What is the value of c?

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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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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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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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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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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Answer:

It is B: A180 mm side length

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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The area of the quilt block 112.5 square inches.

The correct option is B: one hundred twelve and one half in²

The area of the quilt block = area of a rectangle + area of a triangle

Ares of rectangle = length * breadth

Area of rectangle = 7.5 inches * 13 inches

Area of rectangle = 97.5 square inches

Area of the triangle = base/2 * height

base = 5 inches

height = 6 inches

Area of triangle = 5/2 inches * 6 inches

Area of triangle = 15 square inches

The area of the quilt block = 15 square inches + 97.5 square inches

The area of the quilt block = 112.5 square inches

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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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Answer:

Step-by-step explanation:

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

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

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

Proportionately, if Tony spent a total of 140 minutes studying for his algebra test, and this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test, the time Tony spent studying for his biology test was 132 minutes.

Proportion refers to the equation of two or more ratios.

Ratios show the relative size of a value compared to another.

Proportions are fractional values like ratios.

The total minutes Tony spent studying for his algebra test = 140

5 more than 3minutes = 8 minutes

140 > 132 by 8 minutes (140 - 8)

The time spent studying biology = 132

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Answer:

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

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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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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Answer:

Step-by-step explanation:

your going to have to show anwser choices

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!

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:

20s + 36t - 24

Step-by-step explanation:

4(5s + 9t - 6)

20s + 36t - 24

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

Work Shown:

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(26) = \frac{x}{5.7}\\\\x = 5.7*\tan(26)\\\\x \approx 2.78007575482541\\\\x \approx 2.8\\\\[/tex]

Make sure your calculator is in degree mode.

The Perimeter of the pentagon ABCDE is 17 units.

If two points in coordinates plane P(a, b) and Q(c, d) then the distance between these points are

PQ = √(c-a)² + (d-b)²

Given:

The coordinates of Pentagon are  A (4, 3), B (7, 3), C (8, 0), and D (2, -3) and E(0, 1).

Using Distance formula

AB = √(7-4)² + (3-3)²

AB = √9

AB = 3

BC = √(8-7)² + (0-3)²

BC = √1 + 9

BC = √10

CD = √(2-8)² + (-3-0)²

CD = √36  + 9

CD = √45

CD = 3√5

DE = √(0-2)² + (-3-1)²

DE = √4 + 16

DE = √20

DE = 2√5

So, Perimeter of the pentagon ABCDE = AB+BC+CD+DE+EA

                                                                 = 3 + √10 + 3√5 + 2√5

                                                                 = 3 + √10 + 5√5

                                                                 = 17.342 unit

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Answer: 22

Step-by-step explanation:

Just because it is right yk.

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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Answer:

9

Step-by-step explanation:

54÷6= 9

27÷3= 9

18÷2= 9

hence the answer is 9.

Answer

Step-by-step explanation:

The function represented by the graph is y = |x + 1|

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The equation of the graph is an absolute value graph

An absolute value graph is represented as

y = |x|

The function is shifted left by 1 units

So, we have

y = |x + 1|

Hence, the function is y = |x + 1|

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