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3 years ago

Select 2 of the following

Mathematics

1 answer:

siniylev [52]3 years ago

3 0

Answer:

OPTION C: The ratio is a constant.

OPTION E: The ratio is equal to b.

Step-by-step explanation:

Given: $f(x) = a.b^x$

The ratio of f(x + 1) and f(x) = $\frac{f(x + 1)}{f(x)} = \frac{a.b^{x + 1}}{a.b^x}$

Since, $a^{x + 1} = a^x. a$

$\implies \frac{f(x + 1)}{f(x)} = \frac{a.b^x.b}{a.b^x}$

Cancelling out $a.b^x$ we get:

$\frac{f(x + 1)}{f(x)} = b$

This shows that the ratio is always a constant and that constant is equal to b.

You might be interested in

Three numbers are in the ratio 3:9:10. If 10 is added to the last number, then the three numbers form an arithmetic progression.

MrRa [10]

Answer:

 The numbers are 6, 18, and 30 

Step-by-step explanation:

If the three numbers are in the ratio of 3:9:10,

let the numbers be 3x, 9x and 10x.

If 10 is added to the last number to form an arithmetic progression

Then, 3x 9x (10x+10) are the progression

The common difference of an arithmetic progression (d) = T₂ - T₁ = T₃ - T₂

T₂-T₁ = T₃ - T₂ .............. Equation 1

Where T₁ = first term of the progression, T₂ = Second term of the progression, T₃ = third term of the progression

Given: T₁ = 3x, T₂ = 9x, T₃ = 10x +10

Substituting these values into equation 1

9x-3x = (10x+10)-9x

Solving the equation above,

3x = 10+x

3x-x = 10

2x = 10

x = 10/2

x = 2.

Therefore the numbers are 6, 18, and 30 

7 0

4 years ago

Which two values of x are roots of the polynomial below?

Julli [10]

Answer:

B. and C.

Step-by-step explanation:

1. Set the polynomial equal to zero:

x² + 5x + 7 = 0

2. Plug the given values of a, b, and c into the quadratic formula:

$x=\frac{-5+-\sqrt{5^{2}-4(1)(7) } }{2(1)}$

3. Solve the square root:

$x=\frac{-5+-\sqrt{25-4(1)(7)} }{2(1)}$

$x=\frac{-5+-\sqrt{25-28} }{2(1)}$

$x=\frac{-5+-\sqrt{-3} }{2(1)}$

4. Simplify the rest:

$x=\frac{-5+-\sqrt{-3} }{2}$

5. Separate the solutions:

$x=\frac{-5+\sqrt{-3} }{2} , x=\frac{-5-\sqrt{-3} }{2}$

Thus, options B and C are the answers.

hope this helps!

4 0

2 years ago

Tim has an encyclopedia in 5 volumesA–C, D–F, G–J, K–N, and O–Z. Other than alphabetically (ascending or descending), how many w

Ira Lisetskai [31]

The first book can be any one of the 5.
   For each of those . . .
The 2nd book can be any one of the remaining 4.
   For each of those ...
The 3rd book can be any one of the remaining 3.
      For each of those . . .
The 4th book can be either of the remaining 2.
   For each of those . . .
The 5th book is the last one remaining.

Total number of ways to arrange the 5 books is

   (5 · 4 · 3 · 2 · 1) = 120 .

Cross off alphabetically ascending (1 way), and alphabetically
descending (1 way), and you're left with (120 - 2) = 118 ways.

6 0

3 years ago

Read 2 more answers

Tell whether the triangle is a right triangle. Show Work.

Yakvenalex [24]

Answer:

This is not a right triangle because the hypotenuse is less than the two sides and aren't equal when following the Pythagorean thm

Step-by-step explanation:

To confirm if a triangle is a right triangle, we must use the Pythagorean thm

a^2 + b^2 = c^2

23^2 + 11.4^2 = 21.2^2

529 + 129.96 = 449.44