Find the area of the polygon.

Answer:

It takes 22.52 years for the balance to triple in value.

Step-by-step explanation:

Continuous compounding:

The amount of money earned using continuous compounding is given by the following equation:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.

Interest rate of 5%.

This means that [tex]r = 0.05[/tex], and thus:

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = A(0)(1+0.05)^t[/tex]

[tex]A(t) = A(0)(1.05)^t[/tex]

Time for the balance to triple?

This is t for which [tex]A(t) = 3A(0)[/tex]. So

[tex]A(t) = A(0)(1.05)^t[/tex]

[tex]3A(0) = A(0)(1.05)^t[/tex]

[tex](1.05)^t = 3[/tex]

[tex]\log{(1.05)^t} = \log{3}[/tex]

[tex]t\log{1.05} = \log{3}[/tex]

[tex]t = \frac{\log{3}}{\log{1.05}}[/tex]

[tex]t =  22.52[/tex]

It takes 22.52 years for the balance to triple in value.

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

Explanation:

A sequence is simply a list of values. There may or may not be a pattern to the list, though usually in a math class your teacher would use a pattern.

A series is where we add partial sums of a certain sequence to form a new sequence. For example, let's say A = {44, 44, 44, ...} is one sequence and we could form a list of partial sums to be B = {44, 88, 132, ...} The 88 is from adding the first two terms of sequence A together. The 132 is from adding the first three terms of sequence A. This process is continued forever.

For a series to be convergent, the terms must approach some finite single value. They likely won't actually reach this value but they should get closer and closer (think of it like an asymptote). When I formed series B shown above, note how the terms keep growing. It turns out they won't stop growing either and that means the series diverges to positive infinity. So we rule out choice B. The same happens for choices A and C as well.

To make sure the series approaches some finite value, the underlying sequence its based on must have the terms approaching 0. Choice D seems to have this happen. The terms of the sequence are getting smaller and smaller. Adding on smaller pieces will produce terms in a series that would likely get us closer to some finite target.

Keep in mind that not all decreasing sequences have a converging series. A famous example would be the harmonic sequence {1, 1/2, 1/3, 1/4, ...} which its series does not converge. The proof of this lengthy so I'll leave it out.

In the case of choice D, it is a geometric sequence with a = 120 as the starting term and r = 0.8 as the common ratio. The series converges to

S = a/(1-r) = 120/(1-0.8) = 600

Answer:

hope this helps

Step-by-step explanation:

Answer: The correct option is B.

Step-by-step explanation:

(x+5)(2x-1)=3(x+5)

Multiply the parentheses

2x^2 - x + 10x - 5 = 3x + 15

Collect like terms

2x^2 + 9x - 5 = 3x + 15

Move the expression to the left hand side and change its sign, then equate it to 0

2x^2 + 9x - 5 - 3x -15 = 0

Collect like terms

2x^2 + 6x - 20 = 0

Divide each term of the equation by 2

x^2 + 3x - 10 = 0

Rewrite the expression in factorized form

x^2 + 5x - 2x - 10 = 0

Factor the expression

x(x + 5) - 2(x + 5) = 0

(x + 5) (x - 2) = 0

Separate into possible cases but when the product of factors equals 0, at least one factor is 0.

x + 5 = 0———equation (1)

x - 2 = 0———-equation (2)

Solve the equations

x + 5 = 0———equation (1)

Make x the subject

x = 0 - 5

x = -5

x - 2 = 0———equation (2)

Make x the subject

x = 0 + 2

x = 2

Hence, the possible values of x are -5 and 2.

Answer:

9 games.

Step-by-step explanation:

You need to find 75% of 12. 75% is equal to three fourths. 12 divided by 4 is 3, so one fourth of 12 is 3. 3 times 3 is 9, so three fourths (75%) of 12 is 9.

Answer:

The statement that best describes the incenter of a triangle is that, it is the point where the three angle bisectors of the triangle intersect. In geometry, an incenter of a triangle is described as the triangle center.

Step-by-step explanation:

follow me

Answer:

D. The point where the three angle bisectors of the triangle intersect

Step-by-step explanation:

Answer:

This system has infinite solutions and it would be much easier to solve it by elimination but substitution it is.

Step-by-step explanation:

-3x+3y=9

-x+y=3

Isolate either x or y in any of the equations. I'll go with the second.

y = 3+x

Now substitute this for y in the first equation.

