Identifying Characteristics of an Exponential Function
Consider the function f(x) = (6). What is the value of the growth factor of the function?
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The length of the sides RS, ST and TR are √72, √41 and √37 in the scalene triangle RST.

The distance between any two points A(a,b) and B(c,d) in the plane is given by,

AB = √((c-a)²+(d-b)²)

Here, it is given that the points of the triangle are R(-4,4) S(-2,-2) T(2, 3).

The triangle is scalene so length of every side is different.

Now, Using the above formula,

RS = √((2+4)²+(-2-4)²)

RS = √(36+36)

RS = √72

ST = √((2+2)²+(3+2)²)

ST = √(16+25)

ST = √41

TR = √((2+4)²+(3-4)²)

TR = √(36+1)

TR = √37

So, Brian is correct, the triangle is a scalene triangle.

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Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:

x² = y² + z²

where x is the hypothenuse and y, z are the legs of the right angle triangle.

To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.

x² = y² + z²

15² = 2² + z²

z² = 15² - 2²

z² = 221

z = √221

z = 14.87 feet

The height is 14.87 feet

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the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65

They need at least $1,150

They have already saved $700

They are selling shirts with a profit of $7.00 per shirt

If they sell n number of shirts, they will earn n times $7.00

Since they have already 700, they will earn a total of 700 + 7n

If this quantity has to be equal or greater to 1,150, we can write:

1150 <= 700 + 7n

if we solve this inequality for n:

1150 <= 700 + 7n

1150 - 700 <= 7n

450 <= 7n

450/7 <= n

64.28 <= n

Since the number of shirts has to be an integer (you can not sell "part" of a shirt)

n >= 65

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[tex] \underline{ \large \rm Solution} : [/tex]

[tex]\rm Given : [/tex]

Two equations are -

[tex] \rm Procedure : [/tex]

Considering the equations as (i) and (ii) respectively

From equation (i) -

put this value of y in equation (ii) -

Next thing to do would be to put value of x we got in equation (i) to get y

Values asked are :

[tex] \rightarrow \rm y = - 4[/tex]

[tex] \rightarrow \rm x= - 2[/tex]

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Answer:

$821.2

Step-by-step explanation:

cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2

We spent a total of 40.2 + 24.5+ 37.8 = $102.50

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.

Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.

We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.

You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.

Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.

You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.

We spent a total of 40.2 + 24.5+ 37.8 = $102.50

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Thus, 0 itself is the sole position at which [0,∞] and (0,∞] are separated. Since it is in [0,∞] the set is closed. Given that it is not in (0,∞), the set is open interval.

A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The collection of numbers such that 0 x 1 and the collection of all real numbers are other examples of intervals.

the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).

Because they are the most basic sets whose "length" (or "measure" or "size") is straightforward to define, real intervals are crucial in the theory of integration. The Borel measure and finally the Lebesgue measure result from extending the notion of measure to more intricate sets of real numbers.

Interval arithmetic is a broad numerical computing technique that automatically generates assured enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are at the centre of this technique.

Therefore, 0 itself is the sole place at which [0,∞] and (0,∞] have a boundary. Due to its location in [0,∞] the set is closed. Since it is not in (0,∞), the set is unclosed.

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Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.

2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

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Answer: The ship is going to another planet.

Step-by-step explanation:

I hate i-ready,

Your welcome mate

here in equation function, John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.

To create an equation, multiplying and dividing are used to separate constants and variables. In an equation, terms in various forms on each side of the equality sign are equal. John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.To create an equation, multiplying and dividing are used to separate constants and variables.

so we have,

John had paid $8.00 an hour and waits tables

Therefore,

In 29 hours, he earns -

[tex]= 40 X 8\\= 320 $[/tex]

Via tups, he earned 210.50$

So, in total he earns

[tex]= 320 + 210.50\\= 530.50 $[/tex]

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Answer:   B

Step-by-step explanation:   [tex]8x-5x=3x\\3+9=12\\[/tex]

Hope this helps any

Answer:

B. 3x+12

Step-by-step explanation:

8x+3-5x+9

First combine the x. So, 8x-5x=3x

Next combine the 3 and the 9. So, 3+9=12

After you combined like terms your equation now looks like: 3x+12

Hope it helped you.

