solve for the angles.
[23] ABD = 42°, DBC = 35°
(4x - 2) + (3x + 2) = 77°
4x+ 3x + 2 - 2 = 77°
4x+ 3x= 77°
7x= 77°
x= 11°
-
ABD = (4x - 2) = (4(11°) - 2) = 44° - 2 = 42°
DBC = (3x + 2) = (3(11°) + 2) = 33° + 2 = 35°
[24] ABD = 62°, DBC = 78°
(4x - 8) + (4x + 8) = 140°
4x + 4x + 8 - 8 = 140°
4x + 4x = 140°
8x = 140°
8x = 140°
x = 17.5°
-
ABD = (4x - 8) = (4(17.5°) - 8) = 70° - 8° = 62°
DBC =(4x + 8) = (4(17.5°) + 8) = 70° + 8° = 78°
pls help i don’t know how to do this
Answers
Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]
[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]
Find two positive numbers whose product is 81 and whose sum is a minimum. (enter your answers as a comma-separated list. )
Answers
Answer: 18
Step-by-step explanation: the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.
Prove the cofunction identity using the addition and subtraction formulas. sec 2 − u = csc(u) use a reciprocal identity, then apply a subtraction formula to simplify
Answers
Proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We have to prove that the cofunction identity using the addition and subtraction formulas.
sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We can prove this by using the identities given below:
[tex]sec(u)=\frac{1}{cos(u)}[/tex]
[tex]\frac{1}{sin(u)} =csc(u)[/tex]
cos(a-b) = cos a cos b + sin a sin b
Now the explanation,
[tex]sec(\frac{\pi }{2} -u) = csc(u)[/tex]
By using trignometric identities,
[tex]cos(u)=\frac{1}{sec(u)}[/tex] ∴[tex]sec(u)=\frac{1}{cos(u)}[/tex]
So,
[tex]\frac{1}{cos(\frac{\pi }{2}-u) } =csc(u)[/tex]
By substituting the given identities we get,
[tex]\frac{1}{cos(\frac{\pi }{2})cos(u)+sin(\frac{\pi }{2} )sin(u) }[/tex]
= [tex]\frac{1}{0.cos(u)+(1).sin(u)}[/tex]
=[tex]\frac{1}{sin(u)}[/tex]
= csc(u)
csc(u) = csc(u)
Here we proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]-u) = csc(u)
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A day care program has an average daily expense of $75.00. the standard deviation is $5.00. the owner takes a sample of 64 bills. what is the probability the mean of his sample will be between $70.00 and $80.00? step 1. calculate a z-score for $70.00 - step 2. give the probability for step 1. % step 3. calculate the z-score for $80.00 step 4. give the probability for step 3. % step 5. add the probabilities from steps 2
Answers
Answer:
B. 68
Step-by-step explanation:
x is a raw score to be standardized;
μ is the mean of the population;
σ is the standard deviation of the population.
Therefore the mean is zero. Seventy is -1z, or -1 standard deviation.
Step 2: 34.13% of the cases fall between -1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 70 and 75. This, of course, assumes a normal curve.
Step 3: An 80 is +1z or +1 standard deviation assuming a normal curve.
Step 4: Thirty four percent of the cases fall between +1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 75 and 80. This, of course, assumes a normal curve.
Step 5: Score between +1z and -1z, or +1 and -1 standard deviation account for 68.26% of the cases.
The chance of getting a viral infection is 0.0005. out of 10,000 people, about how many of them are expected to get infected?
Answers
The computation shows that the number of people expected to get infected is 5.
How to calculate the value?It should be noted that the chance of chance of getting a viral infection is 0.0005. out of 10,000 people.
Therefore, the number of people expected to get infected will be:
= 0.0005 × 10000
= 5
The number of people expected to get infected is 5.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
Answers
A polygon is a figure that has a given number of sides.
What is a polygon?A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.
a. 12.gon - An interior angle measures 150°
The polygon that has 12 sides is called the Dodecagon.
Given that the sum of the interior angles in a dodecagon is 1800, then each interior angle is; 1,800/12
= 150°
b. 15-gon - An exterior angle measures 24°
The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is 24° then;
360/ 24° = 15 sides
c. 16-gon - The sum of the interior angles is 2,520°
The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 = 157.5°
d. 18-gon - An interior angle measures 160°
A polygon that contains 18 sides is called an octadecagon .
We have;
160 = (n−2) × 180° / n
160n = 180n - 360
360 = 20n
n = 18
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Missing parts;
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
An interior angle measures 150".
An exterior angle measures 24.
The sum of the interior angles is 2520°.
An interior angle measures 160".
The sum of the exterior angles is 180º.
The sum of the interior angles is 2160°.
15-gon
16-gon
12.gon
18-gon
Answer:
15 gon = An exterior angle measure 2416 gon = The sum of the interior angles is 2,52012 = An interior angle measure 15018 = An interior angle measure 160Step-by-step explanation:
Need help with my math please. 31-41.
Answers
Step-by-step explanation:
31) the answer is (98765x9) +3=888888
why if u look at the equation is descending and if u verify the cinjecture u will find out is correct
41)½+¼+⅛+1/16+1/32=1-1/32
just d same reason with (31)
