so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.
in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}[/tex]
now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}[/tex]
AC must be the diameter of the circle.
What is Circle?
A circle is a closed two dimensional figure in which the set of all the points in the plane is equidistance from a center.
Given that;
A circle passes through points A(7, 4), B(10, 6), C(12, 3).
Now,
If AC is diameter of the circle then half the distance of AC is its radius and midpoint of AC is the center of the circle.
Since, B is also on the circle , then distance from B to the center must be same radius distance.
Midpoint of AC is calculated as;
= (7 + 12 / 2 , 4 + 3/2)
= (19/2 , 7/2)
= (9.5 , 3.5)
Now, Distance from A to the center and check the distance of B to the center as;
AM = √(9.5 - 7)² + (3.5 - 4)²
AM = 2.5495
And,
BM = √(9.5 - 7)² + (3.5 - 6)²
BM = 2.5495
So, Distance from A to the center and the distance of B to the center is same.
Thus, AC must be the diameter of the circle.
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Jogging is one of the few sports that has been consistently increasing over the past few years. The number of people jogging (in millions) from the years 2000 to 2009 is given by the equation y equals x plus 16, where x is the number of years after 2000.
a. Use this equation or a graph of it to complete the ordered pair (2, ).
b. Write a sentence explaining the meaning of the answer to part (a).
c. If this trend continues, how many joggers will there be in 2023?
Answer:
a. The ordered pair is (2 , 18)
b. The number of people jogging in year 2002 was 18 millions
c. There will be 39 millions joggers in year 2023
Step-by-step explanation:
* Lets explain how to solve the problem
- The equation y = x + 16 represents the number of people jogging
in millions from year 2000 to 2009 where y is the number of people
and x is the number of years after 2000
- That means at year 2000 the value of x = 0 and the number of people
jogging was 16 millions
- The equation represented graphically by line
a.
- The ordered pair (2 , ?) means x = 2 and we need to find y when x = 2
- Substitute x by 2 in the equation
∵ y = x + 16
∵ x = 2
∴ y = 2 + 16 = 18
* The ordered pair is (2 , 18)
b.
∵ y represents the number of people jogging in millions
∵ x represents the number of years from year 2000
- That means the number of people jogging in year 2002 was 18
millions
* The meaning of the answer of part (a) is :
The number of people jogging in year 2002 was 18 millions
c.
- If this trend continues means the equation will be the same for years
after 2009
∵ In year 2023 ⇒ x = 23
∵ y = x + 16
∴ y = 23 + 16 = 39
* There will be 39 millions joggers in year 2023
What is the area of the shaded region?
21 mm
24 mm
42 mm
48mm
Please help me find the pattern will give brainlist
1:3
3:17
10:66
6:38
Could be any pattern as long as it’s a pattern please help ASAP
Answer: 1:3 2:6 3:9 1:3 is answer
Step-by-step explanation:
A person who weighs 125 pounds on Earth would weigh 47 2/10 pounds on Mercury. Set up a proportion and solve using means and extremes to determine how much a child who weighs 50 pounds on Earth would weigh on mercury.
The amount of weight for a child who weighs 50 pounds on Earth would weigh on mercury would be = 18.88Ib.
How to calculate the weight of a child in Mercury?To determine the weight of a child using means and extremes, the following steps should be taken as follows;
The ratio of the weight of the child on Earth and Moon = 125: 47 2/10
That is; 125: 47.2
Therefore 50Ib on earth would= ?
That I ;
125 = 47.2
50 = X
make X the subject of formula;
X = 50× 47.2/125
= 2360/125
= 18.88Ib.
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Choose the equation that represents a line that passes through points (-6,4) and (2,0).
A) x+2y= 2
B) 2x-y= -16
C) x+2y= -8
D) 2x+y= 4
Please give a detailed explanation on how you solved the problem.
Answer:
A.
Explanation:
Just plug in the points to each equation.
A. x + 2y = 2
Plugging in (-6,4) (-6) + 2(4) = 2 ---> -6 + 8 = 2
Plugging in (2,0) (2) + 2(0) = 2 ---> 2 + 0 = 2
B. 2x + y = -16
Plugging in (-6.4) 2(-6) + (4) = -16 ---> -12 + 4 = -16 --> -8 [tex]\neq -16[/tex]
Because the first point didn't work there is no need to check the second one.
