If $8000 is invested in an account for which interest is compounded continuously, find the amount of the investment at the end of 12 years for the following
interest rates.
(a) 2%
(b) 3%
(c) 4.5%
(d) 7%

Answer:

I think B

Step-by-step explanation:

Uhh

Answer:

Step-by-step explanation:

y = ax² + bx + c

a( - 7)² + b( - 7) + c = 134 ⇔ 49a - 7b + c = 134 ......... (1)

a( - 3)² + b( - 3) + c = 10 ⇔ 9a - 3b + c = 10 ......... (2)

a(5)² + b(5) + c = 50 ⇔ 25a + 5b + c = 50 ......... (3)

(1) - (2)

40a - 4b = 124 ⇔ 10a - b = 31 ........... (4)

(3) - (2)

16a + 8b = 40 ⇔ 2a + b = 5 ........... (5)

(4) + (5)

12a = 36 ⇒ a = 3

2(3) + b = 5 ⇒ b = - 1

9(3) - 3( - 1) + c = 10 ⇒ c = - 20

y = 3x² - x - 20

y = [ 3 ] x² + [ - 1 ] x + [ - 20 ]

Answer:

I would start by adding/subracting the values in the numerator. by doing this you will get [tex]\frac{2}{4-2+3}[/tex] . Then do the same thing on the bottom to get [tex]\frac{2}{-1}[/tex] or -2

Answer:

I would start by adding/subracting the values in the numerator. by doing this you will get \frac{2}{4-2+3}

4−2+3

2

. Then do the same thing on the bottom to get \frac{2}{-1}

−1

2

or -2

Answer:

0.0048cm/s

Step-by-step explanation:

Volume of the spherical balloon is expressed as;

[tex]V = 4/3 \pi r^3\\[/tex]

dV/dt = dV/dr * dr/dt

Given

dV/dt = 5cm³/s

dV/dr = 4πr²

Since V = 972picm³

972π = 4/3πr³

972 = 4/3r³

4r³ = 972 * 3

r³ = (972 *3)/4

r³ = 729

r = ∛729

r = 9cm

dV/dr = 4π(9)²

dV/dr = 324π

dV/dt = dV/dr * dr/dt

5 = 324πdr/dt

dr/dt = 5/324π

dr/dt = 5/324(3.14)

dr/dt = 5/1017.36

dr/dt = 0.0048cm/s

Answer: the triangles are congruent because

Step-by-step explanation: if you put them over lapping and switch the triangles then it would be the same. but you cant use this in your B answer.

Answer:

i cant read it sorry

Step-by-step explanation:

Answer:

T= y+ 3y-7  

Step-by-step explanation

I'm pretty sure you can also write T= 4y-7 as a simplified form of the equation

The formula for T in terms of y can be written as;

T= y+ 3y -7  

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that Dawn is y years old.

So, Rashid is three times as old as Dawn means R = 3y

Hugo is seven years younger than Dawn means H = y - 7

The total of Dawn's age, Rashid's age and Hugo's age is T years.

We can also write T= 4y-7 as a simplified form of the equation

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ2

Answer:

|x+5|=-16/-4

|x+5|=4

x=4-5

x=-1

Answer:

Step-by-step explanation:

-4(x + 5)=-16

-4 x x - 4 x 5=-16

-4x - 20=-16

-4x - 20 + 20=-16+20

-4x=4

-4x/-4=4/-4

x=-1

Answer:

[tex]\boxed {\boxed {\sf 53}}[/tex]

Step-by-step explanation:

This is a right triangle, which we know because of the little square in the corner.

We can use the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse.

In this triangle, 28 and 45 are the legs, because they make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle.

[tex]a=28 \\b=45 \\[/tex]

[tex](28)^2+(45)^2=c^2[/tex]

Solve the exponents.

[tex]784+(45)^2=c^2[/tex]

[tex]784+2025=c^2[/tex]

Add the two numbers.

[tex]2809=c^2[/tex]

Solve for c by isolating it on one side of the equation. c is being squared. The Inverse of a square is the square root. Take the square root of both sides of the equation.

[tex]\sqrt{2809} =\sqrt{c^2}[/tex]

[tex]\sqrt{2809} = c[/tex]

[tex]53=c[/tex]

The third side and hypotenuse of the triangle is 53

[tex]\pink{\sf Third \: side \: of \: the \: triangle = 53}[/tex]

As, the given triangle is a right angled triangle,

Hence, We can use the Pythagoras' Theorem,

[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]

Here,

In given triangle,

Now, by Pythagoras' theorem,

[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]

[tex] \sf : \implies H^{2} = (45)^{2} + (28)^{2}[/tex]

[tex] \sf : \implies H^{2} = 45 \times 45 + 28 \times 28[/tex]

[tex] \sf : \implies H^{2} = 2025 + 784[/tex]

[tex] \sf : \implies H^{2} = 2809[/tex]

By squaring both sides :

[tex] \sf \sqrt{H^{2}} = \sqrt{2809}[/tex]

[tex] \sf : \implies H^{2} = \sqrt{2809}[/tex]

[tex] \sf : \implies H^{2} = \sqrt{(53)^{2}}[/tex]

[tex] \sf : \implies H^{2} = 53 [/tex]

[tex]\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 53}[/tex]

━━━━━━━━━━━━━━━━━━━━━

Answer and Step-by-step explanation:

1. 3(5x - 4) = 8x + 2

15x - 12 = 8x + 2

15x - 8x = 2 + 12

7x = 14

x = 2

2. 9(n + 3) = 7n - 3

9n + 27 = 7n - 3

9n – 7n = -3 – 27

2n = – 30

n = –15

3. 2(10 - 6x) = x - 8x

20 - 12x = -7x

20 = -7x + 12x

20 = 5x

x = 4

4. 5a + 4(3a - 8) = 4 + 13a

5a + 12a - 32 = 4 + 13a

17a - 32 = 4 + 13a

17a - 13a = 4 + 32

4a = 36

a = 9

5. 2y + 18 = 12 - 6(y + 7)

2y + 18 = 12 - 6y - 42

2y + 6y = 12 - 42 - 18

8y = -48

y = -6

6. x - (5 - 3x) = 7x + 4

x - 5 + 3x = 7x + 4

4x - 7x= 4 + 5

-3x = 9

x = -3

7. 8(m - 5) = 2(3m - 8)

8m - 40 = 6m - 16

8m - 6m = -16 + 40

2m = 24

m = 12

8. -4(3 - 6d) = 9(2d - 2)

-12 + 24d = 18d - 18

24d - 18d = -18 + 12

6d = -6

d = -1

9. 7(10 - 3w) = 5(15 - 4w)

70 - 21w = 75 - 20w

-21w + 20w = 75 - 70

-w = 5

w = -5

10. 6t + 3(5t - 4) = 12(2t - 5)

6t + 15t - 12 = 24t - 60

21t - 24t = -60 + 12

- 3t = -48

t = 16

11. 2(9x - 1) = 99 - 7(3 - 4x)

18x - 2 = 99 - 21 + 28x

18x - 28x = 99 - 21+2

-10x = 80

x = -8

12. 6(5k - 8) - 20 = 11(2k - 3) + 3k

30k - 48 - 20 = 22k - 33 + 3k

30k - 68 = 25k - 33

30 - 25k = -33 + 68

5k = 35

k = 7

13. - x - (13 + 4x) = -3(5 - 9x) + 2

-x -13 - 4x = -15 + 27x + 2

-5x - 13 = -13 + 27x

-13 + 13 = 27x + 5x

0 = 32x

x = 0

Given:

Equation of line is [tex]y=\dfrac{1}{4}x-7[/tex].

The perpendicular line passes through (-2,-6).

To find:

The point slope form of perpendicular line.

Solution:

We have,

[tex]y=\dfrac{1}{4}x-7[/tex]

On comparing this equation with [tex]y=mx+b[/tex], we get

[tex]m=\dfrac{1}{4}[/tex]

Slope of given line is [tex]\dfrac{1}{4}[/tex].

Product of slopes of two perpendicular of the lines is -1.

So, [tex]Slope\times \dfrac{1}{4}=-1[/tex]

[tex]Slope=-4[/tex]

Slope of required line is -4 and it passes through (-2,-6). So, the point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

where, m is slope.

[tex]y-(-6)=-4(x-(-2))[/tex]

[tex]y+6=-4(x+2)[/tex]

Therefore, the correct option is A.

Answer:

B

Step-by-step explanation:

1 4/5

Answer:

KJ = 40

Step-by-step explanation:

Usinh the similarity factor, LJ is similar with PR and QR is similar to KJ

and the similarity ratio is 56/42 = 4/3

which means KJ/30 = 4/3 cross multiply expressions

KJ = 40

Answer:

7/ 15

Step-by-step explanation:

2/ 5 × 7/ 6

reduce the numbers

1/ 5 × 7/ 3

multiply

= 7/ 15

hope it helps!

