How much would $500 invested at 9% interest compounded annually be
worth after 4 years? Round your answer to the nearest cent.

Work Shown:

(p+2q)/p = 7/5

(p/p)+(2q/p) = 7/5

1 + 2(q/p) = 7/5

2(q/p) = 7/5 - 1

2(q/p) = 7/5 - 5/5

2(q/p) = (7-5)/5

2(q/p) = 2/5

q/p = (2/5)*(1/2)

q/p = (2*1)/(5*2)

q/p = 1/5

Answer:

q/p = 1/5

Step-by-step explanation:

(p+2q)/p = 7/5

Multiply each side by p

(p+2q)/p *p = 7/5*p

(p+2q) = 7p/5

Multiply each side by 5

(p+2q)*5 = 7p/5 *5

5p + 10q = 7p

Subtract 5p from each side

5p + 10q -5p = 7p -5p

10 q = 2p

divide each side by p

10q/p = 2p/p

10 q/p = 2

Divide each side by 10

q/p = 2/10

q/p = 1/5

Answer:

35

Step-by-step explanation:

Make equations, l = w+5 and 2l + 2w = 150

Substitute w+5 into 2l + 2w = 150

Simplify to get 4w + 10 = 150

Subtract 10 from both sides to get 4w = 140

Divide both sides by 4 and you get 35 as width

Answer:

The width of the field is 35 meters.

Step-by-step explanation:

Recall that the perimeter of a rectangle is given by:

[tex]\displaystyle P = 2(w+\ell)[/tex]

Where w is the width and l is the length of the rectangle.

We know that the perimeter is 150 meters. Thus:

[tex]150=2(w+\ell)[/tex]

Divide both sides by two:

[tex]75=w+\ell[/tex]

We are given that the length is five meters longer than the width. So:

[tex]\ell = w+5[/tex]

Substitute:

[tex]75=w+(w+5)[/tex]

Combine like terms:

[tex]75=2w+5[/tex]

Subtract five from both sides:

[tex]70=2w[/tex]

And divide both sides by two. Hence:

[tex]w=35[/tex]

Thus, the width of the rectangular field is 35 meters.

Answer:

4x^4 + 6x^3 + 5x + 4 poly means many ....polynomial

x^2 + 1 ... two parts bi-nomial

ax^2 + bx + c ... three parts tri-nomial

3x^2y^3 ... one part  monomial

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

cuz

Answer:

trure correct

ok must of luck

Step-by-step explanation:

what does P mean ?

I assume it is perimeter ?

what is the perimeter of a square ?

come on, there is practically nothing in math that is easier to solve.

a square has 4 equal sides.

so, to go one time around the whole square, we have to go along every one of its 4 sides (which are all of equal length).

so, when I get the perimeter number, I know this is the result of all 4 sides added together.

and how can we express having 4 times the same number ? exactly how we say it in English : 4 times the number.

therefore

P = 4 × side length

and from there we can immediately deduct

side length = P / 4 = 3/4 in

now we know how long the sides of the square are.

what is the area of the square ?

like for any rectangle the area is length×width. just that length=width, so that we end up with length×length = length².

therefore, the area is

3/4 × 3/4 = (3/4)² = 9/16 in²

this is important : a length is measured e.g. in inches (in). an area is then measured in square-inches = in²

Answer:

1. x=72, y=, 108

2.x=30, y=72

Step-by-step explanation:

Brainliest please~

Answer: 2.54647909 or 2.55

Step-by-step explanation:

radius=C/2π

r=16/2π

r=16/6.2831853071796

r=2.54647909

Answer:

4

Step-by-step explanation:

f(x) = 16x+12

g(x) = 4x+3

f(x) / g(x) =

Factoring f(x) =4(4x+3)

f(x) /g(x) = 4(4x+3) / (4x+3) = 4

Answer:

13 - x

(18 + x) /2

Step-by-step explanation:

Given :

See = 18 sweets

Tony = 18 sweets

See gives Tony x sweets :

See = 18 - x

Tony = 18 + x

See eats 5 of her sweets:

See's sweets becomes :

18 - x - 5 = 13 - x

Tony eats half of his sweets;

Tony's sweets becomes ;

(18 + x) /2

Answer:

Let the cost of banana per dozen be Rs. x.

