The distance from Chicago to Cleveland to Cincinnati and back to Chicago is 900 miles. The distance from Chicago to Cleveland is 50 miles more than the distance from Cincinnati to Chicago, and the distance from Cleveland to Cincinnati is 50 miles less than the distance from Cincinnati to Chicago. Find each distance and classify the triangle formed by the three cities.

The additional information needed to prove that both triangles are congruent by SAA postulate is:

A. <B ≅ <D and <A ≅ <E

The SAA postulate is a condition that is used to prove that two triangles are congruent if they have two pairs of corresponding congruent angles and a pair of non-included congruent sides.

From the information we have in the diagram, we can deduce that:

AC ≅ EC (one pair of congruent sides)

ACB ≅ ECB (one pair corresponding congruent angles)

Therefore, the additional information needed to prove that both triangles are congruent by SAA postulate is:

A. <B ≅ <D and <A ≅ <E

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The arithmetic sequence AP's 32nd term is estimated to be 127.

An arithmetic progression (AP) in mathematics is a list or sequence of numbers within which each term is acquired by adding a sequence to the term before it.

Finally, the response to the question;

The numbers in the provided sequence are as follows:

34,37,40,43, ...........

There are 32 terms in the series, so we must obtain the 32nd number.

Suppose the first term is 'a₁' = 34.

Suppose 'a₂' = 37 be the second term.

Suppose 'a₃' = 40 be the third term.

The common difference between the two consecutive terms of an AP that are equal is 'd.'

d = a₂ - a₁  

Put the values in the preceding formula; the 32nd term is

d = 37 - 34

d = 3

The nth term equation is now used to calculate.

Substitute all of the values in the formula now.

a₃₂ = a + (n - 1) d

a₃₂ = 34 + (32 - 1)(3)

a₃₂ = 34 + 96 - 3

a₃₂ = 127

Thus, the arithmetic sequence's 32nd term is evaluated to be 127.

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In order to determine the relationship between the time and the amount of money in the account, we would calculate the average rate of change.

The average rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Mathematically, the slope (average rate of change) can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For Tammy's account, we have:

Points (x, y) = (6, 467) (8, 557)

Average rate of change = (557 - 467)/(8 - 6)

Average rate of change = 90/2

Average rate of change = 45.

As time increases, the amount of money in Tammy's account increases. Also, the rate at which the amount of money in the account is increasing is 45 dollars per month.

First of all, we would determine the increment in 6 months as follows:

Increment = $45 × 6

Increment = $270.

Initial amount = $467 - $270

Initial amount of money = $197.

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2.42 km was steve's peak speed in kilometers per hour.

Describe speed -

Given speed is 67.1 cm/s

we know that 1 cm = 10-² m

            and  1 m = 10-³ km

∴   1 cm = 10-5 ∴m

also          1 sec = 1/3600 hr

∴   67.1 cm/s  = [tex]\frac{67.1 * 10^{-5 km} }{\frac{1 hr}{3600 } }[/tex]

or  67.1 cm/s  =  2. 4156 km/hr  or 2.42 km

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Answer:

Step-by-step explanation:

15.23 units

Answer:

Your answer is 20

Step-by-step explanation:

Ok so AB= 25

BC= 15

We need to find AC And the Pythagorean theorem says a²+b²=c²

Since we only got C and B were gonna do subtraction

So 25²-15²= 400

And 400 square rooted is 20

Hope this helps :33333

The solution of the given linear equation in one variable 5(3w - 2) -7= 23  is at w = 8/3.

According to the given question.

We have a linear equation in one variable 5(3w - 2) - 7 = 23.

As we know that, 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.

Thereofre, the solution of the linear equation in one variable 5(3w -2) = 23 is given by

5(3w - 2) -7= 23

⇒ 15w - 10 -7 = 23  ( by distributive rule)

⇒ 15w -7-10 = 23

⇒ 15w -17 = 23

⇒ 15w = 23 + 17     ( adding 17 both the sides)

⇒ 15w = 40

⇒ w = 40/15

⇒ w = 8/3

Hence, the solution of the given linear equation in one variable 5(3w - 2) -7= 23  is at w = 8/3.

