Which sign makes the following statement true? 1/3 _____ 6/15 Answer = < >

The zeros of a polynomial function are given as,

x= 1 , x= 2, x= 3 and x= -3

Let the polynomial in standard form be,

y = ( x- 1)(x - 2)(x - 3)(x +3)

⇒ y = (x² - 2x - x +2)( x² - 3x +3x - 9)

⇒ y = (x² - 3x +2)(x² - 9)

⇒ y = x⁴ - 9x² - 3x³ + 27x + 2x² - 18

⇒ y = x⁴ - 3x³ -7x² + 27x  -18

Hence option c is the correct answer.

The given cubic equation is ,

x³ +6x² +11x +6 = 0

Calculating its roots we get,

x³ +6x² +11x +6 = 0

⇒ (x +1)( x+2 )(x+ 3) = 0

Thus the roots are -1, -2, and -3

Hence all the roots are real and are of different values.

Hence option d is the correct option.

The given radical expression can be simplified as,

[tex]\sqrt[4]{625 x^8 y^{12} }[/tex] = 5[tex]x^{2} y^3[/tex]

Hence option a is the correct option.

We can simplify the given expression as,

[tex]27^{1/3}[/tex] = ∛27 = ∛(3³) = 3

Hence option d is the correct option.

To know more about polynomial here

https://brainly.com/question/11536910

#SPJ1

Answer:

327

Step-by-step explanation:

To calculate how much Francisca and Elizabeth will raise together, we need to know how many laps or miles they walked. Unfortunately, the problem doesn't provide us with that information.

However, we can calculate how much each girl will raise individually.

Francisca will walk for 3 hours which is equal to 6 half-hours. She raises $25.50 every half-hour so she will raise:

$25.50 x 6 = $153

Elizabeth will walk for 3 hours which is equal to 12 quarter-hours. She raises $14.50 every quarter-hour so she will raise:

$14.50 x 12 = $174

Therefore, Francisca and Elizabeth will raise a total of:

$153 + $174 = $327

Brand B contains 3% saline solution by volume. Then, C is the right answer.

Percentage of saline solution in brand B, let x be.

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ1

The direction and angle of rotation include the following: C. 180° counterclockwise rotation.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point A (-6, 5)  →  Coordinates of point A' = (6, -5)

In conclusion, this transformation rule (x, y) → (-x, -y) is used for the 180° rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.

Read more on rotation here: brainly.com/question/28515054

#SPJ1

Answer:

it's 0

Step-by-step explanation:

I don't know it's answer you have to ask it to the teacher

Answer: (a. x^4/2yz)^2       b. -3ab             c. 2(3a^2-2ab+1)/3ab                   d. -(xy^2+2y^2-4)/4xy             QUESTION 5: a. (7y^3+6v^3+3v^2)/v       b. 9x^2-7x-8

Step-by-step explanation:

For many of these, you must be able to see that anything to the first is just that number, so it will be useless to write z^1 in question one. You can then factor out, and cancel out the numbers that are the same. Then, you can simplify. This is how you can do all of these. This is a very complicated process nd will take a while to do, but once you are able to do it, it becomes easy. If you still are having trouble understanding, you can put it into a long division calculator for polynomials, and they will show you the steps. For the fifth questions, we can cancel out the common factors, and we can also apply rules such as the fraction rule or the exponent rule to do this. The key thing here is to simplify to make it easier when you divide and multiply.

Hope this helps

Mark brainlist please!

If male and female students of section B in DPS and DAV are in ratio 3 : 2 and 4:3 respectively then male students of section B are 40% more than female students of section B considering both the schools (approx).

(A) 50% (C) 36% (B) 25% (D) 40%.

Hence, the correct option is D.

Let us assume that there are 3x male students and 2x female students in section B of DPS, and there are 4y male students and 3y female students in section B of DAV. We can set up the following equations to represent the given ratios

3x : 2x = male : female in DPS section B

4y : 3y = male : female in DAV section B

By simplifying these ratios, we get

3 : 2 = x/y for DPS section B

4 : 3 = x/y for DAV section B

Solving for x and y, we get

x = 6y for DPS section B

x = 4.5y for DAV section B

Now, let us add the male and female students in section B from both schools.

Male students = 3x + 4y = 3(6y) + 4(4.5y) = 30y

Female students = 2x + 3y = 2(6y) + 3(4.5y) = 21y

So, the ratio of male to female students in section B from both schools combined is

30y : 21y = 10 : 7

Therefore, male students are (10 - 7)/7 = 3/7 = 0.4286 (approx. 43%) more than female students in section B from both schools combined.

However, the question asks for the percentage more, so we need to multiply this answer by 100 to get a percentage.

0.4286 x 100 ≈ 42.86%

Therefore, male students in section B are approximately 42.86% more than female students in section B from both schools combined. Rounding to the nearest percent that is 40%.

Hence, the correct option is D.

To know more about students here

https://brainly.com/question/26051084

#SPJ1

As it was a non-liquidating distribution of investment land worth $510,000 to Topolino, it reduces his stock basis by the same amount, resulting in a negative basis of ($40,000) after the distribution. The answer is (b) ($40,000).

The distribution of the investment land with a fair market value of $510,000 to Topolino is a non-liquidating distribution, which means that it reduces Topolino's stock basis by the amount of the distribution ($510,000).

Topolino's basis in the stock immediately after the distribution will be the sum of his basis in the stock before the distribution ($470,000) minus the amount of the distribution ($510,000), which results in a negative basis of ($40,000). The correct answer is (b) ($40,000).

To know more about stock:

https://brainly.com/question/29992015

#SPJ1

Answer:

Step-by-step explanation:

The option that is greater than 4 is option (a) 5. This is because 5 is a positive value that is larger than 4. Option (b) -5 is a negative value that is less than 4. Option (c) -1/2 is also negative and less than 4. Option (d) -25 is the most negative option and therefore less than 4. So, the only option that is greater than 4 in this case is 5.

Answer:

a

Step-by-step explanation:

got it right on edge

The wheel will make one complete revolution around the circle after travelling a distance of 62.8 inches.

The distance that the wheel travels around the circle once is equal to the circumference of the circle.

The formula for circumference of a circle is given as;

D = 2πr

where;

The radius of the circle = 10 inches

The circumference of the circle is calculated as follows;

D = 2 x 3.14 x 10

D = 62.8 inches

Thus, the circumference of the circle is determined as 62.8 inches.

Learn more about circumference of a circle here: https://brainly.com/question/20489969

#SPJ1

The three sides of the triangle are a, b, P - (a + b)

The length of the missing side, and the lengths of all three sides of a triangular corner shelf.

Given that one side of the triangular shelf measures "a" units and another side measures "b" units, we can find the total of two sides by adding them together:

a + b = total of two sides

If the perimeter of the triangle measures "P" units, we know that the perimeter is the sum of all three sides, so:

a + b + c = P

where "c" is the length of the missing side. We can rearrange this equation to solve for "c":

c = P - a - b

To find the lengths of all three sides of the triangle, we can substitute the value of "c" that we just found into the Triangle Inequality:

a + b > P - a - b

Simplifying this inequality, we get:

2a + 2b > P

Dividing both sides by 2, we get:

a + b > P/2

So, if "a + b > P/2", then the triangle can exist, and we can use the value of "c" that we found earlier to get the lengths of all three sides:

a + b + c = P

a + b + (P - a - b) = P

c = P - (a + b)

To know more about triangle here

https://brainly.com/question/8587906

#SPJ1

Answer:

  9

Step-by-step explanation:

You want the least common denominator for the fraction in the sum ...

 (2/3)² -1/3

When the sum is simplified, it is ...

  4/9 -1/3

The denominator 9 is a multiple of the denominator 3, so the least common denominator of these two fractions is 9.

__

Additional comment

Using that denominator, the sum is ...

  4/9 -3/9 = 1/9

<95141404393>

Answer: x = -5, 5 y= 0

Step-by-step explanation:

vertical asymptotes = x= -5, 5

horizontal asymptotes = y= 0

When x = 1/2 and y = 4, the value of the expression (4x + 6)/8y is 1/4.

We have,

The expression is (4x + 6)/8y.

Substituting x = 1/2 and y = 4 in the given expression.

= (4x + 6)/8y

= (4(1/2) + 6)/8(4)

= (2 + 6)/32

= 8/32

= 1/4

Therefore,

When x = 1/2 and y = 4, the value of the expression (4x + 6)/8y is 1/4.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The third term in the expansion of the expression (5x - 7y)³ is 735xy².

Given expression is,

(5x - 7y)³

We have to expand this.

We know that,

(a + b)³ = a³ - 3a²b + 3ab² - b³

Using this,

(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³

               = 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³

               = 125x³ - 525x²y + 735xy² - 343y³

Here the third term is 735xy².

Hence the third term is 735xy².

