Use the given information to write an equation of the circle.
center (6,4) , through (2,1)

Answer:

Ratio of homework papers to exit tickets

Mr. Rowley: 8/7

Ms. Rivera: 16/15

These ratios are not equal

8/7 > 16/15

Step-by-step explanation:

Ratio of homework papers to exit tickets

Mr. Rowley: 16:14

Expressed as a fraction this is
[tex]\dfrac{16}{14}[/tex]

Let's simplify the fraction by dividing numerator and denominator by 2. This is essentially dividing by 1 since 2/2 =1 so the fractional value itself is unchanged.

[tex]\dfrac{16 \div 2}{14 \div 2} = \dfrac{8}{7}[/tex]

Ms. Rivera: 64:60
Expressed as fraction this is
[tex]\dfrac{64}{60}[/tex]

Let's simplify the fraction by dividing numerator and denominator by 2
[tex]\dfrac{64 \div 2}{60 \div 2} = \dfrac{32}{30}[/tex]

This can be simplified further by dividing again by 2:
[tex]\dfrac{32 \div 2}{30 \div 2} = \dfrac{16}{15}[/tex]

(We could have divided by 4 the first time also)

[tex]\dfrac{8}{7}[/tex] [tex]\mathrm {\;is\;\bold{not\; equal\;} to\; }[/tex] [tex]\dfrac{16}{15}[/tex]

We can see that if we multiply both fractions by 105 which is the product of the denominators

[tex]\dfrac{8}{7} \times 105 = 8 \times 15 = 120 \rm \;\;\;\;{ (since 105 \div 7 = 15)}\\\\\dfrac{16}{15} \times 105 = 16 \times 7 = 112 \rm \;\;\;\;{ (since 105 \div 15 = 7)}\\\\\\[/tex]

Since we are multiplying both fractions by the same amount to get rid of the denominator it is easy to see which one is bigger

Obviously 8/7 is bigger than 16/15

We could have converted to decimal also and checked
8/7 =     1.14 rounded to 2 decimal places
16/15 =  1.07 rounded to 2 decimal places

1.14 > 1.07 so 8/7 > 16/15

(You can choose which of the above methods you like)

The geometric mean between pair of numbers 8√2/3 and 4√2/3 is 2.67

We know that for a sequence of numbers x1, x2,.., xn

The formula of geometric mean is,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have been given two numbers 8√2/3 and 4√2/3

We need to find the geometric mean between pair of numbers, 8√2/3 and 4√2/3.

Using the formula for the geometric mean,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi=\sqrt{\frac{8\sqrt{2} }{3} \times \frac{4\sqrt{2} }{3}} \\\\\Pi=\sqrt{\frac{32\times 2}{9} } \\\\\Pi=\sqrt{\frac{64}{9} } \\\\\Pi=\frac{8}{3}\\\\\Pi=2.67[/tex]

Therefore, the geometric mean between pair of numbers 8√2/3 and 4√2/3 is 2.67

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We have proved that the West Texas Triangle formed is an isosceles triangle.

The approximate coordinates of three locations is given.

We have to prove that the West Texas Triangle is an isosceles triangle.

What is a triangle ?

A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.

As per the question ;

The West Texas Triangle is an isosceles triangle.

1st location has coordinates (31.9°N , 102.3°W)

2nd location has coordinates (32.7°N , 99.3°W)

3rd location has coordinates (31.4°N , 100.5°W)

Let's represent 1st location as A , 2nd location as B and 3rd as C.

Let's check it.

Using the distance formula ;

AB = √ [ (32.7 - 31.9) ² + (102.3 - 99.3)²]

AB = √ (0.8² + 3²)

AB = √9.64

AB = 3.10

Similarly ;

BC = √ (1.3² + 1.2²)

BC = √3.13

BC = 1.8

And

AC = √(0.5² + 1.8²)

AC = 1.8

The two sides are of equal length , so , we can conclude that this is an isosceles triangle.

Thus , the West Texas Triangle formed is an isosceles triangle.

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Answer:

Use This it will help

Step-by-step explanation:

The median of the numbers which Norberto received in the test is 88.

