All categories

2 years ago

Simplify (4x^2-7x+14)(3x+5x^2-6) Please show work

Mathematics

1 answer:

tatiyna2 years ago

4 0

Answer:

-23x^3+20x^4+25x^2+84x-84

Step-by-step explanation:

1 Expand by distributing sum groups.

4x^2(3x+5x^2-6)-7x(3x+5x^2-6)+14(3x+5x^2-6)

2 Expand by distributing terms.

12x^3+20x^4-24x^2-7x(3x+5x^2-6)+14(3x+5x^2-6)

3 Expand by distributing terms.

12x^3+20x^4-24x^2-(21x^2+35x^3-42x)+14(3x+5x^2-6)

4 Expand by distributing terms.

12x^3+20x^4-24x^2-(21x^2+35x^3-42x)+42x+70x^2-84

5 Remove parentheses.

12x^3+20x^4-24x^2-21x^2-35x^3+42x+42x+70x^2-84

6 Collect like terms.

(12x^3-35x^3)+20x^4+(-24x^2-21x^2+70x^2)+(42x+42x)-84

7 Simplify.

-23x^3+20x^4+25x^2+84x-84

You might be interested in

Sviatoslav solved the quadratic equation x^2-x-1=0 by completing the square. In the process, he came up with the equivalent equa

zimovet [89]

Answer:

$x=\frac{1+\sqrt5}{2}$ and $x=\frac{1-\sqrt5}{2}$

and b= $\frac{5}{4}$

Step-by-step explanation:

We are given that a quadratic equation

$x^2-x-1=0$

We have to solve the equation by completing square and find the value of b.

$(x)^2-2\times x\times \frac{1}{2}+(\frac{1}{2})^2-(\frac{1}{2})^2-1=0$

$(x-\frac{1}{2})^2-\frac{1}{4}-1=0$

$(x-\frac{1}{2})^2-\frac{1-4}{4}=0$

$(x-\frac{1}{2})-\frac{5}{4}=0$

$(x-\frac{1}{2})^2-(\frac{\sqrt5}{2})^2=0$

$(x-\frac{1}{2})^2=(\frac{\sqrt5}{2})^2$

$x-\frac{1}{2}=\frac{\sqrt5}{2}$ and $x-\frac{1}{2}=-\frac{\sqrt5}{2}$

$x=\frac{\sqrt5}{2}+\frac{1}{2}=\frac{1+\sqrt5}{2}$

And $x=\frac{1}{2}-\frac{\sqrt5}{2}=\frac{1-\sqrt5}{2}$

Therefore, $x=\frac{1+\sqrt5}{2}$ and $x=\frac{1-\sqrt5}{2}$

and b= $\frac{5}{4}$

6 0

3 years ago

Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.3, and 0.5, respectively

svetlana [45]

Answer:

Expectation number of books a customer will purchase = 1.3

Step-by-step explanation:

x : 0 1 2

p(x) :0.2, 0.3, and 0.5

Expectation

E(X) = ∑x P(x)

= 0 X 0.2 +1 X 0.3+ 2 X 0.5

= 1.3

Expectation E(X) = 1.3

Expectation number of books a customer will purchase = 1.3

3 0

2 years ago

F(x) = 2x - 1

zubka84 [21]

Answer:

A) h(x)=9x-13

Step-by-step explanation:

f(x) = 2x - 1

g(x) = 7x -12

Add them together

f(x) = 2x - 1

g(x) = 7x -12

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

f(x)+g(x) = 9x-13

h(x) = 9x-13

7 0

3 years ago

Read 2 more answers

Which situation can be represented by the inequality x-56

notsponge [240]

Complete Question:

Which situation can be represented by the inequality x > 56

A. Phil's saving account balance is $56

B. Junichi's garden is wider than 56 ft.

C. Suzanna hiked for less than 56 min.

D. It was colder than 56ºF this morning.

Answer:

Option B

Step-by-step explanation:

Given

$x > 56$

Required

Represent using a real life situation

$x > 56$ implies that the value of x is greater than 56

Examining the options one after the other

a: Account balance is $56

This option shows equality

i.e.

$x = 56$

b: Garden is wider than 56 ft.

Being wider than 56 means being greater 56;

This option shows greater than

So:

$x > 56$

c. Hiked for less than 56 min.

It is evident that this option shows less than

i.e.

$x < 56$

d. Colder than 56ºF this morning.

Being colder means the temperature is less than 56

i.e.

$x < 56$

So: from the list of given options

Only option B answers the question

3 0

3 years ago

Use the diagram to answer the question

Alenkasestr [34]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers