Mathematics College

classify the polynomial

Answers

Answer 1

The classification of the given polynomial is cubic polynomial, the correct option is C.

We are given that;

The equation=3x^3-x^2-x+4

Now,

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

Degree of 3x^3=3

Degree of x^2=2

Degree of x=1

The heighest degree of the polynomial is three of 3x^3.

Therefore, by the polynomial the answer will be cubic polynomial.

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Related Questions

An aeroplane flies from a town X on a bearing of N45°E to another town Y, a distance of 200 km. It then changes course and flies to another town Z on a bearing of S60°E. If Z is directly east of X, calculate, correct to 3 significant figures, a the distance from X to Z by the distance from Y to XZ.

Answers

The distance from X to Z will be 386 km when rounded to 3 significant figures.

The distance from Y to XZ will be 141 km when rounded to 3 significant figures.

How to obtain the distances

To obtain the distances, we need to extend the distances traveled by the airplane and this yields another triangular form. Angle Y = 105°, z = 200 km, and Z = 30°.

y/Sine Y = z/Sine Z

y/Sine 105° = 200/Sine 30°

y = 200 × 0.966/0.5

386 km to 3 significant figures

Also for the distance from Y to XZ,

We assume that the distance from Y to XZ is d

Sine 45°/1 = d/200

d = 200 sine 45°

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What is the volume of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
--
10 yd
9 yd

Answers

The volume of the given cylinder is 2543 cubic yards.

For the given cylinder,

Height of the cylinder = 10 yard

Radius of cylinder = 9 yard yard

Then we have to calculate the volume of this cylinder.

Since we know that,

Volume of the cylinder = πr²h

Where,

r represents radius of cylinder = 9 yard

h represents height of cylinder = 10 yard

Noe therefore,

Volume of the cylinder = π(9)²(10)

= 3.14x 81 x 10

= 2543 cubic yards

Thus,

⇒ Volume = 2543 cubic yards.

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y^2 + 4 = x. for x the independent variable and the dependent variable. Determine whether the relation is a function.

Answers

Answer:

To determine if the given relation is a function, we need to check if there is a unique y-value for every x-value in the relation.

The given relation is:

y^2 + 4 = x

To test for functionality, we need to solve for y in terms of x:

y^2 = x - 4

y = ± √(x - 4)

Notice that for each x-value, there are two possible y-values, one positive and one negative. This means that for a single x-value, there are two potential y-values, violating the condition of a unique y-value for every x-value.

Therefore, the given relation is not a function since it fails the vertical line test, as there are x-values with multiple corresponding y-values.

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A shipping box has dimensions as shown in the diagram. The red, dashed line represents the longest length of item that will fit inside the box. What is the length of the longest item that will fit inside the shipping box?

Enter the correct answer in the box by replacing the values of m and n.

Answers

The red dashed line is the hypotenuse of the right triangle with one leg equal to 24 inches and the other leg equal to 12 inches. Its length is given by the Pythagorean theorem:
space diagonal = V(24^2 +12^2) = V(720) = 12v5
space diagonal = 26.83 ... inches
The length of the longest item that will fit in the box is about 26.83 inches.

Two aircrafts travel from the position P(30°N, 130°W) to Q (50°N, 170°E) all leaving at 0845hrs and at the same speed of 500km/hr. Aircraft A travels due north to the position (50°N, 130°W) and then along a parallel of latitude using the shortest route. Aircraft B travels along a parallel of latitude (30°N, 170°E) and then due north.
(a) If a third aircraft C had left a point R (30°N, 10°W) at the same time as the two above aircrafts left P and flew via the shortest possible distance to point Q, calculate its position when the aircraft A was passing the longitude 180°W. (b) Calculate the arrival local time of the two aircrafts. (5mks) (5mks)

Answers

(a) The time taken by aircraft C to travel the distance from R to the longitude 180°W is 25.92 hours

(b) Since aircraft A departed at 08:45 hrs, the arrival time would be:

Arrival time is 13:14 hrs

Aircraft A would arrive at approximately 13:14 hrs, and aircraft B would arrive at approximately 21:01 hrs local time.

