Ant Farming You have an ant farm with 33 ants. The population of ants in your farm will double
every 3 months. The table shows the population growth of the ants over nine months. Decide whether
the table represents a linear function or a nonlinear function. After one year, how many ants will there
be in the ant farm?
Population of Ants
Number of
0 3 6 9
Months
Population 33 66 132 264
The table represents a __
function.
After one year there will be __ ants in the ant flarm.

Answer:

x = 53

y = 30

Step-by-step explanation:

Step(I):-

Given equations are

x -2y =-7 ...(I)

5x-9y =-5 ..(ii)

The matrix form  AX = B

                    [tex]\left[\begin{array}{ccc}1&-2\\ 5 & -9\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}-7\\-5\\\end{array}\right][/tex]

The determinant

[tex]= \left|\begin{array}{ccc}1&-2\\5&-9\\\end{array}\right| = -9+10 =1[/tex]

By using Cramer's Rule

Δ₁ =      [tex]\left[\begin{array}{ccc}-7&-2\\\\-5&-9\end{array}\right][/tex]



The determinant is     Δ₁ = -9 X -7 - (10 ) = 53

x = Δ₁ / Δ

x = 53

The determinant

Δ₂ =



Δ₂ = -5 +35

     

y = Δ₂/Δ =  30

 x - 2y = -7

5x - 9y = -5​

[tex]D=\left|\, 1\quad-2\atop5\quad-9\right|=1\cdot(-9)-(-2)\cdot5=-9+10=1\\\\\\x=\dfrac{\left|-7\quad-2\atop-5\quad-9\right|}1=-7(-9)-(-2)(-5)=63-10=53\\\\\\y=\dfrac{\left|\, 1\quad-7\atop5\quad-5\right|}1=1\cdot(-5)-(-7)\cdot5=-5+35=30[/tex]

Answer:

(See the attachment)

Step-by-step explanation:

None

cant see the pic

Step-by-step explanation:

Answer:

[tex]y\leq \frac{x}{2}-2[/tex]

Step-by-step explanation:

When dividing/multiplying you flip the inequality sign, and the negative on the x and 2 cancel.

Answer:

-6

Step-by-step explanation:

4−(3+2)2

Add 3 and 2 to get 5.

4−5×2

Multiply 5 and 2 to get 10.

4−10

Subtract 10 from 4 to get −6.

−6

Answer:

Step-by-step explanation:

a). By applying tangent rule in the triangle,

   tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{3}{4}[/tex]

   θ = [tex]\text{tan}^{-1}(\frac{3}{4})[/tex]

   θ = 36.87°

   Therefore, θ < 45°

b). By using cosine rule in this triangle,

   cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{18}{18\sqrt{2}}[/tex]

   cosθ = [tex]\frac{1}{\sqrt{2}}[/tex]

    θ = 45°

c). By using tangent rule,

  tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{8}{2}[/tex]

  θ = [tex]\text{tan}^{-1}(4)[/tex]

  θ = 75.96°

  θ > 45°

Answer:

Please check the explanation.

Step-by-step explanation:

                                           6)

Given the line

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

We know that the slope-intercept form of the line equation is

[tex]y=mx+b[/tex]

where m is the line and b is the y-intercept

Thus, the slope of line = -1/3

We know that parallel lines have the same slope.

Hence, the slope of the parallel line is also m=-1/3

So, substituting m = -1/3 and (3, 1) in the slope-intercept form to find the y-intercept

[tex]y=mx+b[/tex]

[tex]1=\frac{-1}{3}\left(3\right)+b[/tex]

Switch sides

[tex]\frac{-1}{3}\left(3\right)+b=1[/tex]

[tex]-1+b=1[/tex]

[tex]b=2[/tex]

Thus, the equation line in slope-intercept form

[tex]y=mx+b[/tex]

[tex]y=-\frac{1}{3}x+2[/tex]

                                             8)

Given the line

[tex]y=\frac{1}{4}x+1[/tex]

We know that the slope-intercept form of the line equation is

[tex]y=mx+b[/tex]

where m is the line and b is the y-intercept

so the slope of line = 1/4

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be: -4

Thus, subtituting m = -4 and (-1, 4) in the point-slope form

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-4=-4\left(x-\left(-1\right)\right)[/tex]

writing the point-slope form in the slope-intercept form

[tex]y-4=-4\left(x+1\right)[/tex]

add 4 to both sides

[tex]y-4+4=-4\left(x+1\right)+4[/tex]

[tex]y=-4x[/tex]                                

The answer is $10 per adult ticket, and $7 per child ticket. Now lets figure out how to get to that answer. Let's create a chart to help visualize this.

