What is the product of d – 9 and 2d2 + 11d – 4?

2d3 – 7d2 – 103d + 36
2d3 – 7d2 – 95d + 36
2d3 + 7d2 – 95d + 36
2d3 + 7d2 – 103d + 36

Answer:

[tex]\displaystyle \frac{4x + 14}{2} \div \frac{4x + 14}{x - 6} = \frac{x - 6}{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Dividing Fractions - KCF (Keep Change Flip)

Algebra I

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{4x + 14}{2} \div \frac{4x + 14}{x - 6}[/tex]

Step 2: Simplify

Extra:

If we were to graph this, we would need to watch out for domain restrictions or changes because we are combining 2 domains together when 1 of them has a restriction.

Answer:

(x-6)/2

Step-by-step explanation:

Turn the second fraction upside down and multiply two fractions

Answer:

3. See explanation

2. [tex]\displaystyle Yes[/tex]

1. [tex]\displaystyle [2, 1][/tex]

Step-by-step explanation:

3. Substitution, Elimination, and Graphing are ALL three methods to solve a system of equations, whether they are in three variables or two. The only differense is that with graphing, you will easily spot when a system is dependent [Infinitive Solutions], inconsistent [no solution], and\or consistent [one solution]. With elimination, you want to eliminate one set of variables [set to zero] so that it will be alot simpler solving the system, then latre on, substitute whatever value solved for the remaining set of variables back into the system to solve for the eliminated variable. Finally, with substitution, all you have to do is choose which variable you want to solve for in all three equations, or two. It really does not matter which one, as long as you follow the proper universal concept in using the Order of Operations.

2. This is self-explanatory really. The only time you cannot use any method is when the linear equations form parallel lines. Otherwise, you will always have one or infinite solutions.

1. See above imagery

I am joyous to assist you at any time.

8x^3 − 125y^3/(2x + 5y)3 ÷ 4x^2 + 10xy + 25y^2/4x^2 + 20xy + 25y^2

To divide by a fraction, multiply by its reciprocal.

8x^3 − 125y^3/(2x + 5y)^3  ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Simplify the numerator.

Rewrite 8x^3 as (2x)^3.

(2x)^3 − 125y^3/(2x + 5y)^3 ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2  

Rewrite 125y^3 as (5y)^3.

(2x)^3 − (5y)^3/(2x + 5y)^3  ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Since both terms are perfect cubes, factor using the difference of cubes formula,

a^3 − b^3 = (a − b) (a^2 + ab + b^2) where a = 2x and b = 5y.

(2x − (5y)) ((2x)^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3  ⋅ 4x + 20xy + 25y^2/ 4x^2 + 10xy + 25y^2

Multiply 5 by −1.

(2x − 5y) ((2x)^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3   ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2  

Apply the product rule to 2x.  

(2x − 5y) (22x^2 + 2x (5y) + (5y)^2)/(2x + 5y)3    ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y2

Raise 2 to the power of 2.

(2x − 5y) (4x^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3    ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Rewrite using the commutative property of multiplication.

(2x − 5y) (4x^2 + 2 ⋅ 5xy + (5y)^2)/(2x + 5y)^3      ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Multiply 2 by 5.

(2x − 5y) (4x^2 + 10xy + (5y)^2)/(2x + 5y)^3  ⋅ 4x^2 + 20xy + 25y^2/ 4x^2 + 10xy + 25y^2

Apply the product rule to 5y.

(2x − 5y) (4x^2 + 10xy + 52y^2)/(2x + 5y)^3    ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Raise 5 to the power of 2.

(2x − 5y) (4x^2 + 10xy + 25y^2)/(2x + 5y)^3    ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Cancel the common factor of 4x^2 + 10xy + 25y^2.

((2x − 5y)/(2x + 5y)^3) (4x^2 + 20xy + 25y^2)

Multiply

(2x − 5y) (4x^2 + 20xy + 25y^2)/ (2x + 5y)^3

Factor using the perfect square rule.

Rewrite 4x^2 as (2x)^2.

(2x − 5y) ((2x)^2 + 20xy + 25y^2)/ (2x + 5y)^3

Rewrite 25y^2 as (5y)^2.

(2x − 5y) ((2x)^2 + 20xy + (5y)^2)/ (2x + 5y)^3

Check that the middle term is two times the product of the numbers being squared in the first

term and third term.

20xy = 2 ⋅ (2x) ⋅ (5y)

Rewrite the polynomial.

(2x − 5y) ((2x)2 + 2 ⋅ (2x) ⋅ (5y) + (5y)2)/(2x + 5y)^3

Factor using the perfect square trinomial rule a^2 + 2ab + b^2 = (a + b)^2, where a = 2x and  b = 5y.

