Find the length of the segment indicated. Round to the nearest tenth if necessary. Note: One segment of each triangle is a tangent line

The most appropriate choice for polynomial will be given by

1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

2) Zeroes of P(x) = 3, 2i, -2i

3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

What is a polynomial?

An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.

[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]

        [tex]= 24 -40 + 20 -16\\= 0[/tex]

(x - 2)  is a factor of P(x)

[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]

        = [tex](x - 2)(3x^2 - 4x + 2)[/tex]

        [tex]=(x-2)(x -a)(x - b)[/tex]

where,

[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]

[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]

Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]

(x - 3) is a factor of P(x)

[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]

where,

[tex]a = \sqrt{-4}\\a = 2i[/tex]

[tex]b = -\sqrt{-4}\\a = -2i[/tex]

Zeroes of P(x) = 3, 2i, -2i

[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]

x = 2 satisfies the equation

[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]

[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]

[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]

Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4)

[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]

[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]

For  [tex]x^3 -5x^2+3x +1 = 0[/tex]

x = 1 satisfies the equation

[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]

[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]

Roots are x = 1 or x = a or x = b

where,

[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]

[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]

Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

To learn more about polynomial, refer to the link-

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Answer:

The fraction form of the repeating decimal is;

Explanation:

We want to express the repeating decimal 0.2 (2 repeating) as a fraction.

let x represent the fraction;

Then subtract x from 10x;

Then we can divide both sides by the coefficient of x;

Therefore, the fraction form of the repeating decimal is;

Answer:

b. 15 fl. oz

Explanation:

From the question, we are told that 3/4 cup of bleach is needed per 1 gallon of water.

Thus:

Next, we represent the result in the form of the given options:

Using the standard rate of conversion: 1 cup = 8 fl. oz

The volume of bleach added to 2.5 gallons of water is 15 fl. oz.

The given data is:

Rearrange the data in ascending order:

sin C = 3/5

Given:

CB = 32

AC = 40

AB = 24

To find:

sin C

To determine sinC, we will apply the sine ratio:

Population decreasing rate is

18% monthly

Actual population = 500

Then

In 1 month decreases (500/100)• 18 = 90

Population = 500-90= 410

No find (410/100)•18 = 73.8

410-73.8= 336.2

In 3 months

(336.2/100) •18 = 60.5

336.2 - 60.5 = 276 fishes

ANSWER IS 276 fishes remain

Since the coop is in square shape The fencing is in the shape of a square

So equation is 4x=20, x=5

We will determine the angle as follows:

We know that the whole circle contains 360°, so we determine the angle of 0.35 as follows:

So, the measure of the central angle for sector C is 126°.

To get the better deal of the two, we need to find the cost per area of pizza for each deal and compare.

Deal 1: 2 medium 14'' (round) pizza for $14 total

The area of a circle is calculated as

where r is the radius.

The area of the pizza is calculated to be:

Hence, the total area for the two pizzas will be:

The cost per square inch of pizza is, therefore, calculated to be:

The pizza costs $0.011 per square inch.

Deal 2: 1 large 20'' (round) pizza for $13 total

The area of the pizza is calculated to be:

Hence, the cost per square inch of pizza is calculated to be:

The pizza costs $0.010 per square inch.

CONCLUSION:

The better deal will be the deal with the lesser cost per square inch. As can be seen from the calculation, both deals are about the same price per square inch if approximated. However, without approximation, Deal 2 has a slightly lesser cost per square inch.

Therefore, DEAL 2 IS THE BETTER DEAL.

Answer:

True.

The graph is linear, but not proportional.​

Explanation:

Given the graph in the attached image;

The graph is linear because it is a straight line graph.

A linear graph is always straight.

A proportional relationship in which the two components have a constant ratio.

The proportional graph is a straight line graph that passes through the origin (0,0).

Since the given graph does not pass through the origin, it is not a proportional graph.

Therefore, The graph is linear, but not proportional.​

Answer:

44,000

Let me know if its wrong

Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:

Answer

The situation is not biased because it takes a random sample from each group.

Kindly check below

Question 1) We can see that in the column "number of recipients" there is a Geometric Sequence whose common ratio is 5.

2) Therefore, we can fill in those gaps with the following:

3) Thus is the table.

We have to first determine the area of the square. The area of a square can be represented as follows

The number of each square feet each person will requre can be calculated as follows

Answer: [tex]f(x)=x^3 -51x^2 -3x+153[/tex]

Step-by-step explanation:

By the conjugate root theorem, the roots are [tex]\sqrt{3}, -\sqrt{3}, 51[/tex].

