The vertices of a rectangle are at (−1, −5), (3, −5), (3, −7), and (−1, −7). What is the length of the shorter side of the rectangle? Enter your answer in the box

For the function f(x) = tan(x) , the option that cannot be an Asymptote is (a) x = 5π .

An Asymptote is a straight line or curve that a graph approaches but never touches as the input values become larger or smaller.

In mathematical terms, as x approaches positive or negative infinity, the value of the function approaches a fixed constant value or the value of an asymptote.

The function is f(x) = tan(x) ,

the tangent function do not have any horizontal asymptote , and

the vertical asymptotes of tangent function is multiple of π/2 .

the asymptotes of a tangent function are x = π/2 + πn .

From the formula , we can say that it is not possible for the tangent function to have an integer asymptote .

Therefore , (a) x = 5π is not an asymptote of f(x) = tan(x)  .

The given question is incomplete , the complete question is

Which of the following is NOT an asymptote of the function f(x) = tan(x) ?

(a) x = 5π

(b) x = -4.5π

(c) x = -0.5π

(d) x = -3.5π  .

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The probability of the value of p(a ∩ bc ) is 1/54

Probability is a mathematical measure of how likely an event is to occur.

Given that p(a ∪ b) = 2/3, which means the probability of either event a or event b happening is 2/3, we can find the probability of a and b happening simultaneously using the formula for conditional probability.

=> p(a ∩ b) = p(a | b) * p(b) = 1/12,

where p(a | b) is the probability of event a happening given that event b has already happened. We can use this information to find p(b) as follows:

=> p(b) = p(a ∩ b) / p(a | b) = 1/12 / p(a | b)

We also know that p(b ∩ ac) = 1/3, which means the probability of both events b and ac happening is 1/3. We can use this information to find p(b) and p(a | b).

=> p(b) = p(b ∩ ac) / p(ac | b) = 1/3 / p(ac | b)

Finally, using the formula for conditional probability, we can find p(a ∩ bc) as follows:

p(a ∩ bc) = p(a | bc) * p(bc) = p(a | b) * p(b | bc) * p(bc) = p(a | b) * p(b) * p(bc | b) * p(bc)

p(a ∩ bc) = 2/3 * 1/12 *1/3 = 1/54

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A shape must cross a line in order to be reflected.

Because a reflection across BA will map ABC to ABD, the true statement is (c).

A translation only moves a shape up, down, or from side to side; it has no effect on how it appears. An illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape.

here, we have,

Sides AC and AD of both triangles are congruent

Sides BD and BC of both triangles are congruent

The triangles share a common side AB

This means that a reflection over line AB will map both triangles.

Hence, the true statement is (c)

The complete question is given below.

Is there a rigid transformation that maps triangle ABC to triangle ABD? If so, which transformation?

yes, because a translation to the right will map ΔABC to ΔABD

yes, because a rotation about point B will map ΔABC to ΔABD

yes, because a reflection across BA will map ΔABC to ΔABD

no, because no rigid transformation will map ΔABC to ΔABD

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You first have to find 5% of 200,000gbp in order to find the value of the house for the year 2015.

200,000 x 5/100 = 10,000

Therefore by 2015 the house's value was= 200,000 + 10,000= 210,000

however, you cannot keep adding 10,000 thrice over to find the value of the house for the year 2017 as the amount the value increases by each year will change as it is a percentage difference

value for 2016,

210,000x5/100=10,500

Therefore by 2016 the house's value was= 210,000 + 10,500= 220,500

value for 2017,

220,500x5/100=11,025

Therefore by 2017 the house's value was= 220,500 + 11,025= 231,525gbp

Answer:

You first have to find 5% of 200,000gbp in order to find the value of the house for the year 2015.

200,000 x 5/100 = 10,000

200,000+10,000+10,000+10,000=231510

Amount it has increased: 11,025

Step-by-step explanation:

The number of color sequences possible when removing five balls one at a time depends on the number of different colors the balls have.

If there are C different colors, the number of color sequences possible is C^5 (C raised to the power of 5), since for each ball you remove, you have C options for its color.

The number of combinations of colors possible when removing five balls one at a time is given by the binomial coefficient "C choose 5", which represents the number of ways to choose 5 balls out of C different balls, ignoring the order in which they are chosen.

The binomial coefficient can be calculated as:

C choose 5 = C! / (5! * (C-5)!).

Here, "!" denotes the factorial symbol, which is the product of all positive integers up to that number (e.g. 5! = 5 * 4 * 3 * 2 * 1 = 120).

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The helix r(t) = (cos(πt/2), sin(πt/2), t) intersects the sphere x² + y² + z² = 2 in two points and the angle of intersection at every point is 0°.

