Part A: complete the statement below about inscribed quadrilateralsPart B: select all of the statements that are true
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Because the quadrilateral is incribed in a circle, the opposite vetices forms supplementary arcs of the circle, which means that opposite angles of it are supplementary.
This means that the first option is opposite angles and the second is supplementary.
They being supplementaty means that their sum is equal to 180°, so:
[tex]\begin{gathered} m\angle A+m\angle C=180\degree \\ m\angle B+m\angle D=180\degree \end{gathered}[/tex]However, notrhing can be said about congruency of opposite angles, so the first option of part be is not necessarily true.
The second is true, as we showed above.
The third shows a relationship between adjacent angle, which is not necessarily true.
The fourth is false because the opposite angles should add to 180° no 90°.
The last is a property of all quadrilaterals (independetly of them being inscribed or not): the sum of its internal angles is equal to 360°, so the fifth option is true.
So, in part B the only true statements are the second and the fifth.
Related Questions
6 The drawing below represents the frame for an isosceles triangle-shaped roof. The height of the roof is 6 feet. 30° А B What is the distance from Point A to Point B in feet? (G.8b)(1 point) O A. 4V3 OB. 123 O C. 24 O D. 12
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Given the information about the isosceles triangle, we have the following right triangle:
we can find half the distance from A to B by using the trigonometric function tangent as follows:
[tex]\begin{gathered} \tan (30)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{6}{x} \\ \Rightarrow x=\frac{6}{\tan (30)}=\frac{6}{\frac{1}{\sqrt[]{3}}}=6\sqrt[]{3} \end{gathered}[/tex]therefore, the distance from point A to point B is:
[tex]d(A,B)=2\cdot(6\sqrt[]{3})=12\sqrt[]{3}[/tex]Hi, can you help me to solve this exercise please!
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Given that:
[tex]\sin (\theta)=\frac{5}{13}[/tex]And knowing that:
[tex]0\degree<\theta<90\degree[/tex]You need to remember that, by definition:
[tex]\csc \theta=\frac{1}{\sin \theta}[/tex]Therefore, the cosecant of the angle does not exist when:
[tex]\sin \theta=0[/tex]Because the division by zero is not defined.
Therefore, you can conclude that, in this case:
[tex]\csc \theta=\frac{1}{\frac{5}{13}}[/tex]Simplifying, you get:
[tex]\begin{gathered} \csc \theta=\frac{\frac{1}{1}}{\frac{5}{13}} \\ \\ \csc \theta=\frac{1\cdot13}{1\cdot5} \\ \\ \csc \theta=\frac{13}{5} \end{gathered}[/tex]Hence, the answer is:
[tex]\csc \theta=\frac{13}{5}[/tex]helpp.................
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We want to find the median, which is the value that separates the higher half from the lower half of the data
Step 1: organizing the data from the lowest to the highest
We have that
Step 2: finding the middle of the organized data
Step 3: finding the median
Since the data of the middle is the mean between 44 and 46:
[tex]\frac{44+46}{2}=\frac{90}{2}=45[/tex]Answer- A:45º
20.2 = - [tex] \frac{ \times }{0.2} [/tex]+ 3.7 I need help on that
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To solve for x:
1. substract 3.7 in both sides of the equation:
[tex]\begin{gathered} 20.2-3.7=-\frac{x}{0.2}+3.7-3.7 \\ \\ 16.5=-\frac{x}{0.2} \end{gathered}[/tex]2. Multiply both sides of the equation by 0.2:
[tex]\begin{gathered} 0.2\cdot16.5=-\frac{x}{0.2}\cdot0.2 \\ \\ 3.3=-x \end{gathered}[/tex]3. Multiply both sides of the equation by -1:
[tex]\begin{gathered} (-1)\cdot3.3=(-1)\cdot(-x) \\ -3.3=x \end{gathered}[/tex]Then, x is -3.3One serving of 2 cookies has 140 calories.The whole package has 15 servings.how many calories are in the whole package
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Gathering the data
1)
1 serving = 2 cookies = 140 calories
15 serving = ?
2) We can solve this by setting a proportion:
servings calories
1 ---------------- 140
15 -------------- x
x =15 x140
x=2100
Find the area of a circle whose diameter is 27 inches. (Use pie = 3.1416.)