-3x+3(3+x)=9

Distribute the 3

-3x+9+3x=9

Combine like terms:

9=9

0=0

It's infinite

Answer:

Step-by-step explanation:

Finding solutions in a problem like this requires factoring. That means we need to do whatever we have to to isolate the x term. Of course, we have to do it in order of operations but backwards. Begin by adding 2 to both sides to get

[tex](x+4)^2=9[/tex] Now we have to undo the squaring on the left by taking the square root of both sides:

[tex]\sqrt{(x+4)^2}=[/tex] ±[tex]\sqrt{9}[/tex] Taking the square root of a square cancels out both, and of course the square root of 9 is + or - 3:

x + 4 = ±3

The 2 solutions are

x = -4 + 3 which is -1, and x = -4 - 3 which is -7. Choice (3) is the one you want.

Answer:

7/10

Step-by-step explanation:

Out of the ten spins seven landed on blue.

I hope this helps :)

Answer:

The fraction that would represent the part of Pedro's spins that were blue would be [tex]\frac{7}{10}[/tex].

Step-by-step explanation:

In a fraction, there is a numerator and a denominator. In order to get a fraction that would represent the part of Pedro's spins that were blue, you need to put the number of times the pointer landed on blue as a numerator and the total number of spins as the denominator. Therefore a fraction that would represent the part of Pedro's spins that were blue would be [tex]\frac{7}{10}[/tex].

Answer:

Step-by-step explanation:

12inches/foot , 12x132=1,584 inches

The required triangle is possible, the value of the tangent of ∠I is 1.33.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to estimate the measures of one (or both) of the acute angles.

In a right triangle, the tangent of one of the acute angles is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, we are looking for the tangent of ∠I.

Using the Pythagorean theorem, we can find the length of the third side, HJ, of the right triangle:

HI² = HJ² + IJ²

5² = 4² + 3²

25 = 16 + 9

tan(∠I) = opposite/adjacent = HJ/ JI = 4/3

Rounding to the nearest hundredth, we get:

tan(∠I) ≈ 1.33

Therefore, if the triangle is possible, the value of the tangent of ∠I is 1.33.

Learn more about trig ratios here:

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Answer:

160.

Step-by-step explanation:

The area of the base is 64 since each side is 8, 8x8 is equal to 64. Then you have the lateral faces with a length of 8, and a height of 6, which is 48, but since they are triangles, you divide by 2, finally add 24+24+24+24+64 and your final answer is 160.

Answer:

x = 7 is a solution

x = -2 is an extraneous solution

^ CORRECT ANSWER

Step-by-step explanation:

The rational equation is solved and the solutions are 7 and the extraneous solution is x = -2

A rational equation can be defined as an equation that involves at least one rational expression

A rational function is a function of the form f( x )=P( x ) / Q( x ) ,

f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.

A rational function f ( x )=P( x ) / Q( x )

f( x ) = P( x ) / Q( x ) may have a vertical asymptote

The domain is the set of all real numbers for which Q( x ) ≠ 0

Given data ,

Let the rational equation be represented as A

Now , the value of A is

( 3 / ( x²+5x+6 ) ) + ( ( x-1) / (x+2) ) = 7 / (x+3)   be equation (1)

On simplifying , we get

A rational function is a function of the form f( x )=P( x ) / Q( x ) ,

f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.

So , multiplying both sides by ( x²+5x+6 ) , we get

3 + x² + 2x - 3 = 7x + 14   be equation (2)

On further simplification , we get

x² - 5x - 14 = 0

On factorizing the equation , we get

x² - 7x + 2x - 14 = 0

Taking the common factors , we get

x ( x - 7 ) + 2 ( x - 7 ) = 0

( x + 2 ) ( x - 7 ) = 0

So , the two solutions of x are x = 7 and x = -2

Hence , the solutions of rational equation are x = 7 and x = -2

To learn more about rational equations click :

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Answer:

The surface area is 88ft.

Just to let you know just in case if you have the same question is that the formula of finding the surface area of a rectangular prism is A = 2(wl + hl + hw)

Answer:

The first triangle would be D - Right.

Explanation :

Acute angles can't have a single angle greater or equal to [tex]90^o[/tex]

Equiangular triangles have every single angle equivalent.

