LINEAR EQUATIONS AND INEQUALITES Solving a linear equation with several o Solve for v. 3(v-4)-6=-7(-4v+4)-7v Simplify. your answer as much as possible. v

Answer:

C. The account earns 1.2% in yearly interest.

Step-by-step explanation:

The expression 750(1+0.012) represents the amount of money in a savings account earning yearly interest after t years, where t is the number of years since the account was opened.

The expression (1+0.012) represents the interest rate as a decimal. The value 0.012 represents 1.2% in decimal form, which is the yearly interest rate earned by the account.

Therefore, (1+0.012) represents the account's yearly interest rate as a decimal, which is 1.2%.

Answer:

4y^2 - 12y + 9

Step-by-step explanation:

(3-2y)^2 = (3-2y) (3-2y)

Distribute:

3(3) + (3)(-2y) + (-2y)(3) + (-2y)(-2y)

= 9 -6y -6y +4y^2

Combine like terms:

4y^2 -12y + 9

I hope this helps!

Answer:

9 - 12y + 4y²

Step-by-step explanation:

(3 - 2y)²

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

each term in the second factor is multiplied by each term in the irst factor, that is

3(3 - 2y) - 2y(3 - 2y) ← distribute parenthesis

= 9 - 6y - 6y + 4y² ← collect like terms

= 9 - 12y + 4y²

By converting the Cartesian coordinates (1,−5) to polar coordinates with r>0 and 0≤θ<2π r = √26 and θ = 4.909784033953984

To convert the Cartesian coordinates (1,−5) to polar coordinates with r>0 and 0≤θ<2π, we need to use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
Plugging in the given values of x = 1 and y = -5, we get:
r = √(1² + (-5)²)
r = √(1 + 25)
r = √26
θ = tan⁻¹(-5/1)
θ = tan⁻¹(-5)
θ = -1.373400766945016
Since we want 0≤θ<2π, we need to add 2π to θ to get the correct value:
θ = -1.373400766945016 + 2π
θ = 4.909784033953984
So the polar coordinates are:
r = √26
θ = 4.909784033953984

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Answer:

14.75 + 18.75x ≤ 425

Step-by-step explanation:

Total amount they have is $425

Parking for the entire group = $14.75

If x is the number of persons in the group, the cost of x tickets at $18.75 per head
= 18.75x

The total cost incurred
= Parking Cost + Ticket Cost

= 14.75 + 18.75x

This has to be less than equal to 425

So the inequality is

14.75 + 18.75x ≤ 425

i cannot make out the given answer choices clearly, it appears the constant 425 is on the left side in each answer choice - choose the one which is closest to the given answer

By considering the graph, Jade's rate will be 8 dollars profit per kilogram sold.

Since profit is a function of kilograms sold, x is the kilograms sold and y is the profit.

Two points of the line are (35, 0) and (60, 200).

The Rate or slope is given by:

m = y2 - y1/x2 - x1

m = 200 - 0 / 60 -35

m = 200 / 25

m = 8

Therefore, Jade's rate is 8 dollars profit per kilogram sold.

The translated question is "Jada sells ground paprika. Her weekly profit (in dollars) as a function of the amount of paprika she sold that week (in kilograms) is graphed. What is Jade's rate? "

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The time taken to empty one tank is 1000 seconds or 16.67 minutes. Therefore, the total time required to empty all three tanks one after another is 50 minutes (16.67 minutes x 3).

The volume of water that can be emptied through the hole at the bottom of each tank per second is 0.2 liters. Therefore, the time taken to empty 200 liters of water from one tank is:

200 liters ÷ 0.2 liters per second = 1000 seconds

Converting the time to minutes:

1000 seconds ÷ 60 seconds per minute = 16.67 minutes

So, it takes 16.67 minutes to empty one tank. Multiplying this by three gives us the total time required to empty all three tanks:

16.67 minutes x 3 = 50 minutes

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Answer:

x to the power of 67000 to the 5th power.

