Easy math questions giving brainlest

The domain of the inverse of the function f(x) = 5e^x + 3 is found being all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'

The domain of the inverse of a function (if it exists) is the range of the function it is inverse of. Similarly range of the inverse of that considered function is the domain of that considered function.

The function given is:

[tex]f(x) = 5e^x + 3[/tex]

The domain of the inverse of this function is this function's range.

Assuming only real values are allowed, for any real number x, we have:

[tex]e^x > 0[/tex]

And therefore, we get:

[tex]5e^x > 0 \: \forall x \in \mathbb R\\5e^x + 3 > 3 \: \forall x \in \mathbb R\\[/tex]

Also, since the function [tex]f(x) = 5e^x + 3[/tex] is strictly monotonically increasing and continuous, it touches all the values as its output from any real number > 3 till any finitely large number.

Thus, its range is (3, ∞) (it is an interval consisting of all the real numbers > 3)

This is the domain of its inverse function.

Thus, the domain of the inverse of the function f(x) = 5e^x + 3 is found being set of all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)

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Answer:

Below.

Step-by-step explanation:

0.9 = 90/100 fraction and

= 0.90 as a decimal.

Answer:

The answer would be B

Step-by-step explanation:

Hope this helps:)....if not then sorry for wasting your time and may God bless you:)

A right triangle with sides 3 and 4 would have a hypotenuse of 5.

The answer would be:

B. The triangle in question is not a right triangle.

Answer: 48

Step-by-step explanation: i know

Answer:

The answer is A: Spell check

I am going to assume that leg a:

  ⇒ is the horizontal distance between the house and the gas station

     ⇒ Distance for leg a: 6 miles

I am also going to assume that leg b

  ⇒ is the vertical distance between the house and gas station

     ⇒ Distance for leg b: 5 miles

Thus using the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex]

   ⇒ (look at diagram attached for further explanation)

   [tex]a^2+b^2=c^2\\\\6^2+5^2=c^2\\c=\sqrt{6^2+5^2} \\c=\sqrt{61} =7.81[/tex]

Answer: 7.81

Hope that helps!

Answer:

+1

Step-by-step explanation:

Positive 1

Answer:

-ln(| x - 1 |) + -ln(| x - 2 |) + C

Step-by-step explanation:

[tex]\displaystyle \int \dfrac{1}{x^2 -3x +2} dx\\\\\\=\displaystyle \int \dfrac{dx}{x^2 -3\cdot \dfrac 32 \cdot x + \left(\dfrac 32 \right)^2 -\left( \dfrac 32 \right)^2 +2}\\\\\\=\displaystyle \int \dfrac{dx}{\left(x- \dfrac 32 \right)^2 +2- \dfrac 94}\\\\\\=\displaystyle \int \dfrac{dx}{\left(x - \dfrac 32 \right)^2-\dfrac 14 }\\\\\\=\displaystyle \int \dfrac{du}{u^2-\left( \dfrac 12 \right)^2} ~~~~~~~~~~~~~~~~~~;\left[u = x - \dfrac32\implies du= dx\right]\\[/tex]

[tex]=\dfrac{1}{2\cdot\tfrac 12} \ln \left| \dfrac{u-\dfrac 12 }{u+\dfrac 12 } \right|+C~~~~~~~~~~:\left[ \displaystyle \int \dfrac {dx}{x^2 -a^2} = \dfrac 1{2a} \ln \left| \dfrac{x-a}{x+a} \right| +C\right]\\\\\\=\ln\left|\dfrac{x- \dfrac 32 - \dfrac 12}{x-\dfrac3 2 + \dfrac 12 } \right|+C~~~~~~~~~~~~;\left[\text{Substitute back}~u =x- \dfrac 32 \right]\\\\\\=\ln\left|\dfrac{x-2}{x-1} \right|+C[/tex]

The surface area of the barn is 2040 square feet.

A rectangle is a plane shape with four sides and four right angles.

Analysis:

The barn is composed of:

Two straight  long rectangles with dimensions = 10ft x 40ft

Two slant rectangles with dimensions = 10.6ft x 40ft

Two short rectangles with dimensions = 10ft x 14ft

Two triangles, height 8ft and base 14feet

The surface area of barn = 2(10x40) + 2(10.6 x 40) + 2(1/2 x 14 x 8) + 2(10 x 40) = 800 + 848 + 112 + 280 = 2040 square feet

In conclusion, the surface area of the barn is 2040 square feet.

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Answer:

16 11/12

Step-by-step explanation:

7 2/3 + 3 1/4 =

7 8/12 + 3 3/12 =

10 11/12 + 6

16 11/12

Answer: 77

Step-by-step explanation:

[tex]$$Find the range of the list:$$(41,43,52,25,96,19,72)$$The range of a list is given by:(largest element) - (smallest element) \\$(41,43,52,25,\bold{96},19,72)$ We see that the largest element is $96:$ $-(($ smallest element $))+96$\\$(41,43,52,25,96,\bold{19},72)$ We see that the smallest element is $19:$ $96-19$\\$$96-19=77$$Therefore, the range of the set is 77[/tex]

Answer:

9 people

Step-by-step explanation:

The amount spent on tickets

318.5 - 17 = 301.5

If 301.5 was for tickets alone, the number of tickets can buy

301.5/33.5 = 9

Now

our equation is

No of persons=x

Answer: [tex](2, 2), (6, 4), (8, 10), (9, 28)[/tex]