- - - - -A- - - - - C- - - - -T- - - - -

    :     2    :      4     :   $48    :    

    :     5    :        2   :   $64    :                Key:

    :           :             :               :                      A = Adult ( The Y)

    :           :             :               :                      C = Child ( The X)

    :           :             :               :                       T= Total

When we look at it, the total cost is less then what the adult would be when multiplied by 10, and you WOULD have to add the children cost to the adult cost, so lets try it.

Lets do the 2 adult tickets first, 2 x 10 is 20. Now we do 48 - 20 to get how much the cost of the children's 4 needs to equal. We get 28 as the answer. Now we have to do 28 divided by 4, we get 7 as that answer.

Now lets plug that in to the $64 problem and see if that gets us the correct answer.

So the amount of adult tickets for this problem is 5, so we do 5 x 1 which is 50.

Now the amount of children tickets is 2, so lets do 2 x 7, which equals 14.

Now to test if it gets us the correct answer, to do that we do 50 + 14, that equals what we want it to, 64.

Therefor, the correct answer is $10 per adult ticket, and $7 per child ticket.

Hope this helps!

Solution,

y = -x-4......(i)

3x + y =- 16.......(ii)

Now,

Substituting the value of y in equation (ii)

or, 3x + (-x-4)= -16

or,3x - x - 4 = -16

or, 2x= -16 +4

or, x = -12/2

: x = -6

Then,

Substituting the value of x in (i) equation;

or,y= -(-6) - 4

or,y= 6 - 4

: y =2

Answer:

Step-by-step explanation:

150-20/2

Answer:

48

Step-by-step explanation:

If there were 126 students total, and 21 dots. That means that there are 6 students per dot. And since there are 8 dots in the 18 minute mark, that means that there were 48 predicted students.

Step-by-step explanation:

true I think I hope this helps !!!

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-6, 5)

Point (5,  -7)

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Answer:

(9,3)

Step-by-step explanation:

You can just substitute the answer choices in to the equation and see what option works for both equations.

Answer:a

Step-by-step explanation:

Answer is D

the reason it's because you only changed the Y intercept number to a negative so it will shift down the graph 14 units because if you have no adding number then your graph will start at 0 but it's -7 so it starts at -7 so now shift 14 places down

Answer:

Please show the graph, and i will be able to answer it for you.

Step-by-step explanation:

Answer:

nothing

Step-by-step explanation:

there was no mistake at all he did it all correct he subtract 11 from both sides the divided by 2 correctly.

Answer:

2,-1,-2,-1

Step-by-step explanation:

You just replace x with the given numbers

Answer:

12

Step-by-step explanation:

4          6

8         12

12

Answer:

Answer:

12

Step-by-step explanation:

4 6

8 12

12

Ask pelzerzion about this question...

Answer: $38.50

Step-by-step explanation: Find 70% of $55.

Answer:

38.5

Step-by-step explanation:

SO U FIND 10% WHICH IS =5.5

THEN U TIMES IS BY 3 AND ITS =16.5

THEN YOU MINUS 55 BY 16.5

AND THAT IS =38.5

Answer: 48 feet

In order to get the answer you have to plug 12 into the equation you made in part a.

Firstly, let's check your answer to part A.

We know that there is no y-intercept because the line crosses the origin (0,0).

Let's use the slope formula to find the slope:

[tex]\frac{y2 - y1}{x2 - x1} = \frac{20 - 0}{5-0} = \frac{20}{5} = 4[/tex]

So, the slope is actually 4x.

Now, we go on to answer part b.

y = 4x

Plug in the 12

y = 4(12)

y = 48

Therefore Kelvin will have walked 48 feet after 12 seconds.

I hope this helps!!

- Kay :)

Answer:

0.29

Step-by-step explanation:

12 divide by $3.48 is 0.29

Answer:

x=1

Step-by-step explanation:

_3× +1=2(4×_5)

_3×+1=8×_10

-3×_8×=_10-1

11×=_11

=1