All categories

3 years ago

(x2 + 3x + 1)(x2 + x + 2)

1 answer:

Klio2033 [76]3 years ago

5 0

$( x^{2} +3x+1)( x^{2} +x+2) \\ = x^{2} ( x^{2} +x+2)+3x( x^{2} +x+2)+1( x^{2} +x+2) \\ = x^{4}+ x^{3}+2 x^{2} +3 x^{3} +3 x^{2} +6x+ x^{2} +x+2 \\ = x^{4} +4 x^{3} +6 x^{2} +7x+2$

You might be interested in

What is the silk road? What happened on it? Don't copy and paste pleased In your own words pleased NO LINKS NO FILES pleased.

nevsk [136]

Answer:

The silk road was a trading route and some stuff that happened on it was trading, robbings. Some stuff that was traded was gold and silk

Step-by-step explanation:

yuh yw

3 0

3 years ago

Read 2 more answers

SOMEONE PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!

MAXImum [283]

Answer:

Step-by-step explanation:

Let the quadratic equation of the function by the points in the given equation is,

f(x) = ax² + bx + c

If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),

For (0, 8),

f(0) = a(0)² + b(0) + c

8 = c

For a point (-3, -10),

f(-3) = a(-3)² + b(-3) + 8

-10 = 9a - 3b + 8

9a - 3b = -18

3a - b = -6 --------(1)

For (-4, -8),

f(-4) = a(-4)² + b(-4) + 8

-8 = 16a - 4b + 8

-16 = 16a - 4b

4a - b = -4 ------(2)

Subtract equation (1) from equation (2)

(4a - b) - (3a - b) = -4 + 6

a = 2

From equation (1),

6 - b = -6

b = 12

Function will be,

f(x) = 2x² + 12x + 8

= 2(x² + 6x) + 8

= 2(x² + 6x + 9 - 9) + 8

= 2(x² + 6x + 9) - 18 + 8

= 2(x + 3)² - 10

By comparing this function with the vertex form of the function,

y = a(x - h)² + k

where (h, k) is the vertex.

Vertex of the function 'f' will be (-3, -10)

And axis of symmetry will be,

x = -3

From the given graph, axis of the symmetry of the function 'g' is; x = -3

Therefore, both the functions will have the same axis of symmetry.

y-intercept of the function 'f' → y = 8 Or (0, 8)

y-intercept of the function 'g' → y = -2 Or (0, -2)

Therefore, y-intercept of 'f' is greater than 'g'

Average rate of change of function 'f' = $\frac{f(b)-f(a)}{b-a}$ in the interval [a, b]

= $\frac{f(-3)-f(-6)}{-3+6}$

= $\frac{-10-8}{3}$

= -6

Average rate of change of function 'g' = $\frac{g(b)-g(a)}{b-a}$

= $\frac{g(-3)-g(-6)}{-3+6}$

= $\frac{7+2}{-3+6}$

= 3

Therefore, Average rate of change of function 'f' is less than 'g'.

6 0

3 years ago

Factoring Inequalities,<br><br> Please help as I do not know how to progress after this.

Rainbow [258]

The factored inequality is $x^2-3x+6\geq 0$

<h3>Factoring Inequalities</h3>

The given inequality is:

$-x^2+3x-6\leq 0$

This can be further simplified as:

$-(x^2-3x+6)\leq 0$

The inequality can be re-written as:

$x^2-3x+6\geq 0$

Since the question does not state that we should solve the inequality, the simplest we can get after factoring is $x^2-3x+6\geq 0$

Learn more on factoring of inequality here: brainly.com/question/16789297

#SPJ1

7 0

2 years ago

Helping little sis with homework! =) A student says that the solution of 375 = x – 28 is 347. Explain the student’s error and fi

Amiraneli [1.4K]

The student subtracted each side by 28, which is wrong because if u want to cancel -28, you need to add 28 to both sides. The correct answer is 403. I need brainliest answer pls

4 0

4 years ago

A point moves along a straight path. The function f ( t ) = log 2 ( t ) determines the distance (in meters) the point has travel

Marina CMI [18]

Answer:

a) 4.392317 mt

b) 9 seconds

c) $\large f^{-1}(d)=2^d\;sec.$

Step-by-step explanation:

We have

$\large f(t)=log_2(t)$

where t is given in seconds and t in meters.

<em>a)How far has the point traveled 21 seconds after it started moving?</em>

By replacing t=21 in our equation we get

$\large f(21)=log_2(21)=4.392317 \;mt$

<em>b)If the point has traveled 3.16993 meters, how many seconds have elapsed since it started moving?</em>

We need to find a t such that f(t) =3.16993.

This can be accomplished by using the definition of $log_2$

$\large f(t)=3.16993\rightarrow log_2(t)=3.16993\rightarrow t=2^{3.16993}=9\;sec.$

<em>c)Write a function $f^{-1}$ that determines the number of seconds that have elapsed since the particle started moving in terms of the distance (in meters) the particle has traveled.</em>

$f^{-1}$ is given by the definition of log

$\large f^{-1}(d)=2^d\;sec.$

5 0

3 years ago