The second side of a triangular deck is 3 feet longer than the shortest​ side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 80 ​feet, what are the lengths of the three​ sides?

Step-by-step explanation:

Below is an attachment containing the solution.

Paulina and Aliya's equations, 4x+2y=6 and 12x+6y=18, are multiples of each other. This means they represent the same line and indicate an infinite number of solutions rather than a single intersection point typically sought after in a system of distinct linear equations.

Paulina and Aliya have created linear equations to solve a mathematical problem. Paulina has the equation 4x+2y=6 and Aliya has 12x+6y=18. At a glance, these equations may look different, but upon closer inspection, Aliya's equation is actually just Paulina's equation multiplied by 3. This realization is pertinent because it suggests both equations represent the same line. Therefore, these two equations should have the same solution set.

To analytically solve simultaneous equations, one could use methods such as substitution, elimination, or matrix and determinant-based approaches. Using elimination or substitution, we aim to isolate one variable and solve for it. For example, because Aliya's equation is a multiple of Paulina's, if they were meant to be a system of separate lines, one way to solve them would be to simplify Aliya's equation by dividing by 3, revealing it to be identical to Paulina's, which indicates that this system has an infinite number of solutions (all points on the line represented by the equation).

If a system has two distinct equations, elimination involves adding or subtracting equations from one another to eliminate one of the variables, and substitution involves solving for one variable in terms of the other and then substituting this expression into the other equation. When equations are actually multiples of each other, this indicates either an infinite number of solutions or no solutions dependant if the equations are consistent or inconsistent respectively.

The decay factor of the exponential function represented by the provided table is 1/3 as the ratio of the consecutive y-values of the function is consistently 1/3.

The decay factor of an exponential function can be found by comparing the ratio of the y-values of the function.

In the given question, a table of x/f(x) values is provided.

A decay happens if the ratios of the consecutive y-values (outputs) are consistently less than 1.

Let's find the ratio between successive y-values. Between 18 and 6, the ratio is 6/18 = 1/3. Going from 6 to 2, the ratio is 2/6 = 1/3. Lastly, transitioning from 2 to 2/3, the ratio is (2/3)/2 = 1/3.

Since we find the ratio of successive outputs (y-values) to consistently be 1/3, it is safe to say that 1/3 is the decay factor for the exponential function represented by the given table.

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Answer:

  -8

Step-by-step explanation:

Let n represent the number. Then we have ...

  n -3 . . . . the difference of a number and 3

  = . . . . . .  equals

  5 +2n . . . 5 added to twice the number

Adding -n-5 to both sides of the equation gives ...

  n -3 -n -5 = 5 +2n -n -5

  -8 = n . . . . . simplify

The number is -8.

Answer:

She makes 7.8% portion of sales collectively.

Step-by-step explanation:

Let us assume she makes total of 100 calls.

The percentage of calls which are busy or unanswered = 22 %

So, now calculating 22% of 100 , we get:

[tex]\frac{22}{100} \times 100 = 22[/tex]

So, 22 of her calls are UNANSWERED.

Now, let us find out the number of calls successfully made by telemarketer.

Total successful calls = Total Calls made - Number of unanswered calls

                                    = 100 - 22  = 78

So, she makes a total of 78 calls successfully.

Now, he sells subscriptions to 10% of the 78 calls made successfully.

So, now calculating 10% of 78 , we get:

[tex]\frac{10}{100} \times 78 = 7.8[/tex]

So, she sold 7.8 subscriptions in total out of 100 attempts.

Also, as we know 7.8 out of 100  = 7.8% of 100.

Hence, she makes 7.8% portion of sales collectively.

Answer:

  12.37 square inches

Step-by-step explanation:

The area of the dartboard can be figured from the diameter as ...

   A = (π/4)d² = (π/4)(17.75 in)² ≈ 247.4495 in²

There are 20 sectors, all the same size, so the area of one of them is ...

  sector area = (1/2)(247.4495 in²) ≈ 12.37 in²

Answer: There are 15 nickles and 20 dimes.

Step-by-step explanation:

Since we have given that

Let the number of nickles be 'x'

Let the number of dimes be '2x-10'.

Total amount = $2.75

According to question, we get that

[tex]0.1(2x-10)+0.05x=2.75\\\\0.2x-1+0.05x=2.75\\\\0.25x=2.75+1\\\\0.25x=3.75\\\\x=\dfrac{3.75}{0.25}\\\\x=15[/tex]

Hence, there are 15 nickles and [tex]2x-10=2(15)-10=30-10=20[/tex] dimes.

Therefore, there are 15 nickles and 20 dimes.

Final answer:

Mary has 15 nickels and 20 dimes.

Explanation:

Let's solve this problem step-by-step:

Modular division, also known as modular arithmetic, has various applications in cryptography, computer science, and number theory. It is used in encryption algorithms like RSA and in solving congruence equations.

Modular division, also known as modular arithmetic, is a mathematical operation that involves finding the remainder when one number is divided by another. Modular division is commonly used in various mathematical applications such as cryptography, computer science, and number theory.

One application of modular division is in the encryption and decryption of data using modular arithmetic. For example, the RSA encryption algorithm relies on modular division to encode and decode messages.

Another application of modular division is in solving congruence equations. Congruence equations represent the idea of equivalence of numbers modulo a given number. By using modular division, we can determine the solutions to these equations.

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Modular division is used to find remainders in mathematics, but it is not used for dividing polynomials or dividing by zero. It's also not useful for dividing vectors in physics.

Modular division is a mathematical method used to find the remainder of a division problem, but it is not necessarily applicable in all contexts. For example, dividing a polynomial by a polynomial generally does not result in a polynomial, indicating that other methods must be used in this situation. Furthermore, it's important to note that modular division cannot be used to divide by zero, since this is undefined in mathematics. Additionally, within the discipline of physics, modular division is not applicable for operations such as dividing a vector by another vector component by component, as there are no useful physics applications for this type of operation.

Answer:

  see below

Step-by-step explanation:

As always, the coordinate transformations are ...

  a. 180° — (x, y) ⇒ (-x, -y)

  b. 270° CCW or 90° CW — (x, y) ⇒ (y, -x)

  c. 90° CCW or 270° CW — (x, y) ⇒ (-y, x)

___

It can be quick and easy to use a transparency or tracing paper to locate the rotated position of the image.

Step-by-step explanation:

Here, given:

Let us assume the number on Tens place  = M

The number in Units place  = N

So, the actual value of the number   = 10 M + N

The number can be written as MN.

Now, The value of M ( Tens digit) is Less than 5.

So, M  = 1, 2 , 3 or 4  ( 0 not included)

Also, The value of N(Unit digit)  is greater than 7.

So, N  = 8, 9 or 0  ( 0  included)

So, by combining all possibilities for M and N , the possible number chosen by Andy can be expressed as MN :

Number = {18,19,10,28,29,20,38,39,30,48,49 or 40}

Any number can be chosen from the above set as all the numbers match the given restrictions.

The well is 35 feet deep.

Step-by-step explanation:

Given,

Length of rope = 50 feet

Length of remaining rope = 15 feet

Let,

x be the depth of well.

Total length of rope = Length of remaining + Depth of well

[tex]50=15+x\\50-15=x\\x=35[/tex]

The well is 35 feet deep.

Answer:

C

Step-by-step explanation:

The x-axis is more than 7.0 and the y-axis is less than 7.0.

Cheers

Answer:

[tex]2\frac{1}{6}[/tex] pounds.

Step-by-step explanation:

We have been given that Gina's literacy bucket weighs 6 pounds. Her novel weighs 1 4/6 pounds, and her chrome book weighs 2 1/6.

To find weight of bucket after taking out the two items, we will subtract weight of each item from 6 pounds as:

[tex]\text{Weight of bucket}=6-1\frac{4}{6}-2\frac{1}{6}[/tex]

Let us convert mixed fractions into improper fractions as:

[tex]1\frac{4}{6}=\frac{6\cdot 1+4}{6}=\frac{10}{6}\\\\2\frac{1}{6}=\frac{6\cdot 2+1}{6}=\frac{12+1}{6}=\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=6-\frac{10}{6}-\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=\frac{6\cdot 6}{6}-\frac{10}{6}-\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=\frac{36}{6}-\frac{10}{6}-\frac{13}{6}[/tex]

Combine numerators:

[tex]\text{Weight of bucket}=\frac{36-10-13}{6}[/tex]

[tex]\text{Weight of bucket}=\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=2\frac{1}{6}[/tex]

Therefore, the weight of the bucket is [tex]2\frac{1}{6}[/tex] pounds.

Answer:

e) Trend Analysis

The term is 'trend analysis'. This refers to a statistical method used to evaluate and predict future trends based on historical data. This technique is specifically referenced in prediction of labor demand using prior year’s data.

The concept referred to in the question is e. Trend analysis. Trend analysis is a statistical method used to evaluate and predict future trends based on historical data. In the context of labor demand, a trend analysis would involve examining labor demand data from the previous year, identifying patterns and trends within that data, and using statistical models to make predictions about labor demand for the upcoming year.

For example, suppose a company has seen a steady increase in labor demand over the past five years. Based on this trend, they can build a statistical model that predicts an increase in labor demand for the next year as well. This strategy helps companies plan for their future staffing needs, ensuring they have the necessary resources to meet their objectives.

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From the given info (and the linked question) we find

[tex]\cos\alpha=-\dfrac5{13}[/tex]

[tex]\sin\alpha=\dfrac{12}{13}[/tex]

[tex]\sin\beta=-\dfrac45[/tex]

Then using the angle-sum identity for cosine, we have

[tex]\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta[/tex]

[tex]\cos(\alpha-\beta)=\left(-\dfrac5{13}\right)\dfrac35+\dfrac{12}{13}\left(-\dfrac45\right)=-\dfrac{63}{65}[/tex]

Final answer:

To find the exact value of cos(α-β), we use the cosine sum and difference identity and the respective sine and cosine values calculated from the given tangent and cosine values for angles α and β. Using this approach, we find that cos(α-β) equals 63/65.

Explanation:

The exact value of cos(α-β) can be found by using the sum and difference identities for cosine. Since tanα = -12/5, in quadrant II, we can find the corresponding sine and cosine values for α using the Pythagorean identity sin²α + cos²α = 1. For cosβ = 3/5, in quadrant IV, we do a similar procedure to find the sine of β. With both sine and cosine for α and β, we use the identity cos(A-B) = cosA cosB + sinA sinB to find cos(α-β).

To find the sine and cosine for α, given that tanα = -12/5, we know that the opposite side is -12, and the adjacent side is 5, so the hypotenuse using the Pythagorean theorem is √(12² + 5²) = √(144+25) = √169 = 13. Thus sinα = -12/13 (negative because α lies in the second quadrant where sine is negative) and cosα = 5/13 (positive because cosine in the second quadrant is positive).

For β, we already have cosβ = 3/5. The sine can be found using the Pythagorean identity 1 - cos²β = sin²β, which gives sinβ = -√(1 - (3/5)�) = -√(1 - 9/25) = -√(16/25) = -4/5 (negative because β is in the fourth quadrant where sine is negative).

Now, we can find the exact value of cos(α-β) by plugging in the values:

cos(α-β) = cosα cosβ + sinα sinβ = (5/13)*(3/5) + (-12/13)*(-4/5)
= 15/65 + 48/65 = 63/65.

Therefore, the exact value of cos(α-β) is 63/65.

Answer:

D)191 feet

Step-by-step explanation:

Let the height of the light house be |AB| and the Boat be at point C as shown in the diagram.

