help would be appreciated

The age of the car that Devon purchased is given by: Option C: 5 years

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

We can use compound interest's formula (with a bit modification if necessary) whenever there is compounding on a base amount on some fixed rate for some time.

For this case, there is decrement happening, so rate can be taken negative. Thus, we take:

R = -35%

Let the car is T years old.

Then, as we have: Initial price of the car = P = $16000, and the final price of the car = A = $2000, thus, we get:

[tex]A = P(1 +\dfrac{R}{100})^T\\\\2000 = 16000(1 + (-35/100) )^T\\1/8 = (1-0.35)^T\\0.125 = 0.65^T\\\\T = log_{0.65}(0.125)\\T \approx 4.827 \approx 5 \text{ (in years) }[/tex]

Thus, the age of the car that Devon purchased is given by: Option C: 5 years

Learn more about compound interest here:

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Answer:

C 5 years

Step-by-step explanation:

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

Explanation:

In the first parenthesis grouping, we have these three terms

[tex]9x^2y[/tex]

[tex]6xy^2[/tex]

[tex]-3xy[/tex]

and we're dividing each of them over the denominator -3xy.

Think of it like the distributive property. In fact, division is a disguised version of multiplication, which is why the distributive property is not a coincidence. Example: 10/2 = 10*(1/2) = 10*0.5 = 5

If we divide each term over -3xy, then we get these three separate results:

[tex](9x^2y) \div (-3xy) = -3x[/tex]

[tex](6xy^2) \div (-3xy) = -2y[/tex]

[tex](-3xy) \div (-3xy) = 1[/tex]

The last equation is probably self explanatory: any number divided by itself is 1, as long as the number isn't zero. Eg: 4/4 = 1.

The first two equations might not be obvious. For the first equation, we divide the coefficients 9 and -3 to get -3 as the final coefficient on the right hand side. Then the variable terms cancel when pairing them up. Check out the diagram below to see what I mean by this canceling.  It's optional, but it might help to think of [tex]x^2[/tex] as [tex]x*x[/tex]

A similar situation happens in the second equation as well.

After doing those three division operations, we then add up the results to arrive at -3x+(-2y)+1 which is the same as -3x-2y+1

Answer:

s^2 = 324 would mean side length s = 18

Step-by-step explanation:

The square root of 324 would be 18.

A square with side length s has an area of 324 square centimeters. So, the side of the square is 18cm

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = [tex]side^2[/tex]

A square with side length s has an area of 324 square centimeters.

The area of a square = [tex]side^2[/tex]

then s = √324

           =18

Thus, the side of the square is 18cm

Learn more about the area;

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Answer:

2 v 13, 2 Square root 13

Step-by-step explanation:

there's 2 right triangles

a)

10^2 = 6^ + a^2

100 - 36 = a^2

64 = a ^2

a = 8

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

now we know the base of the right triangle = 8

and also the base of the left one = 4

8 + 4 = 12

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

now find x

b)

x^2 = 6^2 + 4^2

x^2 = 36 + 16

x^2 = 52

x = (square root) 52

x = 2 v 13     <---- "v = square root"

Instructions :- Simplify the answer if there is square root

hypotenuse² = perpendicular²+base²

First triangle:-

[tex] {h}^{2} = {p}^{2} + {b}^{2} \\ {10}^{2} = {6}^{2} + {b}^{2} \\ 100 = 36 + {b}^{2} \\ 100 - 36 = {b}^{2} \\ 64 = {b}^{2} \\ 8 = b[/tex]

Second triangle

[tex] {h}^{2} = {p}^{2} + {b}^{2} \\ {x}^{2} = {6}^{2} + {4}^{2} \\ {x}^{2} = 36 + 16 \\ {x}^{2} = 52 \\ x = \sqrt{52} = 7.2 \\ x = 7 \: \: approx[/tex]

Answer:  3a - 2b + 3

Step-by-step explanation:

(3a + 2b - 7) - (4b - 10)

open the bracket

3a + 2b - 7 - 4b + 10

combine like terms

3a + 2b - 4b - 7 + 10

3a - 2b + 3

Answer:

Is there supposed to be an attachment? if so please send it so I can answer your question.

Answer:

x = 8

Step-by-step explanation:

Answer:

x = 8

m∠M = 52°

m∠K = 52°

m∠L = 128°

m∠J = 128°

Step-by-step explanation:

If the given shape is a parallelogram, its opposite interior angles are equal.

⇒ m∠M = m∠K

⇒ 7x - 4 = 5x + 12

Subtract 5x from both sides:

⇒ 2x - 4 = 12

Add 4 to both sides:

⇒ 2x = 16

Divide both sides by 2:

⇒ x = 8

Substitute found value of x into the expressions for each angle to find the measures of the angles:

⇒ m∠M = 7(8) - 4 = 52°

⇒ m∠K = 5(8) + 12 = 52°

As the angles on the same side of the transversal in a parallelogram sum to 180°, then

⇒ m∠J + m∠M = 180°

⇒ m∠J = 180° - m∠M

⇒ m∠J = 180° - 52°

⇒ m∠J = 128°

As m∠L = m∠J  then m∠L = 128°

Answer:

I believe the answers are a and e.

Step-by-step explanation:

Let me know if you want an explanation.

Hope this helps!!!

Answer: 107 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 1/2 x 4 1/2

2x1=2 2+1=3

3/2

2x4=8 8+1=9

9/2

3/2 x 9/2=

3x9=45

2x2=4

45/4

Step-by-step explanation:

By definition, pi is equal to c/d, where c is the circumference and d is the diameter.

This means that C = pi(d).