Letting the leading coefficient be 1,

[tex]f(x)=(x-\sqrt{3})(x+\sqrt{3})(x-51)\\\\=(x^2 -3)(x-51)\\\\=x^3 -51x^2 -3x+153[/tex]

Given the graph:

The length of the shadow = y - x.

• To find x:

• To find y:

Length of the shadow:

ANSWER

Length of the shadow = 11.4 m

we have the functions

so

ANSWER:

The system can only be consistent and independent

STEP-BY-STEP EXPLANATION:

We have to:

• If a system has at least one solution, it is said to be consistent.

• If a consistent system has exactly one solution, it is independent.

• If a consistent system has an infinite number of solutions, it is dependent

• If a system has no solution, it is said to be inconsistent

We know that the system has 2 solutions, and we know that the system is only inconsistent when it has no solution, therefore the correct answer is:

The system can only be consistent and independent

Step 1

compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.

Step 2

Math problem

455 + 229

Compatible numbers

455 + 225 = 680

680 is close to 455+229 = 684

Step 3:

Hence

By compatible numbers, 455 + 229 is more than 650.

The breadth of the room = 6 cm

Since the length of the room is twice its breadth

Then

Length of the room = 2 times 6cm = 12cm

The height of the room = 4cm

Since the shape of the room is a cuboid

The surface area of a cuboid is given as

Substitute l = 12, w = 6 and h = 4 into the formula

This gives

Simplify the expression

Therefore, the total surface area of the room is

Original Car price = $20,000

Price increase after 5 years = 25%

To calculate the price after 5 years, first multiply the original price (20,000) by the percentage increase in decimal form ( divided by 100) to obtain the increase amount:

20,000 x (25/100) = 20,000 x 0.25 = $5000

Finally, add the increase amount to the original price:

20,000+5,000 = $25,000

Answer:

Step-by-step explanation:

(3,9)

(-5*3) +( 3*9) > 12

-15 + 27 > 12

12 > 12

not true

(-5,5)

(-5*5) + (3*5) > 12

-25 + 15 > 12

-10 > 12

not true

(3,-6)

(-5*3) + (3*-6) > 12

-15 + -18 > 12

-33 > 12

not true

(-2,-5)

(-5*-2) + (3*-5) > 12

10 + -15 > 12

5 > 12

not true

(2,8)

(-5*2) + (3*8) > 12

-10 + 24 > 12

14 > 12

(-6,0)

(-5*-6) + (3*0) > 12

30 + 0 > 12

30 > 12

A dime is 10% of a dollar = 10/100 x 100 cent = 10 cents

A quater is 25% of a dollar = 25/100 x 100 cent = 25 cents

Since Karen has 5 more quaters than dimes

let quaters = q

let dimes = d

Then Karen has 5q : d = $ 3.70

$ 3.70 = 3.70 x 100 cents = 370 cents

Given angles are corresponding angles, they are congruent (have the same measure):

Use the equation above to solve x;

You use the value of x=30 to find the measure of corresponding angles:

Solution

We have the function

The graph of the function is

a) To calculate the minimum payment of the balance, you calculate the 2% of $4273.56. You proceed as follow:

(2/100)(4273.56) = 85.47

Hence, the mimum payment of the balance is $85.47

b) You calculate the amount of interest charged this month as follow:

convert the annual percentage rate to decimal form:

21.1/100 = 0.211

divide the previous result by 12 to get the monthly interest rate:

0.2111/12 = 0.0175

multiply the previoues result by the balance:

0.0175 x 4273.56 = 75.143 ≈ 75.14

convert the monthly rate to a percentage:

0.0175 x 100 = 1.75%

Hence, the amount of interest was $75.14, which corresponds to a 1.75%

Answer:

Explanations:

According to the question, we need to determine which of the signs will fit in that will make the expression a binomial.

In simple terms, a binomial is a two-term algebraic expression that contains variable, coefficient, exponents, and constant.

We need to determine the required sign by using the trial and error method.

Using the positive sign (+) first, we will have:

Using the product sign, this will be expressed as:

According to the sum of two cubes;

Comparing this with the expression above, we will see that a = 3y^6 and

b = 4. This means that the resulting expression above can be written as a sum of two cubes to have;

Collect the like terms:

Bobby is right because the measurements were made smaller so the dilation factor must be a number less than 1, and 1/3 is less than 1