1. Explain the difference between circumscribed angles and inscribed angles in relationship to a circle.
2. Explain, in your own words, the steps required to convert any equation of a circle into standard form be completing the square.
3. Explain/define the following terms, or draw a picture and label the terms.
a. radius
b. diameter
c. chord
d. secant
e. tangent
f. point of tangency
9514 1404 393
Explanation:
1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.
If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)
__
2. The general form of the equation of a circle is ...
Ax² +Ay² +Dx +Ey +F = 0
Any equation of a circle can be put in this form. If we divide by A, this can be written as ...
x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A
and the equation can be further transformed to the standard form ...
(x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c
The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.
__
3. Again refer to the attached diagram.
a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.
b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.
c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.
d) A secant is a line containing two points of the circle. Lines CG and CE are secants.
e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.
f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).
Which diagram represents the type of solution to this system of equations?
7x − 12y + z = -1
8x − 10y = 5
21x − 36y + 3z = -3
A.
B.
C.
D.
Answer: The answer should be A.
Step-by-step explanation: When solving the first and third equations, it becomes 0=0. I'm assuming that is one solution. Then 8x-10y=5 should be the other solution. In other words, there is 2 solutions.
The correct diagram represents the type of solution to this system of equations is shown in Option A.
We have to given that,
System of equations are,
7x - 12y + z = -1 .. (i)
8x - 10y = 5 .. (ii)
21x - 36y + 3z = -3 .. (iii)
Now, From equation (i);
Multiply by 3;
3( 7x - 12y + z) = -1 × 3
21x - 36y + 3z = - 3
Which is same as equation (iii).
Hence, Equation (i) and (ii) are parallel to each other.
And, It's a triple relationship.
Thus, Only option A has parallel planes.
So, Option A is true.
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Casey wants to buy a gym membership. One gym has a $176 joining fee and costs $29 per month. Another gym has no joining fee and costs $51 per month.
Part 1 out of 2
In how many months will both gym memberships cost the same? What will that cost be?
Answer:
8 months for cost to be same, cost will be $408
Step-by-step explanation:
x = months
176 + 29x = 0 + 51x
176 = 22x
8 = x
176 + (29*8) = 408
0 + (51*8) = 408
Determine the equation for the line that passes through (2,-1) and (6,5)
Write in point slope form
Write in slope intercept form
Write in standard form
Answer with explanation:
The equation of a line passing through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Equation of line passing through (2,-1) and (6,5) is given by :-
[tex](y-(-1))=\dfrac{5-(-1)}{6-2}(x-2)\\\\\Rightarrow\ (y+1)=\dfrac{6}{4}(x-2)[/tex]
[tex]\\\\\Rightarrow\ (y+1)=\dfrac{3}{2}(x-2)\ \ \ \ \ \text{[point slope form} : (y-y_1)=m(x-x_1)] \\\\\Rightarrow\ y+1=\dfrac{3}{2}x-3\\\\\Rightarrow\ y=\dfrac32x-4\ \ \ \ \ [\text{ slope intercept form} : y= mx+c]\\\\\Rightarrow\ 2y= 3x-2\times4\\\\\Rightarrow\ 2y=3x-8\\\\\Rightarrow\ 3x-2y=8 \ \ \ \ [\text{Standard form : Ax + By = C}][/tex]
What is the y-intercept when a line has a slope of 1/2 and
passes
through the point (2, -1)?
Answer:
-2
Step-by-step explanation:
y=ax+b
Put the numbers into that equation.
-1=1/2*2+b
Simplify:
-1=1+b
-1-1=b
-2=b
Hope this helped! :)
Use synthetic division to determine f(-2) for the function f (x) = 9x^3 - 18x^2 - 16x + 32
Answer: -80
Step-by-step explanation:
What is the y intercept of y =4x
Answer:
origin of the graph (0)
Step-by-step explanation:
because it does not have a b value it is zero if there is no plus or minus a number at the end it is always 0 when dealing with the y=mx+b equation
Given the points P(2, –6) and R(8, 3), what is the component form of Vector PR?
- ⟨6, -3⟩
- ⟨10, -3⟩
- ⟨6, 9⟩
- ⟨10, 9⟩
Answer:
the third one
Step-by-step explanation:
jsut took it
Answer:
It’s C
Step-by-step explanation:
Ms. cooper goes to Panera Bread for dinner and orders the Green Goddess salad. Her total was $8.79. Ms. cooper gave the cashier $10, how much change did she receive?
5. Which is the best first step to solve 5x+12x = 40 by completing the square?
A. Subtract 40 from both sides.
B. Divide all terms by 12.
C. Divide all terms by 5
D. Divide 12 by 2
Answer:
B
Step-by-step explanation:
To make the perfect square the first step is Subtract 40 from both sides option (A) is correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The complete question is:
Which is the best first step to solve 5x²+12x = 40 by completing the square?