C. x + 2y = -8
Plugging in (-6,4) (-6) + 2(4) = -8 ---> -6 + 8 = -8 --> 2[tex]\neq -8[/tex]
Again, because the first point didn't work there is no need to chek the next.
D. 2x + y = 4
Plugging in (-6,4) 2(-6) + (4) = 4 ---> -12 + 4 = 4 --> -8[tex]\neq 4[/tex]
Even though the answer was A. you should still check each on of them because there can always be a mistake in your work.
Answer:
A
Step-by-step explanation:
To find the equation of a line, the first thing that must be determined is the lines gradient. This can be determined by using the formula:
m = (Δy) / (Δx)
m = (4-0) / (-6-2)
m = 4 / -8
m = -0.5
The gradient has been determined, now we determine the y-intercept by using a point it passes through (either point cant be used because the line will pass through bother coordinates given)
y = mx + c (Using the point (2,0))
0 = (-0.5)(2) + c
c = 1
Since we have the y-intercept, a formula can be created for the line, and rearranging it, we can then find the correct option.
y = mx + c
y = (-0.5)x + 1
2y = -x + 2
x + 2y = 2
With a tank of gas, if you can drive 475 miles, your car uses 12 miles per gallon. Write an equation to model this situation
Solve 36+57 on a number line
36
+57
------
93
On a number line: Start at 0. Count forward until you reach 36. Once you've reached 36, Mark it. Then you go forward 57, from the mark you made at 36. You should end up on 93 on the number line.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Temperature (degrees F) 49 55 52 46 47 42 38 Julia measured the high temperature in her town for one week. Using the chart above, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth. Be sure to show your work for finding: the mean of the set of data the distance of each number from the mean the mean absolute deviation
Answer:
[tex]4\dfrac{2}{7}[/tex]
Step-by-step explanation:
How to calculate the mean absolute deviation:
Step 1: Calculate the mean.
[tex]\text{Mean}=\dfrac{49+55+52+46+47+42+38}{7}=47[/tex]
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
[tex]\begin{array}{ccccccc}\text{Sun}&\text{Mon}&\text{Tue}&\text{Wed}&\text{Thu}&\text{Fri}&\text{Sat}\\49&55&52&46&47&42&38\\2&8&5&1&0&5&9\end{array}[/tex]
Step 3: Add those deviations together.
[tex]\sum|\text{mean}-x_i|=2+8+4+1+0+5+9=30[/tex]
Step 4: Divide the sum by the number of data points.
[tex]\text{MAD}=\dfrac{\sum|\text{mean}-x_i|}{n}=\dfrac{30}{7}=4\dfrac{2}{7}[/tex]
Answer:
4 2/7
Step-by-step explanation:
123,608,902.904.Written in words
Answer:
One hundred and twenty three million six hundred and eight thousand nine hundred and two point nine hundred and four. Hope this helps you!
A town’s population has increased 35% during the last 8 years and is now 50,100 people. What was the population 8 years ago?
To find the population 8 years ago, we can set up an equation and solve for the original population. The population 8 years ago was approximately 37,000 people.
Explanation:To find the population 8 years ago, we need to calculate the original population before the 35% increase. Let's assume the population 8 years ago was P.
Since the population has increased by 35% over the last 8 years, we can set up the equation: P + 0.35P = 50100
Simplifying the equation, we have: 1.35P = 50100
Divide both sides of the equation by 1.35 to solve for P: P ≈ 37000
Therefore, the population 8 years ago was approximately 37,000 people.
"One less than
half a number is
a maximum of 19"
Solve the system. -4= x - y 4= -x + y
Answer:
x-y=-4
y-x=4
y=x+4
(x,y)=(1,5),(2,6),(3,7),...
u see it doesn't have a particular answer any pair of numbers with 4 difference will do
Which is an algebraic expression for the word phrase "8 less than the product of 12 and a number x"? A. 12x – 8 B. 8 – 12x C. 12 – 8x D. 8x – 12
Answer:
A
Step-by-step explanation:
A product is the answer you get when you multiply 2 numbers together.
So you are starting backwards. Get the product first.
12*x
Now you want to take 8 away from it.
12x - 8 is what you get.
