Ronin simplified an expression, and his solution is shown below. His teacher told him to verify that they are equivalent by using x = 5. What is the resulting value of both expressions? x + 13 + 2 x minus 4 = 3 x + 9

Answer:

After n passing, the total number of people knowing the secret [tex]= 2^n[/tex].

After 10 passing, 1024 peoples know the secret.

Step-by-step explanation:

Given that each friend can pass the secret to 2 people.

On 1st pass:

Total number of people knowing the secret = 1+1=2

On 2nd pass:

Total number of people knowing the secret = 1+1+1x2=4

On 3rd pass:

Total number of people knowing the secret = 1+1+2+2x2=8

This can be written as [tex]1+1+2+2^2=1+1+2+2^{3-1}=8[/tex]

Or, [tex]1+S_3=8[/tex], where [tex]S_3=1+2+2^{3-1}[/tex].

So, for the [tex]n^{th}[/tex] pass:

Total number of people knowing the secret = [tex]1+1+2+2^2+\cdots+2^{n-1}=1+S_n, where, S_n = 1+2+2^2+\cdots+2^{n-1}[/tex].

As [tex]S_n[/tex] is the sum of geometric progression of n terms having the first term, [tex]a_1=1[/tex], and the common radio [tex]r=2[/tex].

So, [tex]S_n = \frac{a_1(r^n-1)}{r-1}[/tex]

[tex]\Rightarrow S_n =\frac{1(2^n-1)}{2-1}=2^n-1[/tex].

Hence, after n passing, the total number of people knowing the secret

[tex]=1+S_n = 1+2^n-1=2^n.[/tex]

After, 10 passing, put n=10.

Total number pf peoples know the secret [tex]= 2^{10}=1024.[/tex]

Answer:

504 m³

Step-by-step explanation:

The volume of the rectangular prism is V = 504 m³

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the volume of the prism be represented as V

Now , the value of V is

Let the height of the rectangular prism be H = 9 m

Let the length of the rectangular prism be L = 7 m

Let the width of the rectangular prism B = 8 m

where the base area of prism B = L x W = 7 x 8 = 56 m²

Now , the volume of the prism V = B x H

The volume of prism V = 56 x 9 = 504 m³

Hence , the volume of the rectangular prism V = 504 m³

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Answer:

It is not proportional because it does not pass through the origin (0,0)

9514 1404 393

Answer:

Step-by-step explanation:

If a vertical line can be drawn that goes through 2 or more points on the graph, then it is not a function. That will be the case for the two graphs on the left side of your figure.

The two graphs on the right side pass this "vertical line test," so are functional relationships.

upper left: not a function

upper right: is a function

lower left: not a function

lower right: is a function

Answer:

1 2/4

Step-by-step explanation:

Answer:5m/2

Step-by-step explanation:

3m-m/2

(2×3m-1×m)/2

(6m-m)/2=5m/2

Answer:

$2,184

Step-by-step explanation:

$6,500 x 2.8% = annual interest

6,500 x 2.8% = $182 annual interest

$182 x 12 years = interest earned in 12 years.

182 x 12 = $2,184

The value of f(6)=64

Given :

The graph of an exponential function .

Explanation :

We need to find out f(6) using the given graph .

To find f(x), first we find out the function f(x) using the graph .

Pick any two points from the graph (0,1) and (1,2)

General form of exponential function is [tex]y=ab^x[/tex]

Substitute (0,1) in general equation

[tex]1=ab^0\\1=a\\a=1[/tex]

Now we plug in (1,2) in the equation

[tex]y=ab^x\\2=1(b)^1\\2=b\\b=2[/tex]

Substitute a=1, b=2 in [tex]f(x)=ab^x\\[/tex]

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

To find out f(6), we plug in 6 for x  in f(x)

[tex]f(x)=2^x\\f(6)=2^6\\f(6)=64[/tex]

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Answer:I believe the answer is 12

Step-by-step explanation: if you split the triangle into 2 then you can do 1/2bh then add them. (1/2)(2)(3)+(1/2)(6)(3)=12

Answer:

A) The standard form of a linear equation is given as follows;

Ax + By = C

In order to change the above linear equation from standard form to slope and intercept form which is the form y = mx + c, we have;

1) Move the x-variable (and its coefficient) to the right side of the equation as follows;

By = C - Ax

2) Divide both sides of the equation above equation, by the coefficient of y as follows;

By/B = C/B - Ax/B

y = C/B - A/B·x

3) Rearrange the right hand side of the above equation

y = -A/B·x + C/B

The equation given above is in the slope and intercept form, y = m·x + c, where;

m = -A/B

c = C/B

B) Two reasons why it is important to have a slope and intercept form of a linear equation are;

1) The slope and intercept for shows the initial value of the dependent variable, y, when the dependent variable, x is 0 which is the constant term, c, in the equation

2) The slope coefficient term, m, in the slope and intercept form of a linear equation shows the rate of increase of the y-coordinate value with a unit increase in x-coordinate value.