To calculate the position of aircraft C when aircraft A was passing the longitude 180°W, we need to determine the distance and direction between R (30°N, 10°W) and Q (50°N, 170°E) via the shortest route.

Distance between R and Q:

The latitude difference between R and Q is 50°N - 30°N = 20°. As each degree of latitude is approximately 111 km, the distance in terms of latitude is 20° × 111 km = 2,220 km.

The longitude difference between R and Q is 170°E - 10°W = 180°.

At the latitude of 40°N (midpoint between 30°N and 50°N), each degree of longitude is approximately cos(40°) × 111 km = 70.7 km.

The distance in terms of longitude is 180° × 70.7 km = 12,726 km.

Using the Pythagorean , the shortest distance between R and Q is:

Distance = √((2,220 km)² + (12,726 km)²)

≈ 12,960 km

Speed of aircraft C is 500 km/hr.

The time taken by aircraft C to travel the distance from R to the longitude 180°W is:

Time = Distance / Speed

= 12,960 km / 500 km/hr

≈ 25.92 hours

Since the aircraft A and aircraft C departed at the same time, when aircraft A was passing the longitude 180°W, aircraft C would also be at the same longitude, assuming they maintained a constant speed.

(b) To calculate the arrival local time of the two aircraft, we need to consider the time taken for each leg of their respective routes.

For aircraft A:

Distance from P to (50°N, 130°W) = (50°N - 30°N) × 111 km/degree

= 2,220 km

Time taken = Distance / Speed

= 2,220 km / 500 km/hr

= 4.44 hours

Since aircraft A departed at 08:45 hrs, the arrival time would be:

Arrival time = Departure time + Time taken

= 08:45 + 4.44 hours

≈ 13:14 hrs

For aircraft B:

Distance from (30°N, 170°E) to Q = (170°E - 130°W) × cos(40°) × 111 km/degree = 6,282 km

Time taken = Distance / Speed

= 6,282 km / 500 km/hr

= 12.564 hours

Since aircraft B departed at 08:45 hrs, the arrival time would be:

Arrival time = Departure time + Time taken

= 08:45 + 12.564 hours

≈ 21:01 hrs

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If I have $25. How many cheeseburgers can I get if they are 2.50 each?

Answers

Answer:

We can get 10 cheeseburgers.

Step-by-step explanation:

To find out how many cheeseburgers we can buy if:

we have $25 andeach cheeseburger costs $2.50,

we can divide the money we have by the cost of each cheeseburger.

To make the division simpler, we can multiply both numbers by 10.

$25 / $2.50 = $250 / $25

From this form of the division, we can clearly see that the amount of money we have is 10 times the cost of one burger because it is 25 with a 0 on the end, which is the result of multiplying by 10.

Therefore, we can get 10 cheeseburgers.

The quilt is made of squares with diagonals.
The length of BD is 4.
a. Find the length of AE. Round answer to the hundredths.
b. Find the area of square ABCD.

Answers

Round answer to the hundredths.

a. AE = 4√2 ≈ 5.66
b. Area of square ABCD = 16

If I have 7.55 how many dimes and quarters is it

Answers

Answer:

To convert 7.55 dollars into dimes and quarters, we need to make use of the fact that there are 10 dimes in a dollar and 4 quarters in a dollar. Here's how to do it:

Step-by-step explanation:

1. First, convert the dollar amount into cents: 7.55 dollars x 100 cents/dollar = 755 cents.

2. Next, use long division to find how many quarters are in 755 cents: 755 ÷ 25 = 30 with a remainder of 5.

3. The quotient of 30 tells us that we can use 30 quarters, which equals $7.50.

4. The remainder of 5 cents is less than a quarter, so we cannot use another quarter. Instead, we can use 1 dime, which is worth 10 cents.

Therefore, 7.55 dollars is equivalent to 30 quarters and 1 dime.

