A certain type of lily plant is growing in a pond in such a way that the number of plants is growing
exponentially. The number of plants, N, in the pond at time t is modeled by the function N(t) = ab',
where a and b are constants and t is measured in months. The table shows two values of the function.
t
0
1
N(t)
150
450
Which equation can be used to find the number of plants in the pond at time t?
A. N(t) = 150(1)
B. N(t) = 450(1)
C. N(t) = 150(3)t
D. N(t) = 450(3)

The simplified form of the expression is -46p - 72.

In mathematics, we have to note that if we have an expression, then the expression can be written in the simplest way that is possible and this is called the simplified form of the expression.

We have that if we put the sentences into words;

(-6 1/2p) + (3/4p - 9)

(-13/2p) + (3p - 36/4)

8(-13/2p) + 8 (3p - 36/4)

-52p + 2(3p - 36)

-52p + 6p - 72

-46p - 72

Hence the expression can be said to have been simplified.

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Answer:-6

Step-by-step explanation:

The solution to the equation "Twelve more than p equals 6" is p = -6.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The given equation is:

12 + p = 6

To solve for p, we need to isolate p on one side of the equation.

We can do this by subtracting 12 from both sides:

12 + p - 12 = 6 - 12

p = -6

Therefore,

The solution to the equation "Twelve more than p equals 6" is p = -6.

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The total surface area of the hexagonal pyramid is 237.5 in²

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The surface area of a solid figure is gotten by adding all the individual surfaces area.

Given the hexagonal pyramid with base of 6 inches and the each isosceles triangle has a height of 8 inches. Hence:

Area of pyramid base = 93.5 in²

The lateral face have 6 triangles faces, hence:

Area of each lateral face = 1/2 * base * height = 0.5 * 8 * 6 = 24 in²

Total area of lateral face = 6 * 24 in² = 144 in²

Total surface area = 144 in² + 93.5 in² = 237.5 in²

The surface area is 237.5 in²

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Answer: The graph of the equation y = 1/3x - 1 represents a nonlinear function. A nonlinear function is a function that is not a linear function, which means that the graph of the function is not a straight line. In this case, the equation y = 1/3x - 1 can be graphed and will not be a straight line, which means it is nonlinear. Additionally, the equation has an x in the denominator which is an indication that the function is nonlinear.

Step-by-step explanation:

Answer: search it up its a bit

Step-by-step explanation:

The Arithmetic series is as follows  :  -3423 , - 3443 , -3463 , -3483,.... when d = -20 and a20 = -3803

What is Arithmetic progression?

Arithmetic progression can be defined as the sequence of numbers in which the difference between any consecutive numbers is same.

Given ,

To evaluate arithmetic series.

Given ,

a20 = -3803

and d = -20

an = 197 - 200n

a20 = a+(20-1)d

a20 = a+ 19d

-3803  = a + 19*-20

-3803 = a-380

a = 380 - 3803

a =  - 3423

so, a1 = -3423

a2 = a+d = -3423 + (-20)

a2 = -3443

a3 = a+2d

= -3423 - 2 * 20

= -3463

a4 = a+3d

= -3423 - 2*30

= - 3483

Hence, The Arithmetic series is as follows  :  -3423 , - 3443 , -3463 , -3483,.... when d = -20 and a20 = -3803

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Domain: 4 1 2 3 0  

Range: -5 0 -3 2 -1

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

here, we have,

given that,

        x                               y

-5 0 -3 2 -1                 4 1 2 3 0

let, y=f(x)

which is domain of x-range.

hence, Domain: 4 1 2 3 0  

           Range: -5 0 -3 2 -1

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Direct variation equation for the relationship is y = 4x

y is number of fence posts.

x is number of hours.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

Given,

Edwin installs 40 fence posts in 8 hours

Let the number of fence posts installed be y, x be the hours worked

x and y are in direct proportion,

then,

y/x = 40/5

y/x = 5

y = 5x

Hence, y = 5x is the direct variation equation of relationship.

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i) The graph of y = tan x will be a periodic function with period of 180 degrees, with asymptotes at x = (n+1/2)π, where n is an integer. The graph of y = 4 cos x will be a cosine function with amplitude 4 and period 360 degrees.

ii) The roots of the equation tan x = 4 cos x, denoted by a and ß, can be found by solving the equation tan x = 4 cos x for x. The two solutions will be a and ß, where a <ß.

iii) The equation tan x = 4 cos x can be written as 4 sin^2x+ sin x−4=0 by using trigonometric identities. The value of ß-a can be found by using the quadratic formula on this equation. However, it's not possible to give you an exact value without the specific value of a.

Answer:

Step-by-step explanation:

answer is D my friend.

