All categories

3 years ago

Express the quotient in simplest form. x^2 - 4/ x^3 + 7x^2 divided by x^3 - x^2 - 6x/x^2 + 4x - 21

Mathematics

1 answer:

amm18123 years ago

8 0

You must first transform into a multiplication and then factor to see what you can eliminate.

Explanation:

To transform a fractional division into a multiplication, you have to inverse the numerator and the denominator of the second fraction.

x2−4x3+7x2×x2+4x−21x3−x2−6x

(x+2)(x−2)x2(x+7)×(x+7)(x−3)x(x−3)(x+2)

Since aa=1,a= all real numbers, we can proceed by eliminating factors that appear in the numerator and the denominator.

We are left with x−2/x^3

You might be interested in

Please help meeee Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

Simora [160]

Answer:

<1=33, <2=90, <3=57

Step-by-step explanation:

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

5 0

3 years ago

9.4 the tangent ratio please help on #27 and 28

Ilya [14]

Answer/Step-by-step explanation:

27.

✔️Sin 23 = opp/hyp

Sin 23 = t/34

34*sin 23 = t

t = 13.3

✔️Cos 23 = adj/hyp

Cos 23 = s/34

s = 34*cos 23

s = 31.3

28.

✔️Sin 36 = opp/hyp

Sin 36 = s/5

s = 5*sin 36

s = 2.9

✔️Cos 36 = adj/hyp

Cos 36 = r/5

r = 5*cos 36

r = 4.0

29.

✔️Sin 70 = opp/hyp

Sin 70 = w/10

w = 10*sin 70

w = 9.4

✔️Cos 70 = adj/hyp

Cos 70 = v/10

v = 10*cos 70

v = 3.4

6 0

3 years ago

6 + 2/5b = 12 What does “b” equal?

Elis [28]

Answer:

B = 15

Step-by-step explanation:

Combine multiplied terms into a single fraction

6 + 2b/5 = 12

Subtract 6 from both sides

6 + 2b/5 (-6) = 12 (-6) = 2b/5 = 6

Multiply all terms by the same value to eliminate fraction denominators

2b/5 ( x 5) = 6 (x 5)

Simplify

2b = 30

4 0

3 years ago

Read 2 more answers

Log(x-2)+log2=2logy log(x-3y+3)=0

In-s [12.5K]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right$

$===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}$

$\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac$

$y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D$

$\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D$

4 0

3 years ago

How many ways can a librarian arrange 15 books on a top shelf if she has 20 books from which to pick?

Jlenok [28]

Use the permutation formula
nPr = (n!)/((n-r)!)
20P15 = (20!)/((20-15)!)
20P15 = (20!)/(5!)

The final answer is choice A

8 0

3 years ago

Read 2 more answers