However, since diameter is twice the radius, if we let the radius be r cm, d=2r.

This gives that C=2pi(r).

Answer:

types of waves in physics

Answer:

A

Step-by-step explanation:

the rock lands when it reaches height 0.

so, for what t is h(t) = 0 ?

16t² - 100 = 0

16t² = 100

now we pull the square root on both sides (we can ignore the negative solutions, as negative seconds don't make any sense in our scenario)

4t = 10

t = 10/4 = 5/2 = 2.5 seconds

so, A is correct.

Check the picture below.  When will it reach its height? well, at the vertex, so

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&24\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&50\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+24t+50\implies \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients}[/tex]

[tex]h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+24}t\stackrel{\stackrel{c}{\downarrow }}{+50} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 24}{2(-16)}~~~~ ,~~~~ 50-\cfrac{ (24)^2}{4(-16)}\right)\implies \left( \cfrac{3}{4}~~,~~50-\cfrac{576}{64} \right)[/tex]

[tex]\left(\cfrac{3}{4}~~,~~50+9 \right)\implies \stackrel{\underset{\qquad \downarrow }{\textit{how far up it went}}}{\underset{\stackrel{\uparrow \qquad ~~}{\textit{when it reached it}}}{\left( \cfrac{3}{4}~~,~~59 \right)}}[/tex]

Answer:

42.25π cm²

Step-by-step explanation:

To find the area of the circle, first find its radius.

Formulas needed

Given: circumference= 13π cm

2πr= 13π

Divide both sides by 2π:

[tex]r = \frac{13}{2} [/tex]

r= 6.5 cm

Now, we can find the area by substituting r= 6.5 into the area of circle formula.

Area of circle

= πr²

= π(6.5)²

= 42.25π cm²

Answer:

Step-by-step explanation:

c

so you have to combine like terms so subtract 8 - 4 and the 4 disappears so it be like this

8 - 2x = 4 + x

-4 -2x = -4 + x

4 - 2x = x

next combine the like terms of the 2x so

4 - 2x = x

4 + 2x = +2x

4 = 2x

now you divide 4 by 2 so like this

4 = 2x

2   2

and your answer is x = 2 try to solve the other one if you need help ask me

Answer:

1/5

Step-by-step explanation:

Hope this helps

Answer:

11/5

Step-by-step explanation:

y2-y1/x2-x1

= -3-8/4-9

= -11/-5

= 11/5

Answer:

270 Miles

Step-by-step explanation:

18 miles per gallon

15 gallons

Basically count 18, 15 times

18*15=270

The van can travel 270 miles

Answer;

A=2(W·l+h·l+h·w)

Step-by-step explanation:

multiply all the numbers by eachother  and multiply by 2

· is multiply

For example:

length-12

height-5

width-7

12×5+5×7+7×12=179

179×2=358

With the given budget, the inequality that must be used is:

$5.5*s ≤ $350

We know that the budget is $500.

Then, we know that there is a fixed cost of $150, then the budget left is:

$500 - $150 = $350

With these $350 they pay the food for the students, which costs $5.50 per student.

So the number of students that can go must be such that:

s*$5.50 ≤ $350

There says that the cost in food for the s students must be smaller than or equal to the remaining $350.

So the correct option is the second one.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/18881247

Answer: n = 3

Step-by-step explanation:

divide 3.5n by 3.5n then divide 10.5 by 3.5 which is

n = 3

Answer:

[tex]\boxed{\sf{n=3}}[/tex]

Step-by-step explanation:

To find the value of n, you have to isolate it on one side of the equation.

3.5n=10.5

First, multiply by 10 from both sides.

[tex]\sf{3.5n*10=10.5*10}[/tex]

Solve.

35n=105

Divide by 35 from both sides.

35n/35=105/35

Solve.

105/35=3

n=3

I hope this helps you! Let me know if my answer is wrong or not.

Step-by-step explanation:

what do you mean by "the hard part" ?

anyway,

we need to sum the numbers in every column creating 5 sums.

then we need to multiply these 5 numbers (product) and divide the result by 16 (we need 1/16 of that product).

so, we have

5 + 1 = 6

1 + 6 + 4 + 8 = 19

2 + 1 + 3 = 6

2 + 5 = 7

1 + 0 + 7 = 8

6×19×6×7×8 = 38,304

38,304 / 16 = 2394

that is your code : 2394

Answer:

59

Step-by-step explanation:

VUW is an isoceles triangle, therefore VUW = VWU

tirangles total to 180 so 180 - 62 =118=2VUW

118 ÷2 = 59

Answer:

9

Step-by-step explanation:

5% of 180 = 5/100 x 180

=> 5/10 x 18

=> 90/10

=> 9

Answer:

9

Step-by-step explanation:

5% of 180 = 5/100 of 180

10% = 18 ----->  5% = 9

180 = ?/1000 ------->  180 = 18000 / 100    =  180

5% of 180 = 9

Answer: c=4

Step-by-step explanation:

70-8.76c=34.96

-70             -70

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

-8.76c=-35.04

-35.04/-8.76 = 4

c=4

Answer:

10

Step-by-step explanation:

2(3)+4 = 10

Answer:

x = 10.4

Step-by-step explanation:

This is a supplementary apple which means the angle is equal to 180 degrees. You do 180 - 128 which equals 52. Then you divide 52 by 5 to figure out "x". 52 divided by 5 equals 10.4. So x = 10.4.

To make sure, you can plug in "x" as 10.4. (5 * 10.4) equals 52. 52 + 128 equals 180.

Answer:

52

Step-by-step explanation:

180-128=52

the whole angle is 180