Write an equation of a circle with diameter AB.A(1,1), B(11,11)Choose the correct answer below.A. (X-6)2 + (y-6)2 = 11C. (x-6)2 – (y+6)2 = 50E. (X+6)2 + (y-6)2 = 50G. (X+6)2 – (y + 6)2 = 50
Answers
The question asks us to find the equation of a circle with diameter AB with coordinates:
A = (1, 1), B = (11, 11)
In order to solve this, we need to know the general form of the equation of a circle.
The general form of the equation of a circle is given by:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where,} \\ (a,b)=\text{ coordinates of the center of the circle} \\ r=\text{radius of the circle} \end{gathered}[/tex]We have been given the coordinates of the diameter. This means that finding the midpoint of the diameter
will give us the center coordinates of the circle, which is (a, b).
The formula for finding the midpoint of a line is given below:
[tex]\begin{gathered} (x,y)=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ \text{where,} \\ x_2,y_2=\text{ second coordinate} \\ x_1,y_1=\text{first coordinate} \end{gathered}[/tex]For better understanding, a sketch is made below:
Therefore, let us find the coordinates of the center of the circle using the midpoint formula given above:
[tex]\begin{gathered} a,b=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ x_2=11,y_2=11 \\ x_1=1,y_1=1 \\ \\ \therefore(a,b)=\frac{11+1}{2},\frac{11+1}{2} \\ \\ (a,b)=6,6 \\ Thus, \\ a=6,b=6 \end{gathered}[/tex]Now that we have the coordinates of the center, we now need to find the value of the radius of the circle.
This is done by finding the length from the center of the circle to any side of the diameter.
Let us use from point (6,6) which is the center to the point (11, 11) which is one side of the diameter.
The formula for finding the distance between two points is given by:
[tex]\begin{gathered} |\text{distance}|^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ \text{where,} \\ x_2,y_2=\text{second point} \\ x_1,y_1=\text{first point} \end{gathered}[/tex]hence, we can now find the square of the radius as:
[tex]\begin{gathered} r^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ x_2,y_2=11,11_{} \\ x_1,y_1=6,6 \\ \\ \therefore r^2=(11-6)^2+(11-6)^2 \\ r^2=5^2+5^2 \\ r^2=25+25 \\ \therefore r^2=50 \end{gathered}[/tex]Now that we have the radius, we can now compute the equation of the circle as:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ a=6,b=6,r^2=50 \\ \\ \therefore(x-6)^2+(y-6)^2=50\text{ (Option B)} \end{gathered}[/tex]A graph of the circle is given below:
Related Questions
Use the graph shown to the right to find each of the following
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The x intercept is the value of x at the point where the curve touches the x axis of the graph. Looking at the graph,
x intercept = - 1
It is written as (- 1, 0)
The zeros of the quadratic function is the same as the x intercept. Since the curve touches the x axis at only x = - 1, the zeros would be
x = - 1 twice
What is the equation of the following line written in slope-intercept form? Oy=-3/2x-9/2
Oy=-2/3x+9/2
Oy=3/2x-9/2
Answers
The equation of the line in slope-intercept form is: C. y = -3/2x - 9/2
How to Write the Equation of a Line?If we determine the slope value, m, and the y-intercept value of the line, b, we can write the equation of a line in slope-intercept form as y = mx + b by substituting the values.
Slope of a line (m) = change in y / change in x.
y-intercept of a line is the point on the y-axis where the value of x = 0, and the line cuts the y-axis.
Slope of the line in the diagram, m = -3/2
y-intercept of the line, b = -9/2.
Substitute m = -3/2 and b = -9/2 into y = mx + b:
y = -3/2x - 9/2 [equation in slope-intercept form]
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3) An experiment is designed to compare the average salaries in a particular Position in two competing companies. The null hypothesis is assumed to be that there is no difference in the average salaries of empoty employees in a particular position in the two companies. What is the alternative hypothesis?
Answers
Given:
There are two competing companies.
