22. Write an exponential function to model the situation: You purchase an antique table for $525. Each year t,
the value V of the table increases by 5%

The solution is, the function has factors (x - 5) and, (x+4), and, the zeros of the function f(x)= x² - x - 20, are,(x= 5) or( x= -4) .

Option B. is correct.

Here, we have,

the given function is;

f(x) = x² - x - 20

now, we know that,

The zero of the function is where the y-value is zero. The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph.

here, we have,

zeros:

we can set f(x) =0

and then we can solve for x

f(x)= x² - x - 20 = 0

we can factor it

so, we get :

x² - x - 20 =0

or, x² - 5x + 4x - 20 =0

or, x(x-5) + 4( x - 5) = 0

or, (x - 5) (x+4) = 0

so, we get,

(x= 5) or( x= -4)

Hence, The solution is, the function has factors (x - 5) and, (x+4), and, the zeros of the function f(x)= x² - x - 20, are,(x= 5) or( x= -4) .

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The predicted weight for an infant with a foot length of 9 centimeters is 4 kilograms.

Therefore, the correct answer is: B) 7.

To determine the predicted weight of an infant with a foot length of 9 centimeters, we can refer to the given line model that represents the relationship between body weight and foot length for a group of infants.

From the line model, we can observe that the weight increases as the foot length increases.

Looking at the provided data, we see that the weights corresponding to foot lengths are given as:

Foot length (cm): 0, 2, 4, 6, 8, 10, 12, 14

Weight (kg): 14, 12, 10, 8, 6, 4, 2, 0

By examining the pattern, we can deduce that the weight decreases by 2 kilograms for every increase of 2 centimeters in foot length.

Therefore, to find the predicted weight for a foot length of 9 centimeters, we can subtract 2 kilograms from the weight corresponding to a foot length of 10 centimeters.

Weight for 10 cm - 2 kg = 4 kg

Thus, the predicted weight for an infant with a foot length of 9 centimeters is 4 kilograms.

Therefore, the correct answer is: B) 7

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Answer:

Step-by-step explanation:

To find the values of the given expressions, we first need to find the values of t and b, which are the roots of the equation 2x² + 3x - 1 = 0.

Using the quadratic formula, we can solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 2, b = 3, and c = -1. Plugging in these values, we can calculate t and b:

t = (-3 + √(3² - 4(2)(-1))) / (2(2))

t = (-3 + √(9 + 8)) / 4

t = (-3 + √17) / 4

b = (-3 - √(3² - 4(2)(-1))) / (2(2))

b = (-3 - √(9 + 8)) / 4

b = (-3 - √17) / 4

Now, let's calculate the values of the given expressions:

(a) t² + b²

Substituting the values of t and b:

(t² + b²) = ((-3 + √17) / 4)² + ((-3 - √17) / 4)²

= (9 - 6√17 + 17) / 16 + (9 + 6√17 + 17) / 16

= (35 + 12√17) / 16 + (35 - 12√17) / 16

= 70 / 16

= 35 / 8

(b) (t - b)²

Substituting the values of t and b:

(t - b)² = ((-3 + √17) / 4 - (-3 - √17) / 4)²

= (2√17)²

= 4(17)

= 68

(c) (2 + 1/b²)(b² + 1/t²)

Substituting the values of t and b:

(2 + 1/b²)(b² + 1/t²) = (2 + 1/((-3 - √17) / 4)²)((-3 - √17) / 4)² + 1/((-3 + √17) / 4)²)

= (2 + 16 / (3 + √17)²)((-3 - √17) / 4)² + 16 / (3 - √17)²)

= (2 + 16 / (3 + √17)²)((-3 - √17) / 4)² + 16 / (3 - √17)²)

The final expression cannot be further simplified without knowing the exact values of √17.

The value of x that makes the equation -5(1.2x + 2) = 14.6 true is -1.4

From the question, we have the following parameters that can be used in our computation:

-5(1.2x + 2) = 14.6

Divide both sides of the equation by -5

So, we have the following representation

-5(1.2x + 2)/-5 = 14.6/-5

Evaluate the quotients

This gives

1.2x + 2 = -2.92

Subtract 2 from both sides of the equation

1.2x = -4.92

Divide both sides by 1.2

x = -4.1

Hence, the value of x that makes the equation true is -1.4

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Answer:

red 8/30=4/15

blue. 12/30=2/5

Answer:

2/3

Step-by-step explanation:

Total number of marbles = 8+12+4+6 = 30

(I just realized that there's a total at the bottom! Ooops!)

So Red = 8

Blue = 12

Red OR blue means we add them together; we're only picking 1 time here. (This is different from the other scenarios that you have posted where there's 2 different selections without replacement.)

