The number of mice living in a field triples each year. What type of function
represents this pattern?

It looks like your equation (it's not an identity) is

2 cos(5x) cos(3x) + sin(x) = cos(8x)

Recall that

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==>   2 cos(x) cos(y) = cos(x + y) + cos(x - y)

so that

2 cos(5x) cos(3x) = cos(8x) + cos(2x)

Then the equation simplifies to

cos(8x) + cos(2x) + sin(x) = cos(8x)

cos(2x) + sin(x) = 0

Also recall that

cos(2x) = 1 - 2 sin²(x)

so the equation is quadratic in sin(x) and can be factorized:

1 - 2 sin²(x) + sin(x) = 0

2 sin²(x) - sin(x) - 1 = 0

(2 sin(x) + 1) (sin(x) - 1) = 0

Solve for x :

2 sin(x) + 1 = 0   or   sin(x) - 1 = 0

sin(x) = -1/2   or   sin(x) = 1

[x = arcsin(-1/2) + 2nπ   or   x = π - arcsin(-1/2) + 2nπ]   or   x = arcsin(1) + 2nπ

(where n is any integer)

x = -π/6 + 2nπ   or   x = -5π/6 + 2nπ   or   x = π/2 + 2nπ

Answer:

144 degrees

Step-by-step explanation:

We can use the formula (n-2)(180), where n = number of sides, to find the sum of all the interior angles in the decagon. Since a decagon has 10 sides:

(n-2)(180) = ?

(10-2)(180) = ?

(8)(180) = 1440.

Now, to find one interior angle in the decagon, divide 1440 by the number sides in our polygon (10).

1,440/10 = 144

               = 144 degrees

Answer:

The answer is 2.)

Step-by-step explanation:

Given initial velocity=135 ft/s

& cliff=76 foot

Given quadratic equation

⇒                      (let h=0 it is given)

⇒  

⇒  

⇒    t=8.96≈9 s (the other root is negative)

Hence, rocket will take 9 s to hit the ground after launched.

Answer:  Choice D

0 = 16t^2 + 135t + 76;  9 s

==============================================

Explanation:

The equation we start with is

[tex]h = -16t^2 + vt + c\\\\[/tex]

where v is the starting or initial velocity, and c is the starting height.

We're told that v = 135 and c = 76

We let h = 0 to indicate when the object hits the ground, aka the height is 0 ft.

That means the equation updates to [tex]0 = -16t^2 + 135t + 76\\\\[/tex]

Based on that alone, the answer is between A or D

-------------------

We'll use the quadratic formula to solve for t

We have

So,

[tex]t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-135 \pm \sqrt{135^2 - 4(-16)(76)}}{2(-16)}\\\\t = \frac{-135 \pm \sqrt{23,089}}{-32}\\\\t \approx \frac{-135 \pm 151.9506}{-32}\\\\t \approx \frac{-135 + 151.9506}{-32} \ \text{ or } \ t \approx \frac{-135 - 151.9506}{-32}\\\\t \approx \frac{16.9506}{-32} \ \text{ or } \ t \approx \frac{-286.9506}{-32}\\\\t \approx -0.52971 \ \text{ or } \ t \approx 8.96721\\\\[/tex]

We ignore the negative t value because a negative time duration makes no sense.

The only practical solution here is roughly 8.96721 which rounds to 9.0 or simply 9 when we round to the nearest tenth (one decimal place).

In short, the object will hit the ground at the 9 second mark roughly. Or put another way: the object is in the air for about 9 seconds.

From this, we can see that the final answer is choice D.

Keep in mind that we aren't accounting for any wind resistance. Considering this variable greatly complicates the problem and requires much higher level mathematics. So we just assume that there is no wind at this moment.

Answer:

Don't write the " ^ " that I'm typing, that's just showing its to the power of 2 (squared)

1. x^2 + y^2 = 100

2. (x+1)^2 + (y-8)^2 = 25

3. (x+5)^2 + (y+5)^2 =20

4. x^2 + y^2 = 85

5. x^2 + (y+2)^2 = 40

graph 6) middle of circle (dot) at origin (0,0), 5 out in every direction

graph 7) middle of circle (dot) at (-2, 1), 2 out in every direction

graph 8) middle of circle (dot) at (0, -3), 1 in every direction

graph 9) middle of circle (dot) at (1, 1), 4 in every direction

Step-by-step explanation:

Hope these are right, I just kind of banged them out real quick :)

Answer:

see below

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

36 = s^2

Taking the square root of each side

sqrt(36) = sqrt(s^2)

6 = s

The side length of the pen is 6 ft

To find the perimeter of a square

P = 4s

P = 4*6 = 24

He will need 24 ft of fencing

The two mold populations are equal after 4.5 years and the number of days is 9.2

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the point of intersection to be