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ANSWER:
The area of circle is 572.5566 in^2
STEP-BY-STEP EXPLANATION:
We have that the area of the circle is the following
[tex]A=\pi\cdot r^2[/tex]Where r is the radius, and the radius corresponds to half the value of the diameter, replacing and calculating the area we have left:
[tex]\begin{gathered} d=\frac{27}{2}=13.5 \\ A=3.1416\cdot13.5^2 \\ A=572.5566 \end{gathered}[/tex]Determine the value x needs to be to make the triangles similar
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If both triangles are similar, it means that the ratio of the corresponding sides is proportional. It also means that the corresponding angles are congruent
By comparing both triangles,
2x - 10 = 30
2x = 30 + 10
2x = 40
x = 40/2
x = 20
I not really good at geometry, can you help me, that will mean a lot, thank you!
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oval (option C)
rectangle (option D)
circle (option E)
Explanation:The cross section gotten from a shape depends on the orientation of the plane used in cutting the shape.
If the plane is cutting the cylinder vertically, the cross section obtained will be a rectangle
If the plane is cutting the cylinder horizontally, the cross section obtained will be a circle
if the plane is cutting the cylinder in slant manner, the cross section will be an oval
A line is not a shape and we can't get it whne the plane cuts the cylinder.
Hence, the shapes are oval, rectangle and circle
I make 9.50 per hour work 5hours per day 4days per week What will I earn in a 12 week season
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From the information given, 9.5 is made per hour. This means that in 5 hours, The amount that would be made is
[tex]9.5\text{ }\times5\text{ = 47.5}[/tex]Since he works 5 hours per day, the amount earned per day is 47.5
If he works 4 days per week, then the amount that he would earn per week is
[tex]47.5\text{ }\times4\text{ = 190}[/tex]If he earns 190 per week, then the amount that he would earn in a 12 week season is
[tex]190\text{ }\times\text{ 12 = 2280}[/tex]He would earn 2280 in a 12 week season
At What point is the maximum value found in the system of inequalities graphed below for the functionf(x, y) = x - 2y?
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The correct answer is C. 5,0
Let´s replace on the equation given:
Ashaniea Hinds Question 9-10 Points Mar 05, 10:34:28 AM ? Find the volume of a right circular cone that has a height of 15.2 m and a base with a radius of 16.2 m. Round your answer to the nearest tenth of a cubic meter. Submit Answer Answer: Privacy Policy Terms of Service
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Step 1
List all parameters
Height h = 15.2m
Radius r = 16.2
Step 2
Write formula of volume of a cone
[tex]\begin{gathered} \text{Volume of a cone} \\ =\text{ }\frac{1}{3}\text{ }\pi r^2h \\ =\text{ }\frac{1}{3}\text{ x 3.142 x 16.2 x 16.2 x 15.2} \\ =\text{ }\frac{1\text{ x 3.142 x 16.2 x 16.2 x 15.2}}{3} \\ =\text{ }\frac{12533.7145}{3} \\ =4177.9m^3 \end{gathered}[/tex]Find the length of the line segment between the given points.P106, -2) and P2(-3, 4)
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Circle O is centered at the origin. Point P (1,^3) lies on the circle. What is the radius of the circle?A. 1 unitB. 2 unitsC. 3 unitsD. 4 units
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The circle with its origin at 0, and a point (1, V3) means all points along the circle is the same distance from point zero (origin). From the information provided we can deduce a right angled triangle as shown below.
The points given as
[tex]P(1,\sqrt[]{3})[/tex]means that point P is 1 unit along the x-axis and square root 3 units along the y-axis. Note that the distance between point P and the origin is the radius. We can now solve for the radius by using the Pythagoras' theorem;
[tex]\begin{gathered} a^2=b^2+c^2 \\ \text{Where, a=hypotenuse, b and c=other two sides} \\ r^2=1^2+(\sqrt[]{3})^2 \\ r^2=1+(\sqrt[]{3}\times\sqrt[]{3}) \\ r^2=1+3 \\ r^2=4 \\ r=\sqrt[]{4} \\ r=2 \end{gathered}[/tex]The radius of the circle is 2 units
Option B is the correct answer
List 2 solutions to y = -7x + 5
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Substituting with x = 0 into the equation, we get:
y = -7(0) + 5
y = 0 + 5
y = 5
Substituting with x = 1 into the equation, we get:
y = -7(1) + 5
y = -7 + 5
y = -2
The solutions are (0, 5) and (1, -2)
If x equals 7 and the total is 234 what’s Y
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We are given the following information
[tex]x=7[/tex]And the total is 234 which means
[tex]x+y=234\text{ eq. 1}[/tex]We are asked to find the value of y
Let us substitute the value of x into the eq. 1
[tex]7+y=234[/tex]Subtract 7 from both sides of the equation
[tex]\begin{gathered} -7+7+y=234-7 \\ y=227 \end{gathered}[/tex]Therefore, y is equal to 227.