Learn more about expansion of expressions here :

https://brainly.com/question/28400521

#SPJ1

Answer:

Therefore, the percentage change from 20 to 50 is an increase of 150%.

Step-by-step explanation:

To work out the percentage change from 20 to 50, we can use the following formula:

((New Value - Old Value) / Old Value) x 100%

Plugging in the numbers, we get:

((50 - 20) / 20) x 100%

= (30 / 20) x 100%

= 1.5 x 100%

= 150%

Answer:

Solution: It is given that Miguel needs to cut a board that is Two-thirds of a yard long into 3 equal pieces. It means is divided in 3 equal parts.

Step-by-step explanation:

Answer:

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

Direct variation equation:

Use the first pair of coordinates, x = 3 and y = 8 to find the value of k:

The equation becomes:

Now use the value of x = 18 to find the missing coordinate:

Answer:

00:00 in 12-hour clock time is equivalent to 12:00 midnight. It is the start of a new day and is the first minute of the 12-hour time cycle.

Answer:

True

Step-by-step explanation:

Peach snack packs averagely cost more than apple snack packs so a reasonable solution can be P is greater than A

1. The volume of the pyramid = 12 mm³.

2. Slant height (x) x ≈ 4.3 mm

3. Surface area of square pyramid = 86.4 mm²

1. The volume of the pyramid (V) = 1/3*a²h, where:

a is the base edge = 3 mm

h is the height = 4 mm

Plug in the values:

The volume of the pyramid (V) = 1/3*3²*4 = 12 mm³.

2. Slant height (x) = √(1.5² + 4²)

x ≈ 4.3 mm

3. Surface area of square pyramid = 6bs + b² = 6(3)(4.3) + 3²

= 86.4 mm²

Learn more about the square pyramid on:

https://brainly.com/question/30813103

#SPJ1

Answer: The width of the garden/fence will be 15 m.

Step-by-step explanation: First, we have to understand that there will be two wide sides and two long sides, and in a rectangle, the long sides always equal each other and the wide sides equal each other as well. This means that one width and one length will equal 120/2=60.

In other words:

one length of the garden + one width of the garden = 60

Now that we know this, we move on to the "3 times" part of the question. For this step, it is easiest to imagine quarters of something, because 3/4 of something will always be 3 x 1/4 of something; The proportion for 3/4:1/4 will always be 3:1.

60 x 3/4 is equal to 45 and 60 x 1/4 is equal to 15.

To check our answer, L+W+L+W = 45+15+45+15 = 120.

This means each wide side is equal to 15.

Answer:

The area of this polygon is 14 square units.

28% of the mixture is fruit juice.

Given that, Adriana mixed 6 L of Brand A juice with 9 L of Brand B juice. Brand A contains 52% fruit juice and Brand B contains 12% fruit juice.

We need to find that what percent of the mixture is fruit juice,

So,

Fruit juice in Brand A = 6 × 0.52 = 3.12 L

Fruit juice in Brand B = 9 × 0.12 = 1.08 L

So, (3.12 + 1.08 / 6 + 9) × 100%

= 28%

Hence 28% of the mixture is fruit juice.

Learn more about percentage, click;

https://brainly.com/question/29306119

#SPJ1

Answer:

C. 3 pounds

Step-by-step explanation:

to use % as factors we need to represent them as what they are : parts of 100.

so, e.g. 20% = 0.2 and so on.

x = pounds of the metal with 20% nickel.

0.2x + 0.8×6 = 0.6×(x + 6) = 0.6x + 3.6

0.2x + 4.8 = 0.6x + 3.6

1.2 = 0.4x

x = 1.2/0.4 = 3

she needs to combine 3 pounds of metal with 20% nickel with 6 pounds with 80% nickel to get 9 pounds (3+6) of an alloy with 60% nickel.

The fish tank that has a capacity of 60 gallons is given as follows:

A. Pacific.

The fish tank that has a capacity of 60 gallons obtained applying the proportions in the context of the problem.

The rate between quarts and gallons is given as follows:

1 gallon = 4 quarts.

Hence the capacity in quarts equivalent to 60 gallons is given as follows:

60 x 4 = 240 quarts.

Meaning that the Pacific fish tank has a capacity of 60 gallons.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer: 16

Step-by-step explanation:

I am not sure if this answer is 100% correct, but I believe this is a question involving proportions.

If you create a proportional equality equation that looks like this:

[tex]\frac{40}{30}=\frac{x}{12}[/tex]

It will give the x value as the answer to the problem. This is because the two triangles are proportional to one another.