Fully factor the following polynomials. Explain your thought process with your solution.
a. ????(x) = 2x3 − 25x2 + 53x − 30 [3 marks]
b. ????(x) = x3 + 3x − 4 [3 marks]

Answer:

1/3

Step-by-step explanation:

The exponent -1 indicates that we need to take the reciprocal of the base 3.

So, 3^(-1) = 1/3

Therefore, the answer is 1/3.

Answer:

1/3

Step-by-step explanation:

Rewrite the expression using the negative exponent rule [tex]b^{-n}[/tex] = [tex]\frac{1}{b^{n} }[/tex]

The answer is 1/3

Anthοny is accurate, and had he cοlοred a quarter οf Jacοb's final circle rather than a quarter οf his οwn, they wοuld have cοlοred 12 cοmplete circles.

A circle is a spherical shape that lacks bοrders and edges. In geοmetry, a circle is indeed a clοsed, curved shape having twο dimensiοns.

Tο start, let's cοunt the tοtal number οf circles Anthοny οr Jacοb cοlοred befοre tο lunch:

Anthοny cοlοred 6.25 circles, οr 6 and 1/4 circles.

Jacοb cοlοred 5.75 circles, οr 5 and 3/4 circles.

They cοmbined tο cοlοr a tοtal οf 12 circles (6.25 + 5.75).

Let's nοw imagine that Anthοny cοlοred a quarter οf Jacοb's final circle rather than a quarter οf his οwn. Jacοb cοlοred 5 and 3/4 + 1/4 = 6 circles, while Anthοny cοlοred 6 with 1/4 - 1/4 = 6 circles.

Tοgether, we wοuld have cοlοured 12 circles since 6 + 6 = 12. This is what they desired. Anthοny is therefοre right!

By calculating the tοtal number οf circles that each persοn cοlοured while accοunting fοr the fact that they all cοlοred the very same number οf circles, we can further cοnfirm οur cοnclusiοn:

Anthοny drew 6 circles.

Jacοb filled in 6 circles.

Tοgether, they cοlοred 6 + 6 = 12 circles.

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The value of cos C is 3/5

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

In a right angle triangle, the longest side is called the hypotenuse and the other two sides are called opposite and adjacent. The line facing the acute angle( tetha) is the opposite. The ratio of the sides with the acute angle are called trigonometric ratio.

sin(tetha) = opp/ hyp

cos( tetha) = adj/ hyp

tan(tetha) = opp/adj

In the triangle, using angle C,

opposite = 4

adjascent = 3 and hypotenuse = 5

cos (C) = 3/5

therefore the value of cos (C) = 3/5

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The volume of a cylinder is πr²h.

Given, that H = 2 ft and R = 6 Feet.

So V = πr²h = 3.14 x 6 x 6 x 2

                   = 3.14 * 72

                   = 226.08 ft³

Answer:

The volume of the cylinder is 226.08 feet^3

Step-by-step explanation:

The volume of a 3-d shape with sides straight up is

BaseArea × height.

For a cylinder the base is a circle. Area of a circle is pi•r^2

So the Volume of your cylinder is:

V = pi•r^2 • h

Fill in the info given.

V = 3.14 • 6^2 • 2

= 226.08

The units for volume are cubed, that is, 3rd power.

So 226.08 cubed ft

or 226.08 ft^3

Hope this helps!

Answer: f(-2)=0; yes, the binomial is a factor of the polynomial.

f(-2)≠0; the binomial is not a factor of the polynomi f(2)=0; yes, the binomial is a factor of the polynomial.

f(2)≠0; the binomial is not a factor of the polynomial.

Step-by-step explanation:

The length of MN is equal to: 32.2 ft.

In Mathematics, Pythagorean's theorem is modeled by the following mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the length of sides of a right-angled triangle.

In order to determine the length of MN in right-angled triangle LNM, we would have to apply Pythagorean's theorem.

LN² + MN² = LM²

16² + MN² = 36²

256 + MN² = 1,296

MN² = 1,296 - 256

MN² = 1,040

MN = √1,040

MN = 32.2 ft.