To determine the number of dimes and quarters you can make with $7.55, you need to consider the values of each coin and find a combination that adds up to the given amount.

Let's break it down:

1 dime = $0.10
1 quarter = $0.25

We'll assume you want to use the maximum number of coins possible.

To calculate the number of quarters, divide the total amount by the value of a quarter:

Number of quarters = $7.55 / $0.25 = 30.2

However, you can't have a fraction of a coin, so you'll need to round down to the nearest whole number. Therefore, you can have a maximum of 30 quarters.

To calculate the remaining amount after using all the quarters, subtract the value of the quarters from the total amount:

Remaining amount = $7.55 - (30 * $0.25) = $7.55 - $7.50 = $0.05

Now, we'll calculate the number of dimes. Divide the remaining amount by the value of a dime:

Number of dimes = $0.05 / $0.10 = 0.5

Again, you can't have a fraction of a coin, so you'll need to round down. Therefore, you can have a maximum of 0 dimes.

In summary, with $7.55, you can have a maximum of 30 quarters and 0 dimes.

I hope this helps! :)

Find the indicated angle

A.) 9
B.) 7
C.) 12
D.) 32

Answers

The calculated value of the missing side length in the triangle is (c) 12

How to find the indicated angle

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

The simiar triangles

Using the theorem of corresponding sides, we hav

?/8 = 9/6

Multiply both sides by 8

So, we have

? = 8 * 9/6

Evaluate

? = 12

Hence, the missing side length in the triangle is (c) 12

Answers

Answer:

tan^(-1)(|cos(x)| / (1 + sin(x)))

Step-by-step explanation:

√(1 - sin(x)) / √(1 + sin(x))

(√(1 - sin(x)) / √(1 + sin(x))) * (√(1 + sin(x)) / √(1 + sin(x)))

√((1 - sin(x))(1 + sin(x))) / (1 + sin(x))

√(1 - sin^2(x)) / (1 + sin(x))

Then, using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can substitute cos^2(x) for 1 - sin^2(x):

√(cos^2(x)) / (1 + sin(x))

|cos(x)| / (1 + sin(x))

tan^(-1)(|cos(x)| / (1 + sin(x)))

*Note : the absolute value |cos(x)| is used to ensure the argument of the inverse tangent is always positive.

Trina has a credit card that uses the adjusted balance method. For the first 10
days of one of her 30-day billing cycles, her balance was $780. She then
made a purchase for $170, so her balance jumped to $950, and it remained
that amount for the next 10 days. Trina then made a payment of $210, so her
balance for the last 10 days of the billing cycle was $740. If her credit card's
APR is 17%, which of these expressions could be used to calculate the
amount Trina was charged in interest for the billing cycle?
OA. (30)($780)
365
B.
O C.
D.
0.17
365
0.17
365
0.17
365
30
30
(10 $780+10 $950 +10 $210)
30
10
$780+10$950+10 $740
30
•30) ($570)

Answers

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is (APR / 365) x 30 days x adjusted balance.

What is the adjusted balance method?

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.

Answers

The area of the shaded region is equal to 45 square units.

How to calculate the area of a rectangle?

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

A represent the area of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 8 × 6

Area of rectangle = 48 square units.

Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;

L₁ = 8 - 5 = 3 units.

L₂ = 6 - 4 = 2 units.

Area of right triangle = 1/2 × 3 × 2

Area of right triangle = 3 square units.

For the area of the shaded region, we have:

Area of the shaded region = 48 square units - 3 square units.

Area of the shaded region = 45 square units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Can some one help me with this please

Answers

A) Area of figure is,

⇒ A = 3π (3 + √73) + 4.5π

B) Area of figure is,

A = 89 feet²

We can simplify as;

A) In figure A,

It is make with one cone and one semicircle.

Hence, Area of cone is,

A = πr (r + √h² + r²)

A = π × 3 (3 + √8² + 3²)

A = 3π (3 + √64 + 9

A = 3π (3 + √73)

And, Area of semicircle is,

⇒ A = 1/2 (π × 3²)

⇒ A = 4.5π

Hence, Total area is,

⇒ A = 3π (3 + √73) + 4.5π

B) Figure B is make with a trapezoid and triangle.

