An initial deposit of $1,000 is made into a savings account that is compounded continuously at 3% interest. How much money will be in the account after 18 years?

Answer:

1. x = 5

Step-by-step explanation:

1.

The Trapezoid Midsegment Theorem states that a line segment connecting the midpoints of the legs of the trapezoid is parallel to the bases, and equal to half their sum.

In this problem you can see that 5x - 1 is the midsegment of the trapezoid, so using the rule:

[tex](21 + 27) / 2 = 5x -1[/tex]

solve:

[tex]48/2 = 5x-1\\24 = 5x - 1\\25 = 5x\\x= 5[/tex]

2. Diagonals are congruent

You can see in this picture that the diagonals are not always congruent:

Answer:

Required equations:

Solve by substitution x = 8 - y

Find x:

Answer: 5 adults and 3 students

Equations:

Solve by elimination, subtract the equations:

Find x:

Answer: Gloves cost $8.5, hats cost $6.5

Answer:

Your answer will be 2278 hope this helps

Step-by-step explanation:

if u need the steps just ask me

Answer:

1) They forgot to multiply 2 times (2x+5)

2) x-2 is not equal to -(x+2).

3) The correct expression is [tex]x-1-1+2x=1-3x[/tex]

4) The correct way is [tex]4(2x+3)=3(1-3x)[/tex]

Step-by-step explanation:

1) In this case they forgot to multiply 2 times (2x+5). Let's recall we need to multiply (2x+5) to all terms of the equation.

2) Here, x-2 is not equal to -(x+2). If we see -(x+2) = -x-2 using the distributive property.

3) After multiplying by (3x-2) we will have:

[tex]x-1-(1-2x)=1-3x[/tex]

Apply the distributive property again, we will have:

[tex]x-1-1+2x=1-3x[/tex]

So the correct term is 2x not -2x.

4) When we multiply by (1-3x)(2x+3) on each side of the equation, we will have something like this:

[tex]\frac{4(1-3x)(2x+3)}{(1-3x)}=\frac{3(1-3x)(2x+3)}{(2x+3)}[/tex]

If we see we can simplify the same terms on each side of the equation.

[tex]4(2x+3)=3(1-3x)[/tex]

This is the correct way to do this.

I hope it helps you!

Answer:

d = 9.84 m

Step-by-step explanation:

The dimensions of an envelope are 9 inches by 4 inches.

We need to find the maximum possible length of the pencil.

Let it be d. It can be calculated using Pythagoras theorem such that,

[tex]d=\sqrt{9^2+4^2} \\\\d=9.84\ m[/tex]

So, the maximum possible length of the pencil is 9.84 m./

Answer:

[tex]\sqrt{29} ,6,2\pi ,3\sqrt{8}[/tex]

Step-by-step explanation:

Hello there!

First lets find the value of each irrational number

[tex]6 = 6\\\\\sqrt{29} =5.385164807\\\\2\pi =6.283185307\\\\3\sqrt{8} =8.485281374[/tex]

now we can easily put them in order from least to greatest

5.3,  6,   6.2,  8.4

then we change it to its irrational form

so the correct order would be

[tex]\sqrt{29} ,6,2\pi ,3\sqrt{8}[/tex]

Answer:

your answer will be Option D

Step-by-step explanation:

hope it helps

Answer:

by poop needs 5 more poin

Answer:

15 ft

Step-by-step explanation:

This is another classic case of Pythagoras theorem. To start with, let's assume that the length of the ladder we're looking for is x

We're told that the height of the building the ladder is leaning on is, x - 3

Also we're told that the distance at an adjacent from the ladder is 9 ft.

If we use Pythagoras theorem, we have

x² = (x - 3)² + 9²

x² = x² - 6x + 9 + 81

On rearranging, we have

x² - x² = -6x + 90

6x = 90

x = 90 / 6

x = 15 ft

Therefore, the length of the ladder is found to be 15 ft

Answer:

p=25 degrees

Step-by-step explanation:

70 and 20+2p are verticle angles, so they are equal

70=20+2p

-20-20

50=2p

/2   /2

25=p

Answer:

p = 25 degrees

Step-by-step explanation:

2p = 70 - 20

2p = 50

p = 50 / 2

p = 25

Hope that helps!

Answer:

9x/y³

Step-by-step explanation:

The simplification of the expression 9x⁰y⁻³ will be 9/y³.

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

In another word the mathematics of power or exponent of any number is called indices.