Answer:

5%

Step-by-step explanation:

1500 / 75 = 0.05 as a percentage its 5 %

To solve the quadratic equation 2x² + 12x - 3 = 0, the correct choices are option 1: 2(x² + 6x + 9) = 3 + 18 and option 3: 2(x² + 6x) = 3.

What is a quadratic equation?

Having the form ax² + bx + c = 0, quadratic equations are second-degree algebraic expressions. From the term "quad," which meaning square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way.

The given quadratic equation is 2x² + 12x - 3 = 0.

The first choice for solving the quadratic equation is -

2(x² + 6x + 9) = 3 + 18

Multiply 2 with every number of the other multiplier on the left side -

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

Now, on simplifying it further -

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

The second choice for solving the quadratic equation is -

2(x² + 6x) = -3

Multiply 2 with every number of the other multiplier on the left side -

2·x² + 2·6x = -3

2x² + 12x = -3

2x² + 12x + 3 = 0

The third choice for solving the quadratic equation is -

2(x² + 6x) = 3

Multiply 2 with every number of the other multiplier on the left side -

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0

The fourth choice for solving the quadratic equation is -

x + 3 = 21/2

Dividing 21 by 2 on right hand side -

x + 3 = 10.5

x + 3 - 10.5 = 0

x - 7.5 = 0

The fifth choice for solving the quadratic equation is -

2(x² + 6x + 9) = –3 + 9

Multiply 2 with every number of the other multiplier on the left side -

2·x² + 2·6x + 2·9 = -3 + 9

2x² + 12x + 18 = -3 + 9

Now, on simplifying it further -

2x² + 12x = -3 + 9 - 18

2x² + 12x = -12

2x² + 12x + 12 = 0

The sixth choice for solving the quadratic equation is -

(x + 3)² = 3/2

Apply the formula (a+b)² = a² + 2ab + b² on the left side and divide 3 by 2 on the right side -

x² + 6x + 9 = 1.5

x² + 6x + 9 - 1.5 = 0

x² + 6x + 7.5 = 0

Therefore, the correct choices are option 1 and option 3.

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Inga is solving 2x² + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.

2(x² + 6x + 9) = 3 + 18

2(x² + 6x) = –3

2(x² + =6x) = 3

x + 3 = 21/2

2(x² + 6x + 9) = –3 + 9

(x + 3)2 = 6/2

The value of the variables that make the matrix equation true are x = 5/7, y = 4/9 and z = 13/5.

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.

For instance, consider a matrix with two rows and three columns.

We are given the matrix as;

{8 0 0} = { 7x+3 0 0 }

{ 0 8 0} = { 0 9y-4 0 }

{ 0 0 8} = { 0 0 5z-5}

So, we have 7x + 3 = 8

7x = 5

x = 5/7

Also, 9y-4 = 8

9y = 4

y = 4/9

5z - 5 =8

z = 13/5

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On solving the provided question, we can say that Volume of cylinder, V = [tex]\pi r^2 X h[/tex] => V = 3.14 * 8*8*4 = 803.84 cubic m

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

here,

we have a cylinder

and,

radius, r = 8m

height, h = 4m

Volume, V = [tex]\pi r^2 X h[/tex]

V = 3.14 * 8*8*4 = 803.84 cubic m

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The required inverse of the function at when x = 8 is 3/2.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = 2x + 5

first we need to find the inverse of the function:

Let y = g(x)

y= 2x + 5

Replace y with x

x = 2y + 5

Make y the subject of the formula

2y = x - 5

y = (x - 5)/2

So, the inverse of the expression is [tex]f^{-1}[/tex](x) = (x - 5)/2

Substitute x = 8

[tex]f^{-1}[/tex]((8) = (8 - 5)/2

[tex]f^{-1}[/tex](8)  = 3/2

Hence, the required inverse of the function at when x = 8 is 3/2

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Answer:

$40

Step-by-step explanation:

$28 is the reduced price 30%, i.e. the product has a (100-30)% = 70% of its original value.

Divide the discounted price by the decimal of the percentage it represents with respect to the original price, The result is the original price

70% = 70/100 = 0.7

28/ 0.7 = 40

Hope this helps.

Let x be the number. Then, we have the inequality:

3(x + 15) ≤ 19

Expanding the left side:

3x + 45 ≤ 19

Subtracting 45 from both sides:

3x ≤ -26

Dividing both sides by 3:

x ≤ -8.67

So, the solution to the inequality is x ≤ -8.67, which means that the number x must be less than or equal to -8.67.

The perimeter of the shape is 26.85 inches

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.

The shape consist of a rectangle joined with a semi circle.

