1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Greeley [361]
2 years ago
10

GIVING OUT BRAINLIEST TO WHOEVER GETS ALL OF THEM RIGHT

Mathematics
1 answer:
Thepotemich [5.8K]2 years ago
6 0

Answer:

4) \frac{x}{7\cdot x +x^{2}} is equivalent to \frac{1}{7+x} for all x \ne -7. (Answer: A)

5) \frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}} is equivalent to -\frac{14}{1-5\cdot x} for all x \ne \frac{1}{5}. (Answer: B)

6) \frac{x+7}{x^{2}+4\cdot x - 21} is equivalent to \frac{1}{x-3} for all x \ne 3. (Answer: None)

7) \frac{x^{2}+3\cdot x -4}{x+4} is equivalent to x - 1. (Answer: None)

8)  \frac{2}{3\cdot a}\cdot \frac{2}{a^{2}} is equivalent to \frac{4}{3\cdot a^{3}} for all a\ne 0. (Answer: A)

Step-by-step explanation:

We proceed to simplify each expression below:

4) \frac{x}{7\cdot x +x^{2}}

(i) \frac{x}{7\cdot x +x^{2}} Given

(ii) \frac{x}{x\cdot (7+x)} Distributive property

(iii) \frac{1}{7+x} \cdot \frac{x}{x} Distributive property

(iv) \frac{1}{7+x} Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

7+x = 0

x = -7

Hence, we conclude that \frac{x}{7\cdot x +x^{2}} is equivalent to \frac{1}{7+x} for all x \ne -7. (Answer: A)

5) \frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}}

(i) \frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}} Given

(ii) \frac{x^{3}\cdot (-14)}{x^{3}\cdot (1-5\cdot x)} Distributive property

(iii) \frac{x^{3}}{x^{3}} \cdot \left(-\frac{14}{1-5\cdot x} \right) Distributive property

(iv) -\frac{14}{1-5\cdot x} Commutative property/Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

1-5\cdot x = 0

5\cdot x = 1

x = \frac{1}{5}

Hence, we conclude that \frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}} is equivalent to -\frac{14}{1-5\cdot x} for all x \ne \frac{1}{5}. (Answer: B)

6) \frac{x+7}{x^{2}+4\cdot x - 21}

(i) \frac{x+7}{x^{2}+4\cdot x - 21} Given

(ii) \frac{x+7}{(x+7)\cdot (x-3)} x^{2} -(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})

(iii) \frac{1}{x-3}\cdot \frac{x+7}{x+7} Commutative and distributive properties.

(iv) \frac{1}{x-3} Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

x-3 = 0

x = 3

Hence, we conclude that \frac{x+7}{x^{2}+4\cdot x - 21} is equivalent to \frac{1}{x-3} for all x \ne 3. (Answer: None)

7) \frac{x^{2}+3\cdot x -4}{x+4}

(i) \frac{x^{2}+3\cdot x -4}{x+4} Given

(ii) \frac{(x+4)\cdot (x-1)}{x+4}  x^{2} -(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})

(iii) (x-1)\cdot \left(\frac{x+4}{x+4} \right) Commutative and distributive properties.

(iv) x - 1 Existence of additive inverse/Modulative property/Result

Polynomic function are defined for all value of x.

\frac{x^{2}+3\cdot x -4}{x+4} is equivalent to x - 1. (Answer: None)

8) \frac{2}{3\cdot a}\cdot \frac{2}{a^{2}}

(i) \frac{2}{3\cdot a}\cdot \frac{2}{a^{2}}

(ii) \frac{4}{3\cdot a^{3}} \frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot b}{c\cdot d}/Result

Rational functions are undefined when denominator equals 0. That is:

3\cdot a^{3} = 0

a = 0

Hence, \frac{2}{3\cdot a}\cdot \frac{2}{a^{2}} is equivalent to \frac{4}{3\cdot a^{3}} for all a\ne 0. (Answer: A)

You might be interested in
Can someone show how to divide Divide 5/8 into 2/5
tekilochka [14]

Answer: 1 9/16

Step-by-step explanation:

1. Switch the numerator and the denominator of the second fraction. (5/8 ÷ 2/5 = 5/8 x 5/2)

2. Multiply the two fractions. (5/8 x 5/2 = 25/16)

3. Simplify the answer. (25/16 = 1 9/16)

5 0
2 years ago
ASAP please i need help
Alla [95]

Answer:

1 hr 20 min.

Step-by-step explanation:

5 0
3 years ago
What is the equation of the line 2-3y = 18 in slope-intercept form?
il63 [147K]
The person above me got that horrible wrong, do not put that.

You also wrote the question wrong, please be more careful when posting.

x-3y=18

Move x to the other side by subtracting it since it’s positive.

-3y = -x + 18

Divide the whole equation by -3 to find the value of just 1 y.

-3y/-3 = -x/-3 + 18/-3

y = 1/3x -6
4 0
3 years ago
Margo borrows $500, agreeing to pay it back with 3% annual interest after 14
Akimi4 [234]

Answer:

\$17.50

Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

I is the Final Interest to pay

P is the amount of money borrowed

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=\frac{14}{12}\ years\\ P=\$500\\r=3\%=3/100=0.03

substitute in the formula above

I=500(0.03)(\frac{14}{12})

I=\$17.50

4 0
3 years ago
Compare the decimals 0.29__0.3
Nostrana [21]
<
>
=
Are the answers the first line is for the first question same for the second and 3rd
7 0
3 years ago
Other questions:
  • A contractor is considering a sale that promises a profit of 26,000 with a probability of 0.7 or a loss (due to bad weather stri
    12·2 answers
  • What is the estimated quotient for 5,514÷82?
    7·2 answers
  • Find the Mae sure of each exterior angle of a regular 30 sided polygon
    12·1 answer
  • If tan2A=cot(A+60), find the value of A, where 2A is an acute angle
    10·1 answer
  • Write an equation of the line that passes the point and given slope (1, -1); m=3
    10·1 answer
  • Determine the intercepts of the line
    15·1 answer
  • Can someone help me plslsssssss
    11·1 answer
  • Which exponential equation correctly rewrites this logarithmic equation? log6 18=x
    5·1 answer
  • I literally have a test tomorrow and dont know what to do please help
    6·2 answers
  • Simplify the algebraic expression by combining like terms. -7x² +19x²<br> Simplify your answer.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!