Amount for which bananas are bought = Rs. 840

No. of dozens of bananas for Rs 840  = 840/x

New cost of banana per dozen = Rs. (x + 1)

New No. of dozens of bananas for Rs 840 = 840/x+1

According to given condition,

840/x – 840 / x + 1 = 2

∴ 840[1/x – 1/x+1] = 2

∴ 840 [x+1- x / x(x+1)] = 2

∴ 840 [1/ (x² + x)] = 2

∴ 840 = 2(x² + x)

∴ 2x2 + 2x – 840 = 0

Dividing by 2, we get

x² + x – 420 = 0

x² – 20x + 21x – 420 = 0

∴  x (x – 20) + 21 (x – 20) = 0

∴  x – 20 = 0 or x + 21 = 0

∴  x = 20 or x = –21

∴  The cost of bananas cannot be negative.

∴  x = 20

The original cost of one dozen banana is Rs. 20

hope it helps you

Step-by-step explanation:

Answer:

-i

Step-by-step explanation:

i =i

i^2=-1

i^3= -i

i^4=1

i^5=1

For the missing Y, replace x in the given equations and solve for y.

y = 2(-1) -1 = -2-1 = -3

y = 2(2)-1 = 4-1 = 3

The missing y values are -3 and 3

Step-by-step explanation:

-6(4v) + -6(9) = 42

-24v - 54 = 42

-24v = 42 + 54

-24v = 96

-v = 96/24

-v = 4

v = -4

Answer:

I think it's -33\24 V

Step-by-step explanation:

bc the equation is -6(4v+9)=42

so you would multiply -6 and 4 to get -24V +9=42

so then you would subtract 9 from both sides to cancel out the 9 and get 33

then take 33 over -24 but that isn't able to be devided so it would stay a fraction

Answer:

In addition, from the response shown, using a graphical calculator brings the following benefits:

1) You can write the system of linear equations as big as you want. This is: systems 3 * 3, 4 * 4, 5 * 5.

2) The response to systems of equations greater than 2 * 2 can be complicated when you graph the solution, therefore, the graphing calculator can be much more efficient in these cases.

3) You can write the linear equations in any way. Resolving by hand you should probably rewrite the system of equations to find the solution.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is much simpler to graph and find the intersection points between the equations, which would be the solutions to the system, than graphing it by hand which would lead to some errors.

Answer:

x is any number

y depends on x value

Answer:

how does exercise improve mood

Answer:

3 3/4 tins of food

Step-by-step explanation:

Number of cats = 3

Quantity of food for each cat per day = 1/4 of a tin

Total tins of cat food sue bought = 4 tins

Has Sue bought enough cat food to feed her cats for 5 days?

Quantity of food 3 cats eat per day = Quantity of food for each cat per day × Number of cats

= 1/4 × 3

= 3/4 of a tin

Total Quantity of food 3 cats eat for 5 days = Quantity of food 3 cats eat per day × 5 days

= 3/4 × 5

= (3 * 5) / 4

= 15/4

= 3 3/4 tins of food

Total Quantity of food 3 cats eat for 5 days = 3 3/4 tins of food

Recall,

Total tins of cat food sue bought = 4 tins

Therefore, Sue bought enough cat food to feed her cats for 5 days

Step-by-step explanation:

x²+3x+x+3+x²+4x+2x+8

2x²+10x+11....then solve quadratically

Answer:

Step-by-step explanation:

Hello!

(x + 1)(x + 3) + (x + 2)(x + 4)

x*x = x²

x*3 = 3x

1*x = x

1*3=3

x*x=x²

x*4 = 4x

2*x= 2x

2*4 = 8

x²+3x+x+3+ x² + 4x+ 2x+  8=

2x² + 10x+ 11

Answer:

Step-by-step explanation:

give four apples to each child because 12/3 is 4

Answer:

91

Step-by-step explanation:

Answer:

125.66

Step-by-step explanation:

Answer:

t = -0.22secs and 0.85secs

Step-by-step explanation:

Given the expression

h = –16t² + vt + c.

