If f(x)=5x^3-2 and g(x)=2x1, find (f+g)(x).

Answer:

[tex]p(x) = (x-4)(x - \frac{5}{3})(x - 1)[/tex]

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

We have the polynomial [tex]p(x) = 3x^3-20x^2+37x-20[/tex]

It has a known factor [tex]x - 4[/tex]. This means that the polynomial can be written as:

[tex]p(x) = (x-4)q(x)[/tex]

In which q(x) is a second order polynomial, because p is of the third degree and q is of the first degree(3 - 1 = 2). So

[tex]q(x) = ax^2 + bx + c[/tex]

We have to find a, b and c. Then

[tex]3x^3-20x^2+37x-20 = (x-4)(ax^2 + bx + c)[/tex]

[tex]3x^3-20x^2+37x-20 = = ax^3 + (-4a + b)x^2 + (c - 4b)x - 4c[/tex]

Comparing both sides, we have that

[tex]a = 3[/tex]

[tex]-4c = -20 \rightarrow c = 5[/tex]

[tex]c - 4b = 37[/tex]

[tex]-4b = 32 \rightarrow b = -8[/tex]

Now we find the roots of this polynomial.

[tex]\bigtriangleup = b^{2} - 4ac = (-8)^2 - 4(3)(5) = 64 - 60 = 4[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{4}}{2*3} = \frac{5}{3}[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{4}}{2*3} = 1[/tex]

So, as a product of it's factors, we have that q is:

[tex]q(x) = (x - \frac{5}{3})(x - 1)[/tex]

And p(x)

[tex]p(x) = (x-4)q(x)[/tex]

[tex]p(x) = (x-4)(x - \frac{5}{3})(x - 1)[/tex]

Answer: (x-4)(3x-5)(x-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Age of Qasim =  6 year

Age of Asif = 1 year

Step-by-step explanation:

Let :

Age of Qasim = x

Age of Asif = x -5

After 4 years there age will be:

Age of Qasim = x+4

Age of Asif = x-5+4 = x-1

We are given: Four years later, Qasim will be twice as old as  Asif.

Age of Qasim = 2 (Age of Asif)

x+4=2(x-1)

x+4=2x-2

2x-x=4+2

x=6

So, We get x = 6

The present ages will be:

Age of Qasim = x = 6 year

Age of Asif = x -5 = 6-5 = 1 year

Answer: 10.5/6 - 6.5/6 = 2/3

Step-by-step explanation:

The answer is 10.5/6 - 6.5/6 = 2/3

Answer:

9400.11

Step-by-step explanation:

Answer:

D. 20 cm²

Step-by-step explanation:

The second object is 2 times bigger than the first object. To solve this, take the original area and multiply it by 2:

10 · 2 = 20

Therefore, the second object has an area of 20 cm².

Answer:

A x B = 5/6 x 3/4 = 15/24

Answer = 15/24

Step-by-step explanation:

Answer:

We are asked to find the area of the rectangle that has side lengths of 3/4 yard and 5/6 yard.

We know that area of rectangle is width times length.

To find the area of the given rectangle we will multiply both side length as:

Area of regatangle = width x Lenghth

Area of regtangle = 3/4 x 5/6 yard to the 2 power

Area of regtangle = 1/4 x 5/2 yard to the 2 power

Area of regtangle = 1 x 5/ 4x2 yard to the 2 power

Area of regtangle = 5/8 yard to the 2 power

Therefore, the area of the given rectangle would be 5/8 square yards.

Answer:

The answer is C and E.

Step-by-step explanation:

I just took the assignment and it is C and E.

The expression that represents the population after 5 decades is

100,000 x [tex]2^5[/tex] or 100,000 x 2 x 2 x 2 x 2 x 2.

Options C and E is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

The population of the city = 100,000

Population doubles every decade.

This means,

Population after 1 decade.

= 100,000 x 2

= 200,000

Population after 2 decades.

= 200,000 x 2 x 2

= 800,000

We can write an expression for the population after x decade.

= 100,000 x [tex]2^x[/tex]

The population after 5 decades.

= 100,000 x [tex]2^5[/tex]
= 100,000 x 2 x 2 x 2 x 2 x 2

= 100,000 x 32

= 3200,000

Thus,

The expression is 100,000 x [tex]2^5[/tex] or 100,000 x 2 x 2 x 2 x 2 x 2.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

When a decimal number is multiplied by a power of ten, the product is found by moving the decimal point to the right that many places as the power of ten. For example, in 3.45 × 10 2, the product is obtained by moving the decimal point two places to the right, i.e., 3.452 × 10 2 = 345.2.

