What is the Exponential or Logarithmic function?

Answer:

√25

= √( 5 x 5 )

= 5

√25 = 5

5 is an rational number, not an irrational number.

                 [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Given question:-}}}\rule{50}{1}[/tex]

              Jillian said, "√25 is irrational because it's a square root!" Why is

she incorrect?

    [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

    First let's see if we can simplify √25.

     We can, by using either our calculator or our brains.

       Anyway, √25=5 (5×5=25)

Now, let's take a look at what irrational numbers are.

            [tex]\dagger[/tex] Irrational numbers. This set includes numbers with an infinite

           number of digits after the decimal point. Irrational numbers

           cannot be expressed as fractions (p/q form)

Can [tex]\LARGE\textbf{5}[/tex] be expressed as a fraction? Sure!

This is how it's done:-

[tex]\Large\text{$\displaystyle\frac{5}{1}$}[/tex]

As you can see, 5 is not irrational.

            [tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]

Answer:

x = 1/20 y^2

Step-by-step explanation:

This is a rightward opening  (sideways ) parabola

Directrix = x = -5

Distance formula form point x,y  to directrix and focus are equal:  

(x - -5)^2 = (x-5)^2 + y^2

x^2 + 10x + 25 = x^2 - 10x  + 25 + y^2

20x = y^2

x = 1/20 y^2

Answer:

9

Step-by-step explanation:

For the equation x² - 6x = 5 the coefficient of the term x is -6

(-6/2)2 = 9

The given equation can be written as

x2 - 6x + 9 = 5 + 9

x2 - 6x + 9 = 14

We can write it as

(x - 3)2 = 14

Take square root on both sides.

|x - 3| = √14

We get

x = 3 + √14

In other case,

- x + 3 = √14

x = 3 - √14

Therefore, 9 should be added to both sides of the equation to complete the square (x2 - 6x = 5).

What number should be added to both sides of the equation to complete the square (x2 - 6x = 5)?

Summary:

The number that should be added to both sides of the equation to complete the square (x2 - 6x = 5) is 9.

Answer:

74

Step-by-step explanation:

(23-3)+(6×9)

(20) +(54)

=74

Check the picture below.

[tex]\stackrel{parent}{y=x^2}\hspace{5em}y=\stackrel{A}{4}(\stackrel{B}{1}x\stackrel{C}{-2.5})^2\stackrel{D}{-3} \\\\\\ \hspace{7em} \begin{array}{llll} \textit{stretch by }4\cdot 1\implies 4\\\\ \textit{translated by }\frac{2.5}{1}\implies 2.5\textit{ to the right}\\\\ \textit{downwards shift by }3 \end{array}[/tex]

Answer:

Ray, you need the slope-intercept formula  y=mx+b

Step-by-step explanation:

Next you'll need 2 points,  any points are fine.  Just find two easy ones along the line.  I'll just pick  Point 1  as P1 = ( 0,4)  and point 2 as P2 = (4,0) because they are easy to work with.

next use

point P1 (0,4)  in the form (x1,y1)

point P2(4,0)  in the form (x2,y2)

slope = m

m = (y2-y1) / (x2-x1)

m = (0-4) / (4-0)

m = -4 / 4

m = -1

now use the point slope with one of the points,  to find the slope-intercept form.

y - y1 = m(x -x1)

y - 4 =  -1(x-0)

y -4 = -x

y = -x + 4

note:

y = mx +b

y = (-1)x + b    is the form.   see?

Answer:

y = mx + b

m = slope

b = intercept

From the graphic:

(x₁, y₁) = (0, 4)

(x₂, y₂) = (4, 0)

[tex]\frac{y-y_{1} }{y_{2} -y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} } \\\\\frac{y-4 }{0 -4} =\frac{x-0 }{4 -0 } \\\\\frac{y-4}{-4} =\frac{x}{4} \\\\(y-4)4=-4x\\\\y-4=-x\\y=-x+4\\[/tex]

Answer:

C) 10,000,000

Step-by-step explanation:

Data provided in the question:  

- The phone number is of 7 digits

- we have choices from 0-9

meaning 10 number of choices, 0 1 2 3 4 5 6 7 8 9

we have 10 choices out of 10 for each of the 7 blanks

Therefore,

The total number of different phone numbers can there be in one area code that can be formed

= 10 × 10 × 10 × 10 × 10 × 10 × 10

= 10^7

= 10,000,000

The distance between J(-5, -3) and K(1, 5) on the coordinate plane is about 10 units.

An equation is an expression that shows the relationship between two or more numbers and variables.

Point J is at (-5, -3) while point K is at (1, 5), hence:

[tex]JK=\sqrt{(5-(-3))^2+(1- (-5))^2} =10\ units[/tex]

The distance between J(-5, -3) and K(1, 5) on the coordinate plane is about 10 units.

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Answer:

67.38 degrees

Step-by-step explanation:

this is a right triangle so we can use sohcahtoa

we want to calculate angle A

we know the side opposite to A as well as the hypotenuse. 13 is the hypotenuse because it is opposite the right angle

thus, sin(A) = opposite/hypotenuse = 12/13

arcsin(12/13) = A ≈ 67.38 degrees

Answer:

Vol_prism = 48 (all answers should have the units cm^3)

Vol_pyramid = 25

Vol_cyl = 37.68

Vol_cone = 12.56

Vol_sphere = 113.04

Step-by-step explanation:

This was a very compact problem (5 problems!) You read the chart top to bottom and each column is a different problem.

Vol of a prism:

V = l×w×h = 4×4×3

= 48 cm^3

Vol of a pyramid:

V = 1/3Base•h

= 1/3 (5×5)•3

= 25 cm^3

Vol of a cylinder:

V = pi•r^2•h

= pi•2^2•3

= pi•4•3

= 12pi = 12(3.14)

= 37.68 cm^3

Vol of cone:

= 1/3pi•r^2•h

= 1/3pi•2^2•3

= 4pi = 4(3.14)

= 12.56 cm^3

Vol of a sphere:

V = 4/3pi•r^3

= 4/3 pi•3^3

= 4/3 pi•27

= 36pi = 36(3.14)

= 113.04 cm^3

Pheewwwww! That was a lot! Hopefully you are just reviewing all your volume formulas. Hope this helps!

Answer:

3/10 or 30%

Step-by-step explanation:

Add all of the marbles: 5+2+3=10

Then use a fraction to represent the three purple marbles: 3/10

That porportion is your answer

Answer: 85 lbs

Step-by-step explanation:

$107.95 / $1.27 = 85 pounds of dog food

Answer:

-40%

Step-by-step explanation:

NV = new value

OV = old value

percent change = (NV - OV)/(OV) × 100%

percent change = (30 - 50)/(50) × 100%

percent change = -20/50 × 100%

percent change = -40%

Answer:

Yes if Greg and his partner can both eat 18 inch pizza then together they can eat a 36 inch pizza

Step-by-step explanation:

18+18=36

x(36) is greater then or equal to 36 making this equation true

Answer:

[tex](\frac{2}{3})^{3} (\frac{1}{5}.\frac{2}{3} )^{-3} (\frac{1}{5})^{4} =(\frac{2^{3} }{3^{3} }) (\frac{2}{8} )^{-3} (\frac{1^{4}} {5^{4} })[/tex]

                          [tex]=(\frac{2^{3} }{3^{3} }) (\frac{2^{-3} }{8^{-3} } ) (\frac{1^{4}} {5^{4} })[/tex]

                          [tex]=\frac{2^{3} .2^{-3}.8^{3}. 1 }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{1.8^{3} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{(2^{3}) ^{3} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{2^{9} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{512}{27.625}[/tex]

                          [tex]=\frac{512}{16875}[/tex]

[tex]\text{Given that,}\\\\P(x) = 2x^4 -5x^2 +3x -9\\\\P(6) = 2\cdot 6^4 -5 \cdot 6^2 +3 \cdot 6 -9 \\\\~~~~~~~=2592-180+18-9\\\\~~~~~~~=2421\\\\\text{Hence the answer is option D.}[/tex]

Step-by-step explanation:

x + 2x + 6 = 27

3x + 6 = 27

x + 2 = 9

x = 9 - 2

x = 7

2 × 7 = 14

14 + 6 = 20

x=-4

Step-by-step explanation:

see the picture for full solution

The exponential function is P = 5.63(1.0145)ⁿ. And the population of the city in 2018 is 6.1379 million, the number of the years when the population of the city is 10 million is 40 years, and the doubling time will be 49 years.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

In​ 2012, the population of a city was 5.63 million. The exponential growth rate was 1.45​% per year.

Then the exponential function will be given as

P = 5.63 (1.0145)ⁿ

Where P is the population (in million) and n is the number of years.

Then the population of the city in 2018 will be

n = 2018 - 2012 = 6

Then we have

P = 5.63 (1.0145)⁶

P = 5.63 x 1.0902

P = 6.1379 million

The number of the years when the population of the city is 10 million.

    10 = 5.63 x (1.0145)ⁿ

1.776 = (1.0145)ⁿ

Taking log both sides, then we have

log 1.776 = n x log 1.0145

            n = 39.90

            n ≅ 40 years

Then the doubling time will be

2 = (1.0145)ⁿ

Taking log on both sides, then we have

log 2 = n x log1.0145

      n = 48.1489

      n ≅ 49 years

More about the exponent link is given below.

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Answer: Pretty Simple; an easy equation could be 10 + 4 = 14.

Step-by-step explanation:

A more difficult equation might be (10(8) - 70) + 4 = 14

:)

Answer:

7x2=14

8+6=14

7+7=14

5x2.8=14

28/2=14

140/10=14

100-86=14

81(+-)67= 81-67=14

The function f(x) =  x² + 12x is a quadratic function, and the vertex of the function is (-6,-36)

The equation of the function is given as:

f(x) =  x² + 12x

Differentiate the function

f'(x) = 2x + 12

Set the function to 0

2x + 12 = 0

Add -12 to both sides

2x = -12

Divide both sides by 2

x = -6

Set x = -6 in the function f(x)

f(-6) =  (-6)² + 12(-6)

Evaluate

f(-6) =  -36

Hence, the vertex of the function is (-6,-36)

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Answer:

the vertex of the function is (-6,-36)

Step-by-step explanation:

Pls add brainliest pls

Answer :The constant of proportionality is  K = 2/3

Answer:

x = √51

Step-by-step explanation:

The given figure is a right triangle.

Using the Pythagorean Theorem to find x

The sentences here are all simple sentences and all begin with the same word.

A paragraph is used to show a complete thought. It is important that a paragraph ought to be presented in complete sentences. However the sentences here are all simple sentences and all begin with the same word.

The reasons pointed out above makes the paragraph appear clumsy and boring to read. The writer should revise the paragraph and introduce a more complex sentence structure as well as the use of pronouns where neccessary.

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Answer:

B

Step-by-step explanation:

edge 22

Answer:

1/12

Step-by-step explanation:

probability of tails is 1/2

probability of 1 out of 6 is 1/6

so 1/2 x 1/6 = 1/12