Step-by-step explanation:

The first four ordered pairs using the two sequences are:[tex](2, 2), (6, 4), (8, 10), (9, 28)[/tex]

The first rule is to add 10, then divide by 2 starting from 2

Add/Divide:

[tex]10=2+10=12[/tex]

[tex]2=12[/tex]÷[tex]2=6[/tex]

Add/divide again:

[tex]10=6+10=16[/tex]

[tex]2 = 20[/tex]÷[tex]2 = 10[/tex] [tex]2=16[/tex]÷[tex]2=8[/tex]

Add/divide again:

[tex]10=8+10=18[/tex]

[tex]2=18[/tex]÷[tex]2=9[/tex]

I believe it’s C, convert 0.188 into a fraction

Answer:

x = -1/2.

Step-by-step explanation:

x^2 - 4 = (x - 2)(x + 2)  so if we multiply each term by x^2 -4 we get:

2 - 1(x - 2) = 3(x + 2)

2 - x + 2 = 3x + 6

2 + 2 - 6 = 3x + x

4x = -2

x = -1/2.

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

1. Multiply both sides of the equation by the LCM (x - 2)(x + 2):

[tex]\frac{2}{x^{2} -4} (x-2)(x+2)[/tex]

factor x² - 4 by rewriting it as x² - 2²

x² - 2² = (x + 2)(x - 2)

now we have;

[tex]\frac{2}{(x+2)(x-2)} (x-2)(x+2)[/tex]

cancel the common factors (x - 2)(x + 2)

= 2

-------------------------------

[tex]\frac{-1}{x+2} (x-2)(x+2)[/tex]

cross cancel the common factor (x + 2)

[tex]\frac{-1}{x-2}=-(x-2)=-x+2[/tex]

-------------------------------

[tex]\frac{3}{x-2} (x-2)(x+2)[/tex]

cross cancel the common factor (x - 2)

3(x + 2)

distribute the 3

3x + 6

-------------------------------

combining all new values, we have;

2 + (-x) + 2 = 3x + 6

-x + 4 = 3x + 6

2. Isolate x:

-x + 4-4 = 3x + 6-4

-x = 3x + 2

-x-3x = 3x-3x + 2

-4x = 2

-4x/-4 = 2/-4

x = [tex]-\frac{1}{2}[/tex]

hope this helps!

Answer:

x=2,3

Step-by-step explanation:

[tex] {x}^{2} - 5x + 6 = 0 \\ {x}^{2} - 2x - 3x + 6 = 0 \\ x(x - 2) - 3(x - 2) = 0 \\ (x - 2)(x - 3) = 0 \\ either \: x = 2 \: \: \: \: \: or \: x = 3[/tex]

Answer:

  an = 40 -7(n -1)

Step-by-step explanation:

The given sequence has terms with a common difference, so it is an arithmetic sequence. The formula for the general term of an arithmetic sequence applies:

  an = a1 +d(n -1)

__

The first term of the given sequence is ...

  a1 = 40

The common difference for this sequence is ...

  d = 33 -40 = -7

Using these values in the equation for the n-th term, we have ...

  an = 40 -7(n -1) . . . . . explicit formula for the n-th term

Answer:Here, a=3, b=-10 and c=2. Substitute the values, Therefore, the discriminant of is 76.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

Answer:

0.315  to nearest thousandth.

Step-by-step explanation:

7e^3x − 4 = 14

7e3x  = 18

e^3x = 18/7

3x = ln(18/7)

x = ln(18/7) / 3

= 0.31482.

Step-by-step explanation:

using indices..

(7.2x 10³)/(1.2x10^5)

7.2/1.2 = 6

10³/10^5 = 10-²

answer = 6x 10-2

(c)

Answer:

$111222.02

Step-by-step explanation:

This year = Last year * (100%-9%)

This year = 122222 * 91% = 111222.02

It's around 1 to 3

So

From 35 it's 1,2,3

From 5500 samples of 35

Now

If 1 comes from each

If 2

If 3

Answer:

1

Step-by-step explanation:

because parentheses go first so 2 x 3 = 6 minus 1 = 5 minus 4 = 1

Answer:

2

Step-by-step explanation:

i got 20/8 from multiplying same with 1/2

20/8 - 1/2 = 2

Answer:

x = 27

Step-by-step explanation:

because the angles are on a line that means they add up to 180

18 + x + 5x = 180

then combine like terms

18 + 6x = 180

then you subtract 18 from both sides

6x = 162

lastly divide both sides by 6

x = 27

The volume of the cylinder is 471.43 cm³.

The volume of the cone is 157.14 cm³.

The volume of the sphere is  523.81 cm³.

The shape that would hold the most volume is the sphere.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = πr²h

Where:

π = 22/7

r = radius

22/7 x 5² x 6 = 471.43 cm³

Volume of a cone = 1/3 x volume of a cylinder

1/3 x  471.43 cm³ = 157.14 cm³

What is the volume of a sphere?

Volume of a sphere = 4/3 x pi x r³

4/3 x 5³ x 22/7 = 523.81 cm³

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Answer:

49.7359 units²

Step-by-step explanation:

Area = πr²

Circumference = 2πr

2πr = 25

πr = 12.5

r = 12.5 / π = 3.97887

π(3.97887)² = 49.7359 units²

Hope this helps