Select the correct answer.In triangle ABC, AB = 12, BC = 18, and m B = 75°. What are the approximate length of side AC and measure of XA?OA. AC = 18.9;m A = 66.9°OB AC = 20.3; m XA = 34.8°O c. AC = 18.9;m A = 37.8°OD. AC = 20.3; m A = 58.9°ResetNext
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The triangle described is shown below (this is not the correct triangle but we need something to help):
To find the lenght of side AC we need to use the law os cosines:
[tex]AC^2=AB^2+BC^2-2(AB)(BC)\cos B[/tex]In this case we have:
[tex]\begin{gathered} AC^2=12^2+18^2-2(12)(18)\cos 75 \\ AC^2=356.19 \\ AC=\sqrt[]{356.19} \\ AC=18.9 \end{gathered}[/tex]Now, to find angle A can use the law of sines:
[tex]\frac{\sin A}{BC}=\frac{\sin B}{AC}[/tex]Then:
[tex]\begin{gathered} \frac{\sin A}{18}=\frac{\sin 75}{18.9} \\ \sin A=\frac{18}{18.9}\sin 75 \\ A=\sin ^{-1}(\frac{18}{18.9}\sin 75) \\ A=66.9 \end{gathered}[/tex]Therefore the correct answer is A.
Find the volume of the space not taken up by the volleyball.
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Given that a volleyball is shipped in the cubical box.
The diameter of the ball is = 8.15 inches
So the radius will be r = 8.15/2 inches = 4.075
Now, the diameter of the ball will be the side of the cube as it is inside the box.
Then the side of the cube is a = 8.15 inches
Hence, the volume of the cubical box will be
[tex]\begin{gathered} V=a^3 \\ V=8.15\times8.15\times8.15\text{ in}^3 \\ V=541.343375\text{ in}^3 \end{gathered}[/tex]Now the volume of the ball
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\frac{4}{3}\times3.14\times4.075\times4.075\times4.075\text{ in}^3 \\ v=283.303033 \end{gathered}[/tex]Now the required volume will be
= V - v = 541.343375 - 283.303033 cubic inches
= 258.040342 cubic inches
After round-off, the answer will be 258 cubic inches.
Therefore the space left will be 258 cubic inches.
on the diagram shown of two intersecting lines if the angle of 2 equal 130 degree what would the degree of angles at 1, 3 and 4 equal
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In the diagram shown in the picture, both lines intersect forming 4 angles.
The angles that share a vertex but not sides, meaning that they are on the opposite side of the X shape, are vertically opposite angles:
Vertically opposite angles are equal so that:
∠1=∠3
∠2=∠4
We know that ∠2= 130º, since ∠4 is equal to ∠2, then ∠4= 130º
Now ∠1 and ∠2 are on the same line, which means that they are a linear pair.
Linear pairs are adjacent supplementary angles, which means that their sum is equal to 180º
Knowing this we can calculate the measure of ∠1 as follows:
[tex]\begin{gathered} \angle1+\angle2=180º \\ \angle1+130=180 \\ \angle1=180-130 \\ \angle1=50º \end{gathered}[/tex]Finally, ∠1 and ∠3 are equal so ∠3=50º
So the measures for the angles are:
[tex]\begin{gathered} \angle1=50º \\ \angle2=130º \\ \angle3=50º \\ \angle4=130º \end{gathered}[/tex]Find the area of the rectangle that has a perimeter of 8x + 12 units and a length of 2x − 3 units.
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We are given the following information.
Perimeter of rectangle = 8x + 12 units
Length of rectangle = 2x − 3 units
Recall that the perimeter of a rectangle is given by
[tex]P=2(L+W)[/tex]Where L is the length and W is the width of the rectangle.