If a child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft, then;

v = 10, c = 3

Since we are to let h = 0, then the equation becomes:

0 = –16t² + 10t + 3

Multiply through by a minus sign

16t² - 10t - 3 = 0

Factorize the reulting expression:

t = -(-10)±√(-10)²-4(16)(-3)/2(16)

t = 10±√100+192/32

t = 10±√292/32

t = 10±17.09/32

t = 10-17.09/32 and 10+17.09/32

t = -7.09/32 and 27.09/32

t = -0.22secs and 0.85secs

Answer:

0.8 s

Step-by-step explanation:

I got it right in grandpoint.

Answer:

105

Step-by-step explanation:

Because the lines are parallel, we know that those angles have to add up to 180. so we just do

x+75=180

or 180-75=105

x+75°=180°

x=180°-75°

x=105°

or

180°-75° = 105°

please mark this answer as brainlist

Answer:

how?

Step-by-step explanation:

i didnt get this question

Answer:

(8,-22)

Step-by-step explanation:

I took the quiz and did my work on paper but the paper got wet and I don't remember the steps I did

Recall the triple angle identity for cosine:

cos(3x) = cos³(x) - 3 sin²(x) cos(x)

… = cos³(x) - 3 (1 - cos²(x)) cos(x)

… = 4 cos³(x) - 3 cos(x)

and the definition of secant,

sec(x) = 1/cos(x)

So we have

sec(x) cos(3x) = 0

(4 cos³(x) - 3 cos(x))/cos(x) = 0

cos(x) (4 cos²(x) - 3)/cos(x) = 0

If cos(x) ≠ 0 (this happens at the endpoints of the interval [-π/2, π/2]), we can simplify this to

4 cos²(x) - 3 = 0

cos²(x) = 3/4

cos(x) = ±√3/2

But since -π/2 < x < π/2, we know cos(x) > 0, so we ignore the negative case:

cos(x) = √3/2

==>   x = π/6 and x = -π/6

The solution of the given trigonometric equation by using trigonometric identities is [tex]\frac{\pi }{6} \ and \frac{-\pi }{6}[/tex].

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

[tex]cos(3x) = 4cos^{3}(x) -3cos(x)[/tex]

According to the given question.

We have an equation

[tex]sec(x)cos(3x) = 0[/tex]

Since, the above equation can be written as by using trigonometric identities

[tex]sec(x)cos(3x) = 0\\\implies \frac{1}{cos(x)} (4cos^{3} x-3cos(x))=0[/tex]

Solve the above equation for x.

[tex]\implies 4cos^{2} x -3= 0[/tex]

[tex]\implies 4cos^{2}x = 3\\ \implies cos^{2} x = \frac{3}{4} \\\implies cos x = \sqrt{\frac{3}{4} } \\\implies cos x = \pm\frac{\sqrt{3} }{2}[/tex]

In the given domain [tex][\frac{-\pi }{2}, \frac{\pi }{2} ][/tex] we know that cosx > 0. Therefore, we take only positive part

[tex]\implies cosx = \frac{\sqrt{3} }{2} \\\implies x = cos^{-1} \frac{\sqrt{3} }{2} \\\implies x = \frac{\pi }{6}, and \frac{-\pi }{6}[/tex]

Hence, the solution of the given trigonometric equation by using trigonometric identities is [tex]\frac{\pi }{6} \ and \frac{-\pi }{6}[/tex].

Find out more information about trigonometric identities here:

https://brainly.com/question/12537661

#SPJ2

Step-by-step explanation:

Mark me as the brainliest

Answer:

24°

Step-by-step explanation:

cos ? = 41/45

? = arccos 41/45

? = 24

Answered by GAUTHMATH