The equation of the circle (x + 6)^2 + y^2 = 121 has a radius of 11 and a center located at (-6 , 0).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 6)^2 + y^2 = 121, is in standard form, then
h = -6
k = 0
r = 11
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A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and a free concert ticket to every 100th caller. When will the station first give away all three prizes to one caller?
The radio station awarded all three prizes to the 300th caller.
What is termed as the LCM?LCM is an abbreviation for "Least Common Multiple." The smallest multiple which two or even more numbers have now in common is defined as the least common multiple.The least amount divisible from both numbers is the LCM of two numbers.Discovering the lowest common denominator (LCD) of 2 or more fractions is a common application of LCM.To estimate the one caller to receive the all three prices, find the LCM of 15, 25 and 100.
LCM of 15, 25 and 100 is as follows;
3 15, 25, 100
----------------------
4 5, 25, 100
-----------------------
5 5, 25, 25
----------------------
5 1, 5, 5
-----------------------
1, 1, 1
LCM = 3×4×5×5
LCM = 300
Therefore, the radio station will first award all three prizes to the 300th caller.
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Evaluate the quantity negative four thirds squared all cubed.
4,096 over 729
1,024 over 243
negative 1,024 over 243
negative 4,096 over 729
The value of the given expression is 4,096/729. Therefore, option A is the correct answer.
The given expression is ((-4/3)²)³.
We need to evaluate the given expression.
What are exponents?A number's exponent indicates how many times the number has been multiplied by itself.
Now, ((-4/3)²)³=((-4/3)×(-4/3))³
=(16/9)³
=(16/9)×(16/9)×(16/9)
=(16×16×16)/(9×9×9)
=4,096/729
The value of the given expression is 4,096/729. Therefore, option A is the correct answer.
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Points A,B,C are collinear and B is between A and C. Given AB=12 and AC=19, what is BC?
Answer:
BC = 7
Step-by-step explanation:
Due to the segment addition postulate, AB + BC = AC
Substitute: 12 + BC = 19
BC = 7
8+3(4+6)divided by 2 =
Answer:
23
Step-by-step explanation:
8+3(4+6)/2
8+3(10)/2
8+30/2
8+15
=23
please give me a brainlist
A company sells two different sizes of exercise balls. The ratio of the diameters is 15: 11 . If the diameter of the smaller ball is 55 centimeters, what is the volume of the larger ball? Round to the nearest tenth.
The volume of the larger ball the company sells is 220,893.2 cubic centimeters.
If the diameter of the smaller ball is 55 centimeters, and the ratio of the diameters of two different sizes of exercise balls is 15 : 11, then
diameter of larger ball / diameter of smaller ball = 15 : 11
diameter of larger ball = 15 (55 cm) / 11
diameter of larger ball = 75 cm
If the diameter of the larger ball is 75cm, and half of the diameter is the radius, then:
r = D/2
r = 75cm/2
r = 37.5 cm
Solving for the volume of the larger exercise ball using the formula for the volume of the sphere given by:
V = 4/3πr^3
V = 4/3π(37.5 cm)^3
V = 220,893.2335 cubic centimeters
Rounding off to the nearest tenth.
V = 220,893.2 cubic centimeters
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Write Each Number As A Fraction Or A Mixed Number.
-0.7 repeating
-0.04 repeating
-4.45 repeating
-2.191919...
Simply divide by the decimal points to make it a fraction and then divide to make it a mixed fraction. The answer is
a) 7/10
b) 4/100
c) 40 45/10
d) 20 19/10
Represent the number as fraction or mixed number
Fractions are defined as the parts of a whole. The whole can be an object or a group of objects. In real life, when we cut a piece of cake from the whole of it, then the portion is the fraction of the cake.
Mixed Number is the combination of a whole number and a fraction. The numerator and denominator are part of the proper fraction that makes the mixed number. It is two-part in a fraction that helps to make the mixed number. Mixed fraction can only be made when the numerator is greater than denominator.
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ill make the points bigger answer the question
hi
area of rectangle is Length * width
Length is : 3 +1/3 so 9/3 +1/3 = 10/3
width : 5 + 2/3 = 15/3 + 2/3 = 17/3
so Area = 10/3 * 17/3 = 170/9
Area is 170/9
Answer
Step-by-step explanation:
first we have to multiply length of rectangle and width of rectangle according to it's formula and then change it to improper fraction
I forgot to write the unit at the end of answer which should be yd²
Describe the similarities and differences between a common difference and a common ratio.
