Elena bought six guppies at the beginning of the month. One month later, the number of guppies in her
tank had doubled. Her guppy population continued to grow in this same manner. (16 pts.)
a. Create a function 9 to model the growth of the Elena's guppy population, where g(n) is the number
of guppies at the beginning of each month and n is the number of months that have passed since
she bought the six guppies.
g(n) =
(2 pts.)

Answer:

Step-by-step explanation:

We are given the following quadratic equation, 3x² - 1 = 7x, which requires us to find its possible solutions using the quadratic formula.  

The quadratic formula is given by:

[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]

We will use this formula to solve for the roots or the solution of the given quadratic equation.

Step 1: transform the given equaton into standard form.

First, we must subtract "7x" from both sides of the equation:

3x² - 7x - 1 = 7x - 7x

3x² - 7x - 1 = 0     ⇒   This is the standard form of the given quadratic equation where a = 3, b = -7, and c = - 1.

Step 2: Plug in the values for a, b, & c into the quadratic formula.

The derived values for a, b, & c from the previous step are:  a = 3, b = -7, and c = - 1.  Substitute these values into the following quadratic formula:

[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]

[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{(-7)^2-4(3)(-1)}}{2(3)}}[/tex]

Step 3: Following the PEMDAS Order of Operations, start by applying the Power rule of Exponents  [tex]\displaystyle\mathsf{(a^m)^n = (a^{m*n})}[/tex] (under the radical) :

[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{49-4(3)(-1)}}{2(3)}}[/tex]

Step 4: Next, multiply the integers under the radical, PEMDAS Order of Operations.

[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{61}}{2(3)}}[/tex]

Step 5: Multiply the integers in the denominator, and apply the multiplication integer rule, -(-a) = a.

[tex]\displaystyle\mathsf{x\:=\:\frac{7\pm\sqrt{61}}{6}}[/tex]

Step 6: Separate the solutions.

[tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex]  , and   [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]  

Therefore, the solution to 3x² - 1 = 7x  are:  [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex],  [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex].

Quadratic equation

Quadratic function

Standard form

Parabola

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Answer:

228 inches

Step-by-step explanation:

There are 12 inches in a foot.

19 × 12 = 228

Answer:

27

Step-by-step explanation:

Base is 6 - (-3) = 9

height is 1 - (-5) = 6

so Area = 9 * 6/2 = 27

Answer:

Solutions: (0,11) ; (1,15) ; (2, 19)

Step-by-step explanation:

y - 3 = 4(x +2)

y - 3 = 4x + 8

y = 4x + 8 + 3

y = 4x + 11

When x = 0 , y = 11                      (0,11)

When x = 1  ; y = 4 +11 = 15         (1, 15)

When x = 2 ; y = 8 + 11 = 19        (2 , 19

Answer: f = 3x -7 /  x

Step-by-step explanation:

fx=(x−3)(3)+2

Step 1: Divide both sides by x.

fx/x =  3x -7 / x

f = 3x  -7  / x

Answer: f = 3x -7 /  x

» What is the slope of the line passing through the points (-1, – 7) and (-9, - 2)?

— — — — — — — — — —

_______________❦︎_______________

Answer:

Area = 1/2 × base × height

A = 1/2 × 5 × 3,3/5

= 9

The consecutive ages of the siblings mean that each sibling is a year older than the younger sibling

All the options cannot be the sum of their ages

Represent the age of the smallest sibling with x.

So, the sum of their ages is:

[tex]Sum =x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5[/tex]

Evaluate the like terms

[tex]Sum =6x + 15[/tex]

When the sum is 95 (from the options), we have:

[tex]6x + 15 = 95[/tex]

Subtract 15 from both sides

[tex]6x = 80[/tex]

Divide by 6

[tex]x = 13.3[/tex] -- this is not an integer

When the sum is 95 (from the options), we have:

[tex]6x + 15 = 125[/tex]

Subtract 15 from both sides

[tex]6x = 110[/tex]

Divide by 6

[tex]x = 6.875[/tex] -- this is not an integer

When the sum is 167 (from the options), we have:

[tex]6x + 15 = 167[/tex]

Subtract 15 from both sides

[tex]6x = 152[/tex]

Divide by 6

[tex]x = 25.33[/tex] -- this is not an integer

When the sum is 205 (from the options), we have:

[tex]6x + 15 = 205[/tex]

Subtract 15 from both sides

[tex]6x = 190[/tex]

Divide by 6

[tex]x = 31.67[/tex] -- this is not an integer

When the sum is 233 (from the options), we have:

[tex]6x + 15 = 233[/tex]

Subtract 15 from both sides

[tex]6x = 218[/tex]

Divide by 6

[tex]x = 36.33[/tex] -- this is not an integer

Hence, all the options cannot be the sum of their ages

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Answer:

Step-by-step explanation:

Answer:

y = 17

Step-by-step explanation:

11 = y - 6

prove that the value of y is 17

11 = y - 6

proven

Hello.

Let's solve this equation for y.