A. Subtract 40 from both sides.B. Divide all terms by 12.C. Divide all terms by 5D. Divide 12 by 2We have a quadratic equation:
5x²+12x = 40
To make the perfect square:
First, subtract 40 from both sides.
5x²+12x - 40 = 40 - 40
5x²+12x - 40 = 0
Thus, to make the perfect square the first step is Subtract 40 from both sides option (A) is correct.
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Solve for A if ñ=3.14 and r=3.
Answer:
28.26
Step-by-step explanation:
The question gives the first three digits of π, which is 3.14, and it gives us the radius, which is 3. So, just substitute them into the formula and you’ll get 3.14(3^2). Solve it and the final answer is 28.26.
Hope this helps! :)
The graph of F(x), shown below, resembles the graph of G(x) = x^2?, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Answer:
D
Step-by-step explanation:
Slope is negative, derivative of x shows that -3 is the maximum in C/D but C is not negative
The function F(x) = -3(x + 3)^2 + 3.
The correct option is (D).
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A variable y is said to be a function of the independent variable x if there is a relationship between them.
As per the given data:
We are given the equation of the functions G(x) and we have to find out the equation of the function F(x).
Equation of G(x) = x^2
For a left shift of 3 units x → x + 3.
⇒ y = (x + 3)^2
For a change in concavity, if the curve, multiply by -3.
⇒ y = -3(x + 3)^2
For an up shift of 3 units y → y -3.
⇒ y - 3 = -3(x + 3)^2
The function F(x) comes out to be:
F(x) = -3(x + 3)^2 + 3
Hence, The function F(x) = -3(x + 3)^2 + 3.
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A barrel of 20 apples has 2 rotten apples and 18 good apples. 7 apples are selected at random from the barrel. What is the expected number of good apples selected
Answer:
Expected value = 7 x 0.9 = 6.3
Step-by-step explanation:
Probability of getting a good apple is 18/20 = 0.9
Probability of getting a bad apple is 2/20 = 0.1
This follows a binomial distribution because either you get a good apple or a bad apple.
The expected value of a binomial distribution is given as n*p where n is number of trials and p is the probability of success.
In this case our number of trials is 7 and the probability of success is 0.9, since the trials are for getting good apples.
Hence
n = 7
p = 0.9
Expected value = 7 x 0.9 = 6.3
HELP!!! ASAP PLEASE The temperature dropped 4 1/2 degrees each hour for 5 hours. By how many degrees did the temperature fall during those 5 hours?
Answer:
22.5 degrees.
Step-by-step explanation: Just change the half to 0.5 so then times 4.5 times 5.
Answer:
22 1/2
Step-by-step explanation:
I did the quiz
State all integer values of x in the interval (2,8) that satisfy the following inequality:
5x + 4 > 19
Answer:
3,4,5,6 and 7
Step-by-step explanation:
Given
[tex]5x + 4 \ge 19[/tex]
Required
State the values of x within 2 and 8
[tex]5x + 4 \ge 19[/tex]
Collect Like Terms
[tex]5x \ge 19 - 4[/tex]
[tex]5x \ge 15[/tex]
Divide both sides by 5
[tex]\frac{5x}{5} \ge \frac{15}{5}[/tex]
[tex]x \ge 3[/tex]
(2,8) is an open interval which means that 2 and 8 are not inclusive of the values of x.
So:
The values of [tex]x \ge 3[/tex] are: 3,4,5,6 and 7
Bob wants to distribute his fish and plants equally without having any left over. Help Bob find how many aquariums he needs. Use the fish and plant images to answer these questions. Insert the image of the fish and plant just like in Task 1’s introduction.
Part A
Insert images of the plant and the fish in the space provided to arrange the 24 fish and the 18 plants into sets so that each set has the same number of fish and the same number of plants and none are left over. (In each set, the number of plants does not have to be equal to the number of fish.) Write an expression for the total number of fish and plants in each set.
answer: 6
Step-by-step explanation:
you have 6 containers. you out 4 fish in each and then 3 plants in each.
-15 = z/-2. what does z = ?
Answer:
I think it's 30 but I'm not 100% sure
Some one help me please
Answer:
I think it would be a
Step-by-step explanation:
I think it would be a because when you divide by a negative number the sign flips
Can someone please help me?
Answer:
24 square inches
Step-by-step explanation:
First box: 3 x 4 = 12
Second box: 3 x 4 = 12
Added together = 24
Write an Equivalent Expression by combining like terms for 2x+3x+y+2y
Answer:
5x+3y
Step-by-step explanation:
2x+3x=5x since they have the same variable.
y+2y
1y+2y u can put a 1 so that would be 3y
5x+3y
16. Patrick turned out for the track team and lost 5.62 kilograms during the season. After the season
finished, he gained back 1.4 kilograms.
a. One of the decimals should be written as negative number. Which one is it and why?
b. Find the sum of the two numbers to determine the total change in Patrick's weight
Answer:
A: the 5.62 kilograms should be negative, since he is losing weight.