Let's assume that the central axis of the helix is z

Given r(t) = (cos(πt/2), sin(πt/2), t)

Put this point in the sphere equation

cos²(πt/2) + sin²(πt/2) + t² = 2

                                 1 + t² = 2

                                      t² = 1

                                       t = +1, -1

Now, let f = x² + y² + z² - 2

Δf = (fx, fy, fz)

Δf = (2x, 2y, 2z)

At (cos(πt/2), sin(πt/2), t), Δf = (2cos(πt/2), 2sin(πt/2), 2t)

Angle of intersection at t = 1

Δf = (0, 2, 2) and r = (0, 1, 1)

Using dot product:

                           cosθ = (0, 2, 2).(0, 1, 1)/ √(2² + 2²) √(1² + 1²)

                           cosθ = 1

                                 θ = 0°

Angle of intersection at t = -1

Δf = (0, -2, -2) and r = (0,-1, -1)

Using dot product:

                           cosθ = (0, -2, 2-).(0, -1, -1)/ √((-2)² + (-2)²) √((-1)² + (-1)²)

                           cosθ = 1

                                 θ = 0°

Hence, the angle of intersection at every point is 0°

The given question is incomplete. The complete question is

"The helix r(t) = (cos(πt/2), sin(πt/2), t) intersects the sphere x² + y² + z² = 2 in two points. Find the angle of intersection at each point."

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To calculate the coordinates of B, we use 7 = √(x-4)^2 + (y-5)^2

Pythagoras Theorem states that "In a right- angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".

The sides of this triangle have been named Perpendicular, Base and Hypotenuse. The hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

Given:

To calculate the coordinates for point B, we can use the Pythagorean Theorem.

In this case, we are given point A located at (5, 4).

We also know that the distance from A to B is 7 units.

We can represent this as a right triangle, with point A being one of the legs and the distance of 7 units being the hypotenuse.

Now, using the Pythagorean Theorem, we can calculate the coordinates for point B.

Let consider the coordinates of B (x, y)

The distance between A and B be 7 units. So, we use distance formula,

7 = [tex]\sqrt{ (x - 4)^{2} + (y - 5)^{2}[/tex]

We can do this by setting up the equation 7 = [tex]\sqrt{ (x-4)^2 + (y-5)^2 }[/tex]and then solving for x and y.

To solve for x, we can start by subtracting 4 from both sides of the equation, giving us 3 = [tex]\sqrt{x^2 + (y-5)^2}[/tex]. Now,

we can take the square root of both sides to get x = √3.

Similarly, to solve for y, we can start by subtracting 5 from both sides of the equation,

giving us 2 = [tex]\sqrt{(x-4)^2 + y^2}[/tex]. Now, we can take the square root of both sides to get y = √2.

Therefore, the coordinates for point B are (√3, √2).

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The amount of money that she has to pay per month, next year in rent will be $736.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Lian currently pays 640 per month to rent her apartment she has been told by her landlord that her rent will be increasing by 15% next year.

Then the amount is given as,

A = $640 x (1 + 0.15)

A = $640 x 1.15

A = $736

The amount of money that she has to pay per month, next year in rent will be $736.

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The correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

The algebraic representation of the statement 15 is what percent of 40 is:

40 (x/100) = 15

40x / 100 = 15

40x = 1500

x = 1500/40

x = 37.5

Hence, the correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.

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The equation of line segment AB is y = 3.5x - 0.5.

Line segment AB starts at point A(-1, -3) and ends at point B(3, 11). The equation for this line can be found by calculating the slope and then using the point slope formula, y-y1=m(x-x1).

The slope of the line is m= (11-(-3)) / (3-(-1)) = 14/4 = 3.5.

Using the point-slope formula, we can find the equation of the line:

y-(-3) = 3.5(x-(-1))

y + 3 = 3.5x + 3.5

y = 3.5x - 0.5

Therefore, the equation of line segment AB is y = 3.5x - 0.5.

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If the sale price is 72 with a 64% discount. Then the original price will be $200.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

If the sale price is 72 with a 64% discount. Then the original price is given as,

⇒ $72 / (1 - 0.64)

⇒ $72 / 0.36

⇒ $200

If the sale price is 72 with a 64% discount. Then the original price will be $200.

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The exponential function for the given  data will be y = 5 * [tex]e^{2*7}[/tex]

What is exponential?

The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

Given population is = 5(now)

The time = 7years

r = 2

Exponential growth equation:

N₁ = No e¹t

Where,

N= Population density after time t

N+= Population density at time zero

r = Intrinsic rate of natural increase

e = Base of natural logarithms (2.71828)

So the exponential expression will be y = 5 * [tex]e^{rt}[/tex]

y = 5 * [tex]e^{2*7}[/tex]

Hence, The exponential function for the given  data will be y = 5 * [tex]e^{2*7}[/tex]

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A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended.