Required:
We need to find the alternative hypothesis
Explanation:
If the null hypothesis assumes equal average salaries (i.e. no difference), then the alternative can take on three cases:
A)
One mean is greater than the other
B)
One mean smaller than the other
C)
The means are not equal
Now here A and B sound the same, so I shoukd be more precise,
Which is the upper left quadrant on the coordinate plane?A coordinate plane.Quadrant IQuadrant IIQuadrant IIIQuadrant IV
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The quadrants on the coordinate plane are the following:
then, we have that the upper left quadrant is quadrant II
i need help with this pls
Answers
Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.What is the formula for linear pairs?A two-variable linear equation of the form axe + by + c, with a, b, and c all being real numbers and not equal to zero.The Transitive Property states that if all real numbers x, y, and z are equal, then x=z. Substituting characteristics. If x=y, then x can be swapped to y in any equation or formula.Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing. A linear pair is made up of two angles, and the sum of their measures is 180°.Line pairs can be congruent. Adjacent angles are joined by a vertex. Angles that are similar cross across. A linear pairing is unnecessary.
Therefore, mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.To learn more about the Linear pair theorem refer to:
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divide and Simplify 7/5 ÷7/9
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What we have is a fractional division, this is following expression
[tex]\frac{(\frac{7}{5})}{(\frac{7}{9})}[/tex]For this procedure, it says to multiply the top and bottom ends to get the numerator, and the middle numbers to get the denominator
[tex]\frac{7\cdot9}{7\cdot5}=\frac{9}{5}[/tex]In conclusion after splitting and simplifying this, the answer is 9/5
Question 5 of 8
What is the largest proper fraction less than 1 that can be made by using these
numbers only once: 1, 3, 6, 11 and 12?
Answers
The largest proper fraction that can be formed is 16/17
What is a fraction?
A fraction (from the Latin fractus, "broken") is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line (or before a slash like 12) and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
The largest proper fraction that can be formed is
= 1+3+12/11+6 = 16/17
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10 ptsQuestion 3Find the measure of each interior angle. Round to the nearest hundredth.4x(6x - 90)(3x + 31)(7x+19)X=(4x)" =(6x - 90)(7x + 19)° =(3x + 31)º =
Answers
Alexandre, this is the solution:
Let's recall that the interior angles of a rhombus add up to 360 degrees.
Upon saying that, we have:
4x + 3x + 31 + 6x - 90 + 7x + 19 = 360
20x - 40 = 360
Adding 40 at both sides:
20x - 40 + 40 = 360 + 40
20x = 400
Dividing by 20 at both sides:
20x/20 = 400/20
x = 20
Now, we can calculate each of the angles and prove they add up to 360 degrees, as follows:
• 4x = 4 * 20 =, 80
,• 3x + 31 = 3 * 20 + 31 = 60 + 31 =, 91
,• 7x + 19 = 7 * 20 + 19 = 140 + 19 = ,159
,• 6x - 90 = 6 * 20 - 90 = 120 - 90 = ,30
80 + 91 + 159 + 30 = 360
Explain how you found the diagonal length of the package.
Answers
First find diagonal of base D =√( 10^2 + 10^2)= √200
Then find diagonal lenght L = √ (D^2 + 10^2) = √ (200 + 100) =√300
L= √300 = √3•√100 = √3• 10
L= √3•10 = 10•√3 (by conmutative property)
у = -3х5х + y = 14i need help finding the matrix of this
Answers
3x + y = 0
5x + y = 14
[tex]\Delta\text{ = }\begin{bmatrix}{3} & 1{} & \\ {5} & 1{} & {} \\ {} & {} & {}\end{bmatrix}\text{ = (3 x 1) - (5 x 1) = 3 - 5 = -2}[/tex][tex]undefined[/tex]
the top ten medal winning nations in a in a particular year are shown in the table. use the given information and calculate the median number of bronze medals for all nations round to the nearest tenth as needed
Answers
We have the following:
We know that to calculate the average we must add the corresponding values of bronze medals of each nation and then divide by the number of nations like this
[tex]\begin{gathered} m=\frac{11+7+9+5+5+3+8+4+6+0}{10} \\ m=\frac{58}{10} \\ m=5.8 \end{gathered}[/tex]the median number of bronze medals for all nations is 5.8
Determine whether the figure has line symmetry. If so, draw the line(s) of symmetry.