B: -5.62 + 1.4 is -4.22, which is how many kilograms Patrick lost in total.
Hope this helps :)
Which expression can be used to find The amount of money for camp leader spends on b books
Answer:
Part A: A. 7.50 x b
Part B: $90
Step-by-step explanation:
Part A: The cost of a book is $7.50, so the equation that is going to tell you the total cost of however many books purchased is equation A.
Part B: $90. If the cost of a book is $7.50 and the teacher purchases 12 books, you do $7.50 x 12= $90. You can check the equation by adding $7.50 12 times. You will get the same result.
A store is having a sale with a 19% discount on all merchandise. Write an
equation representing between the regular cost of merchandise (r) and
the discount received (d).
Your answer
Answer:
3
Step-by-step explanation:
A business person is desperate to better organize their business. They hire you to act as an efficiency expert. As you review their situation, you notice they file all of their receipts and documents into one overflowing folder. Their workspace is very messy with many piles of papers and useless knick-knacks. They mention difficulty finding important documents and have forgotten important dates and events due to their clutter. Write a formal letter to your client offering tips on ways to make their business more organized and efficient. Make sure your letter has specific examples which can improve the business' organization.
Answer:
Simply have neat and organized ways to save files. You can do this with file cabinets or by having digital copies of all the files to get rid of the clutter. I would recommend the second option.
Step-by-step explanation:
I got it right
The formal letter to the client offering tips on ways to make his business more organized and efficient is;
51, broad street,
Times Square Church,
New York City.
2/12/2021
The General Manager,
Clad financial services Ltd,
Brooklyn, New York city.
Dear Mr. Bill Wilkinson,
Letter of advice on more organized and efficient business.
I am writing with respect to the need to have a more organized and efficient office. Since resumption into this role as an efficiency expert, I have noticed that specific files and documents are very difficult to locate due to unorganization and untidiness.
With respect to the issue of unorganization and untidiness, I have some neat and organized ideas that can be used to save files. This can be can done by making use of file cabinets and also by creating and saving digital copies of all the files in order to get rid of some of the files and documents occupying a lot of space in the office.
Secondly, I will also like to add that unwanted papers or files should be thrown away and the files on the shelf should be properly labeled for easy identification.
Regards.
Frank Johnson,
Efficiency Expert.
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What’s the common factor for 72 and 84
Answer:
Step-by-step explanation:
This is the general method for doing this problem. First factor these numbers into primes.
72: 2 * 2 * 2 * 3 * 3
84: 2*2 * 3 * 7
Now each number has at least two 2s
Each number has at least one 3
The highest common factor is 2 * 2 * 3 = 12
3 6/12 +4 1/2 tell me what it is
Answer:
8
Step-by-step explanation:
3 + 4 = 7
6/12 + 1/2 = 1
7+1 = 8
:)))))))))))))))))))))
Answer:
Please check the explanation.
Step-by-step explanation:
1)
From the graph, taking the two points
(3, -5)
(-3, 5)
The slope between (3, -5) and (-3, 5) will be:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{5-\left(-5\right)}{-3-3}[/tex]
[tex]m=-\frac{5}{3}[/tex]
Therefore, the slope is:
[tex]m=-\frac{5}{3}[/tex]
2)
1ST METHOD
We know that the y-intercept of the graph of the linear function can be determined by setting x=0 and solving for y
As the graph crosses the y-axis at x=0From the graph, it is clear that:
at x=0, y=0
Thus, the y-intercept is: (0, 0)
2ND METHOD
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where 'm' is the slope and 'b' is the y-intercept
substituting the point (3, -5) and m=-5/3 in the slope-intercept form
[tex]y=mx+b[/tex]
[tex]-5=\frac{-5}{3}\left(3\right)+b[/tex]
[tex]\frac{-5}{3}\left(3\right)+b=-5[/tex]
[tex]-5+b=-5[/tex]
[tex]b=0[/tex]
Thus, the y-intercept is: (0, 0)
3)
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
substituting m=-5/3 and b=0 to determine the equation line in the slope-intercept form
[tex]y=\frac{-5}{3}x+0[/tex]
Therefore, the equation line in the slope-intercept form is:
[tex]y=\frac{-5}{3}x+0[/tex]
where m=-5/3 and b=0
$599 TV: 12% discount
Answer:
After the discount $527.12
You save $71.88
Step-by-step explanation:
The data was modeled with a linear best-fit function. What was the initial
purchase price?
X Y
4. 5,000
7. 6,875
9. 8,125
12. 10,000
A. $625
B. $2,500
C. $5,000
D. $5,625
Answer:
c
Step-by-step explanation:
Find the maximum value of the function
f(x) = –22 – 15.9x – 57 to the nearest hundredth.