Step-by-step explanation:

Answer:

Let's start by using the formula for mixing two solutions to set up an equation. The formula is:

(concentration of solution 1) x (volume of solution 1) + (concentration of solution 2) x (volume of solution 2) = (concentration of resulting solution) x (total volume of resulting solution)

In this problem, solution 1 is the 25% sugar syrup, solution 2 is the 10% sugar syrup, and the resulting solution is 15% sugar syrup. We are also given that the total volume of the resulting solution is 120 grams. Let's use x to represent the volume of the 10% sugar syrup that is mixed with the 25% sugar syrup. Then we can write:

(0.25)(120-x) + (0.10)(x) = (0.15)(120)

Simplifying this equation, we get:

30 - 0.25x + 0.10x = 18

0.15x = 12

x = 80

Therefore, we need to mix 80 grams of the 10% sugar syrup with 40 grams of the 25% sugar syrup to get 120 grams of 15% sugar syrup.

To find the amount of pure sugar in the 120 grams of 15% syrup, we can use the fact that the concentration of pure sugar in the resulting solution is 15%. That means that 15% of the 120 grams is pure sugar. We can find this by multiplying 120 by 0.15:

120 x 0.15 = 18

So there are 18 grams of pure sugar in the 120 grams of 15% syrup.

The pair of integers to be used to rewrite the middle term when factoring 6t^(2)+5t-4 by grouping is (5t - 4) and (6t^2 + 5t). By factoring by grouping, we can factor the middle term out of the polynomial and then factor the remaining terms separately.

First, the middle term is factored out of the equation. This is done by multiplying the first and last terms together, which in this case is (6t^2)(-4). This results in the equation 6t^2 + 5t - 4 being rewritten as 6t^2 + (5t - 4)(-4).

Next, the remaining terms are factored separately. The first term, 6t^2, is a perfect square and can be factored as (3t)(2t). The second term, (5t - 4)(-4), can be factored by taking out a common factor from each term. In this case, the common factor is (-4). This results in the equation being rewritten as (3t)(2t) + (-4)(5t - 4).

The final step is to group the terms together and factor out the greatest common factor. In this equation, the greatest common factor is (3t)(-4). Thus, the equation 6t^2 + 5t - 4 can be rewritten as (3t)(-4)(2t + 5).

In conclusion, the pair of integers used to rewrite the middle term when factoring 6t^2 + 5t - 4 by grouping is (5t - 4) and (6t^2 + 5t).

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The final answer is 2x^3 +x^2 +3x+5 = (2x^2 + 3x + 6)(x−1) + 11.

(2) To solve the inequality |2x − 5| ≤ 9, we need to split it into two separate inequalities and solve for x:
2x − 5 ≤ 9 and 2x − 5 ≥ −9
2x ≤ 14 and 2x ≥ 4
x ≤ 7 and x ≥ 2
The solution in interval notation is [2, 7].

(3) To find the inverse of the function f(x) = 5/(6x−1), we need to switch the x and y values and solve for y:
x = 5/(6y−1)
6y−1 = 5/x
6y = 5/x + 1
y = (5/x + 1)/6
The inverse function is f^(-1)(x) = (5/x + 1)/6.

(4) To find fg and fg, we need to plug in the functions for x and simplify:
fg(x) = f(g(x)) = √(x^2−11x+30−4) = √(x^2−11x+26)
fg(x) = g(f(x)) = (√x−4)^2−11(√x−4)+30 = x−8√x+16−11√x+44+30 = x−19√x+90
The domain of fg is all real numbers greater than or equal to 26, and the domain of fg is all real numbers greater than or equal to 0.

(5) To find the equation of the line perpendicular to y = 35 x − 4 and passing through the point (1, 2), we need to find the slope of the perpendicular line and use the point-slope form:
The slope of the original line is 35, so the slope of the perpendicular line is -1/35.
Using the point-slope form, y − y1 = m(x − x1), we get:
y − 2 = −1/35(x − 1)
y = −1/35x + 2 + 1/35
y = −1/35x + 71/35
The equation of the line in slope-intercept form is y = −1/35x + 71/35.

(6) To divide 2x^3 +x^2 +3x+5 by x−1 using long division, we need to divide each term of the dividend by the divisor and find the remainder:
2x^3 ÷ x = 2x^2
2x^2(x−1) = 2x^3−2x^2
(x^2 +3x+5) − (2x^3−2x^2) = 3x^2 +3x+5
3x^2 ÷ x = 3x
3x(x−1) = 3x^2−3x
(3x+5) − (3x^2−3x) = 6x+5
6x ÷ x = 6
6(x−1) = 6x−6
5 − (6x−6) = 11
The final answer is 2x^3 +x^2 +3x+5 = (2x^2 + 3x + 6)(x−1) + 11.

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a. 240 students were surveyed in all. b. 60 students chose blue. c. The number of students who chose purple is 7, green is 10, others is 7 students.

In mathematics, a proportion is a statement that two ratios or fractions are equal. A proportion can be expressed as an equation of the form:

a/b = c/d

where a, b, c, and d are numbers, and b and d are not equal to zero. This equation can also be written in the form of a cross product:

ad = bc

This equation means that the product of the numerator of one fraction and the denominator of the other fraction is equal to the product of the denominator of the first fraction and the numerator of the second fraction.

a. If 20% of the students surveyed chose yellow and 48 students chose yellow, we can set up the following proportion to find the total number of students surveyed (let "x" be the total number of students):

20/100 = 48/x

Solving for x, we get:

x = 240

Therefore, 240 students were surveyed in all.

b. 25% of the students surveyed chose blue, so the number of students who chose blue is:

25/100 x 240 = 60

Therefore, 60 students chose blue.

c. We are given that 3% of the students surveyed chose purple, and 4% chose green. To find the number of students who chose purple or green, we can add the two percentages and find the corresponding portion of the total number of students:

3/100 + 4/100 = 7/100

So 7% of the students surveyed chose purple or green. The number of students who chose purple is:

3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)

Similarly, the number of students who chose green is:

4/100 x 240 = 9.6 (rounded to the nearest whole number, this is 10)

We are also given that 3% of the students surveyed chose "other". Therefore, the number of students who chose "other" is:

3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)

So 7 students chose "other".

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Answer:

Step-by-step explanation:

based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number8957647h3ny4y4y7

Answer: $170

Step-by-step explanation:

6x + 18(6) = 1128.

6x + 108 = 1128

6x = 1020

x = 170

The price of one ticket is 170

Using Pythagoras theorem, the size of the TV will be 65 inches.

What is Pythagorean Theorem?

The Pythagorean Theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right triangle. It states that in any right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

In equation form, the Pythagorean Theorem can be written as:

a² + b² = c²

where a and b are the lengths of the two legs and c is the hypotenuse.

Now,

We can use the Pythagorean theorem to find the diagonal measure of the television screen.

In this case, the height and width of the screen form the legs of a right triangle, so we can use the following equation:

(diagonal)² = (height)² + (width)²

Substituting the given values, we get:

(diagonal)² = (32)² + (57)²

(diagonal)² = 1024 + 3249

(diagonal)² = 4273

Taking the square root of both sides

diagonal = √(4273) ≈ 65.37

Therefore, the size of the TV screen, as measured diagonally, is approximately 65 inches (rounded to the nearest whole number).

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Sky can run 3 miles per hour faster than her sister rose can walk. If Sky ran 12 miles in the same time it took Rose to walk 8 miles, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.

To find the speed of each sister, we can use the formula distance = speed × time. We can set up a system of equations to solve for the speeds of Sky and Rose. Let s be the speed of Sky and r be the speed of Rose. Then we have:

12 = s × t (equation 1)
8 = r × t (equation 2)

We are also told that Sky can run 3 miles per hour faster than Rose, so we can write:

s = r + 3 (equation 3)

Now we can substitute equation 3 into equation 1 and solve for t:

12 = (r + 3) × t
t = 12 / (r + 3)

Next, we can substitute this value of t into equation 2 and solve for r:

8 = r × (12 / (r + 3))
8(r + 3) = 12r
8r + 24 = 12r
24 = 4r
r = 6

So the speed of Rose is 6 miles per hour. We can use equation 3 to find the speed of Sky:

s = 6 + 3
s = 9

So the speed of Sky is 9 miles per hour. Therefore, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.

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The speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.

Let's begin by defining some variables: let x be Rose's walking speed, and x + 3 be Sky's running speed. Since we know that Sky ran 12 miles and Rose walked 8 miles in the same amount of time, we can write an equation to represent this:

12 / (x + 3) = 8 / x

Cross-multiplying and simplifying gives us:

12x = 8x + 24

4x = 24

x = 6

So Rose's walking speed is 6 miles per hour, and Sky's running speed is 6 + 3 = 9 miles per hour.

Therefore, the speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.

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2x+7y+2z+10=0 is the equation of the plane passing through A(-2, 0, -3) and B(1, -2, 1) that lies parallel to the line through C(-2, -13/5, 26/5) and D(16/5, -13/5, 0).

The equation of the plane passing through a point (a,b,c) can be written as A(x-a) + B(y-b) + C(z-c) = 0, where A, B and C are the coefficients of the normal vector to the plane.

So, the equation of the plane passing through a point (-2,0,-3) can be written as A(x+2) + B(y) + C(z+3) = 0,...i)

Now the plane also passes through the point (1,-2,1) so A(1+2) + B(-2) + C(1+3) = 0,

So, 3A-2B+4C=0.........ii)

Now, the direction cosines of CD is

l= 16/5 +2= 26/5

m= -13/5+13/5 = 0

n= 0-26/5 = -26/5

For a plane and line to be perpendicular Dot product of the direction cosines must be zero

or A*26/5 +  B*0 + C*-26/5=0

or, A=C.....iii)

Putting this in i) 7A-2B=0 or, A=2B/7....iv)

putting iii) and iv)

A(x+2) + B(y) + C(z+3) = 0

or, A(x+2) + B(y) + A(z+3) = 0

or, 2*B*(x+2)/7 + B(y) + 2*B*(z+3) /7= 0

or 2*(x+2)/7 + y + 2*(z+3) /7= 0

or 2x+7y+2z+10=0

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Answer:

0.5

Step-by-step explanation:

0.5

Answer:

100°

Step-by-step explanation:

∠A and ∠B are supplementary angles, which means:

∠A° + ∠B° = 180°

[tex](2x) + (2x + 20) = 180[/tex]

Expand the parenthesis and solve for x:

[tex]2x + 2x + 20 = 180[/tex]

[tex]4x + 20 = 180[/tex]

[tex]4x = 180 - 20[/tex]

[tex]4x = 160[/tex]

[tex]x = \frac{160}{40}[/tex]

∴[tex]x = 40[/tex]

Substitute the value of x to determine the measurement of ∠B:

[tex]2(40) + 20[/tex]

[tex]80 + 20[/tex]

= 100°

If Jason claims no allowances this year, $17 more will be deducted from his weekly check for taxes compared to last year when he claimed one allowance.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

The amount of money deducted from Jason's paycheck for taxes depends on the number of allowances he claims.

Claiming more allowances reduces the amount of taxes withheld from his paycheck while claiming fewer allowances increases it.

If Jason claimed 1 allowance last year, his employer would have withheld taxes from his paycheck based on that information.

If he claims no allowances this year, more taxes will be withheld.

To calculate how much more will be deducted from his weekly check if he claims no allowances, we need to know his tax bracket and the amount of taxes that will be withheld for each allowance.

Assuming Jason is paid on a weekly basis, we can use the IRS tax withholding tables for 2021 to estimate the additional amount of taxes that will be withheld if he claims no allowances.

Using these tables, we find that for a single person earning $232.50 per week, claiming no allowances would result in an additional withholding of $17 per week.

Therefore, claiming no allowances would result in an additional withholding of $17 per week.

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Solving a linear equation we can see that he can afford to pay the monthly fee for 28 months

We know that there is an initial fee of $300 plus $7 per month, so the total cost after x months is:

C = 300 + 7*x

And we know that Julio has $500 set aside, then the equation that we need to solve is:

500 = 300 + 7x

500 - 300 = 7x

200 = 7x

200/7 = x = 28.5

Rounding down we get 28.

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The result of alternately adding and subtracting the terms in the nth row of Pascal's triangle is given by the formula

[tex]n C 0 - n C 1 + n C 2 - ... + (-1)^n \times n C n = 0.[/tex]

The binomial theorem and patterns in Pascal's triangle can be used to simplify the given expressions.

Here are the simplified versions of each expression:

9 C 0 + 9 C 1 +…+ 9 C 9 = 2^9 = 512

12 C 0 − 12 C 1 + 12 C 2 −…− 12 C 11 + 12 C 12 = 0

r=0 ∑ 15 15 C r = 2^15 = 32768

r=0 ∑ n n C r = 2^n

If r=0 ∑ n n C r = 16384, then [tex]2^n[/tex] = 16384, so n = 14.

The sum of the squares of the terms in the nth row of Pascal's triangle is given by the formula:

[tex](n C 0)^2 + (n C 1)^2 + ... + (n C n)^2 = 2^{(2n-1).[/tex]

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Peter ended up with 31 beads, and Dan ended up with 28 beads.

What is the fraction?

A fraction is a mathematical expression that represents a part of a whole. It is written in the form of a ratio between two numbers, with the top number called the numerator and the bottom number called the denominator.

Let's represent the number of beads that Peter and Dan had at the start by P and D, respectively. Then we can set up an equation based on the information given in the problem:

After giving away 1/4 of his beads, Peter had 3/4 of his original number of beads, which is (3/4)P.

After giving away 1/5 of his beads, Dan had 4/5 of his original number of beads, which is (4/5)D.

According to the problem, both had the same number of beads left after giving away some of their beads:

(3/4)P = (4/5)D

We also know that Peter had 7 more beads than Dan at the start:

P = D + 7

We can use substitution to solve for D:

(3/4)(D+7) = (4/5)D

9D/20 + 21/20 = 4D/5

D = 35

So Dan had 35 beads at the start. Using the equation P = D + 7, we can find that Peter had:

P = D + 7 = 35 + 7 = 42

After giving away 1/4 of his beads, Peter had (3/4)P = (3/4)*42 = 31.5 beads, which we can round down to 31 beads since we're dealing with whole numbers of beads. After giving away 1/5 of his beads, Dan had (4/5)D = (4/5)*35 = 28 beads.

Therefore, Peter ended up with 31 beads, and Dan ended up with 28 beads.

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Rearranging this equation gives a quadratic equation[tex]length^2 - 3 length - 75 = 0[/tex]

Let's start by using the formula for the volume of a rectangular prism:

Volume = length x width x height

We know that the volume is 900 cubic meters and the width is 12 meters. Let's substitute these values into the formula:

[tex]900 = length \times 12 \times height[/tex]

Now we need to use the information about the height. We know that the height is 3 meters shorter than the length, so we can write:

height = length - 3

Substituting this into the formula gives:

[tex]900 = length \times 12 \times (length - 3)[/tex]

Simplifying this equation gives:

[tex]900 = 12 length^2 - 36 length[/tex]

Dividing both sides by 12 gives:

[tex]75 = length^2 - 3 length[/tex]

Therefore, Rearranging this equation gives a quadratic equation:

[tex]length^2 - 3 length - 75 = 0[/tex]

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The series converges.

1. This is an alternating series, and therefore, the series converges by the Alternating Series Test. This is because the sequence of the absolute value of the terms, {|3n+5|}^(1/3), is a monotonically decreasing sequence, and it is bounded. To determine how many terms are necessary to get within 0.05 of the sum, we use the formula:

Sn≈s​[infinity]​+a1r1/1−r

where a1 is the first term, and r is the common ratio. In this case, we have a1 = (3+5)^(1/3) = 2, and r = (-1)^(1/3) = -1. Thus, Sn ≈ 2 + (2)(-1)/1 - (-1) = 4.

Since the series is alternating, it is absolutely convergent.

2. This series is also an alternating series, so it is absolutely convergent by the Alternating Series Test. The sequence of the absolute value of the terms, {|3n+4|}^(1/ln(5n+2)), is a monotonically decreasing sequence, and it is bounded. Therefore, the series converges.

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a) maximum profit 20.5.

b) maximum profit 20,025.

c)  price 10.35

The given function, f(p)=-50p+2050p-20,700, is not a degree 3 polynomial. It is a degree 1 polynomial or a linear function. Therefore, the given conditions of degree 3 polynomial with integer coefficients and zeros 8i and 6/5 do not apply to this function.

Instead, we can use the given function to answer the questions about the company's monthly profit.

(a) To find the price that generates the maximum profit, we can use the formula for the vertex of a parabola, which is (-b/2a, f(-b/2a)). In this case, a = -50 and b = 2050.
The price that generates the maximum profit is -b/2a = -2050/(2*-50) = 20.5.

(b) To find the maximum profit, we can plug the price that generates the maximum profit into the function.
f(20.5) = -50(20.5) + 2050(20.5) - 20,700 = 20,025.

