A rectangle is 13 feet long and has a diagonal that is 20 feet long. What is the length of the width?

The measure of side AB of the triangle is given by equation AB = 3.5 cm

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔACE

Let the second triangle be represented as ΔBCD

The measure of side AC = 14 cm

The measure of side EC = 84 cm

The measure of side ED = 21 cm

Now , ΔACE is similar to ΔBCD

So , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

AB / AC = ED / EC

AB / 14 = 21 / 84

Multiply by 14 on both sides of the equation , we get

AB = ( 1/4 ) 14

AB = 3.5 cm

Therefore , the value of AB is 3.5 cm

Hence , the measure of side AB of triangle is 3.5 cm

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If the mechanic told Mr P that it will cost 50$ an hour to fix his car, then 50x will be the cost which Mr P has to pay.

An expression is combination of variables, numbers and operators.

Given that Mr P’s had some car issues and he took it into the car shop.

The mechanic told him that it will cost 50$ an hour to fix his car.

We need to find Mr P has to pay for car.

Let x represents the number of hours.

$50x represents the amount Mr P has to pay for car.

Hence, the expression 50x represents the cost Mr P has to pay for car.

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If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

Given f(x) = 4x + 13 and g(x) = 10x − 2

We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.

Let the equation be (f + g)(x) = f(x) + g(x)

substitute the values in the above equation, we get

= (4x + 13) + (10x − 2)

simplifying the above equation, we get

= 4x + 13 + 10x − 2

= 4x + 10x − 2 + 13

= 4x + 11

Therefore, the expression (f + g)(x) be 4x + 11.

The completed question is:

The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.

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Answer:

Step-by-step explanation:

3.8 liters = 38deciliters

Answer:

3.8 litres =38 deciliters

PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

163/30

Step-by-step explanation:

4 3/5 in mixed number form would be 23/5

5/6 remains 5/6 as it is not greater than 1, therefore it cannot be simplified.

23/5 + 5/6

in order to add, we have to make the denominators alike. the least common multiple is 30. so we have to not just multiply the denominators by whatever results in 30, but also the numerators.

23 times 6 = 138

5 times 6 = 30

5 times 5 = 25

5 times 6 = 30

138/30 + 25/30

at this point, we can simply just add the numerators

163/30

i hope this helps

The type of sampling that Huw is using is called Convenience Sampling.

Explanation:

Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.

Answer:The price of 10 pounds of cheese is 15.84$

Step-by-step explanation:

It's simple

In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences.

Number  mathematical entity used to represent a quantity or magnitude it can be symbol or a combination of symbol used to denoted a quantity such as 2573 or 8 1 number are used in a variety of context including counting measuring and computing they are also used to denote the size or amount of something such as a number of people in a room or the number of apples in a basket number play an important role in mathematics including algebra geometry and calculus.

Based on the above figures, the hospital would require a staffing of approximately 62 nurses on Shift A, 93 nurses on Shift B, 68 nurses on Shift C, and 27 nurses on Shift D. This would equate to a total of 250 nurses, which is the number of nurses the hospital has on its staff.

The hospital can adjust the staffing needs by taking into account the amount of nurses needed to provide the necessary patient care. If the shift with the highest number of patients (Shift B) requires additional nurses, the hospital could move nurses from the shift with the lowest number of patients (Shift D). This would result in fewer nurses on Shift D, but would allow for more nurses on Shift B.

In order to ensure that nurses are working in a safe and comfortable environment, the hospital should also take into account the nurses' own preferences. If nurses prefer to work certain shifts, the hospital can adjust the staffing levels accordingly. This can help create a better work-life balance for the nurses, which can, in turn, improve their job satisfaction and performance.

In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences. This way, they can maintain a safe and comfortable environment for their nursing staff, while also ensuring that they have enough nurses to provide the necessary care to their patient.

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Each wand costs $83, found by dividing the total cost of $498 by the total number of items, 6 (4 cloaks and 2 wands), resulting in $498 / 6 = $83.