So basically prob(red OR blue) = prob(red) + prob(blue)

So 8/30+12/30 = 20/30

20/30 = 2/3

The probability that a number greater than 4 is rolled is 1/3

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in percentage.

Probability = sample space / total outcome

sample space here is 5 and 6 since these are the numbers greater than 4 Ina six sided die

The total outcome is 6, because there are six numbers in the die

Probability = 2/6 = 1/3

Therefore the probability of rolling a number greater than 4 is 1/3

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Using the interval 25 - 30 income, the recommended monetary range for the monthly rental budget for the mechanic is $841.75 and $1,010.10.

Mathematically, the range is the lowest and highest value.

The range may also refer to the difference between the highest value and the lowest value in a data set.

The mechanic's hourly pay rate = $32.50

Hours worked per week = 35 hours

Federal and state taxes = 21%

Savings = 5%

Gross pay for the month = $4,550 ($32.50 x 35 x 4)

Federal and state taxes = $955.50 ($4,550 x 21%)

Savings = $227.50  ($4,550 x 5%)

Net Pay = $3,367 ($4,550 - $955.50 - $227.50)

Lower bounds of the interval = 25

Upper bounds of the interval = 30

Recommended range for monthly rental budget = $841.75 (3,367 x 25%) and $1,010.10 ($3,367 x 30%)

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The domain and range for the function shown in the graph above include the following:

D. D: [-∞, ∞]

    R: [-10, ∞]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-10, ∞] or y ≥ -10

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Answer:

Arithmetic sequence is [tex]a_n=-10n+5[/tex]

93rd term is -925

Step-by-step explanation:

Each subsequent term is decreased by 10 and the first term is -5, so we can generate an arithmetic sequence:

[tex]a_n=a_1+(n-1)d\\a_n=-5+(n-1)(-10)\\a_n=-5-10n+10\\a_n=-10n+5[/tex]

So, the 93rd term would be:

[tex]a_{93}=-10(93)+5=-930+5=-925[/tex]

a) Bekele should deposit approximately Br. 4,071.56 at the end of every quarter to meet the objective of the down payment.

b)  we find that the monthly mortgage payment should be approximately Br. 3,421.91.

c)  we find that the total interest paid on the mortgage is approximately Br. 422,288.60.

d)  we find that the total amount paid over the entire period of the mortgage is approximately Br. 1,231,487.60.

a) To determine how much Bekele should deposit at the end of every quarter to meet the objective of the down payment, we can use the sinking fund formula. The formula for the future value of a sinking fund is:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

FV is the future value or the down payment amount (Br. 100,000),

P is the periodic deposit we need to find,

r is the annual interest rate (10% or 0.10),

n is the number of compounding periods per year (4, since it is compounded quarterly),

and t is the number of years (5).

Plugging in the values into the formula, we can solve for P:

100,000 = P * ((1 + 0.10/4)^(4*5) - 1) / (0.10/4)

Simplifying the equation, we have:

100,000 = P * (1.025^20 - 1) / 0.025

Now, we can solve for P:

P = 100,000 * 0.025 / (1.025^20 - 1)

Calculating the value, we find that Bekele should deposit approximately Br. 4,071.56 at the end of every quarter to meet the objective of the down payment.

b) To determine the amount of the monthly mortgage payment to discharge the mortgage within 30 years, we can use the formula for the monthly mortgage payment (PMT) of an amortizing loan:

PMT = (P * r) / (1 - (1 + r)^(-n))

Where:

P is the principal amount of the loan (Br. 400,000, obtained by subtracting the down payment from the total cost),

r is the monthly interest rate (12% divided by 12 months, or 0.01),

and n is the total number of monthly payments (30 years multiplied by 12 months, or 360).

Plugging in the values into the formula, we can calculate the monthly mortgage payment:

PMT = (400,000 * 0.01) / (1 - (1 + 0.01)^(-360))

Using a calculator or spreadsheet, we find that the monthly mortgage payment should be approximately Br. 3,421.91.

c) To calculate the total interest paid on the mortgage, we can subtract the principal amount from the total amount paid over the entire period. The principal amount is Br. 400,000, and the total amount paid over the entire period can be obtained by multiplying the monthly mortgage payment by the total number of payments (360).

Total interest paid = (Monthly mortgage payment * Total number of payments) - Principal amount

Total interest paid = (3,421.91 * 360) - 400,000

Using a calculator, we find that the total interest paid on the mortgage is approximately Br. 422,288.60.

d) The total amount paid over the entire period of the mortgage can be calculated by multiplying the monthly mortgage payment by the total number of payments:

Total amount paid = Monthly mortgage payment * Total number of payments

Total amount paid = 3,421.91 * 360

Using a calculator, we find that the total amount paid over the entire period of the mortgage is approximately Br. 1,231,487.60.

