Some banks now use continuous compounding of an amount invested. In this case, the equation that models the value of an initial investment of P dollars in t years at an annual
interest rate of r is given by A = Pelt. Using this equation, find the value in 5 years of an investment of $2000 that earns 7% annual interest. (Round your answer to the nearest cent.)

Answer:

P= (5.5, 8)

Q=(8.5,5)

Step-by-step explanation:

Coordinates of L: (2,7)

Coordinates of M: (9,9)

Coordinates of N: (8,1)

Midpoint formula is: [tex]\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]

P is the midpoint of LM, so the coordinates of P will be ((2+9)/2,(7+9)/2)

P's coordinates are (5.5, 8)

Q is the midpoint of MN, so the coordinates of Q will be ((9+8)/2,(9+1)/2)

Q's coordinates are (8.5,5)

Answer:

$64188.26

Step-by-step explanation:

→ Calculate the increase in decimal multiplier

( 100 + 3 ) ÷ 100 = 1.03

→ Multiply this by the salary raised to the power of 16

40000 × ( 1.03 )¹⁶

→ Solve

$64188.26

Answer:

$806275

Step-by-step explanation:

type it exactly like that, ap*x

Answer:

70°

Step-by-step explanation:

90 + 20 + x = 180

110 + x = 180

x = 180 - 110

x = 70°

Answer:

60 degrees

Step-by-step explanation:

The angles are 30 and 90 degrees ( i think it was 30 degrees it wasn't a clear picture. )

A triangle it 180 degrees in total.

SO if we add 30 and 90

30 + 90 = 120

We'll get 120.

We then suptract 120 from 180

180 - 120 = 60

So the degree of x will be 60 degrees.

120 + 60 = 180

Answer:

A The ratio of the areas is the square of the ratio of the side lengths.

Step-by-step explanation:

10  x 3.5 = 35 and would be the same size each

35 x 35 = 1225

Ratio of areas = 10x10 and 10x3.5 x 10 x 3.5 = 100 : 1225 = 4: 49

Therefore just from doing this we can find easily by referring back to ratio above shown.

D IS NOT TRUE This means the ratio of the areas (1225) is the square root of the ratio (sqrt1225=35) of the side lengths (35:35) is not true

sqrt 1225 is 35 and becomes a square root of the area

Where matching this to ratio of sides is not true as 35:35= 1:1 and the ratio to the sides are not the same as ratio of two areas. But when we square we get the answer right.

when we cross multiply (division) we find find the ratio of areas 100:1225 is NOT TRUE AND NOT SAME AS ratio 10:35

We therefore left with DIVIDING THE ratio SIDES AS SIMPLIFIED into the Areas ABOVE to show-

1225/49 = 25 same   here we have the area same ratio as

100/4 = 25 same

10:35 = 3.5^2  + 3.5^2 =12.50 + 12.50 = 25

A IS TRUE. as when we square the ratio 1=3.5 and add them together 1=3.5^2 +3.5^2 we get answer = 25

Answer:

A. The ratio of the areas is the square of the ratio of the side lengths. Is correct.

Hope this helps!

Answer:

85 km

Step-by-step explanation:

[tex]68^{2} +51^{2} =c^{2}[/tex]

4,624+2,601 = [tex]c^{2}[/tex]

7,225 =[tex]c^{2}[/tex]

Square both side and you get your answer 85km

Answer:

[tex]y=-\frac{3}{2}x-15[/tex]

Step-by-step explanation:

The slope intercept form is y=mx+b, where m is the slope and b is the y intercept.

So, all we have to do is make y the subject.

[tex]-3x-2y=30\\-2y=3x+30\\y=\frac{3x+30}{-2} \\y=-\frac{3}{2}x-15\\\\[/tex]

Answer:

y = (3/2)x - 15

Step-by-step explanation:

For it to be in slope intercept form, y has to be the subject of the equation, so it's a simple matter of rearranging the equation.

Original:

-3x - 2y = 30

and we want y to be the subject, so we start moving terms:

-3x = 30 + 2y

-3x - 30 = 2y

now it's just a matter of dividing both sides by 2 to give y as the subject

(-3/2)x - 15 = y

y = (-3/2)x - 15

Answer:

( 1 , -3 ) for every +1 on the x line you go -3 on the y I hope this is what you need

Answer:

27

Step-by-step explanation:

start with {5*(13-8)+12/6}

simplify to get:

(5*5)+12/6

simplify to get:

25+12/6

simplify to get:

25+2

simplify to get your answer:

27

Answer:

3/4

Step-by-step explanation:

you can make it into a fraction just putting it like this 9/12

well 12 - 9 = 3

so we divide by it

9÷3 = 3

12÷3 = 4

lastly you put these as a fraction

3/4

I hope this helps :)

Answer:

