You deposit $4300 in an account that earns 2% per year simple interest. The equation that represents this situation is: A(n) = 4300 + (n - 1)(0.02 • 4300) How much will you have in the account at the beginning of the 8th year? Round your answer to the nearest dollar. A. $10,320 B. $4988 C. $4902 D. $4386

Answer:

[tex]a_{n}[/tex] = 100n - 112

Step-by-step explanation:

Given the recursive formula

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 100 with a₁ = - 12

This tells us that any term is found by adding 100 to the previous term

That is common difference d = 100 and a₁ = - 12

The explicit formula for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d , thus

[tex]a_{n}[/tex] = - 12 + 100(n - 1) = - 12 + 100n - 100 = 100n - 112

Answer:

100 = 100n - 112

Step-by-step explanation:

Answer:

Central angle of θ

[tex]\dfrac{A}{\pi r^2} =\dfrac{\theta}{2\pi}[/tex]

[tex]A=\dfrac{\theta r^2}{2}, (\theta$ in radians)[/tex]

Step-by-step explanation:

Suppose a sector of a circle with radius r has a central angle of θ.

Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the central angle of θ to the measure of a full rotation of the circle.

A full rotation of a circle is 2π radians.

This proportion can be written as:  [tex]\dfrac{A}{\pi r^2} =\dfrac{\theta}{2\pi}[/tex]

Multiply both sides by [tex]\pi r^2[/tex]

[tex]\dfrac{A}{\pi r^2} *\pi r^2=\dfrac{\theta}{2\pi}*\pi r^2[/tex]

Simplify to get:

[tex]A=\dfrac{\theta r^2}{2}[/tex]

Where θ is the measure of the central angle of the sector and r is the radius of the circle.

Answer:

Suppose a sector of a circle with radius r has a central angle of θ. Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the CENTRAL ANGLE to the measure of a full rotation of the circle. A full rotation of a circle is 2π radians. This proportion can be written as A/πr^2 =θ2π. Multiply both sides by πr2 and simplify to get A= θ/2 r^2 , where θ is the measure of the central angle of the sector and r is the radius of the circle.

Step-by-step explanation:

i hope this helps a bit

Answer: A rectangle

Step-by-step explanation:

Answer:

Step-by-step explanation:

Zeros mean basically the values of x which make y = 0.

(x + 4)(x - 1) = y

x^2 + 3x - 4 would be a quadratic function whose zeros are -4 and 1

Answer:

I think the correct answer is

A. (-2)

Step-by-step explanation:

This answer seems the most reasonable compared to the others

Hope this helps!

Answer: (-2)

Step-by-step explanation: The international standard symbol for inch is in (see ISO 31-1, Annex A) but traditionally the distance is denoted by a double prime, which is often approximated by double quotes, and the foot by a prime, which is often approximated by an apostrophe. For example, three feet two inches can be written as 3′ 2″. Symbol: in or ″ (the double prime)

HOPE IT HELPS!

Answer:

(3y - 11z)2

Step-by-step explanation:

hahaha hello again

Step-by-step explanation:

(3y - 11z)(3y - 11z)

9y^2: 3y 3y

121z^2: 11z 11z

(3y - 11z)(3y - 11z)

9y^2 - 33yz - 33yz + 121z^2

9y^2 - 66yz + 121z^2

Answer:

You could only draw one triangle because the other side of the triangle can only be one value. This is because when the angle measure between two sides and the length of the sides is given, the length of the other side is fixed. This is also modeled by the SAS principle of congruence.

Answer:

Step-by-step explanation:

You can draw 2 triangles

Answer:

A. 6

E. -4

Step-by-step explanation:

x² - 2x - 24 = 0

x            - 6

x              4

(x - 6)(x + 4) = 0

Set each parenthesis equal to 0:

(x - 6) = 0

Isolate the variable, x. Add 6 to both sides;

x - 6 (+6) = 0 (+6)

x = 0 + 6

x = 6

(x + 4) = 0

Isolate the variable, x. Subtract 4 from both sides:

x + 4 (-4) = 0 (-4)

x = 0 - 4

x = -4

x = -4, 6 are your solutions, or A. &  E.

~

Answer:

[tex] \boxed{A. \: 6 \: \: \: and \: \: \: E. \: -4} [/tex]

Step-by-step explanation:

[tex] = > {x}^{2} - 2x - 24 = 0 \\ \\ = > {x}^{2} - (6 - 4)x - 24 = 0 \\ \\ = > {x}^{2} - 6x + 4x - 24 = 0 \\ \\ = > x(x - 6) + 4(x - 6) = 0 \\ \\ = > (x - 6)(x + 4) = 0 \\ \\ = > x - 6 = 0 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: x + 4 = 0 \\ \\ = > x = 6 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: x = - 4[/tex]

Answer:

Ah! Thank you for a little challenge!