Let us substitute the values of perimeter and length and solve for width.
[tex]\begin{gathered} P=2(L+W) \\ 8x+12=2(2x-3+W) \\ 8x+12=4x-6+2W \\ 8x-4x+12+6=2W \\ 4x+18=2W \\ 2W=4x+18 \\ W=\frac{4x+18}{2} \\ W=2x+9 \end{gathered}[/tex]Recall that the area of a rectangle is given by
[tex]A=L\cdot W[/tex]Substitute the values of length and width
[tex]\begin{gathered} A=L\cdot W \\ A=(2x-3)\cdot(2x+9) \\ A=2x\cdot2x+2x\cdot9-3\cdot2x-3\cdot9 \\ A=4x^2+18x-6x-27 \\ A=4x^2+12x-27 \end{gathered}[/tex]Therefore, the area of the rectangle is
[tex]A=4x^2+12x-27[/tex]A teacher tells a class that the mean raw score on a test was 58. Alex has a raw score of 73 and a z-score of 1.25. What was the standard deviation on the test? (Round to the nearest tenth)
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Given:
Mean raw score(population mean), μ = 58
z-score, Z = 1.25
Raw score, x = 73
To find the standard deviation, σ, use the Z-score formula below:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Rewrite the equation for σ:
[tex]\sigma=\frac{x-\mu}{Z}[/tex]Now, substitute value into the formula:
[tex]\sigma=\frac{73-58}{1.25}=\frac{15}{1.25}=12[/tex]Therefore, the standard deviation on the test is = 12
ANSWER:
12
I need help with this practice I’m struggling to solve it, I have already attempted it but I’m dealing uneasy on my final answer
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Answer:
y = 7 csc ( x /2) - 2
Explanation:
The parent csc x function has the range ( - ∞, -1] U [1,∞ ) infinity, meaning its "width" is 2. Now our function has range ( - ∞, -9] U [5,∞ ), with a width of 5 - (-9) = 14, which is two times as much as that of the parent function function. This tells us that the function is vertically stretched by a factor of 14 / 2 = 7, and so we have
[tex]y=7\csc x[/tex]Now, the parent function csc x has vertical asympototes at x = 0 and x = π. Our function, however, has consecutive asymptotes at x = 0 and x = 2 π. Meaning our functin is streched horizontally by a factor of 2. Therefore, we do x --> x / 2 and so we have
[tex]y=7\csc (\frac{x}{2})[/tex]Lastly, we observe that the function is not symmetric about the x-axis, whereas the parent function is. This tells us that some vertical shifting is involved. How much vertical shifting exactly?
We find the answer by finding the midpoint
[tex](-9+5)/2[/tex][tex]=-2[/tex]which is the vertical shift.
Therefore, the final form of our function is
[tex]\boxed{y=7\csc (\frac{x}{2})-2}[/tex]which is our answer!
18. For the simple interest loan whose terms are given below, find the future value, or the amount due at the end of the specified time.Principal:$6900Interest rate:3.6%Time:1 yearsFuture value: $
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To determine the interest we need to pay, we need to use the following expression:
[tex]A=P(1+rt)[/tex]Where A is the final amount, P is the principal, r is the interest rate and t is the elapsed time.
[tex]\begin{gathered} A=6900(1+\frac{3.6}{100}\cdot1)_{} \\ A=6900(1+0.036)_{} \\ A=6900(1.036) \\ A=7148.4 \end{gathered}[/tex]The due amount is 7148.4
A bag has 20 marblesif 40% of the marbles are green, how many marbles are there?
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Answer:
There are 20 marbles in the bag and 8 of them are green
Explanation:
We need to calculate 40% of 20 marbles, so:
[tex]20\times40\text{ \% = 20}\times\frac{40}{100}=8[/tex]Therefore, there are 20 marbles in the bag and 8 of them are green
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question.Listed below are foot lengths in inches of randomly selected women in a study of a country's military in 1988. Are the statistics representative of the current population of all women in that country's military?
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Given:The given data is (in inches)
9.6, 9.8, 10.2, 9.8, 9.7, 8.9, 10.3, 9.9, 9.3, 10.2, 10.2.
Required:
(a) Mean
(b) Median
(c) Mode
(d) Mid-Range
Explanation:
Let us first arrange the data in ascending order
8.9, 9.3, 9.6, 9.7, 9.8, 9.8, 9.9, 10.2, 10.2, 10.2, 10.3
(a) Mean
The mean of data is sum of observations divided by number of observations
[tex]\begin{gathered} Mean=\frac{8.9+9.3+9.6+9.7+9.8+9.8+9.9+10.2+10.2+10.2+10.3}{11} \\ Mean=9.809 \end{gathered}[/tex](b) Median
Since there are 11 terms, so median is
[tex]\frac{11+1}{2}=\frac{12}{2}=6th\text{ term}[/tex]So median is
[tex]Median\text{ = }9.8[/tex](c) Mode
Mode is most occured frequency
so here 10.2 occurs most of the time (3 times)
[tex]Mode=10.2[/tex](d) Mid range
Mid range is average of least and highest frequency
[tex]Mid\text{ range = }\frac{8.9+10.3}{2}=9.2[/tex]Final Answer:
(a) Mean = 9.809
(b) Median = 9.8
(c) Mode = 10.2
(d) Mid range = 9.2
I don't understand how to add negative fraction with a positive
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The addition of negative fraction to a positve fraaction is simply subtraction of fractions with sign of result depend upon the sign of larger fraction.
Simplify the fraction.
[tex]\begin{gathered} -\frac{4}{5}+\frac{6}{5}=\frac{6}{5}-\frac{4}{5} \\ =\frac{6-4}{5} \\ =\frac{2}{5} \end{gathered}[/tex]Answer is 2/5.
James had three times as many pickles as dimes. If the total value of his coins was $1.00 how many of each did he have?
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James had four dimes and twelve nickels if he had three times that many nickels as dimes.
Describe the equation?An equation is indeed a statement stating that two expressions containing variables and/or numbers are equal. In essence, equations seem to be questions, and attempts to find systematic answers to these questions are the driving forces behind development of mathematics.Provided that James must have three times quite so many nickels as dimes as well as a total coin value of $1.00,
1 $ = 20 nickels
1 $ = 10 dimes
Let the dimes are x, thus the nickel is 3x.
5 × 3x + 10x = 100
15x + 10x = 100
25x =100
x = 4
The number of nickels is found as; 3x4 = 12.
As we know, if James will have three times so many more nickels as dimes, he would have four dimes and twelve nickels.
To know more about equation, here
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1. Match each inequality to the meaning of a symbol within it.a. h > 50o less than or equal tob.h <20º greater thanC. 30 hgreater than or equal to
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There are 4 inequality signs:
[tex]\begin{gathered} <\colon less\, than \\ \le\colon less\, than\, or\, equal\, to \\ >\colon greater\, than \\ \ge\colon greater\, than\, or\, equal\, to \end{gathered}[/tex]So:
A is:
[tex]>[/tex]So, A is greater than.
B is:
[tex]\le[/tex]So, B is less than or equal to.
C is:
[tex]\ge[/tex]So, C is greater than or equal to.
Suppose that the relation S is defined as follows.S={(6,0), (-2, 2), (3, -2), (6, 7)}Give the domain and range of S.Write your answers using set notation.domain =0,0,...range = 0=Хs?
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For the given relation:
[tex]S=\lbrace(6,0),(-2,2),(3,-2),(6,7)\rbrace[/tex][tex]\begin{gathered} \text{Domain:}\lbrace6,-2,3\rbrace \\ \\ \text{Range:}\lbrace0,2,-2,7\rbrace \end{gathered}[/tex]In the figure below, m NLM = 60° and mZPLR = 102°. What is mZOLM? M N 0 60° ? L 102° R P 1200
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angle NLM +angle OLM = angle NLO = angle PRL
angle OLM +60=102
angle OLM =102-60
angle OLM =42
what is the meaning of mathemathics
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Mathematics is a little difficult to define once it is really huge and there are many ways to define it but in a simple way Mathematics is a cience that studies parterns. With mathematics we can analyze the world and understand the paterns and translate it into numbers. For example, imagine you have a lot of apples, than a mathematician arives and translate it into numbers and says you have 20 apples. Now you understand the fact you have apples in a different way, the way math does, through numbers. This is just a simple example. Mathematics is present all around us. To build a plane, an iphone, a house or a website you need some knowledge in mathematics.