(x, y) = (4.5, 3)

The means that the two mold populations are equal after 4.5 years

Given that

A(d) = 100e⁰.²⁵ᵇ

We have

100e⁰.²⁵ᵇ = 1000

Divide by 100

e⁰.²⁵ᵇ = 10

So, we have

0.25d = ln(10)

Evaluate

0.25d = 2.3

Divide

d = 9.2

Hence, the number of days is 9.2

Read more about exponential functions at

https://brainly.com/question/2456547

#SPJ1

Answer:

No

Step-by-step explanation:

The Rectangle A is occupied by 5 unit Squares on its length and 3 unit Squares on its width .....and we know one unit square in a grid is equal to 1 cm

hence.......A=L×W

Area = 5 unit Squares ×3 Unit Squares

Area of A= 15 unit Squares .

The Square B is occupied by 3 unit Square on each side thus.....Area =S×S

Area of B = 3 unit Squares × 3 Unit Squares

Area of B = 9 unit Squares.

Hence the answer is no ....9 isn't the double of 15

Answer:

t3 = 8, t5 = 14

Step-by-step explanation:

t3 = 2 + (3-1) × 3

t3 = 2 + (2) × 3

t3 = 2 + 6

t3 = 8

t5 = 2 + (5-1) × 3

t5 = 2 + (4) × 3

t5 = 2 + 12

t5 = 14

Answer:

(a).5/12

(b).10 players

Step-by-step explanation:

a.

⅓+¼=7/12

Remaining=5/12

b.5/12of 24 =10 players

The statement if two noncollinear rays join at a common endpoint, then an angle is created is a DEFINED TERM.

A defined term is a sentence or expression used to define a concept, statement or confusing words.  

From the question shown,  we can see that a statement was created which is defined  as "If two noncollinear rays join at a common endpoint, then an angle is created". This can be said to be a defined term since there are presence of keywords that made the statement meaningful and easily understandable.

Hence we can conclude that the statement is neither postulate, theorem nor an undefined term rather we can say it is a DEFINED term.

Learn more about definition here: https://brainly.com/question/9823471

The person above is correct defined term :)

Answer:

f(x +1 ) =14

Step-by-step explanation:

12= f(x +1) -2

f(x +1) = 12 +2

f (x+1 ) = 12

Answer:

Multiply 800 by 1.022^7 because 1.022^(n-1)

Step-by-step explanation:

Series and sequences.

Answer:

A).

1) A

2) U

3) S

4) J

5) T

6) M

7) H

8) B

9) Y

10) L

s(-5,-1)

k(-3,1)

f(0,5)

p(5,1)

also the value of L is (-4,4)

E (-2,-3)

N(2,1)

Answer:

We have:

4 red panels

5 yellow panels

1 bankrupt panel

7 blue panels

2 free spin panels

for a total of:

4 + 5 +1 + 7 + 2 = 19 panels.

And we can assume that all the panels are equal, so the probability of landing on every single one is the same.

a) Probability of a spin landing on a red panel.

This will be equal to the quotient between the number of red panels (4) and the total number of panels (19)

P = 4/19 = 0.211

b) Probability of a spin landing on anything but a blue panel

There are 7 blue panels and a total of 19 panels.

then 19 - 7 = 12 panels are not blue.

The probability of not landing on a blue panel will be equal to the quotient between the number of panels that are not blue (12) and the total number of panels (19)

P  = 12/19  = 0.632

c)  Probability of a spin landing on a yellow or red.

There are 4 red and 5 yellow ones, so there are 4 + 5 = 9 panels that are either red or yellow.

The probability is computed in the same way as in the above cases, here we have:

P = 9/19 = 0.473

d)  Probability of a spin landing on any non-color panel.

The non-color panels are:

1 bankrupt panel and 2 free spin panels, for a total of 3 non-color panels.

The probability is computed in the same way as above, so we get:

P = 3/19 = 0.158

Answer:

Vertex= (0,4)

Domain= x: all real number

Range: ( - ∞, 4] or y ≤ 4

OAmalOHopeO

Answer:

50%

Step-by-step explanation:

The question asks who has taken fewer than 19 courses.

So first we look at how many are fewer than 19.

There are 4 that are fewer than 19: 12, 9, 5, 17

So.. 4/8    (8 is the total number of options)

To find the percentage you...

A 45-45-90 triangle follows a unique pattern. It has two congruent sides and one side that = x * sqrt(2).

If AC = 9sqrt(2), then AB is also 9sqrt(2).

To find CB, we need to multiply 9sqrt(2) by sqrt(2).