$5.38 per pound

Step-by-step explanation:

70/13=5.384615

5.38x13=69.94

Answer:

1

Step-by-step explanation:

Answer: I would see the councilor and see if that can help thats what I did they gave me option and I also could have had a pass to eat with a teacher or I could eat in there office :)

Answer:

i

Step-by-step explanation:

you have to write about the remaining people if they had gas problems and write what happened next maybe he was arrested for the sauce made Thanks

a) The value of  [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]

b) The rate of change of the angle with respect to x is -0.000308rad/m

Find the complete question and diagram attached

Form the right-angled triangle shown:

Adjacent side = x

Opposite side = 250m

angle of elevation  = [tex]\theta[/tex]

Using the SOH CAH TOA identity

[tex]tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}[/tex]

Hence the value of  [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]

b) If x = 450m

[tex]\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\[/tex]

Differentiate both sides with respect to "x"

[tex]sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}[/tex]

Substitute x = 450m and [tex]\theta = 60^0[/tex] into the resulting expression to have:

[tex]\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308[/tex]

Hence the rate of change of the angle with respect to x is -0.000308rad/m

Learn more here: https://brainly.com/question/15580615

Answer:

57+20= 90 (false)

40+39= 79 (true)

Answer:

14 * 9(-9) - 8 = 1142               9 - 45(-3) + 7 = 151

Step-by-step explanation:

14 * 9(-9) - 8 = 1142               9 - 45(-3) + 7 = 151

(This one is true)                  (This one is false)

Answer:

3.4

Step-by-step explanation:

will 3.4 is is rounded of 54256 in decamal

Answer:

No

Step-by-step explanation:

Kenji's kite uses more paper

Answer:

53 in.

Step-by-step explanation:

17 + 24 + 12=53

don't forget the in.

Answer:

-4 and -2✓6+3

Step-by-step explanation:

use pemdas

1(1-8)÷✓1 + 3

-7÷1+3

-4

6(6-8)÷✓6+3

-12÷✓6+3

multiply fraction by ✓6 on bottom and top to get rid of square root on bottom

-12✓6÷6+3

divide -12 by 6 and put radical next to it

-2✓6+3

Answer:

sorry I can't understand the word

(a) 305 (?)

(b) Fields, monroe

(c) Treevale

Answer:

7x3=21

Step-by-step explanation:

7+7+7=21, 7x3=21

Answer: answered

A motorcycle can go 50 miles using one gallon of gas. About how many gallons of gas will be used to go 150 kilometers? (Hint: 1 mile is approximately 1.6 kilometers)

Step-by-step explanation:

Answer:37.5

Step-by-step explanation:

Answer:

104 ft²

Step-by-step explanation:

The area of the rectangle is represented by the following:

8ft x 10 ft = 80 ft

The area of the triangle is represented by the following:

(6ft x 8ft) divided by 2 = 24

By combining the values, you get 104 square feet.

Answer:

Step-by-step explanation:

27 ) 2x² - x - 1 = 0

2x² - 2x +  x  - 1 = 0

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

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

x - 1 = 0  ; 2x + 1 = 0

x = 1   ;     2x = -1

                  x = -1/2

x = 1 ; -1/2

Option b

28) Area of a rectangle = 24 cm²

length * width = 24

(3x +2 )(2x -1) = 24

3x(2x -1) + 2(2x - 1) = 24

3x *2x - 3x *1 + 2*2x - 2*1 = 24

6x² -3x + 4x - 2= 24

6x² + x - 2 -24 = 0

6x² + x - 26 = 0

6x² -12x + 13x - 26 = 0

6x(x - 2) + 13(x - 2) = 0

(x -2)(6x +13) = 0

x = 2      {Ignore 6x + 13 as it gives negative value}

length = 3x + 2 = 3*2 + 2 = 6 + 2 = 8 cm

Width  = 2x - 1 = 2*2 - 1 = 4 - 1 = 3 cm

29) Area of square = 900 cm²

Side² = 900

(5x)² = 900

25x² = 900

x² = 900/25

x² = 36

x = √36 = √6*6

x = 6 cm

30) base = b cm

height = b + 2

Area of triangle =  24 cm²

[tex]\dfrac{1}{2}base*height = 24\\\\\dfrac{1}{2}*b*(b+2) = 24\\[/tex]

b(b + 2) = 24*2

b² + 2b = 48

b² + 2b - 48 = 0

b²  - 6b + 8b  - 48 = 0

b(b - 6) + 8(b - 6) = 0

(b - 6) (b + 8) = 0

b - 6 = 0    {Ignore b +8 = 0 as it gives negative value}

b = 6 cm

height = 6+ 2 = 8 cm

Answer:

though the answers given don't make sense. the best given answer is A. angle 3 should be 113 instead of 103