Match the vocabulary word to the definition

Identify the initial value in each formula below, and state whether the formula models exponential growth or

Hitman42 [59]

Answer: Hello mate!

the equation is written is:

f(t) = 2 / 3 (3)t

And is hard to work with this, but let's try:

I will interpret this function in two ways:

f(t) = (2/3^(3t)) in this case, the exponential part is in the denominator, so when t increases, the denominator also increases, if the denominator increases, the value of the function decreases, then, in this case, we have an exponential decay.

second case:

f(t) = (2/3)^(3t) the case is similar.

we know that 2/3 < 1

now, (2/3)^3t = (2^3t/3^3t)

3 is a number bigger than 2, then 3^3t > 2^3t, meaning that when t increases, bot denominator, and numerator increases, but the denominator increases faster, this means that we still have an exponential decay.

5 0

3 years ago

Please find me the value of x

erastova [34]

Answer:

x = 60°

Step-by-step explanation:

See picture below. When two parallel lines are cut by a transversal there are some special relationships.

4 0

1 year ago

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Two shapes are shown below, one isosceles triangle and one rectangle. The dimensions can be represented by algebraic expressions

liberstina [14]

Answer:

Perimeter of Isosceles Triangle = 16 units

Step-by-step explanation:

Area of rectangle is given by the formula;

Area = 1/2 × base × height

From the diagram, base = 6x - 6 and height = 6x - 8

Thus,Area = 1/2 × (6x - 6) × (6x - 8)

Area = (3x - 3)(6x - 8) = 18x² - 42x + 24

Secondly, area of rectangle is given by;

Area = length x breadth

So, area of rectangle in question = (6x - 9)(3x - 2) = 18x² - 39x + 18

We are told both the area of the triangle and the rectangle are the same, so let's equate both areas;

18x² - 42x + 24 = 18x² - 39x + 18

18x² will cancel out and rearranging, we have;

24 - 18 = 42x - 39x

6 = 3x

x = 6/3

x = 2

Plugging 2 for x for the height and base of the triangle, we have;

base = 6(2) - 6 and height = 6(2) - 8

Base = 6 and height = 4

So,let's find the slant height of the isosceles triangle.

Dividing the base by 2,we have; 6/2 = 3

So,using Pythagoras theorem, let the slant height be h, so we have;

h² = 3² + 4²

h² = 9 + 16

h² = 25

h = √25

h = 5

2 slant sides of isosceles triangle are the same. So perimeter = 5 + 5 + 6 = 16 units

8 0

2 years ago

Which of the following could be the equation for a parabola that opens down with the vertex (-11,-28)?

Mekhanik [1.2K]

Answer:y=-5(x+11)^2 -28

Step-by-step explanation: Okay think about what you know about translations and transformations of parent functions. In this case, the parent function is x2. So what now?

First, the problem states that the parabola opens DOWN. This means that you should look for a negative leading coefficient. This narrows your options down to C or D. (-5 is the leading coefficient)

Now starting with the x2, the vertex would be at (0,0), but in this problem it is at (-11,-28). That means it was TRANSLATED 11 spots in the negative x-direction and 28 spots in the negative y-direction.

Look at your options, when a number is being added directly unto the x variable, such as in answer C, it moves in the negative x-direction. This tells you that C has to be your answer.

I hope that helps!

8 0

2 years ago

Classify the following triangle. Check all that apply.

klasskru [66]

Answer:

Step-by-step explanation:

a. scalene : Reason: all angles and sides are different measurements.

f. acute : all the three angles are acute (Less than 90)

5 0

2 years ago

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