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The probability that the die will land on a vowel is 0.2.

It is given in the question that the die is 20-sided and has all of the letters of the alphabet except for Q, U, V, X, Y , and Z .

We have to find the probability that the die will land on a vowel.

Possible outcomes of vowels = A, E, I  and, O

Hence, number of possible outcomes = 4

We know that,

Total number of outcomes = 20

Hence,

Probability that the die will land on a vowel = 4/20 = 1/5 = 0.2

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Answer:

place the dot on 8, -6, and 12

Step-by-step explanation:

The coordinates of the point on the directed line segment from (1, -3) to (7, 5) that partitions the segment into a ratio of 1 to 3 is; (x, y) = (2.5, 0.5)

The formula for partitioning a line segment in the ratio m:n is;

(x, y) = (mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)

We are given the ratio as 1:3 with the coordinates as;

(1, -3) and (7, 5). Thus;

m = 1 and n = 3

x1 = 1

x2 = 7

y1 = -1

y2 = 5

Thus;

(x, y) = (1*7 + 3*1)/(1 + 3), (1*5 + 3*-1)/(1 + 3)

(x, y) = (10/4, 2/4)

(x, y) = (2.5, 0.5)

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Using rational numbers, Jackson supports more education funding as he  7/20 > 6/20.

Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number.

According to Kirsten, 24% of federal tax dollars should fund education

⇒ 24% = 24 / 100

⇒ 6/25

According to Jackson, $0.35 of every tax dollar should go toward education

⇒ 0.35 = 35 / 100

⇒ 7/20

As we can infer that 7/20 > 6/20

So Jackson supports more education funding.

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f (5) =  -19 is the output for the given input .

How can you tell whether a function is linear or not?

f(x)= -4 x+1

Put x = 5    ⇒   - 4 ×  + 1

                 ⇒   -20 + 1

                 ⇒   -19

Therefore f (5) =  -19

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The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 467) and (10, 647)

The rate of change is calculated as

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

So, we have

Rate = (647 - 467)/(10 - 2)

Evaluate

Rate = 22.5

This means that the rate of change is $22.5

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 22.5

So, we have

y = 22.5(x - x1) + y1

Using one of the points, we have

y = 22.5(x - 6) + 467

Set x = 0

So, we have

y = 22.5(0 - 6) + 467

Evaluate

y = 332

Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

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Based on the number of people going to see the movie and the price of the snacks, the total that Genesis would pay if she bought 6 snacks is $78.

The amount that Genesis would pay if she bought x snacks is 60 + 3x.

The total cost to Genesis can be found as:

= (Number of people going to watch movie x Price of ticket) + (Price per snack x number of snacks)

= (4 people including Genesis x 15) + (3 x 6)

= 60 + 18

= $78

The amount that Genesis would pay if she got x snacks is:
=  (Number of people going to watch movie x Price of ticket) + (Price per snack x number of snacks)

= (4 x 15) + (3 × x)

= 60 + 3x

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Line segments are congruent if they have the same length.

∠ ACB ≅ ∠ ABC

Segments of the same length are said to be congruent. Collinear points are those that share a line. A mathematical assertion that can be validated is known as a theorem. A point that separates a segment into two congruent segments is the segment's midpoint.

Line sections are harmonious assuming that they have a similar length. You can utilize tick imprints to demonstrate harmonious line sections. In the triangle underneath, line fragments Stomach muscle and BC are harmonious.

Harmonious portions are sections that have a similar length. ≅ Focuses that lie on a similar line are called collinear. A hypothesis is a numerical explanation that can be demonstrated. The midpoint of a section is a point that separates the portion into two harmonious fragments.

