!!WILL MARK BRAINLIEST!! Write in slope-intercept form an equation of the line that passes through the given points.

Answer:

[tex]\mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

[tex]g(n )= (05)2^n[/tex]

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

SOLUTION:

If we represent g(n) with  t;

Then

[tex]\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}[/tex]

Taking logarithm of both sides; we have :

[tex]\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Answer:

-3

Step-by-step explanation:

[tex]f(x)=-2x^3+x^2-2 \\\\f(1)=-2(1)^3+(1)^2-2= \\\\-2+1-2=\\\\-3[/tex]

Hope this helps!

Answer:

The true statements are

The domain for f(x) is the set {-5, -3, 0, 2, 6, 7, 9, 10, 13}

f(-3) = 2

Extra:

x -5 -3 0 2 6 7 9 10 13

f(x) 1 2 3 0 1 2 3 0 1

Answer:

0.1875 as a decimal and 18.75% as a percent

Step-by-step explanation:

0.1875 is the decimal. Move point over 2 spots right to get percent.

Answer:

see below

Step-by-step explanation:

Let's call the width w. The length would then be 2w - 6. Since the area of a rectangle = length * width the answer is 208 = (2w - 6) * w.

Answer:

5 ounces

Step-by-step explanation:

Mr. Landry prepares 30 pounds of cake batter each morning and he uses half of the cake batter to make large cupcakes.

This means that he uses 15 pounds of cake batter.

He makes 48 cupcakes with the batter.

Therefore, the number of pounds of batter he uses per cake is:

15 / 48 = 0.3125 pounds

We have to convert it to ounces.

1 pound = 16 ounces

=> 0.3125 pounds = 16 * 0.3125 = 5 ounces

He uses 5 ounces of cake batter for each cake.

Answer:

5 ONCES

Step-by-step explanation:

sry i had caps on but i did the math

Answer:

Step-by-step explanation:

If the two cone are similar then the heights are the same

let us find the height of the bigger cone

[tex]volume of cone= \frac{1}{3} \pi r^2h[/tex]

For the bigger cone

r= 3cm

v= 66cm^3

[tex]66=\frac{1}{3}*3.142*3^2*h\\ 66=\frac{28.278}{3} *h\\h*28.278=198\\h=\frac{198}{28.278} =7cm[/tex]

For the smaller cone

r=2cm

v=?

h=7cm

[tex]v=\frac{1}{3}*3.142*2^2*7\\\v=\frac{87.976}{3} \\\\\v=29.30cm^3[/tex]

Answer:

19.6

Step-by-step explanation:

[tex]66=(\frac{3}{2} )^{3} =\frac{27}{8}[/tex]

[tex]\frac{66 x8}{27} = 19.5555555556=19.6[/tex]

[tex]x=[/tex] · [tex]( multiplication symbol )[/tex]

13 years

Step-by-step explanation:

17 + 15 + 23 + 23 + 23 =101 / 5 = 20.2

Mean before was 20.2

In order for the mean to be 19, all those numbers would have to add up 114 to be divided by 6 and have a mean of 19

114 / 6 = 19

114-101 = 13 is that number

17 + 15 + 23 + 23 + 23 + 13 = 114 / 6 = 19

Answer:

Step-by-step explanation:

49 is a perfect square, since it equals 7*7; 56 is not. If you have 35.2 and 37T, 36 is the perfect square between the two integers. Take the square root of the perfect square. If you have your square roots for memory, you know that the square root of 36 is equal to 6.

Answer:

y = 5

Step-by-step explanation:

y + 6 = –3y + 26

Add 3y to each side

y+3y + 6 = –3y+3y + 26

4y +6 = 26

Subtract 6 from each side

4y+6-6 = 26-6

4y = 20

Divide by 4

4y/4 = 20/4

y = 5

The solution of y in the equation y + 6 = - 3y + 26 is,

⇒ y = 5

We have to given that;

Expression is,

⇒ y + 6 = - 3y + 26

Now, We can simplify as;

y + 6 = - 3y + 26

Add 3y to each side

y + 3y + 6 = - 3y + 3y + 26

4y + 6 = 26

Subtract 6 from each side

4y + 6 - 6 = 26 - 6

4y = 20

Divide by 4

4y/4 = 20/4

y = 5

Thus, The solution of y in the equation y + 6 = - 3y + 26 is,

⇒ y = 5

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Answer:

8a^3.

Step-by-step explanation:

(a+b)^3=a^3+b^3+3a^2b+3ab^2

(a-b)^3=a^3-b^3-3a^2b+3ab^2

(a+b)^3+(a-b)^3=2a^3+6ab^2

According to the question

(a+b)^3+(a-b)^3+6a(a^2-b^2)

Put in the value

=2a^3+6ab^2 +6a^3–6ab^2

=8a^3

In the simplest form expression (a + b)³ + (a - b)³ + 6a(a² - b²) can be written as,  8a³

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Given that,

A algebraic identity,

(a + b)³ + (a - b)³ + 6a(a² - b²)

It is known that,

(a + b)³  = a³ + b³ + 3ab(a + b)

(a - b)³  =  a³ - b³ - 3ab(a - b)

So, now we can substitute expressions

(a + b)³ + (a - b)³ + 6a(a² - b²)

a³ + b³ + 3ab(a + b) + a³ - b³ - 3ab(a - b) +  6a(a² - b²)

a³ + b³ +  3a²b + 3ab² + a³ - b³ -3a²b + 3ab² + 6a³ - 6ab²

8a³

Hence, the simplest form is 8a³

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Work Shown:

1/500 = 0.002 is the probability of winning $390

3/500 = 0.006 is the probability of winning $230

16/500 = 0.032 is the probability of winning $170

Multiply the probabilities with their respective winnings

0.002*390 = 0.78

0.006*230 = 1.38

0.032*170 = 5.44

Then add up those results

0.78+1.38+5.44 = 7.60

which is the expected value.