Yes
No
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Yes, the given figure has the horizontal symmetry.
What is a line of symmetry?Line symmetry is a type of symmetry about reflections. When there is at least one line in an object that divides a figure into two halves such that one-half is the mirror image of the other half, it is known as line symmetry or reflection symmetry. The line of symmetry can be in any direction - horizontal, vertical, slanting, diagonal, etc.
The horizontal line of symmetry divides a shape into identical halves, when split horizontally, i.e., cut from right to left or vice-versa.
The given figure has horizontal symmetry.
Yes, the given figure has the horizontal symmetry.
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Find the product. Write your answer in scientific notation. (6.5 X 10^8) X (1.4 x 10^-5) =
Answers
Evaluate the product of the expression.
[tex]\begin{gathered} (6.5\times10^8)\cdot(1.4\times10^{-5})=6.5\cdot1.4\times10^{8-5} \\ =9.1\times10^3 \end{gathered}[/tex]So answer is 9.1X10^3.
two seventh of a number is 30 less than the number . find the number
Answers
Let x = the number
So, the given situation can be expressed as:
[tex]\frac{2}{7}x=30-x[/tex]Then, solve for x:
[tex]\begin{gathered} \frac{2}{7}x+x=30-x+x \\ \frac{9}{7}x=30 \\ \frac{7}{9}\cdot\frac{9}{7}x=30\cdot\frac{7}{9} \\ x=\frac{210}{9}=\frac{70}{3} \end{gathered}[/tex]Answer: the number is 70/3
Solving Equations ** Reminder need to show ALL work **
Answers
solution
For this case we have the following equation:
[tex]\frac{3}{4}x-5=4[/tex]Then we can add 5 in both sides and we got:
[tex]\frac{3}{4}x=9[/tex]Then we can multiply both sides by 4/3 and we got:
[tex]x=9\cdot\frac{4}{3}=12[/tex]And the final solution for this case is x= 12
Just the number 2 please a ball is tossed in the air in such a way that …..
Answers
Note that a quadratic function is increasing and decreasing at exactly half between the roots.
The roots are the point on the ground when tossing the ball into the air.
So we need to get the roots of the given equation.
Roots are the values of x when y = 0
[tex]\begin{gathered} y=-x^2+6x \\ 0=-x^2+6x \\ 0=-x(x-6) \\ -x=0\Rightarrow x=0 \\ (x-6)=0\Rightarrow x=6 \end{gathered}[/tex]So the roots are 0 and 6, this will be the x coordinate or the point on the ground.
Since the equation is increasing halfway and decreasing up to the ground, the halfway point is the midpoint between the roots.
Midpoint = (0 + 6)/2 = 3
Therefore, the ball's height is always decreasing at 3 < x < 6
The answer is 3 < x < 6
See photo for problem
Answers
a. the amount of liquid in the tank: 5580 liters
b. The amount of liquid should be added to fill the tank 100% capacity : 450 liters
We have been given a right circular conical tank.
h = 4 m and r = 1.20 m
We know that the formula for the volume of cone is,
V = πr²h/3
The volume of the tank would be,
V = (π × r² × h)/3
V = (π × 1.20² × 4)/3
V = 18.09/3
V = 6.03 m³
Let h1 be the height of liquid level in the tank and V1 be the volume of the liquid in the tank.
h1 = 3.70 m
V1 = (π × r² × h1)/3
V1 = (π × 1.20² × 3.70)/3
V1 = 16.74 / 3
V1 = 5.58 m³
V1 = 5580 liters
The amount of liquid need to added to fill the tank 100% of capacity.
V2 = V - V1
V2 = 6.03 m³ - 5.58 m³
V2 = 0.45 m³
V2 = 450 liters
Therefore, a. the amount of liquid in the tank: 5580 liters
b. The amount of liquid should be added to fill the tank 100% capacity : 450 liters
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The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.
Answers
The graph of the given function is attached below.
x intercept means if there will be no khakis shipped, then there will be 120 jeans shipped.
Also, y -intercept means if there will be no jeans shipped, then there will be 90 khakis shipped.