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The  evaluated logarithmic expression is: [tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = 2\log[10] + 2\log[x] + \frac{1}{3}\log[y] \][/tex]

Expression mentioned in the question :[tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right][/tex]. . The first property we will use is the Product Rule , so this   can be expressed as: [tex][ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = \log[10x^{2}] + \log[\sqrt[3]{y}] \].[/tex] We can now apply the Power Rule to the first term, which states that the logarithm of a power is equal to the exponent times the logarithm of the base. This can be expressed as: \[ \log[10x^{2}] = 2\log[10x] \]

We can now apply the Quotient Rule to the second term, which states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. This can be expressed as: [tex]\[ \log[\sqrt[3]{y}] = \frac{1}{3} \log[y] \].[/tex] Substituting this back into the original equation gives us:[tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = 2\log[10x] + \frac{1}{3}\log[y] \][/tex]

We can now evaluate this expression without using a calculator. The two logarithmic terms can be rewritten as:[tex]\[ \log[10x] = \log[10] + \log[x] \,  \[ \log[y] = \log[y] \][/tex]
Substituting this back into the original equation gives us: [tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = 2\log[10] + 2\log[x] + \frac{1}{3}\log[y] \[/tex]

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Answer:

-137

Step-by-step explanation:

23, 15, 7, -1, -9,-17...........

    -8  -8   -8  -8.....

∴ -8n+23

if n = 20

-8(20)+23=-137

Answer:

-137

Step-by-step explanation:

The pattern is -8 every term so

15 + (-8(20-1)) = -137

its pretty much multiplying the rate by what term you want. you subtract the 1 because you started with the first term.

Answer:

E

Step-by-step explanation:

My answer

[tex] \frac{2}{5} [/tex]

The area of Circle B could be about 300 in², about 900 in², or about 2,700 in² depending on its radius.

To determine which one is correct, you would need to know the radius or diameter of the circle.

Use the formula for the area of a circle, which is

A = πr²,

where A is the area and

r is the radius.

If you have the radius, plug it into the formula and calculate the area.

Compare the calculated area to the options provided (300 in², 900 in², or 2,700 in²)

to determine which one is closest to the area of Circle B.

Without more information about Circle B's radius or diameter, it is impossible to determine the exact area from the

options given.

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Answer:

The number of nickels and quarters in the bank are 87 and 56, respectively.

Step-by-step explanation:

Let's denote the number of nickels in the bank as "n" and the number of quarters as "q". Then we can set up a system of two equations based on the given information:

n + q = 143 (equation 1, representing the total number of coins)

0.05n + 0.25q = 18.35 (equation 2, representing the total value of the coins)

To solve this system, we can use substitution or elimination method. Let's use elimination method here:

Multiplying equation 1 by 0.05, we get:

0.05n + 0.05q = 7.15 (equation 3, obtained by multiplying equation 1 by 0.05)

Subtracting equation 3 from equation 2, we get:

0.2q = 11.2

Dividing both sides by 0.2, we get:

q = 56

Substituting this value of q into equation 1, we get:

n + 56 = 143

n = 87

Therefore, there are 87 nickels and 56 quarters in the bank.

Hopefully this helped you! If not, I'm sorry! If you need more help, ask me! :]

The probability that exactly 5 of the invoices will be paid within ten working days is 19.34% or 0.1934.

This is a binomial distribution problem, with n = 12 (the sample size) and p = 0.5 (the probability of success, which is an invoice being paid within ten working days). We want to find the probability that exactly 5 of the invoices will be paid within ten working days.

Using the binomial probability formula, the probability of exactly 5 invoices being paid within ten working days is:

P(X = 5) = (12 choose 5) * (0.5)^5 * (1-0.5)^(12-5) = 0.1934

Where (12 choose 5) is the binomial coefficient, which represents the number of ways to choose 5 invoices from a sample of 12.

Therefore, the correct answer is 0.1934 rounded to four decimal places.

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At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Therefore the probability density function has inflection points at x = μ ± σ.

The probability density function (PDF) of a normally distributed random variable is defined as:

f(x) = 1/(σ√2π) e-(x - μ)²/2σ²

where μ is the mean,

σ is the standard deviation.

This equation has two inflection points at x = μ ± σ. To show this, we differentiate the equation twice with respect to x.

f'(x) = -(x - μ) / σ² e-(x - μ)²/2σ²

f''(x) = [-(x - μ)² / σ³ - 1] e-(x - μ)²/2σ²

At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Thus, we have proved that the PDF of a normally distributed random variable has inflection points at x = μ ± σ.

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Answer:

width is 3 inches, length is 11 inches.

Step-by-step explanation:

Let l be the length and w be the width.

We have:

[tex]l = 2w + 5[/tex]

[tex](2w + 5)(w) = 33[/tex]

[tex]2 {w}^{2} + 5w = 33[/tex]

[tex]2 {w}^{2} + 5w - 33 = 0[/tex]

[tex](w - 3)(2w + 11) = 0[/tex]

[tex]w = 3[/tex]

[tex]l = 2(3) + 5 = 11[/tex]

The mathematical equation f(w) = w² - 6w provides a representation of the remaining surface area, measured in square meters, of the field following the construction of the basketball court.