Side note: This game is not a fair game because mathematically a "fair game" is defined as such where the expected value is 0; ie, neither the player nor the dealer win and things break even.

Answer.

x=156

How to solve

x /6 +6=32

1 /6 x+6=32

1 /6 x+6−6=32−6

1 /6 x=26

6*( 1/ 6 x)=(6)*(26)

x=156

Answer:

y = 5(2)ˣ

Step-by-step explanation:

numbers are doubled for y as x is changing by 1

it indicates exponential growth with y intercept 5 and rate 2:  y = 5(2)ˣ

Answer:

The answer is 7x²

Step-by-step explanation:

Since we have to add the two polynomials together, we write it as A+B=7x²+3xy-3xy. Now, we simplify, and we are left with A+B=7x²

Answer:

72

Step-by-step explanation:

The sum of exterior angles is 360

360-57-68-32-59-72 =. 72

Answer:

21.66666667

Step-by-step explanation:

3x-4(0)=65

3x=65

x=21.66666667

You replace y wil 0 when you are sovling for x

Answer:

AA similarity

Step-by-step explanation:

Respective angles of both triangles are 40°, 50° and 90°

AA similarity is the case:

Answer:

5^18 in index form is the answer :)

Step-by-step explanation:

(5^3)^6

In a polynomial like this the rule is that,

(a^m)^n

= a^m*n (multiply the exponents)

So let a be 5

m be 3 and n be 6

5^3^6

= 5^3*6

= 5^18

Answer:

The answer above is wrong it actually b

The function shown in the graph is option b.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

We have from the graph that graph touches the x axis at 2 and at a point between 0 and 1.

That is,

f(x) = 0 when x = 2

Substitute the value of x as 2 in the functions given in the option when x > 1 and find those functions which give y = f(x) = 0.

It is only possible for options 'a' and 'b'.

When x = 2, -2 + 2 = 0.

Also we have the point, when x = 1, y = 1.

x = 1, then -2x + 2 = 0 ≠ 1

x = 1, then -x + 2 = -1 + 2 = 1

So when x = 1, f(x) should be of the form f(x) = -x + 2.

Correct option is option b.

Hence the correct definition of the function is option b.

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Answer:

x = 12

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(6+x) *6 = (4+23) * 4

(6+x) *6 = 27*4

6(6+x) = 108

Divide each side by 6

6+x =18

Subtract 6 from each side

6+x-6 =18-6

x = 12

Answer:

A= 61

B=119

Step by step:

a; interior angle

180-(27+92)

=180(119)

=61

b; exterior angle

180-61

=119

Answer: 61 and 119

Step-by-step explanation:

Answer:

(6-√21,  6+√21)

Step-by-step explanation:

x^2 - 12x = -15

(x - 6)^2 - 36 = -15

(x - 6)^2 = 21

x - 6 = ± √21

x = 6  ± √21

The solution set of the given equation is (6-√21,  6+√21)

Given is an equation, x² - 12x = -15 we need to solve it by completing the square.

Solving the equation,

x² - 12x = -15

(x - 6)² - 36 = -15

(x - 6)² = 21

x - 6 = ± √21

x = 6  ± √21

Therefore, the solution set is (6-√21,  6+√21)

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Answer:

A. y = 5/4(x - 1)

Step-by-step explanation:

The equation of a line can be written in the form:

[tex]\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

From the points given,

y1 = 0

y2 = 5

x1 = 1

x2 = 5

Therefore:

[tex]\frac{y - 0}{x - 1}= \frac{5 - 0}{5 - 1} \\\\\frac{y}{x - 1} = \frac{5}{4}[/tex]

Cross multiply:

4y = 5(x - 1)

y = 5/4(x - 1)

A. y = 5/4(x - 1)

Step-by-step explanation:

The equation of a line can be written in the form:

From the points given,

y1 = 0

y2 = 5

x1 = 1

x2 = 5

Therefore:

Cross multiply:

4y = 5(x - 1)

y = 5/4(x - 1)

Answer:

Step-by-step explanation:

The equation modeling the situation is ;

y = 25x + 80

We want to know what the y-intercept mean in this question

Mathematically, the equation of a straight line is ;

y = mx + c

where c is the y intercept and m is the slope

What we should understand is that at the y intercept which is 80 here, the value of x is 0

Now since y means the amount of money spent and x is number of chairs bought, the value 80 means that the amount spent when he bought 0 number of chairs is 80

Now going by the question, since he bought 0 chairs here and we still have some cost, definitely he spent the money on other things which of course might be the amount spent in purchasing some tables

Answer:

Step-by-step explanation:

So basically, what you have to do is first find the area of the floor. The area can be split into 3 shapes, a quarter of a circle, a square, and a rectangle.

Quarter of circle: (3.14r^2)/4

3.14(100)/4

314/4

78.5

Square: s^2

100

Rectangle: lw

600

Total: 78.5+100+600

778.5

Cost: $2335.50

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