The similarity between common difference and common ratio is that both are used to find the next term, but common difference is added while common ratio is multiplied.
Common difference (d) is defined as the difference between consecutive terms in an arithmetic sequence. It is determined by subtracting the term from the preceding term. For example, in an arithmetic sequence 2, 5, 8, 11,…, the common difference is 5-2=3 or 8-5=3.
The sequence will be: a, a+d, a+2d, a+3d,… a+nd.
In the general form:
d=an -an-1, where an is the nth term and an-1 is the preceding term.
Common ratio (r) is defined as the quotient between consecutive terms in a geometric sequence. It is determined by dividing the term by the preceding term. For example, in an geometric sequence 2, 4, 8, 16,…, the common ratio is 4/2=2 or 8/4=2.
The sequence will be: a, ar, ar^2, ar^3,…ar^n.
In the general form:
r=an/an-1, where an is the nth term and an-1 is the preceding term.
Hence, both common difference and common ratio shows relationship between consecutive terms in a sequence. Common difference is added to the term to find the next term while common ratio is multiplied to the term to find the next term.
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Solve the following:
-(6x + 6) +2=-6x-3
Answer:
no solution
Step-by-step explanation:
- (6x + 6) + 2 = - 6x - 3 ← distribute parenthesis on left side and simplify
- 6x - 6 + 2 = - 6x - 3
- 6x - 4 = - 6x - 3 ( add 4 to both sides )
- 6x = - 6x + 1 ( add 6x to both sides )
0 = 1 ← not possible
this indicates the equation has no solution
Answer:
No Solution, 0 = 1
Step-by-step explanation:
a) Simplify both sides of the equation.
−(6x + 6) + 2 = −6x − 3
−6x+ −6 + 2 = −6x + −3
(−6x) + (−6 + 2) = −6x − 3
−6x + −4 = −6x − 3
−6x − 4 = −6x − 3
b) Add 6x to both sides.
−6x − 4 + 6x = −6x − 3 + 6x
−4 = −3
c) Add 4 to both sides.
−4 + 4 = −3 + 4
0 = 1
The beta club is selling gift baskets to raise funds. Each basket sells for $13 and costs $6.50 to make. Write and expression to model a profit the beta club earns for each basket b sold.
The expression that models a profit P the beta club earns for each basket b sold is:
P = 6.50b
or
P = 13b - 6.50b
Given,
The beta club is selling gift baskets to raise funds.
Each basket sells for $13 and costs $6.50 to make.
We need to write an expression to model a profit the beta club earns for each basket b sold.
How do find profit?The profit is given by:
Profit = Selling price - cost price.
We have,
Selling price = $13
Cost price = $6.50
Find the expression for the profit.
The expression can be written as:
P = b ( 13 - 6.50 )
= 6.50b
or
P = 13b - 6.50b
Where b = number of baskets.
Thus the expression that models a profit P the beta club earns for each basket b sold is:
P = 6.50b
or
P = 13b - 6.50b
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Point A is chosen at random on BE- . Find the probability of the event.
P(A is on DE-)
The probability of the event P(A is on [tex]\bar{DE}[/tex]) is 9/26.
Probability:
Probability defines the possibility of the event.
And it can be calculated as,
Probability = favorable event / total event
Given,
Point A is chosen at random on [tex]\bar{BE}[/tex].
Here we need to find the the probability of the following event.
P(A is on [tex]\bar{DE}[/tex]).
Let us consider the following image, in order to solve this.
Based on the image we have identified that the probability of the event P(A is on [tex]\bar{DE}[/tex]) is calculated by dividing the length of DE by the length of BE.
So, the probability of the event P(A is on [tex]\bar{DE}[/tex]) is,
P(A is on [tex]\bar{DE}[/tex]) = (length of DE) / (length of BE)
Apply the values then we get,
P(A is on [tex]\bar{DE}[/tex]) = 9 / ( 5 + 12 + 9)
P(A is on [tex]\bar{CD}[/tex]) = 9 / 26
Therefore, the probability of the event P(A is on [tex]\bar{DE}[/tex]) is 9/26.