The median is a measure of central tendency that is used to signify the relative middle point of a data-set.

The scores of the last five spelling test are : 88, 81, 93, 85, and 98

Here n = 5 and we have to arrange the data in an ordered form.

81 , 85 , 88 , 93, 95

So the formula to calculate the median is given by

median = (n+1)/2 th term of the data set.

hence median = 3rd data = 88

Again the mean of the data is :

(81+85+88+ 93+ 95) ÷ 5 = 440 ÷ 5 = 88

Hence the median of the data is 88 and the mean is also 88.

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Answer: Area, S = 36 [tex]cm^{2}[/tex]

Step-by-step explanation:

What is the Area of a Triangle?

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e.

                               A = 1/2 × b × h.

Given data,

Area of shaded triangle S = 1/2 *b*h

We can write,

                    Area = S

                     Base = b

                     Height = h

we get,

                Base b = 6cm

                Height h = 12cm

h=12 cm  height of isosceles triangle ,

           Area = 1/2 * b*h

We can substitute b and h values,        

            Area= 1/2* 6 * 12

                    = 1/2 * 72

                    = 36

So, Area, S = 36 [tex]cm^{2}[/tex]

Therefore,

                          Area, S = 36 [tex]cm^{2}[/tex]

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Answer:

y = 11

Step-by-step explanation:

Let's solve your equation step-by-step.

[tex] \rightarrow \sf \: y {}^{2} =121[/tex]

Step 1: Take square root.

[tex] \sf \: y=± \sqrt{121} [/tex]

y=11 or y=−11

Step-by-step explanation:

slope=m=-4

equation-y=mx+c

equation-y=-4x+c

input y and x to find c

x=-1

y=-1

-1=-4(-1)+c

-5=c

therefore equation is

y=-4x-5

the function f(x) is invertible on the intervals:

B: -7 ≤ x ≤ -4

C : 1 ≤ x ≤ 3

A function f(x) can only be invertible if it is one-to-one in its domain, where one-to-one means that each output is related to only one input.

So, if for two different values x₁ and x₂ we have that:

f(x₁) = f(x₂) = y, then the function is not invertible.

So here what we need to do is identify in which interval is the function one-to-one.

If you look at the last option, we have the interval [1, 3]

We have that f(1) = 2, and then the function increases until f(3) = 4

In that interval the function is cleraly one-to-one, so, on that interval, we can find an inverse function to f(x).

Similarly, on the second option [-7, -4] we also can see that:

f(-7) =  2

And then the function increases until f(-4) = 4

Then the function is also invertible on that interval.

We conclude that the function f(x) is invertible on the intervals:

B: -7 ≤ x ≤ -4

C : 1 ≤ x ≤ 3

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Answer:-3<x<-1 is incorrect, all else are correct.

Step-by-step explanation:

Based on the side-angle-side congruence theorem (SAS),

Missing statement is: ΔHIK ≅ ΔHJK

Missing reason is: SAS

If there are two pairs of congruent sides and a pair of included corresponding congruent angles in two triangles, then based on the side-angle-side congruence theorem (SAS), the two triangles are congruent to each other.

The two triangles have the following:

Two pairs of congruent sides which are: HI ≅ HJ, and HK ≅ HK

One pair of included corresponding congruent angles which is: <IHK ≅ <JHK.

This means that both triangles are congruent triangles based on SAS.

Therefore,

Missing statement is: ΔHIK ≅ ΔHJK

Missing reason is: SAS

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Both Tetsuya and Mason are interested in finding the probability that a red marble will be chosen out of the bag. We will decide if either of them is correct.

In statistics, what does a probability mean?

Tetsuya  P( R) = 4/17

Mason  P( R ) = 1 - 4/18

P ( R) = Favorable outcome/ possible outcome

The number of favorable outcomes is the number of red marbles in the bag, so it is equal to 4. The number of possible outcomes is the number of all marbles in the bag. Let's find it.

                     4 + 7 + 5 + 2 = 18

We have enough information to find the probability that a red marble will be chosen P(R).

                              P( R) = 4/18

Tetsuya used the wrong number of possible outcomes in the denominator. Let's look at Mason's solution. They wanted to use the probability of complementary events. However, they found the probability that a selected marble is not red.

                   Mason  P( R ) = 1 - 4/18

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The solution of the given linear equation in one variable 3(x+1)=9+2 x is at x = 6.

According to the given question.

We have a linear equation in one variable.

3(x + 1) = 9 + 2x

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Therefore, the solution of the given linear equation in one variable is given by

3(x + 1) = 9 + 2x

⇒ 3x + 3 = 9 + 2x

⇒ 3x - 2x = 9 - 3

⇒ x = 6

Hence, the solution of the given linear equation in one variable 3(x+1)=9+2 x is at x = 6.

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Answer:

d

Step-by-step explanation:

The equation of the line -4x + y = 10 has -5/2 and 10 as its x- and y-intercept, respectively.

The equation of a line is an equation containing variable(s) and constant(s) and can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The x-intercept of a line is the value of x when y = 0 while the y-intercept of a line is the value of y when x = 0.

For an equation written in standard form ax + by = c, the x- and y-intercept is as follows:

x-intercept = c/a

y-intercept = c/b

If the equation of the line is -4x + y = 10, then its x- and y-intercept is as follows:

x-intercept = c/a = 10/-4 = -5/2

y-intercept = c/b = 10/1 = 10

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Applying the exterior angle of a triangle theorem, m∠G = 40°.

According to the exterior angle theorem of a triangle, we have the following equation that is derived:

11x - 4 + 55 = 23x + 3

11x + 51 = 23x + 3

11x - 23x = -51 + 3

-12x = -48

-12x/-12 = -48/-12

x = 4

m∠G = 11x - 4 = 11(4) - 4

m∠G = 40°

Thus, applying the exterior angle of a triangle theorem, m∠G = 40°.

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Answer:

The answer is 6.

Step-by-step explanation:

Simply by calculation.

The first five terms of each sequence is  20 , 22, 24, 26 ,28.

What is a term:

In algebra, an algebraic expression is formed by a term or a group of terms together. Term in math is defined as the values on which mathematical operations occur in an algebraic expression.

Now , the mathematical expression.

a1 =20 an =an−1​ +2,n>1

putting n=2 a2 =a2−1+2 =a1+2 =20+2=22

h=3 a3 =a3−1 +2 =a2+2 =22+2=24

x=4 a4 =a4−1+2 =a3 +2 =24+2=26

n=5 a5​ =a5−1​ +2 =a4+2 26+2=28

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Answer:

10%

The increase of her score would be 7 so 7 over 70 which would = to .10 and .10 as a percent is 10%.

                         Expression                               Property used

Step 1   1 x 3/2 x (-5) x 3 x (-4)        Inverse Property of Multiplication

Step 2  1 x (-4) x 3/2 x (-5) x 3        Associative Property of Multiplication

Step 3  1 x [ (-4) x 3/2 ] x (-5) x 3  Commutative Property of Multiplication

Step 4  1 x [-6] x (-5) x 3                Identity Property of Multiplication

Step 5  -6 x (-5) x 3

The inverse property of multiplication refers to multiplying a number with it's reciprocal. This is applied while transforming from division to multiplication as division is the inverse of multiplication.

Associative property of multiplication is applied while multiplying several values, Hence rearranging the terms will still give same answer.

This property has it that the order of the multiplication do not matter, hence multiplication can start with any order.

This property refers to multiplication of a value with one, such multiplication usually return same value as the product.

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The distance between the point  [tex]\frac{4}{5}[/tex] and [tex]\frac{-1}{6}[/tex] is [tex]\frac{9}{10}[/tex] or 0.9.

Given point are [tex]\frac{4}{5}[/tex] and [tex]\frac{-1}{6}[/tex]

In decimal form,

[tex]\frac{4}{5}=0.8[/tex]

[tex]\frac{-1}{6} =-0.1[/tex]

Plot that two point on a number line.

Number line means a straight line with numbers arranged at equal segments or intervals throughout its length is known as a number line. A number line is often shown horizontally and can be extended indefinitely in any direction.

In the figure we can see the number plotting.

The points between those points is the distance between the  [tex]0.8[/tex] and [tex]-0.1[/tex].

Therefore, the distance between the point  [tex]\frac{4}{5}[/tex] and [tex]\frac{-1}{6}[/tex] is [tex]\frac{9}{10}[/tex] or 0.9.

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Answer: 678.584in^3

Step-by-step explanation:

Volume= π*(6^2)*6 = 678.584in^3

The initial amount and rate of change given a table for a linear function are $65 and $86, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 476) and (10, 736)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (736 - 476)/(10 - 6)

Evaluate

Rate = 65

This means that the rate of change is $65

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 65

So, we have

y = 65(x - x1) + y1

Using one of the points, we have

y = 65(x - 6) + 476

Set x = 0

So, we have

y = 65(0 - 6) + 476

Evaluate

y = 86

Hence, the initial amount and rate of change given a table for a linear function are $65 and $86, respectively

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Answer:

the answer is -3

Step-by-step explanation:

I took the quiz on k12

Answer:

1800

Step-by-step explanation:

hope this works for you :)

Answer:

x<-3

see the number line attached

make sure the number line has an open circle at -3

Hello,

[tex] - 9x + 9 > 36[/tex]

[tex] - 9x > 36 - 9[/tex]

[tex] - 9x > 27[/tex]

[tex]x < \frac{27}{ - 9 \:} \: \: because \: - 9 < 0[/tex]

[tex]x < - 3[/tex]

If this rate of change continues, the attendance for the year 2012 will be 468973.

Slope(m) for given two points (x₁,y₁) and (x₂,y₂)  is calculated using the formula

m=(y₂-y₁)/(x₂-x₁)

in the given question ,we will take year as x coordinate and the attendance as y coordinate.

Given " The attendance in 2001 was 450,746" , So

The point becomes (2001,450746)

and "the attendance in 2005 was 457,373" So

the point becomes (2005,457373)

Now as we have the two points , slope can be calculated as

m=(457373-450746)/(2005-2001)

m=6627/4

m≅1657

Hence the rate of change is 1657 persons per year

It is given in the question that rate of change remains constant.

To predict the attendance for the year 2012.

Let the attendance for the year 2012 be x.

we have (2001,450746) and (2012,x)

let m=1657, x₁=2001 , y₁=450746 , x₂=2012 , y₂=x

m=(y₂-y₁)/(x₂-x₁)

Substituting the values we get  

[tex]1657=\frac{x-450746}{2012-2001} \\ \\ 1657=\frac{x-450746}{11}[/tex]

By cross multiplying we get

[tex]1657*11=x-450746\\ \\ 18227=x-450746\\ \\ x=450746+18227\\ \\ x=468973[/tex]

Therefore , The attendance for the year 2012 will be 468973.

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   The equation that defines the parabola with vertex at the origin and focus at (0, -4) is

y = -x²/16

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The canonical equation of a parabola is given by

(x - h)² = 4p(y - k)

   The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v = (0, 0)

f = (0, -4) This means that the focus is on the negative part of the y-axis, the form of the equation of this parabola is y = x²

(x - 0)² = 4p(y - 0)

Focus:

f = (0, 0 + p)

(x - 0)² = 4*-4(y - 0)

(x)² = 16(y)

y = -x²/16

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The slope of the given equation of line is [tex]\frac{A}{B}[/tex] and the y-intercept is [tex]\frac{-C}{B}[/tex]

Given: -Ax + By = -C

=> y = [tex]\frac{A}{B}x+ \frac{-C}{B}[/tex]

As we know that the slope-intercept form of an equation of a line is given by: y = mx + c, where:

On comparing the given equation of the line with this form, we get:

m = [tex]\frac{A}{B}[/tex] and c = [tex]\frac{-C}{B}[/tex]

Hence, The slope of the given equation of line is [tex]\frac{A}{B}[/tex] and the y-intercept is [tex]\frac{-C}{B}[/tex].

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