(2x − 5y) (2x + 5y)^2/ (2x + 5y)^3

Cancel the common factor of (2x + 5y)^2 and (2x + 5y)^3.

Factor (2x + 5y)^2 out of (2x − 5y) (2x + 5y)^2.

(2x + 5y)^2 (2x − 5y) / (2x + 5y)^3

Cancel the common factors.

 2x − 5y / 2x + 5y

Answer:

This may be wrong but: (2x - 5y) ((2x)^2 + 10xy + (5y)^2) over (2x + 5y) (4x^2 + 10xy + 25y^2)

Step-by-step explanation:

Answer:

The multiple choice question is A

one of the zeros is x=2

Answer:

Choice C

Step-by-step explanation:

A geometric sequence is usually one that multiply or divide to get to the next number in the sequence. So let's go through them to see which one gets multiplied since all of the choices are increasing.

Choice A:

[tex]1^{+3},4^{+1},5^{+4},9^{+5},14[/tex]

Nope that's not what we're looking for.

Choice B:

[tex]3^{+3},6^{+3},9^{+3},12^{+3},15[/tex]

This would be a perfect arithmetic sequence but not the type of sequence we are looking for.

Choice C:

[tex]6^{*3},18^{*3},54^{*3},162[/tex]

Yes! See how this one is multiplying by 3 and not adding or subtracting.

Choice D:

[tex]3^{+2},5^{+3},8^{+5},13^{+7},21[/tex]

Nope this is not it either.

Answer:

x = (-4 - z)/y

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-4 = xy + z

Step 2: Solve for x

Answer:

it can be answer that it could be posstive

Answer:

Its B :)

Step-by-step explanation:

Look at the graph points and match them with the choices

Answer:

The first choice

Step-by-step explanation:

Perpendicular lines intersect to form right angles, like the x- and y-axis on a coordinate plane.

Answer:

option 1 or A

Step-by-step explanation:

it is the definition of perpendicular lines

2y = 7x + 6 or the simplified version would be y = 7/2x + 3

Step-by-step explanation:

u just gotta know that slope intercept form is the equation y=mx+b

Answer:

y=7x-8

Step-by-step explanation:

y=mx+b........slope-intercept form

where m=slope,b=y-intercept

y=7x-8

Answer:

V2 has more room than the Aquarium.

Step-by-step explanation:

Step-by-step explanation:

according to pythagoras theorem

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2

therefore,

x2 = (4)2 + (4)2

x2 = 16 + 16

x2 = 32

x = √32

hence, x = 4√2

Answer:

53 caramelos

Step-by-step explanation:

El número total de caramelos en el frasco = 180 caramelos

Para Laura

Laura se ha comido la décima parte de un frasco

1/10 × 180 caramelos = 18 caramelos

Por Marta

Marta una novena

1/9 × 180 = 20 caramelos

Por Cristina

Cristina una quinta.

1/5 × 180 = 36 caramelos.

De lo que queda, Juan se ha comido la mitad.

La cantidad de caramelos que quedan se calcula como:

180 - (18 + 20 + 36)

= 180 - 74

La cantidad de caramelos que quedan = 106 caramelos

Para juan

De lo que queda, Juan se ha comido la mitad.

= 1/2 × 106

= 53 caramelos

¿Cuántos dulces quedan?

= 106 caramelos - 53 caramelos

= 53 caramelos

Por tanto, quedan 53 caramelos.

Step-by-step explanation:

(3x+24)°=(8x-11)°

24+11=8x-3x

35=5x

x=7

Answer:

49i^3u−21i^3x+9x

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

y°=70

Step-by-step explanation:

the angles inside a triangle must add up to 180 degrees, and thus the unknown interior angle is 180°-40°-30°=110°

this interior angle and the exterior angle are supplementary to each other and thus 110°+y°=180°

so y°=70°

you could also have used the theorem that states that the interior angles sum not adjacent to the exterior angle would equal the exterior angle

Answer:

[tex]63[/tex]

Step-by-step explanation:

Let number of nickels be [tex]x[/tex]

Number of dimes be [tex]y[/tex]

Number of quarters be [tex]z[/tex]

Total number of coins is [tex]185[/tex]

[tex]x+y+z=185[/tex]

Number of dimes is 5 more than quarters

[tex]y=5+z[/tex]

[tex]x+(5+z)+z=185\\\Rightarrow x+2z=180\\\Rightarrow x=180-2z[/tex]