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HELP!!!!!!10pts
the question is penned below
The reasons for statements 2 and 3 are
statements 2 vertical opposite anglesstatements 3 sum of the angles are 180 degreesWhat is vertically opposite angle?Vertical opposite angles are angles formed when two lines intersect one another. When the lines intersect the angles facing each other or opposite the next is called the vertical opposite angle. The angles formed in this case are equal
Following the figure angle 3 and angle 2 are vertical opposite angles and they are equal. They are formed by intersection of the the parallel line L and the diagonal line running across. Similarly, angle 1 and angle 4 are vertical opposite angles since angle 1 and angle 4 face each other at the point of intersection.
What is supplementary angles?When the sum of two angles is equal to 180 degrees, such angles are called supplementary angles. These angles usually lie on a straight line and the angle on a straight line is 180 degree
Considering the given figure angle 3 and angle 5 are supplementary angles. that is to say that their sum is 180 degrees.
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find the area for each parallelogram
Answer:
Hello im sorry but I am unable to answer this.
Step-by-step explanation:
There is no parallelogram shown to answer.
Eight people arrive at the ticket counter of starlite cinema at the same time. in how many ways can they line up to purchase their tickets?
40320 ways can they line up to purchase their tickets.
What in mathematics is a permutation?
The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.given that n = 8 people
1st person have 8 choices to take ticket &
2nd person have 7 choices & 3rd person have 6 like that 8 people can purchase their tickets in = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ways
= 8 !
= 40320
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A coin is filmed using stop-motion animation so that it appears to move.
b. Describe the translation from A to C using a translation vector.
The translation of a coin from A to C using a translation vector is ;
Vector AC = (7, 3).
What is termed as translation?A translation in arithmetic a structure left or right and/or up or down. The translated shapes appear to be of the same size as the initial structure, indicating that the shapes are congruent.
Whenever the shape is moved to the left by k units, replace x with x - k.Whenever the shape is moved to the right by k units, replace x with x + k.Whenever the shape is moved by k units, replace y with y + k.Whenever the shape is moved by k units, replace y with y - k.Now, as per the given question.
See the given figure.
The coordinates if the points A and C are.
A = (-3, -1) and C = (4, 2)
The translation from A to C is estimated as;
AC = (4 + 3) ,(2 + 1)
Translation AC = (7, 3)
Thus, the given point A shifts 7 units to its right and then 3 units up to the point C.
Therefore, the representation of the translation of A and C in the form of
translation vector is AC = (7, 3).
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Factor the following polynomial completely: 6x^2+12x+6
The correct answer is 6(x+1)2
Explain in full detail how this answer is achieved
The given polynomial, 6•x² + 12•x + 6, can be factored by rearranging and looking for the common factors to give;
6•x² + 12•x + 6 = 6•(x + 1)²
How can the given polynomial be factored?The given polynomial is presented as follows;
6•x² + 12•x + 6
The coefficients in the terms and the constant have a common factor of 6, which gives;
6•x² + 12•x + 6 = 6•(x² + 2•x + 1)
x² + 2•x + 1 = x² + x + x + 1
x² + x + x + 1 = x•(x + 1) + 1•(x + 1)
x•(x + 1) + 1•(x + 1) = (x + 1)•(x + 1) = (x + 1)²
Therefore;
x² + 2•x + 1 = (x + 1)²
6•(x² + 2•x + 1) = 6•(x + 1)²
6•x² + 12•x + 6 = 6•(x² + 2•x + 1)
Therefore;
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Consider ABC and DFE. Triangle DFEis "blank" triangle ABC. since triangle ABC uses "blank" to map onto triangle DFE, the triangles "blank"
According to the question, the triangles ABC and DFE are mapped with each other.
Triangle DFE is right-angled triangle with ABC. And triangle ABC uses acute-angled theorem to mapped onto triangles DFE. Finally, the triangles are scalene triangles.
What is triangle?
The triangle can be defined as a polygon shape with three sides as well as three vertex. Depending upon the sides as well as angles, the triangles can be differentiated.