Answer:

9 a) degree is 4 and variable is 0 and co efficient is z

b) degree is 5 and the constant term is 7

Answer:

x=26°

Step-by-step explanation:

3x-14+x+90=180

4x-14=90

4x=104

x=104/4

x=26°

Answer:

Step-by-step explanation:CAN I HAVE YOURE POINTS AND ITS THE SECOND ONE

Answer:

∠ 2 = 75°

Step-by-step explanation:

∠ 6 and ∠ 2 are corresponding angles and are congruent, thus

∠ 2 = ∠ 6 = 75°

Answer:

5

Step-by-step explanation:

because thats the answer

Answer:

P'(0,0), E' (3,3), N'(6,3), T'(6,-3), A'(3,-3)

Step-by-step explanation:

1.The dilation is by a scale factor of 3/4 meaning it's less than one, meaning the image will get smaller.

2.To find the new coordinates, multiply 3/4 by each number in the coordinate pair. For example 4x3/4 is 3 making (4,4) (3,3).

Answer:

hi

Step-by-step explanation:

im adding an answer so u can giveee the guy brailiestz

Answer:

376.8 m²

Step-by-step explanation:

The formula for finding the surface area of a cylinder is SA=2πr²+2πrh, where r is the radius of the base and h is the height of the cylinder. Using the diameter of the base, we can first calculate that the radius of the base is 10/2=5 meters. Then, we can plug our values into the equation.

SA=2πr²+2πrh

SA=2π(5)²+2π(5)(7)

SA=2π(25)+2π(35)

SA=50π+70π

SA=120π

Because the question asks us to use 3.14 for π, we plug that into our equation.

SA=120(3.14)

SA=376.8 m²

I hope this helps!

Step-by-step explanation:

x-5(x+1)=10

x-5x-5=10

-4x-5-10=0

-4x-15=0

-4x=-15

x=-15/-4

x=3.75

sorry...the answer is wrong..dont write

Answer:

no solution

Step-by-step explanation:

Given

- 5 | x + 1 | = 10 ( divide both sides by - 5 )

| x + 1 | = - 2

To have a solution the right side of the equation must be positive or zero

No absolute value can have a negative solution

Thus the equation has no solution

Answer:

Step-by-step explanation:

J is correct.. that function can never be less than 2

Answer: x-3y+21=0

Step-by-step explanation:

move the constant to the left then divide both sides then booom

Answer:

It actually (70, 195)

Step-by-step explanation:

The point that represents the location of the beetle 5 seconds after starting are;  (70, 195).

The pair of parametric equations to model the path of the beetle is;

x(t)= 14t and y(t)= 37t + 10

An animation shows a beetle crawling in a straight line from the point (0, 10) to the point (28, 84) in 2 seconds.

Proving the answer;

At t(0,10), x = 0 and y = 10

Thus;

For X-coordinate;

x(0) = 14(0)

x(0) = 0

Similarly;

For y-coordinate;

y(0) = 37(0) + 10

y(0) = 10

That corresponds with the coordinate t(0, 10).

At t = 2 seconds, we have;

For x-coordinate;

x(2) = 14(2)

x(2) = 28

Similalry, for the y-coordinate;

y(2) = 37(2) + 10

y(2) = 160

Now, At t = 2 seconds, we have;

For x-coordinate;

x(5) = 14(5)

x(5) = 70

Similalry, for the y-coordinate;

y(5) = 37(5) + 10

y(5) = 195

The point that represents the location of the beetle 5 seconds after starting are;  (70, 195).

Read more about Parametric Equations at;

brainly.com/question/10165611

#SPJ5

Answer:

0/-25

Step-by-step explanation:

You use the slope formula the first x value you divided by the second x value and then put that at the numerator which equals 0 and the repeat with the y values and put the difference at the denominator and that equals -25

Answer:

SSS

BC = CB (COMMON)

AB = DC (DATA)

AE+EC = DE + EB

Answer:

192

Step-by-step explanation:

Given

4xyz ← substitute given values into expression

= 4 × - 2 × - 6 × 4 = - 8 × - 24 = 192

Answer:

C = 21.98 in

Step-by-step explanation:

C = πd,

where C is the circumference, π equals 3.14, and d is the diameter.

C = πd

C = (3.14)(7)

C = 21.98 in

Hope this helps!

Answer:

The answer is 189.

Step-by-step explanation:

This geometric sequence is actually just a division of 2 for every term downwards. Therefore, we can see the first term is [tex]48 \cdot 2[/tex] which is 96. Hence, we can work our way down from there:

List:

First term: 96

Second term: 48

Third term: 24

Fourth term: 12

Fifth term: 6

Sixth term: 3

Now, all we have to do is to add all the first 6 terms together to get:

[tex]96 + 48 + 24 + 12 + 6 + 3[/tex]

[tex]= 189[/tex]

The answer is 189.

Hope this helped!