Step-by-step explanation:

Answer:

B. -2 *4

Step-by-step explanation:

Answer:

no, it won't be enough because you would need $80.06

Step-by-step explanation:

I just found 6.75% of 75 and added it on

Answer:

A.) 6

B.) 24

C.) $60

Step-by-step explanation:

Given that :

Cost of Mango = $2

Purchase of 6 mangoes earns 2 free mangoes

(a) Robin purchased $36.00 worth of mangoes.

How many free mangoes did Robin get?

$36 / price per Mango

$36 / $2 = 18 mangoes

18 / 6 = 3

Hence, free mangoes (3 * 2) = 6 free mangoes

(b) How many mangoes did he get all together?

18 mangoes + 6 mangoes = 24 mangoes

(c) Peter also bought mangoes. He received 40 mangoes. How much did Peter pay?

Set of mangoes purchased:

40/ (6 + 2) = 40/8 = 5 sets of mangoes

Hence, amount paid :

2 * 6 * 5 sets

$60

Answer:

infinite number of solutions

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

3y = 6x + 9 → (2)

Divide the terms in (2) by 3

y = 2x + 3 → (3)

Since the equations are the same in (1) and (3) , then

The system has an infinite number of solutions

5000

Step-by-step explanation:

because u have to add

Answer:

4602

Step-by-step explanation:

Answer:75 × 62 - 58 + 68 - 58 = 4602

Step-by-step explanation:

Your answer should be:

The three significant figures would be the 9, 0, then 1.

Answer: You need to buy about 10 cans of paint.

Step-by-step explanation:

Given : Diameter of round swimming pool = 59 ft

Radius = half of diameter

= [tex]\dfrac{59}{2}[/tex] ft

Area of circle = [tex]\pi r^2[/tex] , where r= radius

Area of bottom of pool = [tex]\dfrac{22}{7}\times\dfrac{59}{2}\times\dfrac{59}{2}[/tex]

[tex]=\dfrac{38291}{14}\ ft^2[/tex]

Each can of paint cover 300 ft².

So , Number of cans required to cover 1 ft² = [tex]\dfrac1{300}[/tex]

Number of cans required to cover[tex]\dfrac{38291}{14}\ ft^2[/tex] = [tex]\dfrac{38291}{14}\times\dfrac{1}{300}=9.1169047619\approx10[/tex]

Hence, you need to buy about 10 cans of paint.

Answer:

114

Step-by-step explanation:

To evaluate f(7) substitute x = 7 into f(x), that is

f(7) = 268 - 22(7) = 268 - 154 = 114

Answer:

Step-by-step explanation:

Translation right (or left) means change of the x-coordinate.

Translation down (or up) means change of the y-coordinate.

(3, 8)   →    (3+3, 8-5) = (6, 3)

Answer:

Step-by-step explanation:

The difference:

Correct choice:

Answer:

a.) 14.5 minutes longer

Step-by-step explanation:

the average travel time for New Yorkers compare to the United States

= 40.0 - 25.5

= 14.5 min. longer

Answer:

17.2

Step-by-step explanation:

Answer:

18.86

Step-by-step explanation:

8.2 x 4.6 = 37.72

37.72/2 = 18.86

Answer:

18.86

Step-by-step solution:

8.2 * 4.6 = 37.72

divide by two, 18.86

Sorry I couldn't elaborate further, I'm really busy right now. Please contact me if you need any more help and I will be sure to help you more soon.

Answer:

For a line:

y = a*x + b

where a is the slope, and b is the y-intercept.

Any other line with the same slope but different y-intercept will be parallel to this line.

Then if we have two lines like:

y1 = a*x + c

and

y2 = a*x + k

Both of them are parallel to our first line, and as you can see, both of them have the same slope and different y-intercept, then these lines are also parallel.

Now, the statement says that:

"If two lines are parallel to the same line..."

Then we can have the lines:

y1 = a*x + k

y2 = a*x + k

Both of them are parallel to our first line (same slope)

Buth these lines are the same line, then these lines are not parallel to each other (a line is not parallel to itself, because it intersects itself in infinity points), then the actual statement should be:

"If two different lines are parallel to the same line, then they are parallel to each other".

Now, this theorem does not have a particular name, just call it as the above statement.

Answer: 0.27

Step-by-step explanation:

Given that :

Probability of being a strike ; p(strike) = 0.3

Note : the probability of each pitch Beau is independent :

Probability that next three will be a strike :

p(strike) * p(strike) * p(strike)

= 0.3 * 0.3 * 0.3

= 0.27

Answer: b

Step-by-step explanation:

The answer is b because both sides of the table start with zero and both sides of the table have a continues pattern the y side(right). They are increasing by a set # of points(3).

I AM NOT POSITVE ABOUT THE ANSWER, BUT IF I HAD TO GUESS- B WOULD BE THE ANSWER! sorry if its wrong!

Answer:

9x^2-3x - 12

Step-by-step explanation:

(9x^2 + 6x - 7) + (-9x -5)

Simplify the expression:

9x^2 - 3x - 12

Factor:

Add and subtract the second term to the expression and factor by grouping.

3( x + 1 ) ( 3x - 4 )

Standard form:

9x^2 - 3x - 12

I hope this helps :)