9sqrt(2) * sqrt(2) = 9 * 2 = 18

CB = 18

Hope this helps!

Answer:

x = 26

Step-by-step explanation:

x and 64 are complementary angles so their sum is 90

x+64 = 90

x = 90-64

x = 26

Answer:

26

Step-by-step explanation:

90-64=26

~~~~~~~~~~

Answer: The marked price is 40% more than the original price

40% - 25% = 15% or 1450

Marked price = 140%

140 × 1450 ÷ 15 = 13533. 33

Step-by-step explanation:

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let l represent the length of the box and let w represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, h, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

Given:

Teresa has $451 in a personal bank account,and then withdraws $10 per week.

Andrew has $10 in a personal bank account,and then deposits $53 each week.

To find:

After how many weeks will they have the same amount of money in the bank.

Solution:

Let x be the number of weeks after which they have the same amount.

Teresa has $451 in a personal bank account,and then withdraws $10 per week. So, the amount in Teresa's account is:

[tex]\text{Teresa's account}=451-10x[/tex]

Andrew has $10 in a personal bank account,and then deposits $53 each week. So, the amount in his account is:

[tex]\text{Andrew's account}=10+53x[/tex]

They have equal amount after x weeks. So,

[tex]451-10x=10+53x[/tex]

Isolate variable terms.

[tex]451-10=10x+53x[/tex]

[tex]441=63x[/tex]

Divide both sides by 63.

[tex]\dfrac{441}{63}=x[/tex]

[tex]7=x[/tex]

Therefore, they will have the same amount of money in the bank after 7 weeks.

Answer:

Step-by-step explanation:

Arc length of the circle is given by,

Arc length = [tex]\frac{\theta}{360^{\circ}}(2\pi r)[/tex]

Area of the sector of a circle = [tex]\frac{\theta}{360^{\circ}}(2\pi r)[/tex]

22). Arc length of the circle having central angle = [tex]\frac{\pi}{3}[/tex]

                                                                                 = 60°

Arc length = [tex]\frac{60^{\circ}}{360^{\circ}}(2\pi )(7)[/tex]

                 = [tex]\frac{14\pi }{6}[/tex]

                 = 7.33 cm

23). Arc length of the circle having central angle = 225°

Arc length = [tex]\frac{225^{\circ}}{360^{\circ}}(2\pi )(10)[/tex]

                 = 12.5π

                 = 39.27 km

24). Central angle = [tex]\frac{5\pi }{4}[/tex]

                              = [tex]\frac{5\times 180^{\circ}}{4}[/tex]

                              = 225°

Area of the sector = [tex]\frac{225^{\circ}}{360^{\circ}}(2\pi )(11)[/tex]

                               = 43.20 yd²

25). Area of the sector = [tex]\frac{270^{\circ}}{360^{\circ}}(2\pi )(14)[/tex]

                                      = 65.97 yd²

Answer:

here's the answer to your question

Answer: √18

√(4-1)^2 + (5-2)^2

√9 + 9

√18

Answered by Gauthmath must click thanks and mark brainliest

Step-by-step explanation: I would first create a factor tree for these numbers and break them down into their prime factorization.

First, 28 is 7 x 4 and 4 is 2 x 2

Next, 35 is 7 x 5

In our factors tree, a 7 is a factor that is shared so we pull out a 7.

Now, we multiply all of our factors that don't pair up

and in this case, that's a 2, another 2, and a 5.

So our LCM is 7 x 2 x 2 x 5 or 140.

140

the lcm of two non-zero integers ×(28) and y(35) ,is the smallest posetive integer m(140) that is divisibleby both ×(28)and y(35) Without any remainder

Answer:

5.53°

Explanation:

Law of sines.

Answer:

[tex] \frac{21}{4} + \frac{35}{8} \\ = \frac{77}{8} \\ = 9 \frac{5}{8} [/tex]

Answer:

4x² - 5x - 8 = 0

Step-by-step explanation:

Standard form of a quadratic: ax² + bx + c

Move all terms to one side and sort them based on the level of degree:

[tex]4x^2-9x-8=-4x\\4x^2-9x+4x-8=0\\4x^2-5x-8=0[/tex]

Answer:

4x^2 -5x-8 =0

Step-by-step explanation:

ax^2 + bx + c = 0 is the standard form

4x^2 -9x-8 =-4x

Add 4x to each side

4x^2 -9x+4x-8 =-4x+4x

4x^2 -5x-8 =0

Answer:

1/6

Step-by-step explanation:

There are 6 faces on a die, and you can only roll one face only. So, the denominator will be 6 because there are 6 faces, and 1 as the numerator because that's the equal proportion for each face (unless you use two dice)

Answer:

09

Step-by-step explanation: