Design an algorithm to find all the common elements in two sorted lists of numbers.

The rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 can be found using the Rational Root Theorem.

The Rational Root Theorem states that if a polynomial has a rational root, it will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is -1 and the leading coefficient is 1. The factors of -1 are -1 and 1, and the factors of 1 are 1. Therefore, the possible rational roots of this polynomial are -1/1, 1/1, or -1 and 1.

We can test these possible roots by plugging them into the polynomial and seeing if the result is 0.

P(-1) = (-1)^3 + 3(-1)^2 + (-1) - 1 = -1 + 3 - 1 - 1 = 0
P(1) = (1)^3 + 3(1)^2 + (1) - 1 = 1 + 3 + 1 - 1 = 4

Therefore, the only rational root of this polynomial is -1.

So, the rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 are -1.

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Answer:

9

Step-by-step explanation:

54÷6= 9

27÷3= 9

18÷2= 9

hence the answer is 9.

Answer:

It is B: A180 mm side length

The value of x for the given circle is 115°.

Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and properties of objects in space. It includes the study of points, lines, planes, angles, curves, surfaces, and solids.

Using the Angles of Intersecting Chords Theorem,

When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

So, angle x = (190° + 40°)/2  = 115°

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A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.

here, we have,

Given,

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.

Equation:

X + y = 119

y = 119 - x

0.40x + 0.12y = 119 of 0.32

0.40x + 0.12y = 38.08

Using y = 119 -x

0.40x + 0.12(119 - x) = 38.08

0.40x + 14.28 - 0.12x = 3808  Eq(2)

0.28x = 23.8

x = 85

and,

y = 119 - 85

y = 119 - 85

y = 34

Equating values in equation (2),

=0.40(85) + 0.12(34)

=34 + 4.08

=38.08

A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

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Answer:

Step-by-step explanation:

There would be 1,968 people who hold valid passports.

The length of the line segment AB is 11/2 mm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to one side of a triangle divides the other two sides in the same ratio.

Therefore, AC/AB = EC/ED.

22/AB = 44/11.

2/AB = 4/11.

4AB = 22.

AB = 11/2.

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Answer:

180 - 119.4 = 60.6

So the answer is 60.6

Answer:

60.6°

Step-by-step explanation:

Supplementary angles equal 180 degrees. So we can show this with the following equation:

119.4 + x = 180

where x is the measure of the other supplementary angle.

If we subtract 119.4 from both sides, we get the the value of x, which is 60.6.

The length of the slide shown is 15 feet

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let l represent the length of the slide, hence:

sin(53) = 12/l

l = 12/sin(53)

l = 15 feet

The length is 15 feet

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60 kilometers per hour (kph) is equal to  roughly 37.28  long hauls (miles) per hour( mph).

To convert kilometers per hour to long hauls per hour, you can use the following conversion formula:

long hauls per hour =  kilometers per hour x0.621371.

Plugging in 60 kilometers per hour, we get,

long hauls per hour =  60 x0.621371  

long hauls per hour ≈37.28.  

Thus, 60 kilometers per hour is roughly 37.28 long hauls per hour.  

A kilometer (km) is a unit of length or distance used in the metric system. It is roughly original to 0.621  long hauls.

Mile is a unit of length or distance used in the customary system of dimension, primarily in the United States and United Kingdom. One afar is original to 280 bases or 760 yards, which is  roughly 1.609 kilometers in the metric system.

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The weighted average of the numbers is 0.1.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

Given that, average of the numbers -3 and 5 with 3/5

The weight of first number and 2/5 of second number.

Here, -3(3/5)+5(2/5)/2

= (-1.8+2)/2

= 0.2/2

= 0.1

Therefore, the weighted average of the numbers is 0.1.

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1. To decide if the offer presented by your great uncle is to your advantage, you need to consider the time value of money. This means that money available today is worth more than the same amount of money available in the future, due to the potential for earning interest or returns on the money. In this case, you need to compare the value of $1,000 today with the value of $1,200 in five years. If you can earn a rate of return greater than 4% over the next five years, it would be better to take the $1,000 today and invest it to earn a higher return. However, if you cannot earn a return greater than 4%, it would be better to wait and take the $1,200 in five years.