Area of trapezoid is,

A = 1/2 (7 + 13) × 5

A = 20 × 5 / 2

A = 50 feet²

And, Area of triangle is,

A = 1/2 × 6 × 13

A = 39 feet²

Hence, We get;

Area of figure is,

A = 50 + 39

A = 89 feet²

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Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

We have,

The composite figure has a cone and a semicircle.

So,

Area of cone = 1/3πr²h = 1/3 x 3.14 x 3 x 3 x 8 = 753.8 cm³

Area of semicircle = 1/2 x πr² = 1/2 x 3.14 x 3 x 3 = 14.13 cm²

The composite figure has a trapezium and a triangle.

Area of the trapezium

= 1/2 x ( sum of the parallel side) x h

= 1/2 x (7 + 13) x 5

= 1/2 x 20 x 5

= 10 x 5

= 50 ft³

Area of the triangle.

= 1/2 x base x height

= 1/2 x 6 x 8

= 3 x 8

= 24 ft²

Thus,

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

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In ΔNOP, p = 70 inches, n = 97 inches and ∠O=163°. Find ∠N, to the nearest degree.

Answers

Answer:

10°

----------------------

In ΔNOP, we are given:

p = 70 inches, n = 97 inches, ∠O = 163°

Use the law of cosines to find side o:

o² = n² + p² - 2(np)cos(∠O) o² = 97² + 70² - 2(97)(70)cos(163°) o² = 27295.61o = 165.2

Now, use the law of sines to find ∠N:

sin(∠N) / n = sin(∠O) / o sin(∠N) / 97 = sin(163°) / 165.2sin(∠N) = 97*sin(163°) / 165.2sin(∠N) = 0.17m∠N = arcsin (0.17)m∠N = 9.78° ≈ 10°

So, ∠N is approximately 10°.

NO LINKS!! URGENT HELP PLEASE!!!

Answers

The flowcharts for each proof are shown in the image attachments below.

For problem 1, we use the SSS (side side side) congruence theorem.

Problem 2 uses SAS (side angle side). It might help to rotate one of the triangles in problem 2 so the marked angles align.

A metal is composed of copper and zinc in the ratio 3:2 by volume. Find the volume of a piece of the metal which contains 42 cm³ of copper.

Answers

Answer:

70 cm³

Step-by-step explanation:

let the total volume be x

copper : zinc = 3:2

copper ==>

3/5 *x = 42

make x the subject if formula

x = 42*5/3

:. x = 70 cm³✅✅

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Using a Net to Find the Surface Area of a Triangular Prism.

Answers

Answer:

Step-by-step explanation:

Surface area is 90in^2

(08.01 MC)
Which of the following is the graph of f(x)=x²-5x +4?

Answers

Answer: C

Step-by-step explanation:

If I plugged in 0 for x, You get 4 for y. This is the y-intercept

(0,4)

The only graph that goes through (0,4) is C.

Find the inverse for: f(x) = 2x^2-3

Answers

Unless we restrict its domain, a quadratic function doesn't have the inverse.

Write the slope-intercept form of the equation for each line.

Answers

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

The measured width of the office is 30mm. If the scale of 1: 800 is used, calculate the actual width of the building in metres

Answers

Answer:

Step-by-step explanation:

which expression can be used

Answers

Answer: The answer is A.

Step-by-step explanation: The surface area of a triangular prism is given by A = b h + ( b 1 + b 2 + b 3 ) l units 2 where is the base of a triangular face, is the height of a triangular face, , , and are the sides of the triangular base, and is the length of the prism.

I need help with this Piece-Wise Function Please

Answers

With f(1), we're being given an x-value of 1.

Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.

f(1) = 1 - 2 = -1

Segment RT has endpoints R(1,1) and T (-7, -2) what are the coordinates of the midpoint of RT?