(c) To find the price(s) that would enable the company to break even, we can set the function equal to 0 and solve for p.
0 = -50p + 2050p - 20,700
20,700 = 2000p
p = 10.35

Therefore, the price that would enable the company to break even is 10.35. There is only one price that would enable the company to break even.

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In a triangle EAC, F is the centroid and two medians, then the required expressions are 10x² + 2y , 5x² +y respectively.

The centroid is the centre point of the object. It is a point at which three medians of a triangle meet. Properties :

We have a triangle AEC, with centroid point F. Here, two medians of triangle AEC. Here, AD = 15x² + 3y, we have to determine the expression for bigger and smaller parts of median. As we know, centroid point F, divides median into ratio, 2: 1, i.e., bigger divided part/smaller divided part = 2/1

First expression for bigger divided part of median = (2/3) (15x² + 3y)

= 10x² + 2y

second expression for smaller divided part of median = (1/3) ( 15x² + 3y)

= 5x² + y

Hence, required expression are 10x² + 2y and 5x² + y.

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81-100. ------2

1-20----------2

21-40---------4

41-60----------1

61-80----------1

Answer:

A. The quantities that change in this problem situation are the number of books Ben orders and the total cost. The quantities that remain constant are the cost per book ($12) and the shipping and handling charge per order ($5).

The independent variable is the number of books Ben orders, as this is the variable that Ben has control over and chooses to change. The dependent variable is the total cost, as it depends on the number of books Ben orders.

B.
(imagine this as a chart)

Number of books                                                                            Total cost

1                                                                                                               $17

2                                                                                                              $29

3                                                                                                               $41

5                                                                                                              $65

10                                                                                                             $125

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To create this table, we used the formula:

Total cost = (Cost per book x Number of books) + Shipping and handling charge

For example, when Ben orders 3 books, the total cost is:

Total cost = ($12 x 3) + $5 = $41

Similarly, when Ben spends $65, the number of books he can order is:

Number of books = (Total cost - Shipping and handling charge) / Cost per book

Number of books = ($65 - $5) / $12 = 5

And so on for the other values in the table.

Answer:

See below

Step-by-step explanation:

Let x be he cost per book and y be the total cost including shipping and handling.

The relevant equation is

y = 12x + 5

A. Variables are number of books ordered(x) and total cost(y)
The constant is the shipping and handling cost

Since the total cost depends on the number of books ordered, the independent variable x = number of books

The total cost y is the dependent variable

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B. Cost of 1 or 2 books can be found by plugging in x = 1 and x =2 into the equations and solving for y
Total Cost of 1 book = 12(1) + 5 = $17
Total cost of 2 books = 12(2) + 5 = 24 + 5 = $29

To compute the number of books that can be ordered for different total cost amounts is obtained by substituting for y and solving for x

For $41:
41 = 12x + 5
41 - 5 = 12x

36 = 12z

x = 36/12 = 3 books

For $65:
65 = 12x + 5
65 - 5 = 12x
60 = 12x
x = 60/12 = 5 books

For $125:

125 = 12x + 5
125 - 5 = 12x
120 = 12x
x = 120/12 = 10 books

Here is the table

Number                            Total Cost(y)
of books (x)                    

          1                                  $17

          2                                 $29

          3                                  $41

          5                                  $65

          10                                 $125

The answer is sin(2x) = 0.8824.

If cot(x) = 5/3, we can use the identity cot(x) = 1/tan(x) to find the value of tan(x). Therefore, tan(x) = 1/(5/3) = 3/5.

Now, we can use the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x). First, we need to find the values of sin(x) and cos(x).

Since tan(x) = 3/5, we can use the Pythagorean identity 1 = sin^2(x) + cos^2(x) to find the values of sin(x) and cos(x).

Let's assume sin(x) = 3/a and cos(x) = 5/a. Then, we can plug these values into the Pythagorean identity and solve for a:

1 = (3/a)^2 + (5/a)^2

1 = 9/a^2 + 25/a^2

1 = 34/a^2

a^2 = 34

a = √34

Therefore, sin(x) = 3/√34 and cos(x) = 5/√34.

Now, we can plug these values into the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x):

sin(2x) = 2(3/√34)(5/√34)

sin(2x) = 30/34

sin(2x) = 0.8823529411764706

To 4 decimal places, sin(2x) = 0.8824.

the answer is sin(2x) = 0.8824.

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