State the postulate or theorem you would use to prove each pair of triangles congruent.
a) SSS
b) SAS
c) ASA
d) AAS
e) HL
f) Not possible

Problem 1

[tex]f(n) = 59,000\left(1.08^{n-1}\right)[/tex]

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Explanation:

The right hand side for choice A is in the form [tex]a(r)^{n-1}[/tex] which is the nth term of a geometric sequence.

The 1.08 represents an increase of 8% because,

1.08 = 1 + 0.08 = 100% + 8% = 108%

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Problem 2

[tex]\frac{(y-60)^2}{144} + \frac{x^2}{100} = 1[/tex]

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Explanation:

The ellipse is 20 inches wide, which cuts in half to 10 inches. This is the corresponding value plugged into the denominator of the 'x' fraction, as x deals with the horizontal component. So we'll have a^2 = 10^2 = 100 in the denominator under the x term. Only choice C has this, so this is the answer we go for. For the vertical component, we cut 24 in half to get 12, then square it to get 144, which explains the denominator for the y term.

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Problem 3

30 feet; major axis

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Explanation:

Pick the larger denominator 225. Apply the square root to get 15. Then double this value to land on 30. This is the length of the major axis which is the longer axis through the center of the ellipse. The major axis also passes through both foci.

Let's say points P and Q are any two random points on the ellipse. The longest segment PQ can get is 30 feet.

Answer:

Step-by-step explanation:

That will be a square with a diagonal of 20

side length of 20sin45

and area of (20sin45)² = 200 units²

prove it you say?

Area of a rectangle is base times height

A = bh

With a radius of 10, the diagonals of any rectangle inscribed will be 20 units

20² = b² + h²

h = [tex]\sqrt{400 - b^2}[/tex]

A = bh

A = b[tex]\sqrt{400 - b^2}[/tex]

Area will be maximized when the derivative is set to zero

           dA/db = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]

                   0 = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]

b²/[tex]\sqrt{400 - b^2}[/tex] =  [tex]\sqrt{400 - b^2}[/tex]

                  b² = 400 - b²

                2b² = 400

                  b² = 200

                  b = [tex]\sqrt{200}[/tex]

h = [tex]\sqrt{400 - b^2}[/tex]

h = [tex]\sqrt{400 - \sqrt{200}^2 }[/tex]

h = [tex]\sqrt{200}[/tex]

A = bh

A =  [tex]\sqrt{200}[/tex]•[tex]\sqrt{200}[/tex]

A = 200 units²

Answer:

8/25 of the people in the stadium are children.

Step-by-step explanation:

45 + 23 = 68

100 - 68 = 32%

32/100 simplified is 8/25

Answer:

8 because the pattern goes up by 2 each time

Answer:

8

Step-by-step explanation:

In 2008, up to 405 messages could be sent without spending more than $ 100.

Since in 2008, text messages were charged per text, and some carriers charged $59 for a basic text package of 200 texts and 20 cents per text after that, while today, most packages include unlimited text and data but cost closer to $ 100 a month, to determine the range of text messages you can send with the 2008 plan without spending more than $100, the following calculation must be performed:

Thus, in 2008, up to 405 messages could be sent without spending more than $ 100.

Learn more about maths in https://brainly.com/question/25908673

Step-by-step explanation:

absolutely. there is no mathematical problem to solve.

just do what the instructions tell you.

that is an exercise for you to get a feeling what is what.

Answer:

2 and 3

Step-by-step explanation:

7/3=2 1/3

So it lies between 2 and 3

2 1/3 is lesser that 3 but more than 2.

Answer:

x³ - 8x² - 20x

Step-by-step explanation:

Zeroes: 10, 0, -2

Factors are: (x - 10), (x - 0), (x + 2)

Multiply all factors to get expression:

(x - 10)x(x + 2) = x(x - 10)(x + 2)

= x(x² - 10x + 2x - 20)

= x(x² - 8x - 20)

= x³ - 8x² - 20x

Answer:

hope it helps.

stay safe healthy and happy.

Answer:

In bold below.