Therefore, Bekele will need to deposit approximately Br. 4,071.56 at the end of every quarter to meet the down payment, make monthly mortgage payments of Br. 3,421.91, pay a total of approximately Br. 422,288.60

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The reference angle of -210 is 30 degrees and the sketch of the angle is attached

From the question, we have the following parameters that can be used in our computation:

Angle = 210 degrees

Rewrite as

θ = 210 degrees

The above angle is in the third quadrant

So, we subtract 180 degrees from it to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 210 - 180

Evaluate the difference

Reference angle = 30 degrees

Hence, the reference angle is 30 degrees and the sketch of the angle is added as an attachment

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The area of the shaded portion of the circle is 329.8 units squared.

The area of the shaded region can be found by subtracting the area of the right triangle from the area of the circle.

Therefore,

area of the triangle = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × 7 × 24

area of the triangle = 168 / 2

area of the triangle = 84 units²

Area of the circle = πr²

let's find the radius of the circle using Pythagoras's theorem,

√24²- 7² = diameter

diameter = √576 - 49

diameter = √527

diameter = 22.9564805665

diameter = 22.96 units

Therefore,

radius = 22.96 / 2 = 11.48 units

Hence,

Area of the circle = 3.14 × 11.48²

Area of the circle = 413.821856

Area of the circle = 413.82 units²

Therefore,

area of the shaded region = 413.82 - 84

area of the shaded region = 329.8 units²

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The solution to all the algebra expressions are:

28) 2³/₁₆

29) 6000

30) 132

28) The area of the rectangle formed by Shana's rug is given by the expression:

Area = Length * Width

Thus:

Area = 2⁵/₈ * ⁵/₆

= ²¹/₈ * ⁵/₆

= 35/16

= 2³/₁₆

29) We are given the number 2641.

Now, from right:

1 is in the units place

4 is in tens place

6 is in hundreds place

2 is in thousands place

If we switch 2 and 6, we will have:

6241 and as such 6 represents 6000

30) The expression is given as:

90 + 7 * (7 - 1)

Using PEMDAS order of operation gives us:

90 + 7(6)

= 90 + 42

= 132

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volume of the sphere is 113.1

The table should be completed by indicating whether each quadrilateral has the given property as follows;

Property                                Parallelogram  Rectangle  Rhombus   Square

Diagonals bisect each other    Yes                  Yes              Yes           Yes

Diagonals are congruent ≅       No                  Yes               No            Yes

Each diagonals bisects             Yes                   No               Yes           Yes

opposite ∠s

Diagonals are ⊥                         No                    No              Yes            Yes

In Mathematics and Geometry, two (2) quadrilaterals are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures such as quadrilaterals are considered to be congruent only when their corresponding side lengths are congruent (proportional) and the magnitude of their angles are congruent.

In conclusion, the diagonals of bisect each other in quadrilaterals such as parallelogram, square, rectangle, and rhombus.

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The solution to the inequality expression -7x + 13 ≥ 41 is x ≤ -4

From the question, we have the following parameters that can be used in our computation:

-7x13_>41

Express properly

So, we have

-7x + 13 ≥ 41

Subtract 13 from both sides of the inequality

So, we have

-7x + 13 - 13 ≥ 41 - 13

Evaluate the difference

-7x ≥ 28

Divide both sides of the inequality by -7

x ≤ -4

Hence, the solution to the inequality expression is x ≤ -4

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The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10

From the question, we have the following parameters that can be used in our computation:

The difference of -10 and the product of p and q

The numbers are given as

p and q

The product of p and q means pq

So, we have the following

The difference of -10 and pq

The difference of -10 and pq means

pq + 10

Hence, the expression is pq + 10

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Answer and Explanation:

First, we can find the factored areas of the circle (the non-shaded area) and the rectangle (which includes the shaded and non-shaded areas).

We can use the rule:

if [tex]x^2 + cx + d = (x + a)(x + b)[/tex], then [tex]c = a + b[/tex] and [tex]d = a \cdot b[/tex].

__

[tex]A_\circ = \dfrac{x+1}{x^2 + 6x + 8}[/tex]

[tex]\boxed{A_\circ = \dfrac{x+1}{(x + 2)(x + 4)}}[/tex]

__

[tex]A_\square = \dfrac{x+1}{x^2 - 6x -16}[/tex]

[tex]\boxed{A_\square = \dfrac{x+1}{(x+2)(x-8)}}[/tex]

Since we want to subtract the area of the circle from the area of the rectangle, we need them to have a common denominator.