The angle of depression of the boat from the top A of the lighthouse is given as 25 degrees

Angle BCA = 25 degrees (Alternate Angles are Equal)

We want to determine the distance of the boat C from the base of the lighthouse B i.e. |BC|

[tex]Tan\alpha =\frac{opposite}{adjacent}[/tex]

Tan 25=[tex]\frac{89}{|BC|}[/tex]

Cross multiply

|BC| X tan 25 =89

|BC| = [tex]\frac{89}{tan 25}[/tex]=190.86 feet

The distance of the boat C from the base of the lighthouse B is 191 feet (to the nearest feet).

The slope of Line m that is parallel to Line l is also 4/9.

The slope of a line determines its steepness and direction. When two lines are parallel, they have the same slope. In this case, Line l is parallel to Line m, and the slope of Line l is 4/9. Therefore, the slope of Line m is also 4/9.

Answer:

36

Step-by-step explanation:

The angles of a pentagon sum to 180(5-2) = 540 degrees, so each angle of a regular pentagon is 540/5 = 108. Therefore, three of these angles sum to $3 * 108 = 324, which means the indicated angle measures 360 - 324 = 36.

Answer:

36

Step-by-step explanation:

The angles of a pentagon sum to 180(5-2) = 540 degrees, so each angle of a regular pentagon is 540/5 = 108. Therefore, three of these angles sum to 3* 108 = 324, which means the indicated angle measures 360 - 324 = 36

Answer:

0.900

Step-by-step explanation:

The easiest way to solve this problem is by putting it into a calculator.

When put into a calculator, the answer comes out to be 0.9004304526, which can be rounded to 0.900, or just 0.9.

Good morning ☕️

Answer:

0.900

Step-by-step explanation:

using a calculator you’ll find:

sin⁻¹(-0.435) = -25.785293878311

now

cos(sin⁻¹(-0.435)) = cos(-25.785293878311)

                           = 0.900430452617

If we round 0.900430452617 to nearest thousandth we get: 0.900

:)

Answer:

the answer is 7

Step-by-step explanation:

angle 30°

x=14/2

x=7

The value of x is 7 cm.

If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle.

y = 14* sin 30°

y = 14* 0.5

y = 7

y = 7cm

The bottom line of a triangle is the base of the triangle, and it can be one of the three sides of the triangle. In a triangle, one side is the base side and the remaining two sides can be the height or the hypotenuse side.

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Answer:

y=-2x

Step-by-step explanation:

First you want to remember rise over run. Your rise is -2 and your run is 1. So -2/1 is your answer. And -2/1 is equal to -2.

Answer:

[tex]\frac{2} {-1}[/tex]=-2

Step-by-step explanation:

Answer:

More. The product of 25 and 3/5 is 15 which is greater than 14.

Step-by-step explanation:

Answer:

-471,861

Step-by-step explanation:

The sum of 9 terms in the sequence –9, 36, –144, 576, ... is -471861.

An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given:

–9, 36, –144, 576, ...

Calculate the ratio of the sequence as shown below,

ratio = 36 / -9

ratio = -4

Calculate the sum of 9 terms as shown below,

S₉ = -9 (1 - (-4)⁹) / (1 - (-4))

S₉ = -9 (1 + 262144) / 5

S₉ = -9 (262145) / 5

S₉ = -2359305 / 5

S₉ = -471861

To know more about the sequence:

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Answer:

The given data is not normal.

Step-by-step explanation:

We are given the following data:

30, 59, 69, 50, 58, 71, 55, 43, 3,  66, 52, 56, 62, 36, 13, 29, 17, 31

Condition for normality:

Mean = Mode = Median

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{800}{18} = 44.44[/tex]

Mode is the most frequent observation of the data.

Since all the value appeared once, there is no mode.

[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]

Sorted data: 3, 13, 17, 29, 30, 31, 36, 43, 50, 52, 55, 56, 58, 59, 62, 66, 69, 71

Median =

[tex]=\dfrac{9^{th}+10^{th}}{2} = \dfrac{50+52}{2}=51[/tex]

Since the mean, mode and median of data are not equal, the data is not normal.

Answer:

Answer:

a) k = 0.1875 m

b) r2 = 0.46875 m

c) q = -1.125*10^-8 C

Step-by-step explanation:

Given:

- The total Length of rod L = 1.5 m

- The total charge of the rod Q = -9 * 10^8 C

- Total section of a rod n = 8

Find:

1. What is the length of one of these pieces?

2. What is the location of the center of piece number 2?

3. How much charge is on piece number 2?

Solution:

- The entire rod is divided into 8 pieces, so the length of each piece would be k:

                                     k = L / n

                                     k = 1.5 / 8

                                     k = 0.1875 m

- The distance from center of entire rod and center of section 2 is 2.5 times the section length

                                     r2 = 2.5*k

                                     r2 = 2.5*(0.1875)

                                     r2 = 0.46875 m

- Assuming the charge on the rod is uniformly distributed. The the charge for each section of rod is given by q:

                                     q = Q / n

                                     q = -9 * 10^8 / 8

                                     q = -1.125*10^-8 C

The length of one of the eight pieces of the rod is 0.1875 m. The center of piece number 2 is at <0.28125, 0, 0> m. The charge on piece number 2 is -1.125e-08 Coulombs.

The problem involves the concepts of electric field, charge distribution, and coordinate system in Physics. Let's answer the question part by part:

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Answer:   [tex]\bold{(a)\quad \dfrac{32}{3}\qquad (b)\quad \dfrac{32}{3}}[/tex]

Step-by-step explanation:

(a) First, find the x-coordinates where the two equations cross

                            y = -1    and   y = 3 - x²

  -1 = 3 - x²

 -4 =     -x²

  4 =       x²

± 2 =       x       → These are the upper and lower limits of your integral

Then subtract the two equations and integrate with upper bound of x = 2 and lower bound of x = -2

[tex]\int_{-2}^{+2}[(3-x^2)-(-1)]dx\\\\\\=\int_{-2}^2(4-x^2)dx\\\\\\=4x-\dfrac{x^3}{3}\bigg|_{-2}^{+2}\\\\\\=\bigg(8-\dfrac{8}{3}\bigg)-\bigg(-8+\dfrac{8}{3}\bigg)\\\\\\=\large\boxed{\dfrac{32}{3}}[/tex]

(b) We know the upper and lower bounds of the y-axis as y = 3 and y = -1

Next, find the equation that we need to integrate by solving for x.

      y = 3 - x²

x² + y = 3

x²       = 3 - y

x         [tex]=\pm\sqrt{3-y}\\[/tex]

[tex]\rightarrow \qquad x=\sqrt{3-y}\quad and \quad x=-\sqrt{3-y}[/tex]

Now, subtract the two equations and integrate with upper bound of y = 3 and lower bound of y = -1

[tex]\int_{-1}^{+3}[(\sqrt{3-y})-(-\sqrt{3-y})]dy\\\\\\=\int_{-1}^{+3}(2\sqrt{3-y})dy\\\\\\=\dfrac{-4\sqrt{(3-y)^3}}{3}\bigg|_{-1}^{+3}\\\\\\=\bigg(0\bigg)-\bigg(-\dfrac{32}{3}\bigg)\\\\\\=\large\boxed{\dfrac{32}{3}}[/tex]

Answer:

14.375 pounds

Step-by-step explanation:

Jesse's dog: 23 lb

Cat: 5/8*23=115/8

Therefore, Jesse's cat weighs 14.375 pounds

Option B:

Point R on the number line best represents [tex]\frac{-6}{2}[/tex]

Solution:

In the number line,

The numbers which are left side of 0 are -1, -2, -3, -4, -5, -6, -7, -8.

The numbers which are right side of 0 are 1, 2, 3, 4, 5, 6, 7, 8.

Q is 6 points left of 0. That is Q = -6

R is 3 points left of 0. That is R = -3

S is 2 points left of 0. That is s = -2

T is 3 points right of 0. That is T = 3

[tex]$\frac{-6}{2}=-3[/tex]

In the number line -3 is the point of R.

Therefore point R on the number line best represents [tex]\frac{-6}{2}[/tex].

Option B is the correct answer.

Answer:

O(n2)

Step-by-step explanation:

the first iteration algorithm of the i-for loop (the outer loop), the j-for loop (the inner loop) will run 2 to

n times which is represented as

(n − 1 times).

the second iteration algorithm of the i-for loop, the j-for loop will run 3 to n times represented as

(n − 2 times).

the third to the last iteration algorithm of the i-for loop, the j-for loop will run n − 1 to n times (2 times).

And the second to the last iteration of the i-for loop, the j-for loop will run from n to n times (1 time)

For the last iteration of the i-for loop, the j-for loop will run 0 times because i + 1 > n.

Now we know that the number of times the loops are run is

1 + 2 + 3 + . . . + (n − 2) + (n − 1) = n(n − 1)/2

So we can express the number of total iterations as n(n − 1)/2.

Since we have two operations per loop (one comparison and one multiplication), we have

2 ·n(n−1)/2 = n

2 − n operations.

So f(n) = n2 − n

f(n) ≤ n2

for n > 1.

Therefore, the algorithm is O(n2) with

C = 1 and k = 1.

Answer:

area = 8a^2 +4ab

Step-by-step explanation:

Area = (4a)(2a + b)

= 8a^2 +4ab

Step-by-step explanation:

[tex]Area of rectangle \\ = base \times height \\ = (4a) \times (2a + b) \\ = 4a \times 2a + 4a \times b \\ = 8 {a}^{2} + 4ab \\ [/tex]

Answer:

general admission tickets  1170

courtside tickets  985

tickets bench seats.  130

Step-by-step explanation:

To solve the problem, it is necessary to generate a system of equations with the information provided by the statement.

First be

x = # general admission tickets

y = # courtside tickets

z = # tickets bench seats.

The first equation would be that they sold nine times more general admission tickets than bench seats tickets.

That is: x = 9 * z (1)

And the second equation is that the number of general admission tickets sold was 55 more than the sum of the number of courtside tickets and bench seats tickets.

That is: x = 55 + y + z (2)

Now the third equation would be the money raised.

28 * x + 43 * y + 173 * z = 97605 (3)

Now if I replace I rearrange (1):

z = x / 9 (4) and replacement in 2, I have:

x = 55 + y + x / 9, rearranging:

y = (8/9) * x - 55 (5)

Now replacing (4) and (5) in 3, we have:

28 * x + 43 * ((8/9) * x - 55) + 173 * (x / 9) = 97605

Solving the above:

x = 1170, therefore

y = (8/9) * 1170 55 = 985

z = 1170/9 = 130

We can confirm this with equation (3)

28 * x + 43 * y + 173 * z = 97605

28 * 1170 + 43 * 985 + 173 * 130 = 97605

450 general admission tickets, 171 courtside tickets, and 50 bench tickets were sold for the Harlem Globetrotter show.

Let's assign variables to represent the number of tickets sold for each category:

Lets  x  = number of general admission tickets sold

Lets  y   = number of courtside tickets sold

Lets  z  = number of bench tickets sold

According to the given information:

The cost of the general admission ticket = $28

The cost of the courtside ticket = $43

The cost of the bench ticket = $173

There were 9 times as many general admission tickets sold as bench tickets: x = 9z

The number of general admission tickets sold was 55 more than the sum of the courtside and bench tickets: x = y + z + 55

The total sales for all three types of tickets was $97,605: 28x + 43y + 173z = 97605

Now, we have a system of three equations with three variables:

x = 9z

x = y + z + 55

28x + 43y + 173z = 97605

We can use substitution or elimination method to solve this system of equations. Solving this system, we find that x = 450, y = 171, and z = 50. Therefore, 450 general admission tickets, 171 courtside tickets, and 50 bench tickets were sold for the Harlem Globetrotter show.

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