To solve for the cost of each wand, we first need to determine the cost of each item (cloak and wand) that Harry bought. We can represent the cost of each item as "x". Since Harry bought 4 cloaks, the total cost of the cloaks is 4 * x. Similarly, since he bought 2 wands, the total cost of the wands is 2 * x.

The total cost of the cloaks and wands that Harry bought was $498, so we can write the equation: 4 * x + 2 * x = $498. This equation represents the total cost of the 4 cloaks plus the 2 wands, which must equal $498.

Next, we can simplify the equation by combining like terms: 4 * x + 2 * x = 6 * x = $498.

Finally, we can find the cost of each item by dividing both sides of the equation by 6: x = $498 / 6 = $83.

Therefore, each wand costs $83.

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Answer:

20(4+3)

Step-by-step explanation:

GCF of 80 and 60 = 20

20*4=80

20*3=60

20(4+3)

hope this helps! :)

The ratio of EP to PF is given as follows:

EP : PF = 2 : 7.

The ratio of EP to PF is obtained applying the proportions in the context of the problem.

Looking at the x-coordinates, we have that:

The ratio must necessarily be the same for the y-coordinates, hence the ratio is given as follows:

EP : PF = 4 : 14.

EP : PF = 2 : 7.

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Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

Step-by-step explanation:

(Pertaining to Part D --- Plugging in variables):

To find the answer to Part D, we must first take the function notation equation from Part C and plug in the appropriate variables needed to find the balance in the bank account after 5 days. So, we plug in '5' for g(x), which would give us g(5). For the other x found in the equation, we also correspondingly replace it with '5'. Our equation now appears as g(5) = -75(5) + 1500.

Finally, we must solve this equation using the order of operations, which simplifies our equation to g(5) = -375 + 1500. We can simplify this further by adding 1500 to -375, giving us the final answer for Part D of $1,125 being the balance in the bank account after 5 days.

Hope that helps!!

Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

We can estimate that there is about 1000 joules of kinetic energy in an average size helium balloon.

The amount of kinetic energy in an average size helium balloon can be estimated using the ideal gas law and the equipartition theorem.

Assuming the balloon is filled with helium at room temperature (around 298 K) and atmospheric pressure (around 1 atm), the volume of the balloon can be estimated to be around 0.5 m^3. The number of helium atoms in the balloon can be estimated using Avogadro's number, which is around 6.02 x 10^23.

Using the equipartition theorem, we can estimate the average kinetic energy of each helium atom in the balloon. At room temperature, each atom has an average kinetic energy of (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K).

Therefore, the total kinetic energy of the helium atoms in the balloon can be estimated as:

KE = (3/2)kT * N

where N is the number of helium atoms in the balloon.

Plugging in the estimated values, we get:

KE = (3/2) * (1.38 x 10^-23 J/K) * 298 K * 6.02 x 10^23

KE ≈ 9.95 x 10^2 J

Therefore, An average-sized helium balloon contains roughly 1000 joules of kinetic energy, according to our estimation. It's important to note that this is just an estimate, and the actual amount of kinetic energy in a helium balloon can vary depending on a number of factors such as the temperature, pressure, and size of the balloon.

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The missing angle is approximately 108.5 degrees.

Law of sines is a trigonometric formula that relates the sides and angles of any triangle. Specifically, the law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.

Using the law of sines:

sin(128°)/15 = sin(x)/12

Multiplying both sides by 12:

sin(x) = 12sin(128°)/15

Taking the inverse sine of both sides:

x = sin^-1(12sin(128°)/15)

x ≈ 108.5°

Therefore, the missing angle is approximately 108.5 degrees.

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The one who types the fastest is Morgan. hence, the correct option is A.

An equation is defined as an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation , the instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We have been given that equation y=39x

Which models the total number of words Alexa can type, where y is the number of words typed and x is the time in minutes.

The data shows the relationship for Morgan.

Then we can conclude that Morgan types the fastest.

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Since the mode is the most frequently occurring data value so -

Option D : None of the alternatives is correct.

What is mode?