Step-by-step explanation:

bf-5k=c(g+2k)

g + 2k = (bf - 5k)/c

g =  (bf - 5k)/c - 2k

[tex]x^2 +18x +90 = 0\\\\\text{Apply quadratic formula,}~~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a} \\\\\text{In this case, a = 1 , b = 18 and c = 90.}\\\\\implies x = \dfrac{-18 \pm \sqrt{18^2 - 4 \cdot 1 \cdot 90}}{2(1)}\\\\\implies x = \dfrac{-18 \pm \sqrt{-36}}2\\\\\implies x = \dfrac{-18 \pm 6i}2\\\\\implies x= -\dfrac{18}2 \pm \dfrac{6i}2\\\\\implies x= -9 \pm 3i[/tex]

1: 1.645

2. 1.28

4: 95% confidence level (12.93, 13.87)

3: No Idea

5: sorry im a bit rusty

Im so sorry for not answering all you questions

Answer:

5/8

6/7

2/3

Step-by-step explanation:

Answer:

Interval Notation (-∞, ∞)

Set-Builder Notation: {x|x ∈ R} (all real numbers = R)

Step-by-step explanation:

I plugged this into a graphing calculator and was able to find the domains by looking at where the lines stopped (they didn't stop) and wrote the f(x) based off of it

Answer: 6. 35 hours

7. 741 Miles

8. 1.5 or 1.54

Step-by-step explanation:

6. 142.20/6=23.7

829.50/23.7=35

7. 117/3=39

39x19=741

8.19/12.35=1.538

Answer: 12.25 ( each side )

Step-by-step explanation

Divide 49 by 4, which is 12.25

Answer:

See below

Step-by-step explanation:

9 and 8.4 are less than 1 apart, so 9-8.4 must be less than 1. The actual difference is 9-8.4=0.6 which verifies that our answers are true since 0.6<1.

Answer:

C

Step-by-step explanation:

Given y ∝ [tex]\frac{1}{x}[/tex] then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = - 2 when x = 14 , then

- 2 = [tex]\frac{k}{14}[/tex] ( multiply both sides by 14 )

- 28 = k

y = - [tex]\frac{28}{x}[/tex] ← equation of variation

Answer: THe Second answer is the correct one

Step-by-step explanation:

Answer:

y = 3x-2

Step-by-step explanation:

Answer:

Calvin's number: 16 Sanjay's number: 6

Step-by-step explanation:

6 x 3 = 18, 18 - 2 = 16

16 / 2 = 8, 8 - 2 = 6

Answer:

Logarithmic functions are the inverses of exponential functions.The logarithmic function y=loga(x)  is called the logarithmic function with base a .

When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.

It is shifted 2 units vertical.(2 units down).

Answer:

Logarithmic functions are the inverses of exponential functions.The logarithmic function y=loga(x)  is called the logarithmic function with base a .

When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.

It is shifted 2 units vertical.(2 units down).

Step-by-step explanation:

8 : 2  

8+ 4 = 12    2 + 1 = 3

12 : 3

12 + 4 = 16   3 + 1 = 4

16 : 4

16 + 4 = 20   4 + 1 = 5

20 : 5

20 + 4 = 24   5 + 1 = 6

24 : 6

24 + 4 = 28   6 + 1 = 7

28 : 7

28 + 4 = 32   7 + 1 = 8

32 : 8

32 + 4 = 36   8 + 1 = 9

36 : 9

36 + 4 = 40   9 + 1 = 10

40 : 10

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer: If the number of cups of cereal is 40, then the number of cups of raisins will be 10.

Have a great day/night! :D

Answer:

$48

Step-by-step explanation:

Each ticket costs 4 dollars.

Step-by-step explanation:

Domain -5 range 5 ,...............

Answer:

1 days= 24 hrs

3 days = 3×1 days

= 3×24 hrs

= 72 hrs

Answer:

60

Step-by-step explanation:

Answer:

2nd answer choice

Step-by-step explanation:

We want to know which one does not have a two digit quotient, or answer. Let us use guess and check since there are only 4 options.

Option 1:

519/6=86 R3

This answer is wrong because it has a two digit quotient

Option 2:

915/7=130 R5

This answer is correct since it has a three digit quotient, but let's find the rest

Option 3:

439/7=62 R5

This answer is wrong because it has a two digit quotient

Option 4:

812/9=90 R2

This answer is wrong because it has a two digit quotient

Therefore option 2 is correct

I will like to know what you need help with?

Answer:

eeeeee

Step-by-step explanation:

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Answer:

14

Step-by-step explanation:

14+28=42, 28/14=2