Tavon has a gift card for $65 that loses $3 for each 30-day period it is not used. He has another gift card for $55 that loses $2.50 for each 30-day period it is not
used
a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal value?
a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal.
(Type an equation. Use integers or decimals for any numbers in the equation)

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

Explanation:

Let's assume that n is not negative. If we tried the smallest nonnegative value, n = 0, then we get

The middle result 0 isn't a natural number. The set of natural numbers is {1,2,3,4,...} which is the set of positive whole numbers.

So we can't use n = 0.

Through trial and error, you should find that n = 9 is the next value we can try such that sqrt(n+16) is a natural number, and so is n/3.

If n = 9, then,

We see that the middle result is now larger than 0 and it's a natural number. The same can be said for the last result as well.

The smallest value of n = 9 is that all of the numbers in the set are natural numbers in {30 + n, n/3, √(n+16)}.

Natural numbers are defined as which range from 1 to infinity, are the most fundamental sort of numbers. Commonly known as positive numbers or counting numbers, these numbers. Natural Numbers are represented by the symbol N.

Assume n is not negative for the whole number. Using n = 0, the smallest nonnegative value, we obtain

30 + n = 30 + 0 = 30

n/3 = 0/3 = 0

√(n+16) = √(0+16) = 4

In the middle result, 0, there is no natural number. The set of positive whole numbers starting with {1, 2, 3, 4, ..} is known as the natural numbers.

Therefore, n = 0 is not a possibility.

We have to determine by trial and error that n = 9 is the next possible value we may test such that √(n+16) is a natural number and so is n/3.

If n = 9, then,

30 + n = 30 + 9 = 39

n/3 = 9/3 = 3

√(n+16) = √(9+16) = 5

The middle result, which is now greater than 0, is a natural number, as can be shown. The final outcome also corresponds to this description.

Thus, the smallest value of n = 9 is that all of the numbers in the set are natural numbers.

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Answer:

you can use a protector for finding the angles and a ruler finding the length of the lines

Answer:

CDO=26cm

AOD=32cm

Step-by-step explanation:

Answer:

862.50

Step-by-step explanation:

First find the amount of increase

750 * 15%

750 *.15

112.50

Add this to the original amount

750+112.50

862.50

Answer:

87

Step-by-step explanation:

number of sausage buns = s

number of custard buns = c

at the start of the day, s = c

at the end of the day

c+27=6(s-68)

since c = s,

s+27=6(s-68)

s+27=6s-408

-5s = -435

s=87

Let us represent:

The number of sausages baked at first =  s

The number of custard buns baked at first =  c

       s - 68

        c + 27

Hence:

c + 27 = 6 (s - 68)

c + 27 = 6s - 408

        c = s

Hence,

c + 27 = 6s - 408

s + 27 = 6s - 408

Collect like terms

408 + 27 = 6s - s

435 = 5s

Divide both sides by 5

435/5 = 5s/5

s = 87

Therefore, the number of sausage buns Sam baked at first is 87 sausage buns.

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Answer:

Step-by-step explanation:

1

When the slope is positive, the graph goes from the lower left to the upper right.

Suppose the graph is y = 0.8x + 2. See the inserted graph to see what happens. See the first graph downloaded to see what the above sentence means. The graph is in red.

2

when b>0 the y intercept is above the x axis. The second graph is y = x + 5. It is in blue. The red graph is the same one as the one above.

Sorry, I'm only allowed 1 download. But the red line is for part 1 and the blue line is for part 2.

Answer:

C. Add 8 to both sides

Step-by-step explanation:

This is done in order to equate the equation to zero so that it relates to the general equation.

[tex] {ax}^{2} + bx + c = 0[/tex]

c is (13 + 8)

Answer:

Option C.

Step-by-step explanation:

Notice that only option B and C involves the vectors in transformation

[tex]A=\begin{bmatrix}4\\2\end{bmatrix}, B=\begin{bmatrix}-8\\-4\end{bmatrix}[/tex]

However, option B is not a defined multification since the dimension of both matrices are not matching. Vector A is 2x1 but the second matrix is 2x2.

Answer:

V = 3.

Step-by-step explanation:

(I'll try.)

v/9 = 4/12

you cancel the common factor which is four.

next, you multiple both sides by nine, which make:

9v

_ = 1 , 9

_____

9 3

,,

and I guess you simplify it, and then it becomes V = 3.

I suck at explaining, so you'll just have to trust me by word.

Answer: Approximately 18.33%

Work Shown:

11/60 = 0.1833 approximately

This decimal converts to 18.33% when moving the decimal point over to the right two spots. Round this value however you need to.

Answer:

cube +27x+27

Hope it is helpfull

Answer:

[tex]x^3+y^3[/tex]

Step-by-step explanation:

[tex]I[/tex] [tex]hope[/tex] [tex]this[/tex] [tex]helped[/tex] [tex]you![/tex]

-[tex]RoseCordelia[/tex]

answer

C = 263.76 m

Step-by-step explanation:

C = 2×pi×r

C = 2×3.14×21

C = 131.88 m

For 2 rounds,

C = 131.88 x 2

C = 263.76 m

Step-by-step explanation:

m^2+ n^2 = (-5)² + 3² = 25+9 = 34

Answer:

34

Step-by-step explanation:

Edmentum/Plato

Answer:

Multiply 7*3

.

5

x√x21

your answer is 5x in square root power of 21

Answer:

1

Step-by-step explanation:

steps are in picture.Ignore hand writing

a (i) The number of standard size is 288 eggs

a (ii) The number of medium size is 1,476 eggs

a (iii) The number of large size is 36 eggs

b (i) The expected profit made from selling the standard size is Gh¢43.2

b (ii) The expected profit made from selling the medium size is Gh¢516.6

b (iii) The expected profit made from selling the large size is Gh¢16.2

The given parameters:

the mean of the distribution, m = 0.06 kg

standard deviation (std) of the distribution, d = 0.009 kg

number of the samples, n = 1800 eggs

(i) Find the position of "less than 0.052 kg (standard size)":

(the standard size is 1 standard deviation below the mean)

(ii) Find the position of "Between 0.052 kg and 0.075kg (medium size)":

(the medium size is between 1 std below the mean and 2 std above the mean)

(iii) Find the position of "Greater than 0.075 kg (large size)":

Check: 288 eggs + 1476 eggs + 36 eggs = 1,800 eggs

(b) the cost of production of an egg = Gh¢0.45

the selling price of the standard size = Gh¢0.60

the selling price of the medium size = Gh¢0.80

the selling price of the large size = Gh¢0.95

(i) The expected profit made from selling the standard size:

Profit = total revenue - cost of production

Profit = 288(0.6) - 288(0.45) = Gh¢43.2

(ii) The expected profit made from selling the medium size:

Profit = total revenue - cost of production

Profit = 1476(0.8) - 1476(0.45) = Gh¢516.6

(iii) The expected profit made from selling the large size:

Profit = total revenue - cost of production

Profit = 36(0.9) - 36(0.45) = Gh¢16.2

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Answer:

9

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

Given worded expression

6 divided by 2 times in brackets 1 plus 2

Convert wordings to numerical expression

6 ÷ 2 × (1 + 2)

Simplify value in parentheses/brackets

=6 ÷ 2 × 3

Simplify by division

=3 × 4

Simplify by multiplication

=[tex]\boxed{12}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

9514 1404 393

Answer:

  A.  2×10³

Step-by-step explanation:

The ratio of diameters is ...

  (189,869 mm)/(98 mm) ≈ 1927.3 ≈ 2000 = 2×10³

The diameter of the peach became about 2×10³ times as large.

Answer:

16

Step-by-step explanation:

The digit '6' is in the ones place.

It is a 2 digit number so the number is between 10 and 24.

=> 16

Answer:

-5

Step-by-step explanation:

-3x + 7 < 11

-3(-5) + 7 < 11

Multiplying two negatives together, makes a positive number.

15 + 7 < 11

22 < 11

22 less than 11 is false, therefore -5 is the correct answer.

The correct answer is 4

Here's the Solution:

Transpose 7 to the right side

Now subtract 11 and 7

HOPE THIS HELPS. GOODLUCK:)

9514 1404 393

Answer:

  (c)  16

Step-by-step explanation:

The figure will be a parallelogram when opposite angles are congruent. We already know X and Z are congruent, so we need to find x so that W = Y.

  x +3 = 2x -13

  16 = x . . . . . . . . . . add 13-x to both sides

Step-by-step explanation:

1. 27

2. 15

3. 22

Answer:

if 9x = 180 degree

Step-by-step explanation:

one x equal to 20 degree

and if 3x= 60 degree the ? = 120 degree

Answer:

∠ ABF = 120°

Step-by-step explanation:

HCI is a straight line , so

3x + 2x + 4x = 180 , that is

9x = 180 ( divide both sides by 9 )

x = 20

∠ ABF and ∠ BCI are corresponding angles and are congruent , so

∠ ABF = 2x + 4x = 6x = 6(20) = 120°

you forgot the main part!

the correct answer is 25

.

your sign will be + not - because when you multiply two negative signs It will be positive

Multiply weeks by minutes per week:

52 x 205 = 10,660 total minutes per year

Work Shown:

205 minutes: 1 week

52*(205 minutes) : 52*(1 week)

10660 minutes : 52 weeks

10660 minutes : 1 year

Answer:

Answer:

$765

Step-by-step explanation:

If an amount of money, P, called the principal, is invested for a period of t years at an annual interest rate r, the amount of interest, I, earned is given by

I =Prt           where

I =interest

P =principal

r =rate

t =time

The following information is given.

Prt=$3,600=4.25%=5 years

Substituting the given information into the simple interest formula and solving for I gives

I =Prt

I =(3,600)(0.0425)(5)

=765

The amount of interest Kelsey earned in 5 years was $765.

Answer:

1) The polar form of that equation will be r= √5cos(2θ)

2) i am stuck on this one (sorry)

Step-by-step explanation:

(i) We know that [tex]x = r\cos{\theta}\:\text{and}\:y = r\sin{\theta}.[/tex] So we can write the given equation as

[tex]r^2\cos^2\theta - r^2\sin^2\theta = 5[/tex]

[tex]\Rightarrow r^2(\cos^2\theta - \sin^2\theta) = 5[/tex]

[tex]r^2 = \dfrac{5}{(\cos^2\theta - \sin^2\theta)}[/tex]

[tex]\:\:\:\:\:=\dfrac{5}{\cos{2\theta}} = 5\sec{2\theta}[/tex]

(ii) Recall that

[tex]\cot{\theta} = \dfrac{\cos{\theta}}{\sin{\theta}}[/tex]

[tex]\csc{\theta} = \dfrac{1}{\sin{\theta}}[/tex]

so we can write r as

[tex]r = 8\cot{\theta}\csc{\theta}[/tex]

[tex]\:\:\:\:= 8\left(\dfrac{\cos{\theta}}{\sin{\theta}}\right)\left(\dfrac{1}{\sin{\theta}}\right)[/tex]

[tex]\:\:\:\:= 8\left(\dfrac{x}{y}\right)\!\left(\dfrac{r}{y}\right) = \dfrac{8xr}{y^2}[/tex]

Upon simplification, we get

[tex]y^2 = 8x[/tex]

9514 1404 393

Answer:

   2440

Step-by-step explanation:

The difference in fixed costs is ...

  37815 -16465 = 21350

The difference in variable costs is ...

  20.50 -11.75 = 8.75 . . . . per book

Then the number of books that must be produced for the difference in variable costs to be equal to the difference in fixed costs is ...

  21350/8.75 = 2440

For production of 2440 books, the costs of the two methods will be the same.

_____

Additional comment

You can write expressions for total cost of each production method. When you set them equal and solve for the number of books, you find the math you end up doing is the same as that shown above.