What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5

Answers

Answer 1

Answer: f′(x)=5 × 1/(xln2)
use derivation

Answer 2

Answer: f′(x)=5 × 1/(xln2)
u need to use

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If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (fxg) (x)?

Answers

Answer:

$(f* g) (x)=3x^3+2x^2+3x+2$

Step-by-step explanation:

Given : If $f(x) = 3x + 2$ and $g(x)=x^2+1$

To find : Which expression is equivalent to $(f* g) (x)$ ?

Solution :

We can write,

$(f* g) (x)=f(x)* g(x)$ ....(1)

We know, $f(x) = 3x + 2$ and $g(x)=x^2+1$

Substituting the values in (1),

$(f* g) (x)=(3x+2)* (x^2+1)$

Multiply term by term,

$(f* g) (x)=3x^3+3x+2x^2+2$

$(f* g) (x)=3x^3+2x^2+3x+2$

Therefore, The expression is equivalent to $(f* g) (x)=3x^3+2x^2+3x+2$

$f(x)=3x+2\nThe\ domain\ D_f=\mathbb{R}\n\ng(x)=x^2+1\nThe\ domain\ D_G=\mathbb{R}\n\nD_f=D_g\ therefore\ (f* g)(x)=f(x)* g(x)\n\n(f* g)(x)=(3x+2)(x^2+1)=3x^3+3x+2x^2+2=\boxed{3x^3+2x^2+3x+2}$

6a-5b=9 2a+5b=23 using the addition method

Answers

Answer:

a = 4

b = 3

:))

Find the area and the circumference of a circle with diameter 5 cm.Use the value 3.14 for it, and do not round your answers. Be sure to include the correct units in your answers.

Answers

The Circumference of the circle is
15.7

and Area is
19.625

What is the area of the figure?40 ft2
84 ft2
96 ft2
can't be determined

Answers

Answer:

$A=80\ ft^2$

Step-by-step explanation:

we know that

The area of the figure is equal to the area of an isosceles triangle (has two equal sides) plus the area of a rectangle

step 1

Find the area of the triangle

The area of the triangle is equal to

$A=(1)/(2)bh$

we have

$b=16\ ft$

To find out the height of the triangle Apply the Pythagorean Theorem

$10^2=(16/2)^2+h^2$

solve for h

$100=64+h^2$

$h^2=100-64$

$h^2=36$

$h=6\ ft$

Find the area of triangle

$A=(1)/(2)(16)(6)$

$A=48\ ft^2$

step 2

Find the area of rectangle

The area of rectangle is equal to

$A=LW$

we have

$L=16\ ft\nW=2\ ft$

substitute

$A=(16)(2)=32\ ft^2$

step 3

Find the area of the figure

Adds the areas

$A=48+32=80\ ft^2$

Answer:

80ft^2

Step-by-step explanation:

John consistently saves7/12
of his monthly salary. John's salary has recently been increased by $312.
As a result of the pay raise, John's monthly savings is now $1512. How much was John's salary before
the pay raise?

Answers

An equation is formed of two equal expressions. John's salary before the pay raise is $2280.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the pay of John before the raise be x.

As it is stated that John's pay was increased by $312. And he saves 7/12 of his pay which is equal to $1512. Therefore, the equation that can represent the current saving John has,

$(7)/(12)(x+312)=1512\n\n(x+312) = (1512 * 12)/(7)\n\nx+312= 2592\n\nx =2592-312\n\nx = 2280$

Hence, John's salary before the pay raise is $2280.

Learn more about Equation:

brainly.com/question/2263981

Answer:

2280

Step-by-step explanation:

As in understandable steps,

1512x12 = 18144

18144 / 7

= 2592

2592 - 312

= 2280

A researcher calculates the expected value for the number of girls in three births. He gets a result of 1.5. He then rounds the result to 2, saying that it is not possible to get 1.5 girls when three babies are born. Is this reasoning correct? Explain.

Answers

yes his reasoning is correct because you can not cut a person in half. you can not be born with half of a body so you would have to round your result to the nearest whole number which in this case is 2 so he would technically be correct

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