Write a flow proof of the Exterior Angle Theorem.
Given: ΔXYZ
Prove: m ∠ X + m ∠ Z = m ∠ 1

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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Answer:

68%

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

calculate the sum for both classes

class 1

[tex]\frac{sum}{20}[/tex] = 64 ( multiply both sides by 20 )

sum = 1280

class 2

[tex]\frac{sum}{10}[/tex] = 76 ( multiply both sides by 10 )

sum = 760

combine the 2 sums and divide by count of both classes for overall mean

overall mean = [tex]\frac{1280+760}{30}[/tex] = [tex]\frac{2040}{30}[/tex] = 68%

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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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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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:

The answer is 6.

Step-by-step explanation:

Simply by calculation.

Answer:

d

Step-by-step explanation:

Answer: 678.584in^3

Step-by-step explanation:

Volume= π*(6^2)*6 = 678.584in^3

The constant of proportionality for the relationship of millimeters of rainwater to time in hours is 48 millimeter/hour.

Given that the measuring tool captures rain falling at a constant.The table shows the height of rainwater in the measuring tool and the number of minutes it rains as shown in attached image.

A ratio is a mathematical comparison between two numbers. In proportion, if two given sets of numbers increase or decrease by the same ratio then the given ratios are said to be proportional.

Now we will calculate the proportion by using the formula

Ratio=(r₂-r₁)/(t₂-t₁)

Here, r₁=4, r₂=8, t₁=5, t₂=10

So, r₂-r₁=8-4=4 and

t₂-t₁=10-5=5

Now, we will convert the time from min to hour by dividing it with 60, we get

t₂-t₁=5/60

Substitute this value in above equation, we get

Ratio=4/(5/60)

Ratio=(4×60)/5

Ratio=4×12

Ratio=48 mm/hr

Hence, the constant of proportionality for the relationship of millimeters of rainwater to time in hours by using the given table is 48 mm/hr.

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P(x) =   =0.1033 , X has a Poisson distribution with a mean of 6.

Describe the Poisson distribution using an example?

Given mean =6

λ=6

To find the probability us ethe below formula

P(X=0)=60 e-6/0!=0.0025

P(X=1)=61e-6 /1!=6e-6 =0.0149

P(X=2)=62e-6 /2!=0.0446

P(X<=2)=P(X=0)+P(X=1)+P(X=2)

        =0.0025+0.0149+0.0446

P(X<=2)   =0.062

P(X=4)=64e-6/4!

            =64e-6  /4.3.2.1

         =64e-6 /24

      P(X=4)  =0.1339

P(X=8)=68 e-6/8!

     =4163.351816/40320

    =0.1033

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The complete question is -

Suppose X has a Poisson distribution with a mean of 6. Determine the following probabilities: P(x = 0) = P(x le 2) = P(x = 4) = P(X = 8) = Round your answers to four decimal places (e.g. 98.7654).

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)

Answer:

x=3

Step-by-step explanation:

8*3 = 24

4*3=12

24-12=12

Answer:

x = 3

Step-by-step explanation:

8x - 12 = 4x ( subtract 4x from both sides )

4x - 12 = 0 ( add 12 to both sides )

4x = 12 ( divide both sides by 4 )

x = 3

the distance between the cars is 3 miles

The rational form of 0.412 is 103/250.

According to the question,  to write the rational expression for the given link by removing the decimal. When the decimal is removed from the numerator then that many zeros will come in the denominator.

Therefore, the rational expression can be written as:

Required expression = 0.412 = 412/1000 = 103/250

Hence, the correct answer for this expression is 103/250.

What is rational expression?

The rational expression can be represented in the form of ratios which has two polynomials in the numerator as well as in the denominator. The value of the denominator term should never be zero.

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According to the Alternate Exterior Angles Theorem, when two parallel lines are severed by a transversal, the resultant alternate exterior angles are congruent if and only if the transversal is itself parallel to the two parallel lines.

So, in the figure below, if k ∥ l then

∠1 ≅ ∠7 and ∠4 ≅ ∠6.

Proof.

Since k ∥ l by the Corresponding Angles Postulate,

∠1 ≅ ∠5.

Also, by the Vertical Angles Theorem,

∠5 ≅ ∠7

Then, by the Transitive Property of Congruence,

∠1 ≅ ∠7

You may use the same strategy to demonstrate that ∠4 and ∠6 are equivalent to establish that they are congruent.

It should also be noted that the opposite of this theorem is true; more specifically, if two lines, k, and l, are sliced by a transversal in such a way that the alternative exterior angles are congruent, then k∥l.