Obtuse angles have only angles greater than [tex]90^o[/tex]

Right triangles have 1 right angle (90 degrees)

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

The second triangle would be an obtuse triangle (A)

Here's an example of an obtuse angle :

(As you can see, it doesn't need to have all 3 sides obtuse, just one)

Answer:

104, 52 degrees

Step-by-step explanation:

A whole circle is 360 degrees.

So ark YX = 360-110-146=104

Z=1/2*YX=52

Answer:

3/5

Step-by-step explanation:

sin theta=opposite/hypotenuse

4/5=opposite/hypotenuse

therefore opposite=4 and hypotenuse=5

for adjacent

using pythagoras theorem

a^2+b^2=c^2

opposite^2 + adjacent^2 =hypotenuse^2

4^2 + adjacent^2 =5^2

16 + adjacent^2 =25

adjacent^2 =25-16

adjacent =[tex]\sqrt{9[/tex]

adjacent=3

cos theta=adjacent/hypotenuse

=3/5

therefore the value of cos theta is 3/5

Answer:

60 cups

Step-by-step explanation:

We can use ratios to solve

20 cups            x cups

---------------  = -------------------

4 loaves             12 loaves

20 * 12 = 4 *x

240 = 4x

Divide by 4

240/4 = 4x/4

60 =x

60 cups

Answer:

73 packs

Step-by-step explanation:

Find how many packs she has to buy by dividing 290 by 4, since each pack has 4 yogurts.

290/4

= 72.5

Since we need a whole number answer, round this up:

72.5

= 73

So, Libby will need to buy 73 packs

Solution :

Sales Revenue

Sales                                                                                   $ 2,400,000

Less:

Sales discount                                $ 8,500

Sales returns and allowances       $ 41,000

                                                                                             $ 48,500

Net Sales                                                                              $ 2,350,500

Cost of goods sold                                                               $ 1,085,000

Gross profit                                                                            $ 1,265,500

Operating expense :

Salaries expenses                         $ 675,000

Advertising expenses                    $ 55,000

Depreciation expense                  $ 125,000

Freight expense                             $ 25000

Insurance expense                        $ 15,000

Total operating expenses                                                 $ 895,000

Operating income                                                              $ 370,500

Non operating income

Interest revenue                            $ 30,000

Rent revenue                                  $ 24,000

                                                                                           $ 54,000

Non Operating expenses  :

Interest expense                                                                 $ 70,000

Income before income tax                                                 $ 354,500

Income tax expense                                                            $ 70,000

Net income                                                                            $ 284,500

The A’ is your reflected shape. The red line is y=-1, or your line  right reflection.  To solve, I counted the distance from the red line on the original triangle, and then the same on the opposite side of the red line, and counted the same distance, plotting the points at the final spot.

Answer:

Triangle RSP is similar to triangle ZXY

Step-by-step explanation:

to be similar triangles the order of the angles must match.

Angle R is 41° so is angle Z

angle S is 54° so is angle X

angle P is 85° so is angle Y

Answer: C

Brainliest Me

Answer:

d

Step-by-step explanation:

Answer:

x = -0.2 and x = -3.5

Step-by-step explanation:

Combine like terms in the given equation, by subtracting 2x^2 from both sides:

6x^2 + 15x + 3 = 2x^2

-2x^2                = -2x^2

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

4x^2 + 15x + 3 = 0

This is a quadratic equation.  We'll find the two solutions using the quadratic equation

      -b ± √(b^2 - 4ac)

x = ---------------------------

                  2a

Here the coefficients of the quadratic are a = 4, b = 15 and c = 3.

Thus, the discriminant b^2 - 4ac is 15^2 - 4(4)(3), or +177

and from that we know we'll find two real, unequal roots.

                                -15 ± √177

The roots are:  x = ------------------- , or x = -0.2 and x = -3.5

                                         8

Answer:

a

c

c

a

Step-by-step explanation:

Answer:

(B). between 2.5 and 3.0 and between 4.0 and 4.5.

Step-by-step explanation:

According to the Question,

From the given table it is clear that the value of function are

 x   |  f(x)  |   Sign

2.0 |  2.8  | Positive  

2.5 |  1.1    | Positive

3.0 | –0.8 | Negative

3.5 | –1.2  | Negative

4.0 | –0.3 | Negative

4.5 |  0.7  | Positive

Therefore, the correct option is B.