Therefore, ∠ ACB ≅ ∠ ABC

The complete question is:

a. Name two unmarked congruent segments.

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Answer:Your answer is X>7

Step-by-step explanation:

Form:

x>7

Interval Notation:

(7,∞)

By solving a linear equation, we can see that after 3 hours Ricardo has $61.91

We know that Ricardo has $132.16, and he rents a jet sky that costs $20 plus $16.75 per hour.

So, the cost of renting the jet sky for x hours is given by the linear equation:

C(x) = $20 + x*$16.75

The cost of renting this for 3 hours is:

C(3) = $20 + 3*$16.75 = $70.25

Subtracting this from what Ricardo had:

$132.16 - $70.25 = $61.91

So the correct option is the second one.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: 2x - 17 = 51 + 61[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x - 17 = 112[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 112 + 17[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 129[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \dfrac{129}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 64.5[/tex]

By elimination, the solution of the system of equations, r + 3s = 7 and 2r - s = 7, is (r , s) = (4 , 1).

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 r and s, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 2.

r + 3s = 7 ⇒ 2r + 6s = 14     (equation 1)

Subtracting the two equations will eliminate the variable r.

2r + 6s = 14     (equation 1)

2r  -   s = 7     (equation 2)

    7s    = 7

s = 1

Substitute the value of s to any of the two equations and solve for r.

2r - s = 7     (equation 2)

2r - 1 = 7

2r = 7 + 1

2r = 8

r = 4

Hence, the solution of the system of equations is (r , s) = (4 , 1).

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The simplification by combining like terms of 4t-(t + 3t)  is 0.

According to the given question.

We have an expression 4t - (t+3t).

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression 4t-(t+3t).

Here 4t, t and 3t both are the like terms.

So, we add and subtract coeffcients of t to simplify the given expression.

Therefore, the simplification of 4t - (t + 3t) is given by

4t -( t+ 3t)

= 4t - t -3t

= 4t - 4t

= 0

Hence, the simplification by combining like terms of 4t - (t + 3t) is 0.

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Answer:

30

Step-by-step explanation:

if x=4 you would take  the x out of 2x and replace it with 4 so it would be 24+6

Answer:

Step-by-step explanation:

in the picture

The probability that he will randomly pull out two quarters in a row is 1/15.

Given that:-

Number of quarters Isaiah has = 3

Number of dimes Isaiah has = 5

Number of nickels Isaiah has = 2

We have to find the probability that he will randomly pull out two quarters in a row.

Probability of getting the first quarter = 3/(3+5+2) = 3/10

After taking out the first quarter, now he is only left with 2 quarter, 5 dimes and 3 nickels.

Hence,

Probability of getting the second quarter = 2/(2+5+2) = 2/9

Hence, probability of getting two quarters in a row = 3/10 * 2/9 = 1/15

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Answer:

C is the correct answer

Step-by-step explanation:

hope you get it right :))

The expression was rewritten using the commutative property of addition

The expressions are given as

(7 + 1) + 9

7 + (1 + 9)

The commutative property of addition states that

a + b = b + a

This means that the expression was rewritten using the commutative property of addition

Also, we have

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18 lines of symmetry the dome have, after excluding the spire of the dome.

36 ÷ 2 = 18

3 row × 36 windows per row, total windows = 108. 36 of them connects a window with the window across to form 1 line of symmetry.

If two additional identical parts that are arranged in an orderly fashion can be divided from a shape, it is said to be symmetrical. As an illustration, if you are instructed to cut out a "heart" from a piece of paper, you need just fold the paper, draw one-half of the heart at the fold, and then cut it out to discover that the second half exactly matches the first half.

Asymmetrical and symmetrical balances are the two types of balance. The two parts of the thing are precisely identical and balanced in symmetrical balance. The two parts of an asymmetrical balance are not similar; rather, separate things are arranged such that they appear to be balanced.

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Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100