When all the sides are different, they comes under scalene triangles. When two sides are equal in a triangle then they are isosceles triangle. And finally, when all the sides are equal they are called as equilateral triangle.
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Answer: Triangle DFE is a rotation and reflection of triangle ABC. Since triangle ABC uses only rigid transformations to map onto triangle DFE, the triangles are congruent.
Step-by-step explanation:
See attached image below for proof
the first package has 17 cards second package has 21 thrid has 22 fourth has 16
The mean number of packages is 19.
How to calculate the mean?It should be noted that mean also means the average of a set of numbers given.
In this case, there are four packages.
The total cards will be:
= 17 + 21 + 22 + 16
= 76
Therefore, the average will be:
= Total cards / Number of package
= 76/4
= 19
Therefore, the mean number of packages is 19.
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The first package has 17 cards second package has 21 thrid has 22 fourth has 16. What is the mean?
What are the center and radius of the circle with the given equation?
b. x²+y²-6 x+14 y=8
The equation of the circle x^2 + y^2 - 6x + 14y = 8 has a radius of √66 and a center located at (3 , -7).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + y^2 - 6x + 14y = 8, then the coefficients are:
D = -6
E = 14
F = -8
If D = -2h and D = -6, then
-6 = -2h
h = 3
If E = -2k and E = 14, then
14 = -2k
k = -7
If F = h^2 + k^2 -r^2 and F = -8, then
-8 = 3^2 + (-7)^2 - r^2
r^2 = 9 + 49 + 8
r^2 = 66
r = √66
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Each hour, 7.5 liters drain from a large water tank. The tank initially held 83 liters of water. What does the expression 83−7.5t represent? the number of hours that have passed the number of hours until there are zero liters left the volume of water left after t hours the volume of water drained after t hours
The expression 83−7.5t represent C. the volume of water left after t hours.
How to illustrate the expression?From the information, each hour, 7.5 liters drain from a large water tank and thee tank initially held 83 liters of water.
Therefore, the expression 83−7.5t represent the volume of water left after t hours.
In conclusion, the correct option is C.
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PLEASE HELP ME ASAP!
Solve the equation for pi
V= pir^2h
The value of pi in the given equation is [tex]\frac{V}{r^2 h}[/tex].
What is the volume of a cylinder?The volume of a cylinder is the capacity of the cylinder, which determines how much material it can hold. In geometry, a specific volume of a cylinder formula is used to calculate how much of any quantity, liquid or solid, can be immersed in it uniformly. A cylinder is a three-dimensional shape with two identical congruent and parallel bases.
The given equation gives us the formula to calculate the volume (V) of the any given cylinder with the help of it's height(h) and base radius (r).
Given, [tex]$\quad V=\pi r^2 h$[/tex]
Divide both sides by h.
[tex]\frac{V}{h}[/tex] = [tex]\frac{\pi r^2 h}{h}[/tex]
V/h = π/[tex]$r^2$[/tex]
Divide both sides by [tex]$r^2$[/tex].
[tex]\frac{V}{r^2 h}[/tex] = [tex]\frac{\pi r^2}{r^2}[/tex]
π = [tex]\frac{V}{r^2 h}[/tex]
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Tiffany has a goal to complete a triathlon. The race consists of a 0.93-mile swim, a 24.8-mile bike ride, and a 6.2-mile run. In training, Tiffany can swim at an average pace of 2.2mph. She rides her bike at an average of 18.2mph and runs at 5.1mph. Estimate how long it will take her to complete the triathlon.
Answer:
3 hours
Step-by-step explanation:
Time = distance / rate
.93 miles / 2.2 mile/hr + 24.8 mile / 18.2 m/hr + 6.2 mile / 5.1 mile/hr = 3.00 hr
Finally, the total time in which Tiffany will complete the race will be 3 hours.
What is speed?speed is a quantity that expresses the relationship between the space traveled by an object. That is, the speed is associated with the change of position of an object in space within a certain amount of time.
Given that The race consists of a 0.93-mile swim, a 24.8-mile bike ride, and a 6.2-mile run.
In training, she can swim at an average pace of 2.2mph. She rides her bike at an average of 18.2mph and runs at 5.1mph.