First, subtract 11 from both sides:

[tex]\mathrm{11-11=y-6-11}[/tex]

[tex]\mathrm{0=y-6-11}[/tex]

[tex]\mathrm{0=y-17}[/tex]

Subtract y from both sides:

[tex]\mathrm{-y=-17}[/tex]

[tex]\Large\boxed{\sf{y=17}}[/tex]

I hope it helps.

Have a nice day.

[tex]\boxed{imperturbability}[/tex]

Answer:

I belive it’s C

Step-by-step explanation:

I don’t know if it’s correct tell me if I’m wrong

By using the image of the polygon and the definition for the parts, we can see that:

a) The vertices are the points where two sides connect, in this case, each letter represents a different vertex, so the vertices of the polygon are A, B, C, D, and E.

b) Adjacent sides are any pair of sides that are connected by a vertex.

For example, DC and CB are connected through vertex C, so these are adjacent sides.

Another pair can be BA and AE.

c) Diagonals are the segments between two non-consecutive vertices.

For example, E and D are consecutive vertices (because there are next to each other). And A and D are non-consecutive vertices.

Then AD is a diagonal. Another example can be EB.

d) The sides of the polygon are the segments between consecutive vertices, in this case, the sides are:

AB, BC, CD, DE, EA.

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Answer:

the first answer is 2/6 and 4/6 both (pick)

Step-by-step explanation:

second is 8/12

third is 9/15

fourth is 16/72

fifth is 2/5,

sixth is 4/10

seventh is 8/18

last one is 2/8

Answer: 1≤x<12

Step-by-step explanation:

The values that are greater than or equal 1 but less than 12 are values ranging from 1 to 11 i.e {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. Note that 1 is included because the number is greater than or equal to 1 (1 included) and less than 12(12 not included).

x≥1 and x< 12

if x≥1, it means 1≤x

combining both inequality

1≤x and x<12

1≤x<12

The interval notation that represent the set S =  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} will be given as S = {x: 1≤x<12}

Answer:

graphing done below.

Step-by-step explanation:

using the formula: y - y₁ = m(x - x₁)

equation:

[tex]\sf y - -5 = \frac{1}{3} (x - - 5)[/tex]

[tex]\sf y +5 = \frac{1}{3} x + \frac{5}{3}[/tex]

[tex]\sf y = \frac{1}{3} x + \frac{5}{3}-5[/tex]

[tex]\sf y = \frac{1}{3} x - \frac{10}{3}[/tex]

Answer:

As Per Provided Information

Given points are (-6,17) & (-6,13).

here

x₁ = -6

x₂ = -6

y₁ = 17

y₂ = 13

We have been asked to find the slope of the line.

Using Formula

[tex] \bf \: m \: = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

m is the slope of line

Put the given value we get

[tex] \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 - ( - 6)}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 + 6}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \dfrac{0}{ - 4} \\ \\ \\ \qquad \sf \longrightarrow \: m = 0[/tex]

Therefore,

Answer:4.8^10 power of 7

Step-by-step explanation:

HCF/GCF 32 and 48

listing factor

32: 1, 2, 4, 8, 16, 32

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

HCF: 16

prime factorization

32: 2 x 2⁴

48: 3 x 2⁴

HCF: 2⁴ = 16

Answer:

Step-by-step explanation:

LCM is least common multiple. It means the least multiple that both 100 and 120 have in common. 600 is the LCM. 20 is the GCF.

Answer:

about 400

Step-by-step explanation:

A .the distribution observation can have two modes

D (last slide) is the graph to the given equation.

As the equation is positive, the line of the graph will give smile shape.

Graph plotted below:

Answer:

T = 1.5

Step-by-step explanation:

If you count all the boxes with T in them there is 6 and if you divide 6 by 9 you get 1.5, 9 divided by 6 = 1.5

Hope this helps!

By finding the number of outcomes that meet each criteria, we will see that the probabilities are:

We know that the fair die has 6 outcomes, so if we roll it twice, there are a total of:

6*6 = 36 outcomes.

To find the probability of getting a given event, we need to find the number of outcomes that make the event true.

A) The sum is greater than 8.

The outcomes that make this true are:

first roll    second roll     sum

 4                   5                 9

 4                   6                 10

5                     5                10

5                    6                 11

6                     3                 9

6                    4                 10

6                     5                11

6                     6                  12

3                     6                   9

So there are 9 outcomes whose sum is greater than 8, so the probability to getting this event is:

P = 9/36 = 0.25

B) The sum is divisible by 5.

The sum must be 5 or 10, the outcomes that give that are:

first roll    second roll     sum

   1                   4                 5

   2                  3                 5

   3                  2                 5

   1                   4                 5

   4                   6                10

  5                    5                10

   6                   4                 10

There are 7 outcomes, so the probability is:

P = 7/36 = 0.194

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Answer:

44 is my answer thank you please ask me questions a little bit easier and not reach the level I am still in jss2 class

Answer:

Step-by-step explanation:

Opposite angles of a rhombus are congruent, so [tex]6x+8=86 \longrightarrow x=13[/tex]

Also, adjacent angles of a rhombus are supplementary, so [tex]86+5z+4=86+7y+3=180 \longrightarrow y=13, z=18[/tex]