We can achieve this by multiplying the area of the circle by [tex]\dfrac{(x-8)}{(x-8)}[/tex] and the area of the rectangle by [tex]\dfrac{(x+4)}{(x+4)}[/tex] because then both fractions will have the denominator [tex](x+2)(x+4)(x-8)[/tex].

[tex]A_\circ = \dfrac{(x+1)(x-8)}{(x + 2)(x + 4)(x-8)}[/tex]

[tex]A_\square = \dfrac{(x+1)(x+4)}{(x+2)(x-8)(x+4)}[/tex]

Now that they have a common denominator, we can subtract them to get the area of the shaded region.

[tex]A_\text{shaded} = A_\square - A_\circ[/tex]

[tex]A_\text{shaded} = \left(\dfrac{(x+1)(x+4)}{(x + 2)(x + 4)(x-8)}\right) - \left(\dfrac{(x+1)(x-8)}{(x+2)(x+4)(x-8)}\right)[/tex]

Now, we can foil out the numerators of each fraction and combining like terms.

[tex]A_\text{shaded} = \left(\dfrac{x^2 + 5x + 4}{(x + 2)(x + 4)(x-8)}\right) - \left(\dfrac{x^2 - 7x - 8}{(x+2)(x+4)(x-8)}\right)[/tex]

↓ rewriting as one fraction ... [tex]\dfrac{x}{y} - \dfrac{z}{y} = \dfrac{x-z}{y}[/tex]

[tex]A_\text{shaded} = \dfrac{ (x^2 + 5x + 4) - (x^2 - 7x - 8)}{(x + 2)(x + 4)(x-8)}[/tex]

↓ distributing the negative

[tex]A_\text{shaded} = \dfrac{x^2 + 5x + 4 - x^2 + 7x + 8}{(x + 2)(x + 4)(x-8)}[/tex]

↓ grouping like terms

[tex]A_\text{shaded} = \dfrac{(x^2 - x^2) + (5x + 7x) + (4 + 8)}{(x + 2)(x + 4)(x-8)}[/tex]

↓ combining like terms

[tex]\boxed{A_\text{shaded} = \dfrac{12x + 12}{(x + 2)(x + 4)(x-8)}}[/tex]

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

Answer:

[tex]b=-\frac{1}{2}, \frac{2}{7}[/tex]

Step-by-step explanation:

Starting from this equation [tex]14b^2-2= -3b[/tex]

We can rewrite it to a quadratic equation:

[tex]14b^2+3b-2= 0[/tex]

Factoring this equation gives us:

[tex](7b-2)(2b+1)=0[/tex]

Now because its a quadratic formula, we have to answers:

[tex](7b-2) = 0\\7b=2\\b=\frac{2}{7}[/tex]

or

[tex](2b+1)=0\\2b=-1\\b=-\frac{1}{2}[/tex]

The solution to each of the equations include the following:

a) x = 25

b) x = 5.

c) x = 6.

d) x = -1.

e) x = 10

f) x = 17

g) x = 3

h) x = 15

i) x = -4

j) x = 0

k) x = 15

l) x = 5

m) x = 13/3.

In this scenario and exercise, you are required to provide a solution to each of the given equations as follows;

Part a.

By subtracting 16 from both sides of the equation, we have:

x + 16 = 41

x + 16 - 16 = 41 - 16

x = 25

Part b.

By collecting like terms and evaluating, we have:

9x – 45 + 4x – 16 = 4

13x = 4 + 45 + 16

13x = 65

x = 5,

Part c.

By collecting like terms and evaluating, we have:

2x – 3 + x – 35 = 2 – 9x – 4

6x = 36

x = 6

Part d.

3 · (x – 2) + 9 = 0

3x - 6 + 9 =0

x = -1

Part e.

8x + 7 – 2x + 5 = 4x + 12 – (x – 30)

x = 10

Part f.

x + (x + 2) = 36

x = 17

Part g

2 · (3x – 2) – (x + 3) = 8

x = 3

Part h

2 · (13 + x) = 41 + x

x = 15

Part i

2 · (x – 3) – 3 · (4x – 5) = 17 – 8x

x = -4

Part j

4x – 3 · (1 – 3x) = –3

x = 0

Part k

4 · (2x) – 3 · (3x – 5) = 12x – 180

x = 15

Part l

6 – x = 4 · (x – 3) – 7 · (x – 4)

x = 5

Part m

3 · (2x – 6) – [(x – (3x – 8) + 2) – 1] = 2 – (3 – 2x)

6x - 18 - [(x – 3x + 8 + 2 – 1] = -1 + 2x

6x - 18 + 2x - 9 = -1 + 2x

6x = 26

x = 13/3

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Complete Question:

Solve the following equations:

Answer:

Step-by-step explanation:

One Fraction:   [tex]\frac{9}{5}[/tex]  

Mixed Number:  [tex]1\frac{4}{5}[/tex]        

Based on the above, the value of the expression 32 x (3+2) + 8 divided by 3 is 162.67.