Amount of money in the jar is $25.25

[tex]0.05x+0.1y+0.25z=25.25\\\Rightarrow 0.05x+0.1(5+z)+0.25z=25.25\\\Rightarrow 0.05x+0.5+0.1z+0.25z=25.25\\\Rightarrow 0.05x+0.35z=24.75[/tex]

[tex]0.05(180-2z)+0.35z=24.75\\\Rightarrow 9-0.1z+0.35z=24.75\\\Rightarrow 9+0.25z=24.75\\\Rightarrow z=\dfrac{24.75-9}{0.25}\\\Rightarrow z=63[/tex]

[tex]y=5+z=5+63\\\Rightarrow y=68[/tex]

[tex]x=180-2z=180-2\times 63\\\Rightarrow x=54[/tex]

So, the number of quarters is [tex]63[/tex].

Answer:

63 is the correct answer :)

Step-by-step explanation:

Answer:

C) $6.46

Step-by-step explanation:

Equations

The price per gallon of milk (m) and the price per gallon of orange juice (j) are given below:

m = 5.71 + 0.25n

j = 4.66 + 0.60n

Where n is the number of months after December 31, 2018.

It's required to find the value of n when both prices are equal:

4.66 + 0.60n = 5.71 + 0.25n

Subtracting 0.25n:

4.66 + 0.60n - 0.25n = 5.71

Subtracting 4.66:

0.60n - 0.25n = 5.71 - 4.66

Operating:

0.35n = 1.05

n = 1.05/0.35

n = 3

The price per gallon of milk for n=3:

m = 5.71 + 0.25*3

m = 5.71 + 0.75

m = $6.46

Answer:

1/25 to get both correct

Step-by-step explanation:

So the probability of getting one choice correct is 1/5

Since 5 choices 1 is correct

now we have to get 2 in a row correct so

1/5*1/5=1/25

Answer:

4321

Step-by-step explanation:

rreer5t66

Answer:

y = 2x - 3.5

Step-by-step explanation:

2x² + 2y = 4x + 2x² - 7

2y = 4x + 2x² - 7 - 2x²

2y = 4x - 7

y = (4x - 7) / 2

y = 2x - 3.5

2x² + 2y = 4x + 2x² - 7

4x + 2y = 4x + 2x² - 7

4x + 2y = 4x + 4x - 7

4x+2y=8x-7

2y = 4x - 7

9514 1404 393

Answer:

  C

Step-by-step explanation:

You can reflect point x across the origin to find is is just above -1. Adding 3 to that value gives a point just above -1+3 = 2. That's where point C is located.

__

Algebraic solution

Algebraically, you can set y = -x +3, and solve for x. That gives you ...

  x = 3 -y

Using the relation given at the start:

  0 < x < 1

  0 < 3 -y < 1 . . . . . substitute for x

Adding y gives ...

  y < 3 < y+1

We can separate this into two inequalities:

  y < 3, and

  3 < y+1

  2 < y . . . subtract 1

Now, we have ...

  2 < y < 3 . . . . . the location of point C

As you can see, it is much easier to use the number line directly to find the desired point.

Answer:

If I did my math right it should be 10.20

Step-by-step explanation:

-78.55 + 128.75 = 50.2

50.2 - 40 = 10.2

And then obviously just add the zero at the end bc its money

Answer:

an equation of the line L will be: y = 1/2x - 2

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

Given the points

Determining the slope between (0, -2) and (6, 1)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(0,\:-2\right),\:\left(x_2,\:y_2\right)=\left(6,\:1\right)[/tex]

[tex]m=\frac{1-\left(-2\right)}{6-0}[/tex]

[tex]m=\frac{1}{2}[/tex]

The y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the point (0, -2), we can determine that at x = 0, the value of y = -2.

Thus,

The y-intercept b = -2

now substituting b = -2 and m = 1/2 in the slope-intercept form of line equation

y = mx+b

y = 1/2x + -2

y = 1/2x - 2

Therefore, an equation of the line L will be: y = 1/2x - 2

Answer:

B) 110.92 u²

Step-by-step explanation:

to find the surface area, find the area of each side and add them together.

here are all 6 sides:

4.5 * 6.8

4.5 * 6.8

4.5 * 2.2

4.5 * 2.2

2.2 * 6.8

2.2 * 6.8

4.5 * 6.8 = 30.6

4.5 * 6.8 = 30.6

4.5 * 2.2 = 9.9

4.5 * 2.2 = 9.9

2.2 * 6.8 = 14.96

2.2 * 6.8 = 14.96

30.6 + 30.6 + 9.9 + 9.9 + 14.96 + 14.96

110.92