Therefore the perimeter of the shape is calculated as:

7+7+ 5+ πd/2

where πd/2 is the circumference of the semi circle

= 7+7+5+(3.14× 5/2)

= 7+7+5+7.89

= 26.85 inches

therefore the perimeter of the shape is 26.85 inches

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To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Answer:

so the answer is

Step-by-step explanation:

-3/2

so how I got this is -4 1/2 would be

-9/2 so your new equation is 3+ -9/2 then you would just do keep change flip so no 3/2 - -9/2 and then you would get -3/2.

Mrs Parkow's 5-digit mystery number is 73248.

Ten thousand is the starting point for five-digit numbers, which go up to ninety-nine million, nine hundred and ninety-nine. Integers are present in the places of ones, tens, hundreds, thousands, and ten thousand in these numbers. Any positive number may be placed at these places, with the exception of 0 at the ten thousand places.

A general 5-digit number can be written as:

a×10000 + b×1000 + c×100 + d×10 + e where a, b, c, and d are single-digit numbers.

a is the ten thousand digit

b is the thousands digit

c is the hundreds digit

d is the tens digit

e is the unit digit.

Let 8 be at one's place that is e

Now, it is given that 8 is in a place that is 10 times less than the place of 4.

This implies 4 is at the ten's place that is d.

Next, it is given that 3 is in a place that is 100 times greater than the place of 4.

That is 100×10 = 1000 place

So, 3 is at the place of b.

The 2 is in a place that is 10 times less than the place of the 3. So, 2 is at the place of c.

The 7 is in a place that is 100 times greater than the 2. That is 100×100 = 10,000 places.

Thus, 7 is at the place of a.

Thus, we obtain

a= 7

b= 3

c= 2

d= 4

e= 8

Therefore, the 5-digit mystery number is 73248.

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The fraction of the spool was used for the project is 4/21

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

Yarm = 2/7

Fraction used  2/3 of the yarn

This means that

Fraction used = 2/3 * 2/7

Evaluate the product

Fraction used = 4/21

Hence, the fraction used is 4/21

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Y-intercept of g(x) at (0,2) therefore correct option is D

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable is called a function.

Given is a function f(x) = 2ˣ

g(x) = 2f(x) = 2(2ˣ)

The y-intercept of g(x) = 2f(x),

Substitute in 0 for x and solve for y

y=2(2⁰)

Anything raised to 0 is 1.

y=2

Y-intercept in point form.

Hence, y-intercept of g(x) : (0,2)

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Answer:

use the calculator

Step-by-step explanation:

that is for they event the calculator

The compound interest at the end of 6 months is $101.2248

Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. The compound interest equals total amount of principal and interest in future (or future value) minus principal amount at present (or present value).

Given here: principal balance=$1265.31  and annual rate is i=8%

Thus compound interest after 6 months is =  [P (1 + i)ⁿ] – P

                                                                       =1265.31(1+0.080¹-1)

                                                                       =101.2248

Hence, the compound interest after six months is $  101.2248

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The circumference of the larger pizza is 12.56 longer than the smaller pizza.

The length around the circle or the perimeter of the circle is called its circumference.

Given that, Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches, and the other was a large cheese pizza with a 7 in. radius.

We need to find how much longer than the circumference of the smaller pizza,

We know that,  

Circumference of a circle = 2πr.

Therefore,

Circumference of the larger pizza = 2 × 3.14 × 7 = 43.96 in

Circumference of the smaller pizza = 2 × 3.14 × 5 = 31.4 in

Therefore,

Subtracting the circumference of smaller pizza from larger pizza to get the difference = 43.96 - 31.4 = 12.56 in

Hence, the circumference of the larger pizza is 12.56 longer than the smaller pizza.

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On solving the provided question, we can say that we have an equation, xy = 8 => x = 8/y; if x increases then y decreases, so it's a inverse variation

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

we have an equation, xy = 8

x = 8/y

if x increases then y decreases, so it's a inverse variation

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Answer: they are equivalent ratios

Answer:

Step-by-step explanation:

1             5
_   div    _
2             3

1/2 x 3/5

1              3
       x            =     3/10
2              5

Answer:

The likelihood of choosing a green marble is (c) Equally likely and unlikely

How to determine the likelihood of choosing a green marble

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

P(green) = five tenths.

Express five tenths as a mathematical expression

So, we have the following representation

P(green) = 5/10

Evaluate the quotient

This gives

P(green) = 0.50

A probability of 0.50 is halfway between 0 and 1

This means that it is likely and unlikely at the same time

Hence, the statement that represents the interpretation of the likelihood of choosing a green marble is (c) Equally likely and unlikely

Answer:

C

Step-by-step explanation: 5/10 is equal to 50% or 1/2 which is equally likely and unlikely.