The rectangular field has an area of length x width, which can be expressed as (2w)(w) = 2w² square meters.

The basketball court has an area of length x width, which can be expressed as (w)(w+6) = w² + 6w square meters.

To find the remaining area of the field after the basketball court is built, we need to subtract the area of the basketball court from the area of the rectangular field.

So the function f(w) representing the remaining area, in square meters, is:

f(w) = 2w² - (w² + 6w)

f(w) = 2w² - w² - 6w

f(w) = w² - 6w

Therefore, the function f(w) = w² - 6w represents the area, in square meters, remaining of the field once the basketball court is built.

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Complete question:

A grounds committee of a housing community plans to build a basketball court in an empty rectangular field.

1. The rectangular field-has a width of 2w meters and a length that is 13 meters longer than its width.

2. The basketball court has a width of w meters and a length that is 6 meters longer than its width.

Which function, f(w), represents the area, in square meters, remaining of the field once the basketball court is built?

The domain of the given function H (t) is 0 ≤ t ≤ 40.

What is the domain of a function?

The collection of all the values for which a function is defined is known as the domain of that function.

We are given that the height of a model rocket, H (t) is a function of time since it was launched, t.

From the graph, we can see that the value of t is represented on the x- axis is ranging from 0 to 40.

Hence, the domain of the given function H (t) is 0 ≤ t ≤ 40.

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The correct response, based on the facts provided, is 625.

What does a math power mean?

When a base number is raised to an exponent in mathematics, the exponent represents how many times the base number has been multiplied, and the base amount is the factor that is multiplied by itself.

What do you call 5 to the power of?

In mathematics and mathematics, the fifth power, or subsolid, of a number, n, is obtained by multiplying five occurrences of n around each other:[tex]n⁵ = n × n × n × n × n.[/tex]The fourth power of a number or the squares of a number of times its cube can also be used to create fifth powers.

5 to the fourth power (also written as 5⁴) is:

[tex]5 × 5 × 5 × 5 = 625[/tex]

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The diagonal of the square bisect the angles. Therefore, the angle x in the square is 60 degrees.

A square is a quadrilateral with each angles equal to 90 degrees. The sum of angles in a square is 360 degrees.

The diagonal of a square is perpendicular to each other. It divided the square into two congruent isosceles triangle.

The diagonal of a square bisects the angles of a square. Therefore, the angles are 45 degrees each after bisection.

Hence, let's find the angle x in the square.

Therefore,

180 - 105 + x + 45  = 180

75 + x + 45 = 180

x + 120 = 180

subtract  120 from both sides of the equation

x + 120 - 120 = 180 - 120

x = 60 degrees

Therefore,

x = 60 degrees

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If BG=BE, we can conclude that triangle BGE is an isosceles triangle.

In a circle, the radius is a line segment that connects the center of the circle to any point on the circle. Therefore, BG and BE are both radii of the circle. In an isosceles triangle, two sides have the same length, and the third side is a different length. In this case, the two sides with the same length are BG and BE, and the third side is GE. Since BG and BE are radii of the circle and therefore have the same length, we can conclude that triangle BGE is isosceles, and the angles opposite BG and BE are congruent.

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Answer:

Option C) is the correct answer.

Add "Spade" to the Card column, with branches to "Even" and "Odd" in the Die column. Thus, option 3 is correct.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο cοmplete the tree diagram, we need tο add the missing branch fοr the spades suit in the card cοlumn.

Here is the cοmpleted tree diagram:

We have added the missing branch fοr the spades suit, which alsο branches intο even and οdd fοr the die rοll. We have alsο filled in the οutcοmes fοr each branch οf the tree, which include the pοssible values fοr the card (2, 3, 4, 5, 6, οr 1 fοr Ace) and the die rοll (even οr οdd).

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Answer:

14

Step-by-step explanation:

6/9 = x+2/24

Cross multiply to expand

9( x + 2) = 24x 6

9x + 18 = 144

Subract 18 from both sides

9x = 126 Divide both sides by 9

X = 14

10/ 2x-9 = 20/9

Cross multiply

20( 2x - 9) = 10 x 9

40x - 180 = 90

Add 180 to both sides

40x = 270

Divide both sides by 40

X = 6.75

Scale question

Convert 240miles to inches

240 x 63, 660 = 15,206,400

Ratio is 3:15,206,400

Reduce to lowest term by divide both sides by 3

Scale is 1: 5068800

Answer:

C

Step-by-step explanation:

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

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 36 square feet.