Step-by-step explanation:

Stay frosty

Answer:

increases

decreases

Step-by-step explanation:

i just did it

9514 1404 393

Answer:

  2.  x ≈ 17.74

  3.  x ≈ 16.64

Step-by-step explanation:

The tangent function relates an angle to the opposite and adjacent sides of a right triangle:

  Tan = Opposite/Adjacent

Here, we're looking for the measure of the side opposite the angle, so we can rearrange this relation to ...

  Opposite = Adjacent×Tan

__

2.  x = 32×tan(29°) ≈ 17.74

3.  x = 13×tan(52°) ≈ 16.64

_____

Hopefully, we've given enough decimal places so that you can round to the precision you need.

Answer:

ggggmd

hsmhdmvx.hffyfylltet

Answer: (2,144)

Step-by-step explanation:

Answer:

2+3 = 5

4+1 = 5

1*5=5

Step-by-step explanation:

Answer:

[tex]2x + 6 = 12 \\ 2x = 12 - 6 \\ 2x = 6 \\ x = \frac{6}{2} \\ \boxed{x = 3}[/tex]

Answer:

All real numbers except for 0, -5, and 5

Step-by-step explanation:

You can't have a zero in the denominator, therefore 0, -5, and 5 can't be solutions to the equation.

Interval notation:

(-infinity, -5) u (-5, 0) u (0, 5) u (5, infinity)

Set-Builder Notation:

{x| x≠ 0, 5, -5}

Explanation:

The formula for calculating the distance between two points is: d = √ ( x 2 − x 1 ) 2 + ( y 2 -y 1 ) 2  Substituting the points from the problem gives: d = √ ( 0 − 5 ) 2 + ( 4 − 1 ) 2   d = √ ( − 5 ) 2 + ( 3 ) 2 d = √ 25 9 d = √ 34 Or d =3 5.8 rounded to the nearest hundredth.

Answer:

247000000

Step-by-step explanation:

10^8 = 10×10×10×10×10×10×10×10

=100000000

or, downloaded=100000000×2.47

=27000000

Answer: 453 more downloads   1,547 more downloads

7,549 more downloads   435 more downloads  ( it will be one of these answers pls help me im doing a quiz) ~cries cutely~

Step-by-step explanation:

An app was downloaded 3,548 times last week. This week the app was downloaded 4,001 times. How many more downloads did the app have this week than last week

Answer: The entire trip is 62.5 miles

Step-by-step explanation:

25 miles = 0.4x

Divide both sides by 0.4

25/0.4 = 62.5 miles

Answer:

x=62

Step-by-step explanation:

all angles should add to 180

180-56=124

124÷2=62

Answer:

Step-by-step explanation:

1st notice that two of the sides are the same length?   ( isosceles ) that mean the two angles at the "base" which is the side that both of the same size legs tie into... that's the side that is 4.5 in the picture.  soooo if both of those angles are the same.. and we know that the angles are going to add to 180 then....  we can say    the the 56° is the same as the one at the other end of the 4.5 side (base) so  2*56°=112°

and then 112° + x = 180°

x = 180-112

x = 68°

:)

Answer:

twelve

Step-by-step explanation:

y=2(3)+6

y=6+6

y=12

thats basically how you do it

Answer:

Stefan originally spent $110.

Stefan made a profit of $44.

Step-by-step explanation:

Given that:

Stefan sold the bike and helmet for $137 and $17

Total amount = 137+17 = $154

This is 140% of the price Stefan originally paid.

Let,

x be the original price paid by Stefan

140% of x = $154

[tex]\frac{140}{100}x=154\\1.4x = 154\\\frac{1.4x}{1.4}=\frac{154}{1.4}\\x=110[/tex]

Therefore,

Stefan originally paid $110 for the bicycle and helmet.

Profit made by Stefan = 154-110 = $44

Hence,

Stefan originally spent $110.

Stefan made a profit of $44.

Answer:

-2.17

Step-by-step explanation:

Answer:

Infinite Solutions

Step-by-step explanation:

3x-7=3x(x-3)+2

3x-7=3x-9+2 - Distributive Property

3x-7=3x-7 - adding the right side together

Answer:

~60•the length of PQ . , the length of QR is 90• Tell me if I'm wrong . sorry if I got it wrong .~

Answer:

90 degrees

Step-by-step explanation:

its a 45-45-90 triangle

Answer:

can you take a picture so I can see I'm trying to help you

Answer:

-6x-9=  1

2x^5-x^4+2x^3-6x^2+2x+4= 5

-4x^3-10^2+7x+5= 3

Step-by-step explanation:

i just did and everything was right

Answer:

uhhh i might be l;ate lol

Step-by-step explanation:

Answer:

No you can not it would come out as a decimal form.

Step-by-step explanation:

3 divided by 2 is 1.5 or 1 1/2

This is not divided evenly between each other

This proves that (no) anything that is a odd number can not be divided equally

Hope that helps