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When 5 winners are randomly selected, the probability that they are all men is 0.0045

Among the contestants in a competition are 45 women and 25 men.

Total persons are = 45+25 = 70

When one winner is chosen, there are 69 people left, when second winner is chosen there are 68 people left and so on.

So, the probability that they are all men is given by:

25/70 *24/69 * 23/68 * 22/67 * 21/66 = 0.0045

Therefore, when 5 winners are randomly selected, the probability that they are all men is 0.0045-

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Multiplication and division properties of equality are stated below.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Multiplication property of equality states that if a real number has been multiplied with the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.

That is, if x = y, then ax = ay, where a is a real number.

Division property of equality states that if a real number has been divided by the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.

That is if x = y, then x/a = y/a.

Hence the multiplication and division property of equality has been stated.

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The total number of different pizzas you can order is 8 x 21 x 4 = 672.

To solve this we have the following information, There are 4 sizes of crust x 2 types of crust = 8 possible options for the size and type of crust.

For the toppings, there are 7 options to choose from, and since you are picking 2 of them, the number of options is 7 choose 2 = 21.

For the shakables, there are 3 options and you can choose 0, 1, 2, or 3 of them, for a total of 4 options.

So the total number of different pizzas you can order is 8 x 21 x 4 = 672.

Therefore, The total number of different pizzas you can order is 672.

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Answer:

Below

Step-by-step explanation:

First find the value of the common vertical side

12/v = v/16

v^2 = 192

v = 8 sqrt 3

Now use pyhtag theorem to find x and y

y^2 = 12 ^2 + (8 sqrt3)^2

y = sqrt (336)   = 4 sqrt (21)

now find x the same way

x^2 = 16^2 + (8 sqrt(3))^2 = 448

x = sqrt (448 ) = 8 sqrt 7

There are 4915200 zombies in the episode 16.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

Given:

In the Walking Dead, the number of zombies doubles every episode.

In the episode 1,

there were 75 zombies.

Then,

y = 75(2)¹⁶

y = 4915200

Therefore, 4915200 zombies.

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Overhead cost applied to Work in Process. and hence Option (c) is correct for the production

Refer to the T-account below:

Manufacturing Overhead

(2)

4,000

(9)

150,000

(3)

15,000

(4)

80,000

(5)

30,000

(6)

25,000

154,000

150,000

Bal.

4,000

Labor costs = $175,000

Production order = $150,000

General factory use = $25,000

Factory overhead applied to production = $23,000

Therefore, the journal entry is as follows:

Work in process A/c Dr. $23,000

      To Factory overhead             $23,000

(To record the factory overhead applied to production

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Answer: D. 2w + 2(2w+3) = 96

Step-by-step explanation:

Perimeter = 2l + 2w

l = 2w + 3

Plug l into the perimeter equation

Perimeter = 2w + 2(2w+3)

Perimeter = 96

96 = 2w + 2(2w+3)

If you want to simplify, w = 22.5

If Jim's credit card statement shows a previous balance of $937.20, and he made a payment of $730 and add a new transaction of $502, if his credit card Annual Percentage Rate (APR) is 15%, then his new balance is $1699.20.

To calculate the new balance, the following steps were taken:

Add the previous balance ($937.20) to the new transaction amount ($502.00) to find the current balance before finance charges

$937.20 + $502.00 = $1439.20

Calculate the finance charges by dividing the annual percentage rate (APR) which is 15% by the number of billing periods in a year (usually 12) and then multiplying the result by the average daily balance.

finance charges = (15% / 12 months) × $1439.20

finance charges = $17.49

Add the finance charges to the current balance before finance charges to find the new balance:

$1439.20 + $17.49 = $1656.69

Finally, subtract the payment amount ($730) from the new balance ($1656.69) to find the updated balance:

$1656.69 - $730 = $1699.20.

Therefore, Jim's new balance is $1699.20.

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The value of the energy E when m=6kg and v=2ms-1​ is;  E = 12 Joules

We are told that the energy E is possessed by a moving object that varies directly as the mass of m and the square of velocity V. Thus, this can be expressed as;

E = kmV²

Where k is the constant of variation

Thus,  when m= 8kg, v=5ms-1 and e =100 joules, we have;

100 = k * 8 * 5²

k = 100/(8 * 5²)

k = 0.5

Thus, when m=6kg and v=2ms-1​, we have;

E = 0.5 * 6 * 2²

E = 12 Joules

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Each month, you must pay $400 toward the balances on these two credit cards. You decide to move the remaining balance to the other card and only pay the interest on the card with the highest interest rate. Fill out the following two tables to help you respond to questions 1-3.