Aisha has 2 chocolates left. You can represent the problem as an equation as follows:

Where x is the total number of chocolates, b is the number of boxes filled and 2 is the remaining chocolates left.

Since we know that Aisha has 50 chocolates, we can substitute this value for x in the equation:

50 = 3b + 2

Solving for b, we find that b = 16. So, Aisha filled 16 boxes and had 2 chocolates left over. The equation is true, and Aisha has 2 chocolates left.

It's worth noting that this is a simple algebraic equation, we can use the same equation to find the number of chocolates given the number of boxes and remaining chocolates, or to find the number of boxes given the number of chocolates and remaining chocolates or to find the remaining chocolates given the number of boxes and the number of chocolates.

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a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:

(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7

b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).

So, the derivative of f(x) = sqrt 25 - x^2 is:

-2x

c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))

so we have: y - 2sqrt(7) = -6(x + 3)

d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).

Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:

g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)

and the limit of g(x) as x approaches -3 is:

lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4

Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.

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Slope = (-2 - 4)/(14 - (-1)) = -6/15

Answer:

25%  

a half is 50%

a quarter is 25%

Answer: It's option C

Step-by-step explanation:

Well 1 quarter is 25

2 quarters is 50

3 quarters is 75

4 quarters is a dollar

The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.

what is a quadratic equation?

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.

where a, b, and c are constant terms and x is the unknown variable.

Here I am using the factoring method to solve a quadratic equation.

Given quadratic equation is

[tex]2x^2 - 5x -12 = 0.[/tex]

By comparing the General form of the quadratic equation we will get

a = 2, b = -5 and c = -12.

2x^2 - (8-3)x - 12 = 0.

2x^2 - 8x + 3x -12 = 0.

2x(x-4) + 3(x-4) = 0

(x - 4) (2x + 3) = 0.

x - 4 = 0 or 2x + 3  = 0

x = 4 or x = -3/2

Given Question is incomplete complete question here:

What are the solutions of the quadratic equation 2x^2-5x-12 =  0?

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The answers for Center of the circle is (-4,3) and radius is 2√10 units.

(x - h)2 + (y - k)2 = r2 is the equation of the center of the circle. The radius (r) is specified as 5 units, while the center's (h, k) coordinates are (0, 0). (x - 0)2 + (y - 0)2 = 52 is the result of substituting the values of h, k, and r in the equation.

Finding the simplified term of the given expression is the goal of simplifying the algebraic statement. We must first understand how to join like terms, factor a number, and the order of operations before we can factorize or simplify the statement. When like words are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.

Examples of  Algebraic Expressions

2x2+3xy+4x+7

Given,

[tex]x^2+y^2+8x-6y-15=0[/tex]

⇒ x².+8x+16–16+y²-6x+.9–9–15=.0

(x+4)²+(y-3)²-16–9–15=0

I.e. (x+4)²+(y-3)²=40

(x+4)²+(y-3)²={2√10}²

Hence center is (-4,3) and radius is 2√10 units.

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One mole consists of 6.02214076×10²³ units which is Avogadro's number. Thus one mole is known as Avogadro's number.

What is one mole?

A mole is 6.02214076×10²³ of any chemical unit, including atoms, molecules, ions, and others. Due to the large number of atoms, molecules, or other components that make up any substance, the mole is a useful measure to utilize. The mole was initially defined as the quantity of atoms contained in 12 grammes of carbon-12, but the General Conference on Weights and Measures declared in 2018 that the mole will only contain 6.02214076×10²³ of some chemical unit as of May 20, 2019.

In chemistry, a mole, sometimes spelled mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, or other predetermined particles.

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Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).

A depiction of two equal variables, one on either side of a "equals" sign, is what constitutes an equation in mathematics. To solve common issues, one can use equations. We frequently look for help with pre algebra to overcome obstacles in real life. Basic mathematical concepts are covered in pre-algebra lessons.