As per the given expression,

9x⁰y⁻³

By the law of indices that, [tex]x^{-m}[/tex] = 1/[tex]x^{m}[/tex]

9x⁰y⁻³ = 9x⁰ × 1/y³

⇒ 9(1)/y³ = 9/y³

Hence "The simplification of the expression 9x⁰y⁻³ will be 9/y³".

To learn more about indices,

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Answer:

Refer to explanation^

Step-by-step explanation:

Find out the value of each card.

4 - 10 = 6

-4 + (-10) which is -4 - 10 = -14

-4 + 10 = 6

4 + (-10) which is 4 - 10 = -6

4 - (-10) which is 4 + 10 = 14

-4 - 10 = -14

-4 - (-10) = -4 - 10 = -14

4 + 10 = 14

Find the cards which have the same value and just match them up.

Answer:

x=−0.292355

Step-by-step explanation:

Answer:

$39

Step-by-step explanation:

First we need to find 35% of 60:

0.35 * 60=21

All we have to do after that is subtract 35% of 60 from 60:

60-21=39

And yeah the answer is 39!

I hope this helped! :)

Answer:

D:21

E:126

F:33

Step-by-step explanation:

3x+18x+5x-2=180

26x-2=180

26x=182

x=7

Answer:

A trapezoid

Step-by-step explanation:

Because a trapezoid has only 1 pair of parallel sides

Answer:

the answer will be 56ef i guesss...

The value of given product is 56ef.

Here,

We have to simplify; 7 x e x f x 8.

What is the product?

When we multiply two numbers, the answer is called the Product.

Now,

The expression is,

⇒ 7 x e x f x 8

After product we get;

⇒ 7 x e x f x 8 = 56ef

Hence, The value of given product is 56ef.

Learn more about the product visit:

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Answer:

C=10

Step-by-step explanation:

A^2 + B^2 = C^2

A=6

B=8

C=?

A^2=36

B^2=64

C^2=100

Answer:

Step-by-step explanation:

c=.2, z=1.5(.2), n=1.5(1.5).2

s+c+z+n=1

s+.2+1.5(.2)+1.5(1.5).2=1

s+.2+.3+.45=1

s+.95=1

s=.05

So Sophia ate 5% of the pizza

Answer:

Sophia ate 5%.

Step-by-step explanation:

Caden ate 20%. Zoe ate 50% more than him, so 150% of 20%. That is 20+half of 20, which is 30. So zoe ate 30%. Noah ate 50% more than her, so 150% of 30%, which is 45%. Add them together and get 95%. That leaves 5% for Sophia to eat.

Answer:

Step-by-step explanation:

Answer:

-957

Step-by-step explanation:

... -915, -929, -943, -957, -971, -985, -999 ...

Answer:

Graph B

Step-by-step explanation:

I typed the equation into Desmo and added a negative and that was the result.

Answer:

Step-by-step explanation:

7(8)?

80 c, 80%, 80/100, .80

$1.20, 120%, 120/100, 1.2

$1.60, 160%, 160/100, 1.6

$1.28, 128%, 128/100, 1.28

Answer:

80c to $1.20: up 50% or x 1.5

$1.20 to 80c: down 33 1/3 % or x 0.6 bar over the 6

80c to $1.60: up 100% or x 2

$1.60 to 80c: down 50% or x 0.5

$1.60 to $1.28: down 20% or x 0.8

$1.28 to $1.60: up 25% or x 1.25

$1.28 to $1.20: down 6 1/4 % or x 0.9375

$1.20 to $1.28: up 6 2/3 % or x 1.06 bar over the 6

Answer:

x=2

Step-by-step explanation:

9x - 3 = 6x + 3

    + 3         + 3

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

9x = 6x + 6

-6x  -6x

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

3x = 6

---    ---

3      3

----------

x=2

Answer:

a)

The point that is equidistant to all sides of a triangle is called the incenter.

The incenter is located at the intersection of bisectors of the interior angles of a triangle.

b)

The point that is equidistant to all vertices of a triangle is called the circumcenter.  

The circumcenter is located at the intersection of perpendicular bisectors of the sides of a triangle.

c)

See the attachment

The blue lines and their intersection shows the incenter.

The red lines and their intersection shows the circumcenter.

As we see the red point- the circumcenter is closer to vertex B.

Answer:

Plug in a 3 every time you see an "x" and the left side should equal the right side

Step-by-step explanation:

Answer:

Yes, his mixed number is correct

Step-by-step explanation:    

     6 3/5    

[tex]\\ 5\sqrt{33} \\[/tex]

  -30

      3