A mode is described as the value in a group of values that occurs more frequently. The value that appears the most frequently is called mode.

The distribution of the mean, median, and mode values will depend on how skewed the distribution is.

The total dependency of mean, median and mode of data is on the asymmetric form of the data.

As a result, mean or mode may be larger than or less than mode.

Therefore, the mode is neither large than mean or median and can never be larger than mean.

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Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To find the area of a parallelogram, we use this equation:

Now that we have this equation, we can apply it to each parallelogram.

Now, we can figure out which has the greatest area.

Therefore, the parallelogram that has the greatest area is 3, or III.

Answer:

III

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

I

A = 3 × 5 = 15 units²

II

A = 5 × 3 = 15 units²

III

A = 4 × 4 = 16 units²

IV

A = 4 × 3 = 12 units²

parallelogram III has the greatest area

After cutting 9 pieces of ribbons, Diego made 14 pieces of wreaths with the remaining roll of ribbon.

For finding the pieces of wreaths we will first obtain the total meter required for 9 pieces of ribbon by multiplying 9 with 0.4 meter and then subtract it from the total meters of the roll of ribbons i.e., 12 meters and then divide the result with 0.6 meter.

Total meter required for 9 pieces of ribbon = 9x0.4 meter

                                                                        = 3.6 meters

Total meter of the roll of ribbon = 12 meters

Meter required per wreath = 0.6 meter per wreath

Meter of roll remaining for making wreaths = 12-3.6

                                                                        = 8.4 meters

Total number of wreath made from the remaining roll

= 8.4 meter / 0.6 meter

= 14 Wreaths

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To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.

The down payment refers to the initial cash payment for the purchase of an item on mortgage.

The down payment is required by the financier to evaluate the buyer's financial readiness.

The cost of the new home = $300,000

Down payment = 20% or $60,000 ($300,000 x 20%)

Mortgage loan required = $240,000 ($300,000 - $60,000)

Bank quoted interest rate = 4.75%

Desired interest rate = 4.5%

Difference in interest rate = 0.25% (4.75% - 4.5%)

Rate of buy down of the quoted interest per point = 0.125%

The number of points to buy down the interest rate = 2 (0.25/0.125)

The cost of each point = 1% of $240,000 = $2,400

The total cost of 2 points = $4,800 ($2,400 x 2)

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A function rule, if a carnival charges $6 to enter and $. 75 per ticket is f(x) = $6 + .75x

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

According to the question,

carnival charges is $6

cost per ticket is $0.75

Let the number of person/tickets be x

and f(x) be the total cost

therefore the function is f(x) = $6 + 0.75x

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Answer:

Step-by-step explanation:

y = 2x:

This is an equation for a straight line in which "y" is proportional to "x" with a coefficient of 2. If you plot this line on a coordinate plane, it will have a slope of 2 and y-intercept of 0.

12 x 12:

This is a mathematical expression for finding the product of 12 and 12. The result is 144. In mathematical writing, it's usually written as "12 * 12 = 144".

The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.

Mathematically, we can express this as:

dP/dt = rP

where P is the population size, t is time, and r is the growth rate.

Assuming a constant growth rate, we can integrate this equation to get:

ln(P) = rt + C

where C is an integration constant. We can solve for C using the initial population estimate:

ln(1200) = r(1980) + C

C = ln(1200) - r(1980)

Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:

ln(7500) = r(2008) + ln(1200) - r(1980)

Solving for r, we get:

r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496

Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:

ln(P) = rt + ln(7500)

ln(P) = 0.0496(12) + ln(7500) = 9.058

P = e^9.058 = 8656

Therefore, the estimated alligator population in the region in the year 2020 is 8656.

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The solution to the system of linear equations associated with the reduced row-echelon form matrix is (0, 0). This indicates that both variables, x and y, have a value of zero.

The reduced row-echelon form of a matrix is the simplest way to represent the solution to a system of linear equations. In the case of a matrix with two rows and two columns, a solution is produced when the matrix is in its reduced row-echelon form. Specifically, for the given matrix, 0 0, the solution to the corresponding system of linear equations is (0, 0). This indicates that both variables, x and y, have a value of zero. This is because the reduced row-echelon form is the simplest way to represent the solution to a system of linear equations. In this form, all the leading entries are ones and all the other entries are zero. Since the matrix is 0 0, this indicates that the solution is (0, 0). This solution can be seen as an ordered pair, where the first value represents the solution for the x variable, and the second value represents the solution for the y variable. In this case, both values are zero, which means that the solution to the system of linear equations is (0, 0).

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The complete question is

The matrix 1 −1 ]5 0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter form matrix(0,0).

In a case whereby three numbers are in the ratio 2:3:5 and the sum of their cube is 34560 then the numbers are  12, 18, and 30.

The given Ratio of three numbers can be expressed as 2:3:5

Then we can represent the three numbers  as: 2x, 3x, and 5x.

We were given the Sum of their cubes as  34560

Thern we can cube them as 2x^3 + 3x^3 + 5x^3 =34560

The we will have 8x^3 + 27x^3 + 125x^3 =34560

Then we have 160x^3 = 34560

x^3 =34560/160

x= 6.

then we can find the values of the ratio as :

2x =( 2×6)

= 12

3x = (3×6 )

= 18

5x = (5×6 )

= 30

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The number that can each terms of the equation be multiplied by to eliminate the decimals before solving is 100

The equation is

5.6j + 0.12 = 4 + 1.1j

The equation is defined as the mathematical expression that shows the relationship between one expression and another expression with equal sign. The equation consist of mathematical operator like addition, subtraction, division and multiplication

The equation is

5.6j + 0.12 = 4 + 1.1j

Here three term has fractional part.

In 0.12 there are two digits after the decimal point to eliminate the decimal number we have to multiply the number with 100 .

Then the equation will become

560j + 12 = 400 + 110j

Therefore, the number is 100

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The given question is incomplete, the complete question is

Which number can each term of the equation be multiplied by to eliminate the decimals before solving?

5.6j + 0.12 = 4 + 1.1j

Rounding off the 1004.8 into 3 significant figures will give 1000.

Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.  

For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.  

Here we have a number    

1004.8 need to be rounded off for 3 significant figures  

Since 4 is less than 5 then the resultant number = 1000  

[ 4 and 8 neglected since 4 < 5]

Therefore,

Rounding off the 1004.8 into 3 significant figures will give 1000.

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The value of x is 80 degrees.

The correct answer is an option (A)

Consider the following figure.

Let us assume that the upper triangle be ABC and the lower triangle be NMC.

We can observe that both the triangles are isosceles triangles, because in both the triangles two sides are congruent.

Consider triangle ABC.

As the triangle is isosceles triangle, from the definition of  isosceles triangle ∠A = ∠B

So, ∠A = 65°

We know that the sum of all the angles of triangle is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠C = 180° - (65° + 65°)

⇒ ∠C = 180° - 130°

⇒ ∠C = 50°

We can observe that ∠ACB and ∠MCN are opposite angles.

So,  ∠MCN = 50°

Also, triangle MNC is also an isosceles triangle.

so, ∠C = ∠N

⇒∠N = 50°

We know that the sum of all the angles of triangle is 180°

⇒ ∠M + ∠N + ∠C = 180°

⇒ ∠M = 180° - (50° + 50°)

⇒ ∠M = 180° - 100°

⇒ ∠M = 80°

Therefore,  x = 80°

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The required we can save $13.86 annually by buying all your turkey at the discount store.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's call the price of turkey per pound at the supermarket "x". Then the price of turkey per pound at the discount store would be x - $0.99.

Since we consume 14 pounds of turkey annually, the cost of the turkey at the supermarket would be 14 × x dollars.

And the cost of the turkey at the discount store would be 14 × (x - $0.99) dollars.

Therefore, the amount you would save annually by buying all your turkey at the discount store is,

= 14 × x - 14 × (x - $0.99) = 14 × $0.99
= $13.86

So, we would save $13.86 annually by buying all your turkey at the discount store.

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