PLEASE HELP!!! What is factoring? Why is it useful to try to factor out the GCF first when factoring? Explain the relationship between factoring and multiplying polynomials. Give an example to help explain. Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6 . What are the key features needed to graph a polynomial function? Explain how to find these key features to sketch a rough graph of a polynomial function. Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.

(x-p)(x-q)

y(x-q) .... let y = x-p

yx - yq ... distribute

x(y) - q(y)

x(x-p) - q(x-p) ... replace y with x-p

x^2 - px - qx + pq .... distribute

x^2 + (-p-q)x + pq

The last expression is in the form ax^2+bx+c with a = 1, b = -p-q and c = pq

The constant term is the term without any variable x attached to it (either x or x^2), so the constant term is pq

Answer:

6 3/5

Step-by-step explanation:

33/5 = 6 R3

Answer:

6.6

Step-by-step explanation:

33÷5=6.6

33 divided by 5equal

Answer:

Area = s² = 4² = 16 sq. In.

Perimeter = 4s = 4(4) = 16 in.

Answer:

0 miles- $50

1 mile- $53

2 miles- $56

3 miles-$59

Step-by-step explanation:

you add $3 to the original 50 as you go each mile.

Answer:

8x²−6xy+20x−15y

Step-by-step explanation:

(4x−3y)(2x+5)

=(4x+−3y)(2x+5)

=(4x)(2x)+(4x)(5)+(−3y)(2x)+(−3y)(5)

=8x²+20x−6xy−15y

=8x²−6xy+20x−15y

Answer:

D

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = lbh ( l is length, b breadth and h is height )

Here l = 7, b = 2 and h = 4 , thus

V = 7 × 2 × 4 = 56 in² → D

Answer:

There is only one solution set.

Step-by-step explanation:

The set can contain any number of solutions or none.

This is all I know, hope it helps.

Intersection point of graph of function is known as solution of the function.

Graph is attached below, in which solution is shown.

1. Here, given that  [tex]3x^2-3x+2=2[/tex]

It can be written as,   [tex]y=3x^2-3x+2\\\\y=2[/tex]

Intersection point of graph of above two equation will be the solution of given function,

Solutions are (1, 2) and (0, 2)

2. Given that , [tex]3x^2-3x-1=x+1[/tex]

It can be written as

                [tex]y=3x^2-3x-1\\\\y=x+1[/tex]

Intersection of graph of above two equation will be the solution of given equation.

Solutions are  (1.721, 2.721) and (- 0.387, 0.613)

Both graph attached below,

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Answer:

Rajesh salary is the median

Step-by-step explanation:

Am not good in explanation

Answer:

1: Ram

Step-by-step explanation:

The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values

if we put these salaries in order we can find out what the median salary is.

32,701 , 45,600 , 52,000 , 67,250 , 71860.

The number in the centre or the middle is 52,000. That is Ram's salary.

The answer is 1. Ram

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Answer:

Step-by-step explanation:

The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;

[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]

Hence the expression 4 raised to 4 is equivalent to 256

Answer:

525 dollars

Step-by-step explanation:

simple interest yearly ( year 11 does not count because the question asking at the amount at the  beginning of year 11)

interest=300*0.075*10= 225

the amount in the account : 300+225=525 dollars

Answer:

c = 152

Step-by-step explanation:

c/8+5 = 24

Subtract 5 from each side

c/8+5-5 = 24-5

c/8 = 19

Multiply each side by 8

c/8*8 = 19*8

c =152

Answer:

D. 152

Step-by-step explanation:

First, subtract 5 from both sides:

c/8 + 5 = 24

c/8 = 19

Multiply both sides by 8:

c = 152

So, the correct answer is D, 152

Answer:

Step-by-step explanation:

The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.

Based on the values given in the table for f(x), the interval of x-values that show the function increasing is (-3, -1).

The value of f(x) was decreasing from 34 until it got to -11 where it then started to rise again. The relevant value of x here is -3.

The value then began to rise until it reached -1 where it then fell to -2. The x value here is -1.

The interval of x-values where the function is increasing is therefore (-3, -1).

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Answer: 4

Step-by-step explanation:

We know that a plane is 2 dimensional surface that extends infinitely far.

The number of points required to define a plane = 3

Here , we have 4 points A, B, C, and D.

So, the number of possible combinations of 3 points to make a plane from 4 points = [tex]C(4,3)[/tex]

[tex]=4[/tex]            [ [tex]C(n,n-1)=n[/tex] ]

Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.

Answer:

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

Step-by-step explanation:

Long division:

13  33

13*2 = 26

33 - 26 = 7

we have: 33/13 = 2 r7

we know that we can rewrite the remainder as 7/13

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

Answer:

mark a dot 2 on the y axis and from there go up one right 3 until you can anymore then go back to the two and go down one left 2

Step-by-step explanation:

There are 12 factors which are perfect squares is 1,  4,  9,  16,  36,  64,  81, 144,  324, 576, 1296, 5184.

Factors can be define splitting the value in multipliable values.

Factorization of 15552
= 1 * 4 * 4 * 4* 9 * 9 * 3

Perfect squares can be formed by above factors are
= 1,  4,  9,  16,  36,  64,  81, 144,  324, 576, 1296, 5184.

Thus, there are 12 factors which are perfect squares is 1,  4,  9,  16,  36,  64,  81, 144,  324, 576, 1296, 5184.

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Answer:

15.60 times 100 divided by 390=4%

Step-by-step explanation:

The required sales tax rate percentage is 4%.

The sales tax for an item was $15.60 and it cost $390 before tax. To find the sales tax rate. Write your answer as a percentage.

the percentage is defined as, the composition of something out of whole inbounds of 100.example 10% of 150 = 10 * 150/100
                                                                = 15
It shows that 10 percent of 150 is 15.

sales tax = $15.60
cost = $390
To get the sales tax percentage we have to find out the tax composition of tax to the cost. So,
Sale tax percent = sale tax/cost  * 100
                            = 15.60/390   * 100
                            = 0.04 * 100
                            = 4 %

Thus, the required sales tax rate percentage is 4%.

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Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Step-by-step explanation:

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

The time will be t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable the dependent variable.

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum.

We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground.

The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

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Answer:

The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6

Step-by-step explanation:

We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.

n/5 ≥ 11

Multiply by 5 on both sides.

n ≥ 55

Now, let's do the second one.

-3y ≤ -18

Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)

y ≥ 6

Answer:

2/6 or 3/9

Step-by-step explanation:

1/3 x 2 = 2/6

1/3 x 3 = 3/9

Answer:

2/6 3/9

Step-by-step explanation:

to find equivalent fractions you can just multiply, or count by the denominator for example, 3 , 6 , 9 and so on and then with the numerator you count how much you went like, if you went to sixths than it was 2 because you skip counted.

Answer:

B. 15 days

Step-by-step explanation:

A=10=1/10 of the job

B=12=1/12 of the job

A+B+C=4=1/4 of the job

A+B

=1/10 + 1/12

=10+12/120

=22/120

=11/60

(A+B+C) - (A+B)

=1/4 - 11/60

=5 - 11/60

=4/60

=1/15

It would take C alone 15 days to finish the job

Answer:

The two polynomials are:

(x + 1) and (x² + x)

Step-by-step explanation:

A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.

Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.

Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.

So,

Let's multiply both numerator and denominator by (x + 1) to get;

(x + 1)/(x(x + 1))

This gives; (x + 1)/(x² + x)

Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.

Answer:

6 quarts

Step-by-step explanation:

8 bags

--------

2 quarts

Multiply top and bottom by 3

8*3 bags

--------

2*3 quarts

24 bags

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

6 quarts

Answer:

6

Step-by-step explanation:

2 quarts of iced tea = 8 tea bags.

x quarts of Iced tea = 24 tea bags

=> 2/8 = x/24

=> Multiply the extremes and means

=> 8x = 48

=> 8x / 8 = 48 / 8

=> x = 6

6 quarts of iced tea can be made with 24 tea bags.

Answer:

Following are the function description to the given question:

Step-by-step explanation:

In the given-question, three functions are used, that can be defined as follows:  

In function 1:

This function is also known as the modulus on the absolute value function, for example:

[tex]f(x)=| x| \left \{ {{x , \ \ \ x>0} \atop {-x, \ \ \ \x<0 }} \right.[/tex]

In the given in the above graph, that is [tex]f(x) = -x , \ \ x<0[/tex]

In function 2:

In this function, It is an algebraic function that is [tex]y=x^2[/tex]

It is also a part of the quadratic polynomial function, and its value is [tex]y=x^2 , \ \ \ x> 0[/tex]  

In function 3:

In this function, it is the cubic polynomial equation that's value is [tex]y=x^3[/tex]

In the graph its value is:

[tex]y=-x^3\\\\and \\ \\\to y= f(x) \\\\ \to y=-f(x)\\[/tex]

Answer:

Step-by-step explanation:

Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.

the total surface of the cone A = πrs+πr² and the volume is expressed as

V = 1/3πr²h

For the surface area of the cone;

Given parameters

radius = 8 cm and slant height s = 15 cm

Total surface area A = π(8)(15) + π(8)²

A = 90π+64π

A = 154π

If π = 3.14

A = 154(3.14)

A = 483.56cm²

A = 483.6cm²

Hence the total surface area of the cone to the nearest tenth is 483.6cm²

For the volume of the cone;

V = 1/3πr²h

Using pythagoras theorem to get the height of the cone;

l² = h²+r²

h² = l²-r²

h² = 15²-8²

h² = 225-64

h² = 161

h = √161

h = 12.69cm

V = 1/3π* (8)² * 12.69

V =  1/3π* 64 * 12.69

V =  1/3*3.14* 64 * 12.69

V = 2550.1824/3

V = 850.06 cm³

V = 850.1 cm³

Hence, the volume of the cone is  850.1 cm³ to the nearest tenth.

Answer:

8π units²

Step-by-step explanation:

center=((-1+3)/2,(-2+2)/2)=(1,0)

[tex]radius~r=\sqrt{(3-1)^2+(2-0)^2} =\sqrt{4+4} =\sqrt{8} \\area~of~circle=\pi r^2=\pi \times (\sqrt{8} )^2=8\pi ~square~units.[/tex]