A
Answer:
A
Step-by-step explanation:
five less than the product of 3 and a number of 40 . Write in an equation
Answer:
I don't get the "number of 40" part, but here's my best shot!
3(40x)-5
Step-by-step explanation:
Answer:
(3*40)-5=115
Step-by-step explanation:
What is the value of x?
x + 1/3 = 9
Enter your answer in the box in simplest form.
Answer:
x= 8 2/3
Step-by-step explanation:
subtract 1/3 from both sides. 9-1/3 is 8 and 2/3.
Maria has 8n-30 marbles, her brother has 5n marbles. How many more marbles does Maria have than her brother
Answer:
3n-30
Step-by-step explanation:
Answer: 3n-30
Step-by-step explanation: plato
Probably a dumb question but how can I solve this without using a calculator? The answer when using a calculator is 0.83 so how can I get that answer without using a calculator?
Answer:
[tex] \frac{25}{30} = .83[/tex]
set it up in an old-fashioned way
using the division method. 30 on the outside and 25 on the inside
Answer:
The answer is 0.833333333 but, to nearest hundredth place is it 0.83.
Step-by-step explanation:
I don't know how they call it in your school but, what we are going to do right now is called long division.
The mass would be the dividend (25) and the volume (30) would be the divisor and the density would be the quotient.
In the past,younglin has painted a total of 5 pictures.She now intends to paint 7 pictures every two weeks.Make a table showing the total number of pictures younglin will have painted at the end of every two weeks.
Answer: see table
Step-by-step explanation:
The number of weeks are multiples of 2 (every 2 weeks) and the number of paintings are multiples of 7 (7 paintings every 2 weeks).
[tex]\begin{array}{c|c}\underline{\text{Week}}&\underline{\text{Paintings}}\\2&7\\4&14\\6&21\\8&28\\10&35\\12&42\\14&49\\16&56\\18&63\\20&70\end{array}[/tex]
Please help me!!!! Number 8 and 9.
Perpendicular to y=1/2-1, x-intercept at4
Answer:
it would be Y= -2x+4
Step-by-step explanation:
To begin, we know that the b value is 4, because that is the x-intercept that is information given, so we can atomatically put that in.
Next we need to find the m value, which can be found by knowing the rules of a perpendicular eqution. to change it you must change the 1/2 and flip the equation and change the signs
soooooo 1/2 would change into 2/1 which is 2 and we would addd the negative sign so
Y=-2x+4
Answer:
the desired equation is y = -2x + 8.
Step-by-step explanation:
Given a line with slope 1/2, we find the negative reciprocal of that to obtain the slope of a line perpendicular to the given line: m = -2.
Recall that at an x-intercept, y = 0. Here we're told that the x-intercept is (4, 0). Therefore, y = mx + b becomes 0 = -2(4) + b, or b = 8.
Then the desired equation is y = -2x + 8.
What inequality is graphed below?
x < -4
x ≤ -4
x ≥ -4
x > -4
Answer:
The answer is x>-4
Answer:
2342423
Step-by-step explanation:
asdadadsada
Please only do 40 (a,b, and c)
a)
well, we know the final score is just the sum of "t" and "i", so hmmm we can just call the final score say "f", thus f = t + i.
b)
student A
f = 30 + 40 => f = 70.
student B
f = 40 + 20 => f = 60.
student C
f = 30 + 50 => f = 80.
c)
the highest score above is from student C or 80, in order to have a higher score than that you would need a final score of 81. You already earned 35 points for "t", so from "i" you'd need 81 - 35 = 46, so if you earn for interpretation 46 points, your final score will be f = 35 + 46 => f = 81.
9. An Integer is 10 times the difference of a rational number and
what is the value of the rational number?
tonal number and 5. If the value of the integer is 124,
Equation
To find the value of the rational number, set up an equation using the representation of the integer as 10 times the difference of the rational number and 5. Solve the equation to find the value of the rational number, which is 17.4.
Explanation:To find the value of the rational number, we can use the given equation: An Integer = 10 times the difference of the rational number and 5.
Let's denote the rational number as x. According to the equation, the integer can be represented as 10(x - 5).
Since the value of the integer is 124, we can set up the equation: 10(x - 5) = 124.
Solving for x, we can divide both sides of the equation by 10 to isolate x: x - 5 = 12.4.
Finally, add 5 to both sides to find the value of x: x = 17.4.
Therefore, the value of the rational number is 17.4.
The population of a city this year [2018] is 34,500. The population is expected to grow by 2% each year. What will be the population if the city in 2025?
A. 39,300
B. 23,180
C. 123,619
D. 39,630
Show that the slope of the segment with the endpoints ( 1/x ,1 )and ( 1/y, y/x ) does not depend on x. Provide your complete solutions and proofs in your paper homework and respond to questions or statements online.
Answer:
Step-by-step explanation:
Givens
y2 = y/x
y1 = 1
x2 = 1/y
x1 = 1/x
Formula
m = (y2 - y1) / (x2 - x1)
Solution
m = (y/x - 1) / (1/y - 1/x)
m = ( (y - x)/x ) / ((x - y)/xy)
m = (-(x - y) / x) / ( (x - y) / xy)
Invert the denominator and multiply
m = ( - (x - y) / x ) * x*y / (x - y) Notice x - y cancels.
m = ( - 1 / x ) * (x*y) Notice the xs will cancel.
m = ( - 1 / y) There are no xs anywhere. The slope is - 1/y
Answer: Hello there!
If you have the set of points (x1, y1) and (x2, y2), the slope of the segment whit this endpoints is:
[tex]a = \frac{y2 - y1}{x2 - x1}[/tex]
Now, we have the endpoints (1/x, 1) and (1/y, y/x), the slope of this segment is:
[tex]a = \frac{y/x - 1}{1/y - 1/x}[/tex]
Let's simplify it:
[tex]\frac{y/x - 1}{1/y - 1/x} = \frac{(y-x)/x}{(x - y)/x*y} = \frac{\frac{y-x}{x} }{\frac{-(y-x)}{y*x} }= y*\frac{\frac{y-x}{x} }{\frac{-(y-x)}{x} } = y*(-1) = -y[/tex]
Then the slope of the segment is a = -y, and it does not depend of x
The following system has no solution.
x+y+z= 15
2x+z = 1
27-z=7
true or false
Answer:
False
Step-by-step explanation:
Let us start with the most obvious one:
27 - z = 7
-27 - 27
_________
-z = -20
z = 20 [Plug this back into the other two equations to get the y-coordinate and x-coordinate of 4½ and -9½]; 4½ = y; -9½ = x
So, the solution is [-9½, 4½, 20].
I am joyous to assist you anytime.
Why is a parallelogram not the same of quadrilateral as a trapezoid? Explain how you know.
A parallelogram has 2 sets of parallel sides. However, a trapezoid only has 1 set.
HI I NEED HELP IVE BEEN DOING HOMEWORK FOR 6 HOURS ummmmm anyways, how do i express this (y^3•y^6 - in picture) in exponential form? i’m stupid so it would mean a lot
y^3 = y * y * y
y^6 = y * y * y * y * y * y
Answer:
Step-by-step explanation:
Find the value of x. If necessary, round to the nearest tenth.
7.3 in.
10.4 in.
5.2 in.
8.8 in.
Answer:
7.3 in
Step-by-step explanation:
area = 27 = 54/2 = (x^2)/2
so what squared is 54?
7.34 whatever inches.
round it down, that's 7.3.
Answer: 7.3 in
Step-by-step explanation:
To find the the value of x, we will simply use the formula of area of a triangle, substitute the values and then solve.
From the diagram above, the height of the triangle is x and also the base of the triangle is also x, the area of the triangle is 27 sq. in
Area of a triangle = [tex]\frac{1}{2}[/tex] base × height
27 = [tex]\frac{1}{2}[/tex] × x × x
27 = [tex]\frac{1}{2}[/tex] × x²
27 = [tex]\frac{x^{2} }{2}[/tex]
cross multiply
2 × 27 = x²
54 = x²
Take the square roots of both-side
√54 = √x²
7.3 = x
x = 7.3
Therefore the value of x is 7.3 in.
if she could have run 400 meters at the same rate as she ran 100 meters, would she have broken the record? Find the difference between her time for 400 meters and the record time.
Answer:
Step-by-step explanation:
It appears i cant answer your question but what i can do is provide this paragraph as a trade for points. Appreciate your help. :)