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
ValentinkaMS [17]
3 years ago
13

Solve 5x(m+n) using the distributive property

Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0

Answer: 5xm+5xn

Step-by-step explanation:

For this exercise it is necessary to remember the following:

1) The Distributive Property states the following:

a(b+c)=ab+ac\\\\a(b-c)=ab-ac

2) The multiplication of signs:

(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-

Knowing this, and having the following expression given in the exercise:

5x(m+n)

You can apply the Distributive property multiplying m and n, which are inside the parentheses, by 5x.

So, you get the following result:

=(5x)(m)+(5x)(n)=5xm+5xn

You might be interested in
How do you find the limit?
coldgirl [10]

Answer:

2/5

Step-by-step explanation:

Hi! Whenever you find a limit, you first directly substitute x = 5 in.

\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{5^2-6(5)+5}{5^2-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{25-30+5}{25-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{0}{0}}

Hm, looks like we got 0/0 after directly substitution. 0/0 is one of indeterminate form so we have to use another method to evaluate the limit since direct substitution does not work.

For a polynomial or fractional function, to evaluate a limit with another method if direct substitution does not work, you can do by using factorization method. Simply factor the expression of both denominator and numerator then cancel the same expression.

From x²-6x+5, you can factor as (x-5)(x-1) because -5-1 = -6 which is middle term and (-5)(-1) = 5 which is the last term.

From x²-25, you can factor as (x+5)(x-5) via differences of two squares.

After factoring the expressions, we get a new Limit.

\displaystyle \large{ \lim_{x\to 5}\frac{(x-5)(x-1)}{(x-5)(x+5)}}

We can cancel x-5.

\displaystyle \large{ \lim_{x\to 5}\frac{x-1}{x+5}}

Then directly substitute x = 5 in.

\displaystyle \large{ \lim_{x\to 5}\frac{5-1}{5+5}}\\

\displaystyle \large{ \lim_{x\to 5}\frac{4}{10}}\\

\displaystyle \large{ \lim_{x\to 5}\frac{2}{5}=\frac{2}{5}}

Therefore, the limit value is 2/5.

L’Hopital Method

I wouldn’t recommend using this method since it’s <em>too easy</em> but only if you know the differentiation. You can use this method with a limit that’s evaluated to indeterminate form. Most people use this method when the limit method is too long or hard such as Trigonometric limits or Transcendental function limits.

The method is basically to differentiate both denominator and numerator, do not confuse this with quotient rules.

So from the given function:

\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}

Differentiate numerator and denominator, apply power rules.

<u>Differential</u> (Power Rules)

\displaystyle \large{y = ax^n \longrightarrow y\prime= nax^{n-1}

<u>Differentiation</u> (Property of Addition/Subtraction)

\displaystyle \large{y = f(x)+g(x) \longrightarrow y\prime = f\prime (x) + g\prime (x)}

Hence from the expressions,

\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2-6x+5)}{\frac{d}{dx}(x^2-25)}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2)-\frac{d}{dx}(6x)+\frac{d}{dx}(5)}{\frac{d}{dx}(x^2)-\frac{d}{dx}(25)}}

<u>Differential</u> (Constant)

\displaystyle \large{y = c \longrightarrow y\prime = 0 \ \ \ \ \sf{(c\ \  is \ \ a \ \ constant.)}}

Therefore,

\displaystyle \large{ \lim_{x \to 5} \frac{2x-6}{2x}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{2(x-3)}{2x}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{x-3}{x}}

Now we can substitute x = 5 in.

\displaystyle \large{ \lim_{x \to 5} \frac{5-3}{5}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{2}{5}}=\frac{2}{5}

Thus, the limit value is 2/5 same as the first method.

Notes:

  • If you still get an indeterminate form 0/0 as example after using l’hopital rules, you have to differentiate until you don’t get indeterminate form.
8 0
3 years ago
What to the tenth power can get you 300
OLEGan [10]

Answer:

1.7689 (rounded to 4 decimal places)

Step-by-step explanation:

Let the number we are seeking be "x", thus we can write the equation as:

x^{10}=300

Since we have raised "x" to the "10th power", to get "x" back again, we need to take 10th root. Same goes for right side, we take 10th root of 300. We will get our answer. The process shown below:

x^{10}=300\\\sqrt[10]{x^{10}} =\sqrt[10]{300} \\x=\sqrt[10]{300} \\x=1.7689

hence, 1.7689 raised to 10th power will give us 300

5 0
3 years ago
What is 3.98 X10 raise to power 10 In standard form
bonufazy [111]
39,800,000,000 is the correct answer, I believe.
3 0
3 years ago
Read 2 more answers
Apparently what I chose was incorrect. Which ones are correct?
ch4aika [34]

Step-by-step explanation:

numbers one two and three are correct

4 0
3 years ago
F(x)=x^2 what is g(x)?<br><br> pls help me
Lady bird [3.3K]
G(x) = ax^2
y = ax^2
5 = a(1)^2
a = 5
Therefore, g(x) = 5x^2
8 0
3 years ago
Other questions:
  • A cube has a volume of 1/8. If the cube holds 24 of these sugar cubes, what is the total volume of the box?
    5·2 answers
  • Please solve with working out <br> simultaneous equations<br> 3x+2y=12<br> 2x+2y=10
    8·2 answers
  • A population of flies, P, over a given amount of time, x, is modeled by the expression
    9·1 answer
  • 20 POINTS AND BRAINLIEST!
    12·2 answers
  • Find the y-intercept of the line on the graph
    7·2 answers
  • Which of the following choices is equivalent to 1 + 8(2x + 3)?
    14·1 answer
  • The area of a rectangle is found by multiplying its length and width together. Calculate the area, in square feet, of the room y
    5·1 answer
  • Please Help Me! This Is Due Soon.
    7·1 answer
  • -2.7+17.8+29.5+8.9=?
    6·2 answers
  • I need help please! In each case below, list the lettered measures for angles or sides in descending order (FROM GREATEST TO LEA
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!