We know that Time = distance / rate
So, total time= 0.93 miles / 2.2 mile/hr + 24.8 mile / 18.2 m/hr + 6.2 mile / 5.1 mile/hr
total time = 3.00 hr
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Find the first five terms of each sequence. aₙ=5-a n₋₁ , where a₁ = 1
The first five terns of the sequence are - 1,4,1,4,1
What is a sequence?
A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
an = 5 - a n-1
a1 = 1
a2 = 5 - (1) = 4
a3 = 5 - (4) = 1
a4 = 5 - (1) = 4
a5 = 5 - (4) = 1
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need help on this plsssssss
Which statement is true based off the parallel line with transversal? Angle 1 has a measure of 135 degrees because it's a consecutive angle with the given angle Angle 7 has a measure of 135 degrees because it's a vertical angle with the given angle Angle 7 has a measure of 135 degress because it's a linear pair with the given angle Angle 3 has a measure of 135 degrees because it's an alternate interior angle with the given angle
Answer:
angle 7 has a measure of 135 degrees because it's a vertical angle with the given angle
the volume of solid hemisphere is 19404cm3 and find its total surface area
Answer:
The volume of a solid hemisphere is 19404 cm3. Its total surface area is. 4158 cm.
Step-by-step explanation:
I hope this will be helpful for you and please like my answer.
10a=22
please help me
Answer:
2.2
Step-by-step explanation:
10 x a = 22
÷10
a = 2.2
Hope this helps!
PLSS HELP I NEED THIS
9r - 177 > - r + 233
9r + r > 233 + 177
10r > 410
^^^Divide both sides
Answer:
r > 41
Alternative form:
r ∈ ( 41, + ∞ ), { r | r > 41 }
It's correct! :)
Find an equation of the circle that has center (-2, 1) and passes through (6, -6).
The [tex](x +2 )^2+(y-1)^2=113[/tex]
The equation of a circle with centre (h,k) and radius r may be written:[tex](x -h )^2+(y-k)^2=r^2[/tex]
We are given (h,k)=(-2,1), so the only unknown is [tex]r^2[/tex].
So,
[tex](x +2 )^2+(y-1)^2=r^2[/tex]
Since the circle passes through (6,−6), the values
x=6, y =−6 will satisfy the equation and we find:
[tex]r^2 = (6-(-2))^2 + (-6-1)^2\\r^2 = (8)^2+(-7)^2\\r^2 = 64 + 49\\r^2 = 113[/tex]
So,
[tex](x +2 )^2+(y-1)^2=113[/tex]
Therefore the equation of the circle that has center (-2, 1) and passes through (6, -6) is [tex](x +2 )^2+(y-1)^2=113[/tex].
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The equation of circle that has center (-2, 1) and passes through (6, -6) is [tex](x+2)^2+(y-1)^2=113[/tex]
The equation of a circle with centre (h,k) and radius r may be written:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We are given (h,k)=(-2,1), so the only unknown is [tex]r^2[/tex].
So,
[tex](x+2)^2+(y-1)^2=r^2[/tex]
Since the circle passes through (6,−6), the values x=6, y =−6 will satisfy the equation and we find:
[tex]r^2=(6+2)^2+(-6-1)^2\\r^2=(8)^2+(-7)^2\\r^2=64+49\\r^2=113[/tex]
So,
[tex](x+2)^2+(y-1)^2=113[/tex]
Therefore the equation of the circle that has center (-2, 1) and passes through (6, -6) is [tex](x+2)^2+(y-1)^2=113[/tex]
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Solve each system by elimination.
2a + 3b = 12 , 5a - b = 13
By elimination, the solution of the system of equations, 2a + 3b = 12 and 5a - b = 13, is (a , b) = (3 , 2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in a and b, a variable should be eliminated by adding/subtracting the two equations.
Multiply first equation 2 by 3.
5a - b = 13 (equation 2)
15a - 3b = 39
Adding the two equations will eliminate the variable b.
2a + 3b = 12 (equation 1)
15a - 3b = 39 (equation 2)
17a = 51
a = 3
Substitute the value of a to any of the two equations and solve for b.
2a + 3b = 12 (equation 1)
2(3) + 3b = 12
3b = 12 - 6
3b = 6
b = 2
Hence, the solution of the system of equations is (a , b) = (3 , 2).
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