Given equation:-
15x + 20y = 1800
Where,
x represents the number of jeans shipped and,
y represents the number of khakis shipped
We have to use the x and y-intercepts to graph the equation.
Putting x = 0 to find the y -intercept, we get,
15(0) + 20y =1800
0 + 20y = 1800
y = 1800/20
y = 90
The coordinates of the point will be (0,90).
Putting y = 0 to find the x -intercept, we get,
15x + 20(0) =1800
15x + 0 = 1800
x = 1800/15
x = 120
The coordinates of the point will be (120,0).
Using the coordinates, we have graphed the graph attached.
Here, x intercept means if there will be no khakis shipped, then there will be 120 jeans shipped.
Also, y -intercept means if there will be no jeans shipped, then there will be 90 khakis shipped.
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How do you solve this??
Answers
Answer:
12-3X=X-3=5
Step-by-step explanation:
-8(4 p -1)-7 p+8( p+1)
Answers
-31p + 16
Explanation:
-8(4 p -1) - 7p+8( p+1)
Open the bracket:
-8(4p) -8(-1) - 7p +8(p) +8(+1)
Simplify:
-32p + 8 - 7p + 8p + 8
Note: the multiplication of opposite sign gives negative number. While multiplication of same sign gives positive number
Collect like terms:
= -32p - 7p + 8p + 8 + 8
= -31p + 16
I am struggling with this question. could you help me please??
Answers
Problem
Solution
Let x = age, W= weight the two variables of interest
We have the following probabilities given:
P(x<37) =0.142
P(W< 2500) = 0.051
P(x <37 AND W<2500)= 0.031
And we want the following probability and we can use the total probability rule:
P(x < 37 OR W< 2500) = P(x<37) +P(W< 2500) -P(x<37 AND W<2500)
If we replace we got:
P(x < 37 OR W< 2500)= 0.142+ 0.051- 0.031= 0.162
Can you please help me out with a question
Answers
The formula for the area of a sector of a circle is:
[tex]A=\frac{\theta}{360}\cdot\pi r^2[/tex]Where
θ is the angle
r is the radius
Given,
θ = 100
r = 7
We substitute into the formula and figure the answer out [remembering to use 3.14159 as π]:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi r^2 \\ A=\frac{100}{360}\cdot(3.14159)(7)^2 \\ A=\frac{5}{18}\cdot(3.14159)(49) \\ A\approx42.76053 \end{gathered}[/tex]Rounding to the nearest thousandth [3 decimal places], we have:
Area = 42.761 square centimetersnowledge Check 01
On November 1, the company rented space to another tenant. A check in the amount of $9,000, representing three months' rent in advance, was received from the tenant on that date. The payment was recorded with a credit to the Unearned Rent Revenue account.
Complete the necessary December 31 adjusting journal entry by selecting the account names from the pull-down menus and entering dollar amounts in the debit and credit columns.
Answers
Debit for unearned rent revenue of $6,000.
Rent Revenue Credit $6,000
What is known as the revenue?The total amount of revenue produced by the purchase of goods or services linked to the company's main operations is referred to as revenue. Because it appears at the top of the revenue statement, revenue, also termed as total sales, is often made reference to as the "top line."For the given question,
It is assumed that the company rented area to another tenant on November 1. On that date, the tenant handed over a check for $9,000, which represented three months' rent in advance. The payment has been recorded as a credit to the account for unearned rent revenue.Now, on December 31, we must prepare this same adjusting entry to record this same Rent Revenue for the two-month period (Nov. 1 to Dec. 31).
For two months, the rent revenue will be 9000×2/3 = $6,000
As a result, the journal entry to track the Rent revenue is as follows:
Debit for unearned rent revenue of $6,000.
Rent Revenue Credit $6,000
(becoming the improvement made for earned Rent Revenue).
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How many times larger is 3 x 10⁹ than 3 x 10⁷ ?
Answers
Answer:
100 times
Step-by-step explanation:
[tex]\frac{10^{9} }{10^{7} }[/tex] = [tex]10^{2}[/tex] = 100
When you are dividing exponents with the same bases, you subtract the exponents.