To solve the expression 32 x (3+2) + 8 divided by 3, we need to follow the rule of operations  of PEMDAS ( that is: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First step- Start by looking at the expression within the parentheses:

(3 + 2) = 5.

32 x 5 + 8 divided by 3.

Secondly, carry out the multiplication:

32 x 5

= 160.

The expression will be : 160 + 8 divided by 3.

Lastly, carry out a division:

8 divided by 3

= 2.67  approx.

The expression will then be: 160 + 2.67.

So one can now add  the two results to be:

160 + 2.67

= 162.67.

Therefore, the value of the expression 32 x (3+2) + 8 divided by 3 is about 162.67.

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Answer:

[tex]\huge\boxed{\sf 1.8 \times 10^3}[/tex]

Step-by-step explanation:

Quotient means "to divide".

[tex]\displaystyle = \frac{4.68 \times 10^6}{2.6 \times 10^3} \\\\\underline{\sf Exponent \ rule:}\frac{a^m}{a^n} = a^{m-n}\\\\= 1.8 \times 10^{6-3}\\\\= 1.8 \times 10^3\\\\\rule[225]{225}{2}[/tex]

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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The average salary of 26 employees is 3750.

The average pay is calculated by dividing the sum of all employee salaries for a company or sector by the total number of employees. It serves as a gauge of the typical pay for workers in a given category.

The average salary of 25 workers in a factory is 2500. This means that the total salary of all 25 workers is 2500 * 25 = 62500.

The salary of the manager is 35000. This means that the total salary of all 26 employees is 62500 + 35000 = 97500.

The average salary of 26 employees is 97500 / 26 = 3750.

Therefore, the average salary of 26 employees is 3750.

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Answer:

ratio of tomato to other ingredients

Step-by-step explanation:

The Pythagorean theorem is a fundamental principle in geometry that pertains to right triangles. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, the Pythagorean theorem can be expressed as:

c^2 = a^2 + b^2

In this equation, 'c' represents the length of the hypotenuse, while 'a' and 'b' represent the lengths of the other two sides, known as the legs of the right triangle.

This theorem enables the calculation of any side length of a right triangle if the lengths of the other two sides are known. It finds wide-ranging applications in geometry, trigonometry, physics, engineering, and architecture.

The name of the Pythagorean theorem originates from Pythagoras, an ancient Greek mathematician credited with its discovery. However, it is worth noting that the concept predates Pythagoras, as various ancient civilizations utilized it prior to his time.

The practical applications of the Pythagorean theorem are numerous. It aids in determining distances, calculating areas, solving problems involving right triangles, and serves as the foundation for trigonometric functions. Its significance in geometry has resulted in its study and application for millennia.

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The correct answer is (a) a bacteria culture triples in size every day describes a exponential function.

We have,

A relation is a function if it has only One y-value for each x-value.

The growth of a population, bacteria culture, or puppy can be modeled by an exponential function if the growth rate is proportional to the current size.

In other words, if the growth rate is constant, then the growth can be modeled by an exponential function.

Out of the three situations given, option (i) is the only one that has a constant growth rate, since the bacteria culture triples in size every day. This means that the growth rate is constant at 200% per day.

Option (iii) has a growth rate that is not constant but increases every year, so it is not best modeled by an exponential function.

Option (ii) also has a growth rate that is not constant, since A plant grows by 1 inch every 4 days regardless of its current height.

Therefore, the correct answer is (a) a bacteria culture triples in size every day describes a exponential function.

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Answer:

8

Step-by-step explanation:

First, you need to find the cost of one video. We know that the cost of 1 video is equal to 4 times the cost of each song. So we will take the cost of a song $1.25 and multiply by four.

$1.25(4) = $5

So if one video costs $5, we now need to find the cost of 12 videos because we need to know how many songs you can purchase after you purchase 12 videos.

12($5) = $60

Now that we know that you have spent $60 on your videos, we need to figure out how many songs you can purchase now that we know you have $10 remaining of the initial $70. To do this, we will divide $10 by $1.25

$10/$1.25 = 8

With $70, given that you have already purchased 12 videos, you can also purchase 8 songs.