2. Interest rates and compounding periods will vary depending on the financial institution and type of account. As an example, let's assume that you are considering a savings account, checking account, and money market account with the following interest rates and compounding periods:

Using a compound interest calculator, the future value of $1,000 in each account after five years would be:

3. The value of money today can be different from its value in the future due to inflation, changes in interest rates, economic growth, and changes in the supply and demand for goods and services. Inflation is one of the biggest factors that can affect the value of money over time. If the rate of inflation is high, the value of money will decrease over time, meaning that the same amount of money will buy fewer goods and services in the future. On the other hand, if the rate of inflation is low, the value of money will increase over time, meaning that the same amount of money will buy more goods and services in the future. Interest rates can also affect the value of money, as higher interest rates can make it more attractive to save money, while lower interest rates can make it more attractive to borrow money. Economic growth and changes in the supply and demand for goods and services can also affect the value of money, as these factors can affect the overall price level of goods and services in the economy.

Answer:

Step-by-step explanation:

EB/BC=15/12=5/4

ED/AC=X+5/Y=5/4

5y=4x+20

y=0.8x+4

Answer:

The area would be 360 because 8 x 6 x 15 = 720 divided by 2 = 360

The equation which is perpendicular to the equation of line passing through the points (-4, 7) (1, 3):

 y = 5/4x + 8.

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

To find the equation of a line that is perpendicular to another line, we need to know the slope of the original line.

The slope of the line passing through (-4,7) and (1,3) is:

m = (3 - 7) / (1 - (-4)) = -4/5

The slope of any line perpendicular to this line would be the negative reciprocal of -4/5, which is 5/4.

Therefore, the equation of a line that is perpendicular to the line passing through (-4,7) and (1,3) would be of the form:

y = 5/4 x + b

where b is the y-intercept.

Among the given options, the equation that matches this form is:

A. y = 5/4 x + 8

So the answer is (A) y = 5/4x + 8.

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An ice cube with a lower volume will melt faster than an ice cube with a higher volume. This is because there is the less mass and surface area for the heat to transfer through, causing the ice cube to melt at a quicker rate.

For example, imagine two ice cubes, one with a volume of 2 cubic centimeters and another with a volume of 4 cubic centimeters. The ice cube with the lower volume (2 cubic centimeters) will melt faster than the ice cube with the higher volume (4 cubic centimeters) because there is less mass for the heat to transfer through.  In conclusion, an ice cube with a lower volume will melt faster than an ice cube with a higher volume. This is due to the fact that there is the less mass and surface area for the heat to transfer through, causing the ice cube to melt at a quicker rate.

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In a case whereby two planes, which are 2235 miles apart, fly toward each other. Their speeds differ by 45 mph. If they pass each other in 3 hours, the speed of slower is 350mph and faster is 395mph.

The concept here is simplification.

Let represent the speed of the slower plane using the( x),

Let us represent the speed of the faster to be ( x + 45)

The distance traveled  that can be associated to the slower plane ( 3x).

then the distance that can be attributed toi that of the faster plane = 3(x + 45).

given that the  total distance=(2235 miles).

[3x + 3(x + 45) ]= 2235

3x + 3x + 135= 2235

[6x ]= 2235-135

6x = 2100

x=350

hence,  the speed of the slower plane is 350

the speed of the faster= x + 45 = 350+45= 395

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The speed of first plane is 350 miles/hour and the speed of second plane is 395 miles/hour .

Given, Distance between the planes = 2235 miles

Let, the speed of the first plane be 'x' miles/hour.

Let, the speed of the second plane be 'x+45' miles/hour.

Since, they are flying towards each other, their speed will get added.

The collective speed of both the planes = (2x + 45) m/h.

A/Q, they pass each other in 3 hours, i.e. they collectively covers the distance of 2235 miles in 3 hours.

We know Distance = Speed × Time

Given, Distance = 2235 miles , Time = 3 hours , Speed = (2x + 45) m/h

                      2235 = 3  × (2x + 45)

                       745 = 2x + 45

                        x = 350 miles/hour.

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The Credit Score is 4274274274274274.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

A phrase is used to describe each number in the series.

Given:

The sum of any three adjacent digits is 13.

The  second digit is 2 and the tenth digit is 4.

So, _2_ _ _ _ _ _ _ 4 _ _ _ _.

Now, the 2nd, 5th, 8th, 11th, 14th digits are equal and so are the 3rd, 6th, 9th, 12th, 15th.

So, the credit card number is 4274274274274274 and the last three digits are 274 which shows the sum is 13.

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Answer:

1. 12 inches

2. 36 inches

Step-by-step explanation: Solve for side b using the Pythagorean therom since this is a right triangle.

[tex]a^2+b^2=c^2[/tex] - Where c is the largest side aka hypotenuse(if you are unsure, look at the side opposite to the right angle)

Substitute the given values to solve for the unknown side

[tex]9^2+b^2=15^2[/tex]

Expand

[tex]81+b^2=225[/tex]

Subtract 81 from both sides

[tex]b^2=144[/tex]

Which means

[tex]b=+-12[/tex]

but since its a triangle in the first quadrant and can only contain positive values, we disregard the negative solution. So b=12.

Lastly, for perimeter, just add all the side lengths together.

[tex]P=9+12+15[/tex]

Which means that the perimeter is 36 inches!

skiing for 5 hours will make the cost of skiing at both ski resorts equal.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, Bunny Hill Ski Resort charges $50 for ski rentals and $5 per hour of skiing, while Black Diamond Ski Resort charges $25 for rentals and $10 per hour of skiing.

Let's define:

x as the number of hours of skiing

C₁ as the total cost of skiing at Black Diamond ski resort

C₂ as the total cost of skiing at Bunny Hill ski resort

At Black Diamond ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:

C1 = 25 + 10x

At Bunny Hill ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:

C₂ = 50 + 5x

We want to find at what point C₁ = C₂, so we set the two equations equal to each other:

25 + 10x = 50 + 5x

Simplifying the equation, we get:

5x = 25

Dividing both sides by 5, we get:

x = 5

Therefore, skiing for 5 hours will make the cost of skiing at both ski resorts equal.

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Answer:

Step-by-step explanation:

your going to have to show anwser choices

Answer:

The area of the land can be found using the formula A = 1/2*D1*D2, where D1 and D2 are the diagonals of the parallelogram. In this case, the area is 1/2*25*12 = 150m^2.

Answer:

180m^2

Step-by-step explanation:

since you said that two sides measure 12 and 17 and the diagonal is 25 you can use herons formula to find the area of each individual triangle then multiply it by two

using heron's formula it gives us the answer of 90 m^2 for one triangle so we can multiply it by two to get the area of the whole shape and 90x2=180m^2

Part A) The figure shows the prism.

Part B) the surface area of the figure is,

⇒ S.A = 270 in²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

By figure,

The shape shows the rectangular prism.

We know that;

The surface area of prism is,

⇒ S.A = 2B + ph

Where, B is base area, p is perimeter and h is height of prism.

Here, The base area of the prism is,

B = 10 × 5 = 50 in²

The perimeter of the base of prism is,

p = 2 (5 + 10)

  = 100 in

Height of prism = 1.7 in

Hence, We get;

The surface area of prism is,

⇒ S.A = 2B + ph

⇒ S.A = 2 × 50 + 100 × 1.7

⇒ S.A = 100 + 170

⇒ S.A = 270 in²

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Answer:

20s + 36t - 24

Step-by-step explanation:

4(5s + 9t - 6)

20s + 36t - 24

We can go any further, so that is the answer.

The volume of the prism is 105 cm³.

Volume of a three dimensional shape is the space occupied by the shape.

Given is a rectangular prism.

Volume of a rectangular prism = l × w × h

Here, l is the length, w is the width and h is the height.

Given that,

l = 7 cm, w = 3 cm and h = 5 cm

Substituting,

V = 7 × 3 × 5

   = 105 cm³

Hence the volume of the given rectangular prism is 105 cm³.

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The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

Similar triangles have the same corresponding angle measures and proportional side lengths.

Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,

The sum of interior angles of a triangle = 180°

Considering Δ ABC,

∠ A + ∠ B + ∠ C = 180°

∠ C = 180°-(22°+75°)

∠ C = 83°

Since, we know that the similar triangles have congruent corresponding angles,

Therefore,

∠ A = ∠ F, ∠ B = ∠  G and ∠ C = ∠ H

Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

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