Answer:
3 x 10^9 is larger than 3 x 10^7 by 2,970,000,000
Step-by-step explanation:
Lola needs 2/3 cup of lemon-lime soda for every 2 cups of punch. Find ____ cups of soda/cup of punch
Answers
We know that
• There are needed 2/3 cups of lemon soda for every 2 cups of punch.
To find the answer, we have to divide.
[tex]\frac{\frac{2}{3}}{2}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the answer is 1/3 of soda/cup of punch.Lin is traveling from Japan to several other countries. The conversion table shows exchange rates between different currencies.
2,000 Yen 16 Euros
40 Euros = 3,125 Indian Rupees
What is the rate of yen per Indian rupee?
0.625
0.64
1.5625
1.6
Answers
The rate of yen per Indian rupee is 1.6
How do you convert currency to another currency?
Divide your current currency by the exchange rate if you are aware of it.
Assume, for instance, that you want to change 100 USD into EUR and the USD/EUR exchange rate is 0.631. Simply multiply 100 by 0.631 to do this, and the result is 63.10 EUR, which is the amount you will receive.
Given, 2000 Yen = 16 Euros
and, 40 Euros = 3,125 Indian Rupees
Find rate of yen per India rupee
1 Euro = 2000/16
1 Euro = 125 yen
And, 1 Euro = 3125/40
1 Euro = 78.125 India rupee
Now, find 1 yen = ? Indian rupee
we know, 1 Euro = 125 yen and 1 Euro = 78.125 India rupee
put the values of euro in India rupee in 1 Euro = 125 yen, we get
78.125 India rupee = 125 yen
1 India rupee = 125 / 78.125
1 Indian rupee = 1.6 Yen
Therefore, the rate of yen per Indian rupee is 1.6
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Triangle A has a 18.3cm side and a 3cm base. Find the hypotenuse.
Answers
Given:
The length of the sides is a=18.3 cm,
The base of the triangle is b =3 cm.
Required:
We need to find the hypotenuse.
Explanation:
Use the Pythagorean theorem.
[tex]c^2=a^2+b^2[/tex]Substitute a =18.3 and b=3 in the equation.
[tex]c^2=18.3^2+3^2[/tex][tex]c^2=343.89[/tex]Take square root on both sides.
[tex]\sqrt{c^2}=\sqrt{343.89}[/tex][tex]c=\pm18.5442[/tex]Length is always positive.
[tex]c=18.54[/tex]Final answer:
The hypotenuse is 18.54cm.
determine the interview on which the function is concave upward and concave downward
Answers
We have to identify the intervals where the function is concave upwards and where is concave downward.
We can differentiate them in a graph as:
We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.
Then, we can write all the intervals as:
[tex]\begin{gathered} (-\infty,-5)\longrightarrow\text{Concave downward.} \\ (-5,-1)\longrightarrow\text{Concave downward.} \\ (-1,4)\longrightarrow\text{Concave upward}. \\ (4,\infty)\longrightarrow\text{Concave downward.} \end{gathered}[/tex]The longest side of a triangle is 5in longer than the shortest side. The medium side is 4 inches longer than the shortest side. If the perimeter of the triangle is 21 inches, what are the lengths of the three sides?
Answers
The perimeter of a triangle is given by the sum of all it is sides.
Now, we have the next measures:
- The longest side of a triangle is 5in longer than the shortest side.
- The medium side is 4 inches longer than the shortest side
Then, the perimeter is given by:
P = (s+5)+(s+4)+s
If the perimeter is P=21 inches:
21 = (s+5)+(s+4)+s
Solve for s:
21 = s+5+s+4+s
21 = 3s + 9
21-9 = 3s
12 = 3s
s = 12/3
s= 4
Therefore,
The shortest side of the triangle is 4 inches.
The medium side is s+ 4 = 4+ 4 = 8 inches
The longest side is s+5 = 4+5 = 9 inches
hey can anyone help me on this im failing school xd
Answers
slope of line is -3 for points (1,0) and (0,3)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From graph let us take two points (1, 0) and (0, 3)
x₁=1, x₂=0, y₁=0,y₂=3
Substitute these values in slope formula
m=3-0/0-1
m=3/-1
m=-3
Hence slope of line is -3.
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