Step-by-step explanation:

To do this, we need to first find our new lengths!

Height= [tex]50+x[/tex]

Radius= [tex]20+x[/tex]

Now, to find the Volume!

Using the volume formula for a cylinder(v=pi*r^2*h)

[tex]v=\pi(20+x)^{2} (50+x)[/tex]

So, we have our equation! let's solve!

[tex]V=\pi*(x^{2}+40x+400)(50+x)\\V=\pi(x^{3} +90x^{2}+2400x+20000)[/tex]

Now, I'm guessing you had trouble with it because it looked really scary.

So what I did in the first step was expand (20+x)^2, and I used the special formula(forgot what else it was called, (a+b)^2=a^2+2ab+b^2)

Next, I multiplied the expand form of that with (50+x), and the way to do that is by multiplying each term in the parentheses with every term in the next parentheses(distributive property).

So, uh, that's it! Not very scary, just a bit of in-head math!

Hope this helps! If you want to learn more or need more help, check out Khan Academy for the "squares of binomials" or "polynomials"

Answer: m∠3 = 30° and  m∠8=  150°  .

Step-by-step explanation:

From the given figure it can be seen that a and b are two parallel lines, where t is transversal intersecting them.

Also, m∠3=x,  m∠8=5x

To find : m∠3, m∠8

Since ∠3=∠5 [Interior alternate angles]

So, m∠5 =m∠3= x

Also, ∠5+∠8=180°  [Linear pair]

⇒ x + 5x = 180°   [Substituted the value of ∠5 and ∠8 in terms of x ]

⇒ 6x = 180°

⇒ x = 30° [Divide both sides by 6]

That means,

m∠3 = 30°

and m∠8= 5(30° ) = 150°

Hence, m∠3 = 30° and  m∠8=  150°  .

Answer:

490.1

Step-by-step explanation:

A=2πrh+2πr2=2·π·6·7+2·π·62≈490.08845

Answer:

See explaination

Step-by-step explanation:

All these questions can be solved remembering that the area of a triangle is the base*height/2

1) 9.8*3.6/2 = 17.64

2) 14*35/2  = 245

3) 8.4*6.9/2 = 28.98

4) For this one, it is important to realize that if a triangle contains 2 perpendicular lines, it is a right triangle, and therefore, those two lines must be the base and the height. So the answer is just 1.8*2.5/2 = 2.25

5)3.2*9.6/2 = 15.36

Answer:

first is 17.64cm second is 245m third is 28.98cm fourth is 15.36

Answer:

D) 330°, 5π/3 , 7π/6 , 2π/3 , π/2

Step-by-step explanation:

Lets clear the question first. We have been given 4 options:

A) π/2 , 330°, 5π/3, 7π/6, 2π/3

B) 5π/3, 7π/6 , 2π/3 , π/2 , 330°

C) π/2, 2π/3 , 7π/6, 5π/3, 330°

D) 330°, 5π/3 , 7π/6 , 2π/3 , π/2

Lets convert all the values into degrees

330° = 330°

π/2 = 180/2 = 90°

5π/3 = 300°

7π/6 = 210°

2π/3 = 120°

Arrange them from greatest to lowest.

330° , 300° , 210° , 120° , 90°

or

330° , 5π/3 , 7π/6 , 2π/3 , π/2

which is option D

Answer:

66 necklaces

Step-by-step explanation:

First determine how many beads Ava has

40 * 100 = 4000

Then divide by the number of beads per necklace

4000/60 =66.66666

Round down for complete necklaces

66 necklaces

Answer:

It is d

Step-by-step explanation:

I did the test

Answer:

You sold 3 of your $19 paintings

Step-by-step explanation:

19x + 29 = 86

19x + 29 - 29 = 86 - 29

19x = 57

19x / 19 = 57 / 19

x = 3

Answer:

Year = 1995 and population = 315

Year = 2015 and population = 715

Step-by-step explanation:

It is given that the population of two different villages is modeled by the given equations:

[tex]y=x^2-30x+540[/tex]

[tex]y=20x+15[/tex]

The population of both villages are same after x years after 1980 if

[tex]x^2-30x+540=20x+15[/tex]

[tex]x^2-30x+540-20x-15=0[/tex]

[tex]x^2-50x+525=0[/tex]

Splitting the middle term, we get

[tex]x^2-15x-35x+525=0[/tex]

[tex]x(x-15)-35(x-15)=0[/tex]

[tex](x-15)(x-35)=0[/tex]

[tex]x=15,35[/tex]

It means, after 15 or 35 years, the population will same.