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The relationship between the number x of days and the total cost represent as piecewise function.

f(x) = -x < 0

      = x if x ≥ 0

The bike store charges $20 for the first day and $15 for each additional day. The relationship between the number x of days and the total cost represent as:

f(x) = 20 , if 0 < x ≤ 1

      = 35,  if 1 < x ≤ 2

      = 50,  if 2 < x ≤ 3

      = 65,  if 3 < x ≤ 4

The absolute value function f(x) = |x| can be written as a piecewise function.

f(x) = -x < 0

      = x if x ≥ 0

Piecewise functions: A piecewise function is made up of two or more functions, each defined on a specific domain. Piecewise functions follow the following format:

f(x)    ⇒ -x,   x < 0

               ⇒  0,  x = 0

                ⇒ x,  x > 0

The piecewise function above is the absolute value function. As you can see, piecewise functions include:

A curly bracket to indicate that the function is comprised of more than one subfunction

The subfunctions that make up the piecewise function

The subdomains corresponding to each subfunction

The domains of the subfunctions cannot overlap, but one function can end where another starts. If different functions were part of the same domain, the piecewise function would not be a function anymore!

To graph a piecewise function, graph each subfunction at the indicated domain. Be wary of the inequality symbols (< , ≤ , > , ≥) and whether they include or exclude the end of the subdomain. If they include the domain, draw a point and fill it in. If they exclude the domain, draw a point but do not fill it in.

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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: 15

Step-by-step explanation:

-15 is 15 units to zero (answer should always be positive)

The measure of the smallest angle is 31°, the middle angle is 67°, and the measure of the largest angle is 82°.

A triangle is a plane shape with three edges and three vertices. All triangles have three internal angles, and the addition or sum of these angles gives 180°. In the question above, the three angles of the triangle are not given, though, we are given some clues as to how we can find them:

        Not much is said about the first angle, so we'll call it angle a.

        We are told that the second angle (angle b) is 5 more than twice

        angle a. The '5 more' means '5+' twice the value of angle a. Thus;

                             angle b = 5 + 2a

        The third angle, angle c is 11 less than 3 times the measure of angle

        a, meaning that angle c is 3 times angle a minus 11, thus;

                            angle c = 3a - 11

The addition of angle a, angle b and angle c gives 180°, hence:

                    a + 5 + 2a + 3a - 11 = 180°

                    a + 2a + 3a + 5 - 11 = 180°

                    6a -6 = 180

                    6a = 180 + 6

                    6a = 186

Dividing both sides by 6,

                      a = 31°

Now that we know the value of angle a, angle b will be

                        5 + 2(31) = 67°

and angle c is  

                        3(31) - 11 = 82°

Hence, the measure of the smallest angle, angle a is 31°, the middle angle, angle b is 67°, and the largest angle, angle c is 82°.

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Answer:

f(- 1) = 6

Step-by-step explanation:

substitute x = - 1 into f(x)

f(- 1) = 2(- 1)² + 4 = 2(1) + 4 = 2 + 4 = 6

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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Answer:

Step-by-step explanation:

what is 20 times 40 plus 67 minus 3

20 × 40 +  67 - 3 =   (remember PEMDAS)

800 + 64 =

864

Answer:864

Step-by-step explanation:

20 x 40 = 800 then you add 800 and 67 then you will get 867 then you subtract 3 that when you get 864

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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   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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Answer:

a = j - g

Step-by-step explanation:

"solve for a" means to get a all by itself on one side of the equation. You can see the beginning of the answer that is provided on your screen says "a = "

We are starting with:

j = g + a

First, subtract g from both sides of the equation.

j - g = a

Now just trade the left and right sides of the equation.

a = j - g

Fill in your answer in the box: j - g

If the tire says P235/65R17, the diameter of your wheel will be 17 inches.

The primary purposes of a car's tires are to carry the weight of the car, transmit traction and braking forces to the road surface, insulate against shocks from the road, and change and maintain the direction of motion.

It offers traction for braking and acceleration and reduces the number of road vibrations that reach the car's body.

It should be noted that the numbers that are written on the tire are vital in knowing the diameter that's illustrated.

In this case, when the tire says P235/65R17, the diameter of your wheel will be 17 inches.

In conclusion, it is 17 inches.

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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%.

Answer:

y=61°

Step-by-step explanation:

(y-8°)+(y+15°)+(y-10°)=180°

y-8°+y+15°+y-10°=180°

3y-3°=180°

3y=180°+3°

3y=183°

3y÷3=183°÷3

y=61°

The value of y from the given triangle can be calculated using the angle sum property as 61.

Given that:

A triangle has three angles given.

The measures of the angles are y - 8°, y - 10°, and y + 15°.

The angle sum property of triangles is defined as the property which states that the sum of the angles of the triangle is 180°.

Equating the angle measures:

y - 8 + y - 10 + y + 15 = 180

Add the like terms together.

3y - 3 = 180

Take 3 as common.

3(y - 1) = 180

Divide both sides of the equation by 3.

y - 1 = 60

Add 1 on both sides.

y = 61

Hence, the value of y is 61.

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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