Here,

the x-intercepts,

In order to determine the x-intercept(s), put in for y and calculate 4x6y=36.

Make the equation work.

x=9 point form x-intercepts.

x-intercept(s): \s(9,0) (9,0)

the y-intercepts, please.

In order to determine the y-intercept(s), replace with and solve for y=.4(0-)6y=36.

Make the equation work.

To continue, tap.

Point shape y=6 y-intercept(s).

The y-intercept is (0, 6).

Write down the junctions.

x-intercept(s): (9,0)

The y-intercept is (0, 6).

Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).

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The length of PG if PG' is 0.5 units is; 3 units.

The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)

Here, given that,

Dilation is simply defined as the shrinking or enlarging of an object by a scale factor.

Now, we are told that Line HG is dilated to form a shorter line H'G'.

We are told that the scale factor is 1/6.

Point P is the center of dilation and if PG' is 0.5 units, then we can write the relation as follows;

Length of PG'/Length of PG = 1/6

Thus;

0.5/length of PG = 1/6

Length of PG = 0.5/(1/6)

Length of PG = 4 units

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Answer:

2x + 2

Step-by-step explanation:

Combine all the like terms:

-5x + 7x -12 + 14 = 2x + 2

Answer:

2x + 2

Step-by-step explanation:

(- 5x - 12) + (14 + 7x) ← remove parenthesis

= - 5x - 12 + 14 + 7x ← collect like terms

= (- 5x + 7x) + (- 12 + 14)

= 2x + 2

Answer: 10.56 cups.

Step-by-step explanation:

1 liter = 4.22 cups; 1.5 liters = 6.34 cups; 2 liters = 8.45 cups; 2.5 liters = 10.56 cups.

The lengths of a,b,c, and d have been derived and expressed in terms of trigonometric ratios below.

As we can see from the figure itself, the value of a = sin θ

This can be written as such because = sin θ = Perpendicular / Hypotenuse

Here, the perpendicular = a and hypotenuse = radius = 1

= sin θ = a

The value of b = tan θ

This is because tan θ = perpendicular/base

Here, the base = radius = 1

= tan θ = b  

The value of c = sec θ

This is because sec θ = Hypotenuse / Base

= sec θ = c

The value of d = cos θ

This is because cos θ = Base / Hypotenuse

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If Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit  she arranges these to form the given shape then the area of shape is 14 Square Units .

The Area of one triangular piece is given as = 1 Sq . Unit ;

The Area of one rectangular piece is = 2 Sq. Unit ;

From the shape given below ,

we can see that the shape has 4 triangular pieces and 5 rectangular pieces .

So , total area of given shape is ⇒[tex]4\times Area Of Triangle + 5\times Area Of Rectangle ;\\[/tex]

Substituting the values of Area ,

we get ;

[tex]Total Area = 4\times 1 +5\times 2[/tex]

= [tex]4+10[/tex]

= 14 Sq . Units .

Therefore , the area of the given shape is 14 Sq. Units .

The given question is incomplete , the complete question is

Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit .

If she arranges these to form a shape as shown below, what would be the area of this shape ?

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Answer:

-2 i think hope this helps

Step-by-step explanation:

Answer:

To find the value of x that makes the expression (4x-6) equal to (8x-6). To do this, you can set the two expressions equal to each other and solve for x:

4x - 6 = 8x - 6

4x = 8x

4x - 8x = 0

-4x = 0

x = 0

So, the value of x that makes (4x-6) equal to (8x-6) is x=0.

Answer:

-4x = -12 Divide each side by '-4'.

If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.

Let d represent the distance that is needed to travel 1 hour

1 hour late decreased to 0.5 hours early = 1.5

Hence,

d/50 + 1.5 = d/35

Simplify

7d + 525 =10d

Collect like terms

525 = 10d - 7d

525 = 3d

Divide both side by 3d

d = 525/3

d = 175

Total number of miles :

Total number of miles = 175 + 35

Total number of miles = 210

Therefore we can conclude that the correct option is C.

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Answer:

y = 3x - 2

Step-by-step explanation: