Which expressions are equivalent to -8/13

The finance charge for Antoni Gaudi's bedroom set purchase is $731.08.

An installment refers to a sum of money that is paid back in parts over a period of time, typically with interest.

A loan is a financial agreement between a lender and a borrower, in which the lender provides the borrower with a specific amount of money or assets, which the borrower agrees to pay back with interest over a predetermined period of time. Loans can be used for a variety of purposes, such as purchasing a home, starting a business, or paying for education.

Based on the given information, the bedroom set sells for $2,650, and the financing requires a 15% down payment, which is $397.50 ($2,650 x 0.15).

Therefore, the amount financed is $2,252.50 ($2,650 - $397.50).

To calculate the finance charge, we need to know the total amount of payments Antoni Gaudi will make over the 42-month period. Each monthly payment can be calculated using the following formula:

Monthly Payment = (Amount Financed x (APR/12)) / (1 - (1 + APR/12)^-n)

Where:

APR is the annual percentage rate (12% in this case)

n is the total number of payments (42 in this case)

Plugging in the values, we get:

Monthly Payment = ($2,252.50 x (0.12/12)) / (1 - (1 + 0.12/12)^-42)

= $70.99 (rounded to the nearest cent)

Therefore, the total amount of payments Antoni Gaudi will make over the 42-month period is $2,983.58 ($70.99 x 42).

The finance charge can be calculated as follows:

Finance Charge = Total Payments - Amount Financed

= $2,983.58 - $2,252.50

= $731.08

Therefore, the finance charge for Antoni Gaudi's bedroom set purchase is $731.08.

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The distance PQ cannot be expressed as k√5, where k is a rational number given that PQ = √18

To find dy/dx, we can use implicit differentiation:

4xy = 2(x² + 4y²) - 9x

Differentiating both sides with respect to x, we get:

4y + 4xy' = 4x + 8yy' - 9

Simplifying and solving for y', we get:

y' = (4x - 4y - 9)/(4x - 16y)

Hence, dy/dx = (4x - 4y - 9)/(4x - 16y).

At point P, the tangent to the curve is parallel to the y-axis.

This means that dx/dy = 0 at P.

We can find the coordinates of P by solving the following equations simultaneously

4xy = 2(x² + 4y²) - 9x

dx/dy = 0

From 4xy = 2(x² + 4y²) - 9x, we have:

4xy + 9x = 2(x² + 4y²)

Dividing both sides by x², we get:

4y/x + 9/x = 2 + 4y²/x²

Since dx/dy = 0, we have:

dy/dx = 0

Using the formula for dy/dx that we derived in part (a), we get:

(4x - 4y - 9)/(4x - 16y) = 0

Solving for y, we get:

y = (4x - 9)/4

Substituting this into 4xy = 2(x² + 4y²) - 9x, we get:

4x * (4x - 9)/4 = 2(x² + 4[(4x - 9)/4]²) - 9x

Simplifying and solving for x, we get:

x = 9/2 and 3/2

Substituting these values of x into y = (4x - 9)/4, we get the coordinates of P:

y = 9/4 and y = -3/4

This means that

P(9/2, 9/4) and P(3/2, -3/4)

At point Q, the tangent to the curve is parallel to the x-axis.

This means that dy/dx = 0 at Q.

Using the formula for dy/dx that we derived in part (a), we get:

(4x - 4y - 9)/(4x - 16y) = 0

Solving for x, we get:

x = (4y + 9)/4

Substituting this into 4xy = 2(x² + 4y²) - 9x, we get:

4 * [(4y + 9)/4] * y = 2([(4y + 9)/4]² + 4y²) - 9 * (4y + 9)/4

Simplifying and solving for y, we get:

y = -3/4, 9/4

Substituting these values of y into x = (4y + 9)/4, we get the coordinates of Q:

x = 3/2 and x = 9/2

This means that

Q(3/2, -3/4) and Q(9/2, 9/4)

Using the distance formula, we can find the distance PQ:

PQ = √[(9/2 - 3/2)² + (9/4 + 3/4)²] or √[(3/2 - 9/2)² + (-3/4 - 9/4)²]

Simplifying, we

PQ = √18 or √18

So, we have

PQ = √18

This gives

k√5 = √18

So, we have

k = √18/√5

Evaluate

k = √3.6

√3.6 is not a rational number

Hence, the distance PQ cannot be expressed as k√5

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The total surface area that needs painting is approximately 487 square inches.

What is the cone total surface area?

The total surface area (TSA) of a cone is given by the formula:

TSA = πr(r + l)

The surface area of a cone can be calculated using the formula:

[tex]Surface Area = \pi r(r + \sqrt{(r^2 + h^2)} )[/tex]

where r is the radius of the base of the cone and h is the slant height of the cone.

Given:

Diameter of the cone = 12 inches

Radius (r) = Diameter / 2 = 12 / 2 = 6 inches

Slant height (h) = 19 inches

Plugging in the values into the formula, we get:

[tex]Surface Area = \pi * 6 * (6 + \sqrt{(6^2 + 19^2)} )[/tex]

Calculating the value inside the square root:

[tex]\sqrt{(6^2 + 19^2)} = \sqrt{(36 + 361) } = \sqrt{397} = 19.92[/tex] (rounded to two decimal places)

Substituting the value back into the formula:

[tex]Surface Area = \pi * 6 * (6 + 19.92) = \pi * 6 * 25.92 = 487.34[/tex] square inches (rounded to two decimal places)

Hence, the total surface area that needs painting is approximately 487 square inches.

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Thus, the height of flagpole from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

Using the trigonometric ratios in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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Answer:

28°

Step-by-step explanation:

If the angles are supplementary, they add up to 180°.

(3x) + (2x + 40) = 180

5x + 40 = 180

     - 40   - 40

5x = 140

x = 28°

Answer: To calculate how many times Francisco will earn interest after keeping the money in the account for 5 years, we need to determine the number of quarters in 5 years.

Since there are 4 quarters in a year, the total number of quarters in 5 years is:

4 quarters/year x 5 years = 20 quarters

Therefore, Francisco will earn interest 20 times over the 5-year period.

To calculate the value of his account in 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time the money is invested (in years)

In this case, P = $5,000, r = 0.03, n = 4 (since the interest is compounded quarterly), and t = 5. Substituting these values into the formula, we get:

A = $5,000(1 + 0.03/4)^(4x5)

A = $5,000(1.0075)^20

A = $5,866.02

Therefore, the value of Francisco's account in 5 years, if he does not make any additional deposits or withdrawals, will be $5,866.02.

Step-by-step explanation:

The product of the binomial (d-1)(d+2)(d-3) is d³-2d²-5d+6.

A binomial is an expression with two terms. For example 3x+4 is an example of binomial and also 3x²+3x is also an example of binomial.

To find the product of (d-1)(d+2)(d-3) , we multiply the three binomial together to give us a polynomial expression.

(d-1)(d+2) = d(d+2) -1( d+2)

= d²+2d-d-2

= d²+d-2

now solving (d²+d-2)(d-3)

= d( d²+d-2) -3(d²+d-2)

= d³+d²-2d-3d²-3d+6

collect like terms

= d³+d²-3d²-2d-3d+6

= d³-2d²-5d+6

therefore the product of (d-1)(d+2)(d-3) is d³-2d²-5d+6

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still 7 inches since translation and rotation do not affect area, angles and the length of the sides. Therefore, if you look at the angles, CA will be the same as DF

Equation of circle in standard form- (x + 1)² + (y + 2)² = 1².  radius of the circle is found as 1. centre -(h,k) =  (-1, -2)

We can solve quadratic equations that lack a factor by completing square.

In order to make the left side of an equation a perfect square trinomial, the equation's form must be adjusted.

Given equation is-

x² + y² + 2x + 4y + 4 = 0

Add and subtract 1 in the equation:

x² + y² + 2x + 4y + 4 + 1 - 1 = 0

rearranging:

(x² + 2x + 1) + (y² + 4y + 4) - 1 = 0

This can be written as:

(x² + 2*1x + 1²) + (y² + 2*2y + 2²) = 1

(x + 1)² + (y + 2)² = 1²  ...eq 1

Thus, the standard form of the equation of circle is:

(x - h)² + (y - k)² = r²  ..eq 2

On comparing eq 1 and eq 2

In which radius of the circle is found as 1.

centre -(h,k) =  (-1, -2)

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Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

slope of line AB is m = 2

line AB crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line AB

a) The angular velocity of the wheel is approximately 1.0667 radians per second. b) The wheel will spin at approximately 10.16 revolutions per minute.

Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point, such as an axis or a center of rotation. It is a vector quantity that describes the rate of change of an object's angular position with respect to time, and is usually expressed in units of radians per second (rad/s) or degrees per second (deg/s).

a) To find the angular velocity of the wheel, we can use the formula:

angular velocity = linear velocity / radius

In this case, the linear velocity of the hamster is 16 centimeters per second, and the radius of the wheel is 15 centimeters. So, we have:

angular velocity = 16 / 15

angular velocity = 1.0667 radians per second

Therefore, the angular velocity of the wheel is approximately 1.0667 radians per second.

b) To find the speed of the wheel in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. There are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the following formula:

angular velocity (in revolutions per minute) = angular velocity (in radians per second) * 60 / 2π

Plugging in the angular velocity we found in part (a), we get:

angular velocity (in revolutions per minute) = 1.0667 * 60 / 2π

angular velocity (in revolutions per minute) ≈ 10.16 revolutions per minute

Therefore, the wheel will spin at approximately 10.16 revolutions per minute.

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Answer:

height= 3cm

Step-by-step explanation:

to find the base of each triangle just half the bottom to get 4cm

a^2+b^2=c^2

a^2+4^2=5^2

a^2+16=25

a^2=9

a=√9

a=3

Answer: 3

Step-by-step explanation:

Using pemdas we know that the parrenthesis comes first. I will do 10-1=9. Now, I need to divide it by three. 9/3=3. 3 is the answer

Answer:

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

Use the formula for permutations:

The number of objects is n = 7 books.

Calculate the factorial:

Answer: a. To find the number of barrels that should be refined to maximize profit, we need to find the critical point of the function P(x), which occurs where the derivative of P(x) equals zero.

P(x) = 8x - 0.02x²

P'(x) = 8 - 0.04x

Setting P'(x) = 0, we get:

8 - 0.04x = 0

Solving for x, we get:

x = 200

Therefore, 200 barrels should be refined to maximize the profit.

b. To find the maximum profit, we substitute x = 200 into the profit function P(x):

P(200) = 8(200) - 0.02(200)²

P(200) = 1600 - 800

P(200) = 800

Therefore, the maximum profit is $800.

Step-by-step explanation:

The three consecutive integers are 18, 19, and 20.

Consecutive integers are integers that follow each other in order, without any gaps, and differ by 1. For example, 3, 4, and 5 are consecutive integers because they follow each other in order and differ by 1.

Let's assume that the three consecutive integers are x, x+1, and x+2. Then, according to the problem statement:

4x + (x+2) = 92

Simplifying this equation, we get:

5x + 2 = 92

Subtracting 2 from both sides, we get:

5x = 90

Dividing both sides by 5, we get:

x = 18

Therefore, the three consecutive integers are 18, 19, and 20. We can check that these integers indeed satisfy the condition given in the problem:

4 times the first integer is 4*18 = 72, and when we add the third integer 20 to it, we get 72 + 20 = 92, as required.

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The probability of exactly 3 successes in 15 trials with a probability of success on a single trial of 0.77 is approximately 0.1648.

To find the probability of exactly 3 successes in a binomial distribution with n=15 trials and a probability of success on a single trial q=0.77, we can use the formula for the probability mass function of the binomial distribution:

P(X=k) = (n choose k) * q^k * (1-q)^(n-k)

Substituting the given values into the formula, we get:

P(X=3) = (15 choose 3) * 0.77^3 * (1-0.77)^(15-3)

P(X=3) = (15!/((15-3)!3!)) * 0.77^3 * 0.23^12

P(X=3) = 0.1648.

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Check the picture below.

[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.

The mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:

  Sin = Opposite/Hypotenuse   ⇒   Opposite = Hypotenuse×Sin

  Cos = Adjacent/Hypotenuse   ⇒   Adjacent = Hypotenuse×Cos

The given triangle will have opposite and adjacent sides of ...

  opposite = (7 in)sin(38°) ≈ 4.31 in

  adjacent = (7 in)cos(38°) = 5.52 in

The leg lengths of the triangle are 4.31 inches and 5.52 inches.

The equation of the form y = c + b logₐX is y = -3 + 3 Log₃X

Recall that Slope-intercept form of a linear equation is where one side contains just “y”. It looks like y = mx + “b” where “m” and “b” are numbers. This form of the equation is very useful because the coefficient of "x" (the "m" value) is the slope of the line and the constant (the "b" value) is the y-intercept at (0, b)

The equation of the line is give as

y-y₁ = m(x-x₁) + c

Where m is the slope and c is the intercept

This implies that

y -3 = m(x -2)

But slope is given as  m = (y₂ - y₁)/(x₂-x₁)

m = (9-3)/ 4-2) = 6/2 = 3

Then, the equation is

y - 3 = 3x - 6

Collecting like terms we have

y = 3x -6+3

y = 3x -3

Writing this in the form y = c + b logₐX

y = -3 + 3 Log₃X

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The equation of the function in the form y = c + b log_a(x) is y = logₓ2

We can start by assuming that the equation is of the form y = c + b log_a(x), where c and b are constants and a is the base of the logarithm.

Using the point (2, 3), we get:

3 = c + b log_a(2)

Using the point (4, 9), we get:

9 = c + b log_a(4)

Simplifying the second equation using the logarithmic identity

loga(4) = 2 loga(2), we get:

3 +  2b loga(2) = 9

Substituting the first equation into this one, we get:

3 = 9 - 2b loga(2)

So, we have

-6 = - 2b loga(2)

Divide

bloga(2) = 3

So, we have

b = 3 / log_a(2)

Substituting this value of b into the first equation, we get:

3 = c + b log_a(2)

3 = c + 3 / log_a(2) * log_a(2)

So, we have

c = 0

Therefore, the equation of the curve is y = (2 / log_a(2)) log_a(x)

We can simplify this equation by using the logarithmic identity log_a(x^b) = b log_a(x):

y = 2 log_a(x) / log_a(2)

y = (2 / log(2)) log(x)

So the final equation is:

y = logₓ2

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The radius of the cylinder is approximately 6.75 inches.

We can use the formula for the volume of a cylinder to solve this problem:

[tex]V = \pi r^2h[/tex]

We know that the volume V is 2,035.75 [tex]in^3[/tex], and the height h is 3 times the radius r. So we can write:

[tex]V = \pi r^2(3r)[/tex]

Simplifying this expression, we get:

V = 3π[tex]r^3[/tex]

To solve for r, we can divide both sides of the equation by 3π[tex]r^2[/tex]:

V/(3π[tex]r^2[/tex]) = r

Substituting the given value for V, we have:

2,035.75/(3π[tex]r^2[/tex]) = r

Multiplying both sides by 3πr^2, we get:

2,035.75 = 3π[tex]r^3[/tex]

Dividing both sides by 3π, we have:

[tex]r^3[/tex] = 2,035.75 / (3π)

Taking the cube root of both sides, we get:

r = [tex](2,035.75 / (3\pi ))^{1/3[/tex]

Using a calculator, we find that:

r ≈ 6.75 inches

Therefore, The cylinder has a radius of about 6.75 inches.

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It would take approximately 26.68 years to double the cost of the car with continuous compounding at an annual inflation rate of 2.6%.

The inflation rate is the rate at which the general level of prices for goods and services is increasing over time. In other words, it measures the percentage increase in the cost of living from one period to another.

In the context of the given problem, the annual inflation rate is 2.6%. This means that, on average, the cost of goods and services is increasing by 2.6% per year. If the cost of a car is $21,000 this year, next year it will be 21,000*(1+0.026) = $21,546. The following year it will be 21,546*(1+0.026) = $22,105.96, and so on.

We can use the formula for continuous compound interest to solve this problem:

[tex]A=Pe^{rt}[/tex]

where A is the final amount, P is the initial amount, e is the mathematical constant e (approximately equal to 2.71828), r is the annual interest rate, and t is the time in years.

In this case, we want to find the time t it takes for the cost of the car to double, so we can set A = 2P and solve for t:

[tex]2P=Pe^{rt}[/tex]

Dividing both sides by P, we get:

[tex]2=e^{rt}[/tex]

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

[tex]t = \frac{ln(2)}{r}[/tex]

Substituting the given values, we get:

[tex]t = \frac{ln(2)}{0.026}[/tex]

t ≈ 26.68 years

Therefore, it would take approximately 26.68 years to double the cost of the car with continuous compounding at an annual inflation rate of 2.6%.