For x=15, years is [tex]1980+15=1995[/tex] and population is  

[tex]y=20(15)+15=315[/tex]

For x=35, years is [tex]1980+35=2015[/tex] and population is  

[tex]y=20(35)+15=715[/tex].

Therefore, population are equation in Year = 1995 and population = 315 or Year = 2015 and population = 715.

Year = 1995 and population = 315

Year = 2015 and population = 715

The equation is

[tex]y = x^2 - 30x + 540\\\\y = 20x + 15[/tex]

Now

[tex]x^2 - 30x + 540 = 20x + 15\\x^2 - 30x + 540 - 20x - 15=0\\\\x^2 - 50x + 525 = 0\\\\x^2 - 35x - 15x + 525=0\\\\x(x - 15) -35(x-15) = 0\\\\(x-15) (x-35) = 0[/tex]

x = 15,35

so,

When x is 15 , the population is = 20(15 )  +15 = 300 + 15 = 315

And, x is 35 , the population is = 20(35 )  +15 = 700 + 15 = 715

Learn more about the population here: https://brainly.com/question/905400?referrer=searchResults

Answer:

d

Step-by-step explanation:

An Irrational Number is a real number that cannot be written as a simple fraction.

one of the examples is [tex]\pi[/tex]

Answer:

1318.8 meters

Step-by-step explanation:

Answer:

1.33 or 133/100

Step-by-step explanation:

formula=area of base x height x 1/3

A=2 x 2 x 1/3 or

A=2 x 2 / 3

A=4 / 3

A=1.33 or 133/100

Answer:

The answer is 4/3 ft^3

Step-by-step explanation:

The formula to find a pyramid is length times width times height divided by 3

Answer:

- 27

Step-by-step explanation:

To find the 8 th term substitute n = 8 into the formula, that is

a₈ = 45 - 9(8) = 45 - 72 = - 27

Answer:

x=19/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(x+5)=2(3x−2)

3x+15=6x+−4

3x+15=6x−4

Step 2: Subtract 6x from both sides.

3x+15−6x=6x−4−6x

−3x+15=−4

Step 3: Subtract 15 from both sides.

−3x+15−15=−4−15

−3x=−19

Step 4: Divide both sides by -3.

−3x

−3

=−19−3

x=19/3

Angle a = 1/2 of the given central angle.

Angle a = 130/2= 65

The answer is 65

Answer:

$0.17

Step-by-step explanation:

2.04/12=0.17

Please mark as Brainliest! :)

Have a nice day.

Answer: 0.17 for 1 pencil

Step-by-step explanation:

Attached the work.

Answer:

52

Step-by-step explanation:

Answer:

x= 12

Step-by-step explanation:

Please see attached picture for full solution.

Feel free to ask if you have any queries :)

Answer:

I18 - xI such that x < 18.

ok, first let's what happens if x = 18:

I18 - xI = I18 - 18I = 0

So, at the moment we have the condition:

I18 - xI > 0.

now, if x is a really large negative number, suppose, x = -100

I18 + 100I = I118I = 118

So, as x can freely move in the negative range, we can see that I18 - xI can be any positive number, so the only restriction that we have is:

I18 - xI > 0.

This means that the domain is:

D = (-∞, 18)

and the range is:

R = (0, ∞)

Answer:

The correct option is;

BC = 4 cm and DE = 4 cm

Step-by-step explanation:

The given sides parameters are;

In ΔABC

AB = 3 cm

AC = 5 cm

In ΔDEF

CD = 3 cm

CE = 5 cm

We note that the point F on ΔDEF is the same as point C on ΔABC

For the two triangles to be congruent, the third side must be equal hence e have;

Where ∠B = ∠D = 90°

Hence, AC² = AB² + BC²

∴ BC = √(5² - 3²) = 4

Similarly,

CE² = CD² + DE²

∴ DE = √(5² - 3²) = 4

Hence the additional information needed to prove that ΔABC ≅ ΔDEF is BC = 4 cm and DE = 4 cm.

Answer:

B.

Step-by-step explanation:

Using Pythagoras theorem

c² = a²+b²

Where c = hypotenuse, a = base and b = perpendicular

So putting the givens

c² = (2√5)² + (6)²

c² = 20+36

c² = 56

Taking square root on both sides, we get

c = √2×2×14

c = 2√14