In its most basic form, interest is computed as a percentage of the principle. The interest you would pay, for instance, would only be 5% of $100 if you borrowed $100 from a friend and agreed to reimburse it with 5% interest: $100(0.05) = $5.

Card Name (APR %) Existing Balance Credit Limit

MarK2 (6.5%) $475.00 $3,000.00

Bee4 (10.1%) $1,311.48 $2,500.00

Savings vs. Debt Portfolio

You must pay off these two credit cards with $400 each month. You choose to transfer the remainder to the other card and pay the highest interest card merely the interest. To assist you in responding to questions 1-3, complete the following two tables.

Higher-Interest Card (Payoff Option)

Month 1 2 3 4 5 6 7 8 9 10

Principal 1311.48 1074.82 814.26 527.38 211.53      

Interest accrued 132.46 108.56 82.24 53.27 21.36      

Payment (on due date) 369.12 369.12 369.12 369.12 232.89      

End-of-month balance 1074.82 814.26 527.38 211.53 0      

Lower-Interest Card

Month 1 2 3 4 5 6 7 8 9 10

Principal 475 475 475 475 475 338.77    

Interest accrued 30.88 30.88 30.88 30.88 30.88 22.02    

Payment (on due date) 30.88 30.88 30.88 30.88 167.11 360.79  

End-of-month balance 475 475 475 475 338.77 0    

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The measure of angle D of the isosceles triangle given above would be = 16°

An isosceles triangle is defined as the type of triangle that has all its three sides less than an acute angle, that is less that angle 90°. Also, all the internal angles of an isosceles triangle= 180°

Total internal angles of the isosceles triangle = 180°

Angle C = 2x + 17

Angle E = 8x - 13

Angle D = X

To calculate D the following is carried out:

180 = 2x+ 17 + 8x - 13 + X

180-17+13 = 2x+8x+X

176 = 11x

X = 176/11

X=16°

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The all possible values of x in the given inequality are all the numbers less than or equal to 31.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Ten less than twice a number is equal to at most 52.

The linear inequality representing this is,

2x − 10 ≤ 52

Adding both sides with 10,

2x ≤ 62

Dividing both sides by 2,

x ≤ 62 / 2

x ≤ 31

Hence all the numbers less than or equal to 31 satisfy the given equation.

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The value of the bond if the rate of interest currently is 6% the value of the bond is Rs. 1,000 and if it is 8% it is 750

Now, According to the question:

A bond is a sort of financial instrument where the issuer (debtor) owes the holder (creditor) a debt and is required, based on the terms, to pay the creditor cash flow at the bond's maturity date as well as interest over a certain period of time. The interest is often due annually, semi-annually, and on occasion less frequently. Bonds give the borrower access to external capital for momentary investments or, in the case of government bonds, for the financing of ongoing expenses. Despite the fact that both bonds and stocks are securities, bondholders hold a position as a creditor and stockholders hold equity in a firm. The main distinction between the two is this.

Value of the bond= V = 1/I = 60/.08 = 750

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Answer:

Step-by-step explanation:

The answer will be 24 because the LCM ( Lowest common Multiple)

of 3 and 8 is 24.

Answer:

24

Step-by-step explanation:

3 x 8 = 24

One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2

The function g(x) = 1x^2 - 4x + 5 and the function h(x) = 2x^2 - 8x + 10x^2 - 4x + 6 are quadratic functions. To find a function f(x) that satisfies the inequality g(x) ≤ f(x) ≤ h(x) for all x >= 0, we need to find a function that lies between these two functions for all x >= 0.

One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2

The intuition behind this choice is that if f(x) is the average of g(x) and h(x), it should be located between these two functions for all x >= 0. To confirm this, we can graph g(x), h(x), and f(x) on the same coordinate plane and see if they satisfy the inequality.

It's important to note that this solution is just one possible choice and there may be other functions that satisfy the inequality g(x) ≤ f(x) ≤ h(x) for all x >= 0.

Therefore, One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2

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The least number of square pieces that Monica can cut from a rectangular cake without wasting any cake is 15 pieces, each 7 inches on a side.

Monica wants to cut a cake into identical square pieces without wasting any cake. To find the least number of square pieces that can be cut from a rectangular cake, we need to find the greatest common divisor (GCD) of the lengths of the sides.

In this case, the GCD of 21 and 35 is 7. This means that we can cut the cake into 7-inch square pieces, and there will be no waste. The number of pieces can be found by dividing each side of the rectangular cake by the side length of the square pieces.

For the 21-inch side, the number of pieces is

21 / 7 = 3

For the 35-inch side, the number of pieces is

35 / 7 = 5

Therefore, the total number of pieces that can be cut from the rectangular cake is

3 * 5 = 15.

In conclusion, the least number of square pieces that Monica can cut from a rectangular cake without wasting any cake is 15 pieces, each 7 inches on a side.

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