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The final value of the annuity due is N165,603.

A series of equal payments paid at regular intervals over a certain time period is known as an annuity. Because they enable people to save a specific sum of money over time and receive consistent payments in the future, annuities are frequently utilised in finance, particularly for retirement planning. The frequency of payments for an annuity might be monthly, quarterly, semi-annually, or annually, and they can be set or variable. Depending on when the payments start, annuities can also be categorised as immediate or deferred.

The effective monthly rate is given as:

[tex]i = (1 + 0.09/12)^{12} - 1 = 0.007434[/tex]

Now, the future value is given by:

[tex]FV = 10000 * ((1 + i)^{120} - 1) / i = 1,473,820.76[/tex]

For annuity due add one payment more to get the value:

FV = FV * (1 + i) = 1,490,304.84

Hence, the final value of the annuity due is N165,603.

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Answer:

mean: 20mins

Step-by-step explanation:

add them all together to get 240

then divide by how many there are

240÷12=20

so the mean is 20mins

The equation of the linear function represented by the table in slope-intercept form is:

y = 3x + 2

We can find the equation of the linear function represented by the table using the slope-intercept form:

y = mx + b

where "m" is the slope of the line and "b" is the y-intercept.

To find the slope, we can use any two points from the table. Let's use the first and last points:

slope (m) = (y2 - y1) / (x2 - x1)

slope (m) = (14 - 5) / (4 - 1)

slope (m) = 3

Now we can find the y-intercept "b" by substituting one of the points and the slope into the slope-intercept form:

y = mx + b

5 = 3(1) + b

5 = 3 + b

b = 2

So the equation of the linear function represented by the table in slope-intercept form is:

y = 3x + 2

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Thus, the unknown side length of rectangle for the given area and one side length is found to be 5.5 m.

Every day, rectangles are all around us. All of these objects—doors in a home, windows in a structure, and books in a library—are rectangles.

Given that:

Area of rectangle A = length * width

width = area / length

width = 11 / 2

width =  5.5

Thus, the missing side of rectangle for the given area and one side length is found to be 5.5 m.

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Complete question:

Find the unknown side length of the rectangle if its area is 11 m² and one of its side is 2 m.

Answer: c. 9

Step-by-step explanation:

Using factorization and simplifying the equations, the points of intersections are (-2, 0), ( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 ) and ( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

We are given two equations:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x + d

and we know that they intersect at x = -4, so we can substitute -4 for x in both equations:

y = 4(-4)² - 3(-4) + 3 = 49

y = (-4)³ + 7(-4)² - 3(-4) + d = -64 + 112 + 12 + d = 60 + d

So, at x = -4, we have y = 49 and y = 60 + d. Since the graphs intersect, these two equations must be equal:

49 = 60 + d

Solving for d, we get:

d = -11

Therefore, the two equations become:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x - 11

We can now set them equal to each other:

4x² - 3x + 3 = x³ + 7x² - 3x - 11

Simplifying and rearranging, we get:

x³ + 3x² - 8x - 14 = 0

We can try to factor this expression by testing possible roots. One possible root is x = 2, because if we substitute 2 for x, we get:

2³ + 3(2)² - 8(2) - 14 = 8 + 12 - 16 - 14 = -10

Since this expression evaluates to a non-zero value, x = 2 is not a root. Similarly, we can test x = -1:

(-1)³ + 3(-1)² - 8(-1) - 14 = -1 + 3 + 8 - 14 = -4

This expression also evaluates to a non-zero value, so x = -1 is not a root. Finally, we can test x = -2:

(-2)³ + 3(-2)² - 8(-2) - 14 = -8 + 12 + 16 - 14 = 6

This expression evaluates to zero, so x = -2 is a root. Using long division or synthetic division, we can divide the cubic polynomial by x + 2 to get:

x³ + 3x² - 8x - 14 = (x + 2)(x² + x - 7)

The quadratic factor x² + x - 7 can be factored using the quadratic formula, giving us:

x² + x - 7 = [ -1 ± √(1 + 4*7) ] / 2

= [ -1 ± 3√(7) ] / 2

Therefore, the three intersection points are:

(-2, 0)

( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 )

( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

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