Because the rectangle has a gap on the left side in the shape of a semicircle, we can first solve for the area of that semicircle.

if you know the radius of a semicircle, you can use the formula:

[tex]A = \frac{\pi r^{2} }{2}[/tex]

But first, we need to solve for the radius.

Because the diameter is twice the size of the radius, we can use this expression:

So, the radius of the semicircle is 2ft.

Inserting 2 into the formula for r:

First, we need to evaluate the exponent:

Dividing 4 by 2 gives:

This simplifies to:

Subtracting that from the area of the rectangle:

36 - 6.28319 = 29.71681 = [tex]29.7ft^{2}[/tex] (Rounded to the nearest tenth)

Therefore, the answer is C.

The coordinates of point P are(0,1)

A part of line which has 2 end points and it is also can be measured

example:

the objects which has starting and the ending point can be taken for consideration

pencil: which is straight and has a fixed length of about 16-22 cm

The intersection of points in a grid system

example the points(25,10) is 25 units long and 10 units up

A(-4,-1) B(6,4) in the ratio 2:3

x1=-4, x2=6,y1=-1,y2=4,m=2,n=3

x=(mx2+nx1)/m+n

=2*6+3*(-4)/2+3

=12-12/5

=0/5

=0

y=my2=ny1/m+n

=2*4+3(-1)/2+3

=8-3/5

=5/5

=1

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An item is regularly priced at 70. Shen bought it on sale for 20% off the regular price. Shen paid 56 for the item on sale.

To determine how much Shen paid for the item on sale, follow these steps:

Find the discount amount

Subtract the discount amount from the regular price.

Calculate the discount amount.

Discount amount = Regular price × Discount percentage

Discount amount = 70 × 20%

Discount amount = 70 × 0.20

Discount amount = 14

Calculate the sale price.

Sale price = Regular price - Discount amount

Sale price = 70 - 14

Sale price = 56

Shen paid 56 for the item on sale.

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If you only have $14 to spend, the park you would attend would depend on the cost of admission and the price of the rides. Assuming that the rides are the same quality at both parks, the decision would come down to which park offers the most affordable pricing.

If Park A charges a $10 admission fee and $2 per ride, you would be able to afford 2 rides with your $14 budget.

If Park B charges a $5 admission fee and $3 per ride, you would be able to afford 3 rides with your $14 budget.

Therefore, if the pricing is as described above, it would be more cost-effective to attend Park B as you would be able to enjoy an additional ride with your budget. However, if the pricing is different or if there are other factors to consider such as distance, location, or amenities, then the decision might change.

Answer:

It's difficult to provide a definitive answer without knowing the specific parks you are considering, but I can offer some general advice on how to choose which park to attend.

First, consider the admission price for each park. If one park has a significantly higher admission price than the other, it may not be worth attending if you only have $14 to spend.

Next, consider the cost of the rides and other attractions at each park. If one park has more expensive rides or requires you to purchase tickets for each ride separately, you may not be able to enjoy as many attractions with your $14 budget.

Finally, consider any other expenses you may incur, such as food, parking, or souvenirs. If one park has significantly higher prices for these items, it may not be the best choice if you are on a tight budget.

Based on these factors, you may want to choose the park that offers the best value for your $14 budget. This could mean choosing a park with lower admission prices and more affordable rides, or a park that offers special deals or discounts that allow you to stretch your budget further. Ultimately, the park you choose will depend on your personal preferences and priorities, as well as the options available in your area.

Step-by-step explanation:

The value of the stock needs to go up by 42.86% to be equal to what the investor first paid for it.

Let's say the investor initially paid $100 for the stock. A 30% decrease in the value of the stock would mean it is now worth $70. To bring the value of the stock back up to $100, it needs to increase by $30, which is 42.86% of the current value ($30/$70).

Therefore, the value of the stock needs to go up by 42.86% from its current value for the investor to break even.

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So, the volume of big cone is 226.08 cu ft for this we have to know about volume.

The area occupied within any three-dimensional solid's borders is known as its volume.

Given, radius of small cone, r = 2 ft

Volume of small cone 25.12 cu ft

[tex]So\ Volume\ of\ small\ cone = \pi rl[/tex]

[tex]25.12 = 3.14 * 2*l[/tex]

[tex]l=\frac{25.12}{3.14\ *\ 2}[/tex]

[tex]l = 4ft[/tex]

Since, cones are similar and bai cone radius is 3 times of small cones then ,

Slant height of big cone = 3 * Slant height of small cone

= 3*4 ft

= 12 ft.

[tex]Volume\ of\ big\ cone = \pi rl[/tex]

[tex]= 3.14*6*12[/tex]

[tex]= 226.08\ cu ft[/tex]

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