Answers

(-3, - 0.5)

The formula to find a midpoint goes as shown below. First take the x coordinates from each set, then add them together. Then take the resulting number and divide that by 2. Which gives you the x coordinate of your midpoint, in this case: -3.

Now repeat this process with the y coordinates from each set. Take both y coordinates, add them together, and divide the sum of them by 2. The result in this case should be: -0.5

Therefore the coordinates of your midpoint are: (-3, -0.5)

how many square are there in 384 sq ft

Answers

The number of squares that are in 384 sq ft is 0

How many square are there in 384 sq ft

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

Area expression = 384 sq ft

The above expression is an area expression

This means that it cannot be compared to quantities other then squares

The term "how many squares" is not an area expression

Hence, there are no squares in 384 sq ft

Answers

It can be seen that each side of the isosceles triangle measures approximately 29.81 meters.

How to solve

The angles at the base of an isosceles triangle have equivalent magnitudes. It can be deduced intelligently that if one of the base angles measures 34°, the remaining base angle must also be 34°.

Let's denote the length of each side as "x."

In a right triangle formed by half of the base, the height, and one of the sides, we can use the tangent ratio:

tan(34°) = height / (x/2)

tan(34°) = 15 / (x/2)

To isolate x, we can rearrange the equation:

x/2 = 15 / tan(34°)

x = (15 / tan(34°)) * 2

By employing a calculator, we have the capability to determine the numerical worth of x.

x ≈ 29.81 m

Therefore, each side of the isosceles triangle measures approximately 29.81 meters.

Answers

The equation for the circle is

(x - 1)² + (y + 2)² = 9

Then the radius is 3 units and the center is (1, -2), the graph is on the image at the end.

How to find the center and radius of the circle?

Remember that for an equation for a circle of radius R and center (a, b), the equation is:

(x - a)² + (y - b)² = R²

Here we have the equation of the circle:

x² + y² - 2x + 4y - 4 = 0

We need to complete squares, we will get:

(x² - 2x) + (y² + 2*2y) = 4

Now we can add in both sides (-1)² and (2)², then we will get:

(x² - 2x + (-1)²) + (y² + 2*2y + (2)²) = 4 + (2)² + (-1)²

(x - 1)² + (y + 2)² = 4 + 4 + 1

(x - 1)² + (y + 2)² = 9 = 3²

Then we can see that the center is (1, -2), and the radius is 3.

The graph of this circle is on the image at the end.

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The value 37 is a solution for the equation 3√√2 sece +7 = 1.
A. True
B. False

Answers

The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.

Given an equation,

3√2 sec θ + 7 = 1

We have to find that whether 3π/4 is a solution for the given equation or not.

Solving the given equation, we get,

3√2 sec θ + 7 = 1

3√2 sec θ = 1 - 7

3√2 sec θ = -6

sec θ = -6 / 3√2

sec θ = -2 / √2

sec θ = -√2

Now, we know that, sec θ = 1/ cos θ

So the equation becomes,

1/ cos θ = -√2

cos θ = -1/√2

Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.

cos 3π/4 = cos (π - π/4) = -cos (π/4) = -1/√2

So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.

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Refer to image attached

Answers

The rationalized form of the expression √(3/5) is √15/5.

To rationalize the denominator of the expression √(3/5), we need to eliminate the square root in the denominator.

We can achieve this by multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of √5 is also √5, so we can multiply the expression by (√5)/(√5):

√(3/5)×(√5)/(√5)

Multiplying the numerator and denominator, we have:

√(3 × 5)/(√(5×5))

Which simplifies to:

√15/√25

√15/5

Therefore, the rationalized form of √(3/5) is √15/5.

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solve each compound inequality. -28 < -4r < 16

Answers

The solution to the compound inequality -28 < -4r < 16 is 7 > r > -4

How to determine the solution to the compound inequality

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

-28 < -4r < 16

Divide through the inequality by -4

so, we have the following representation

-28/-4 < -4r/-4 < 16/-4

When the quotients are evaluated, we have

7 > r > -4

Hence, the solution to the compound inequality is 7 > r > -4