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3 years ago

Solve the following inequality using both the graphical and algebraic approach: .5x+3 > 2x -1.5

1 answer:

8 0

.5x+3 is bigger then 2x-1.5 because .5+3 is 3.5, and 2-1.5 is 1.5. it doesn't matter what x is, because it'll be the same for both 5 and 2. so just ignore x. hope this helps

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given y left parenthesis z right parenthesis equals space fraction numerator z squared minus 1 over denominator z left parenthes

aivan3 [116]

The simplification of the given algebraic expression is;

yz = (z + 1)/z(z - 1)

<h3>How to simplify algebraic expressions?</h3>

We are given y left parenthesis z right parenthesis which is expressed as; yz

Now, we are given the algebraic expression that yz equals space fraction numerator z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction

z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction is expressed as; (z² - 1)/z(z - 1)²

Thus, our main expression is;

yz = (z² - 1)/z(z - 1)²

Factorizing the numerator and denominator gives;

yz = (z + 1)(z - 1)/z(z - 1)(z - 1)

(z - 1) is common to both numerator and denominator and as such, we now have;

yz = (z + 1)/z(z - 1)

Read more about Algebraic Expressions at; brainly.com/question/4344214

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1 year ago

36 and 38<br><br>Steps and explaination please

elena55 [62]

Answer:

36. Limit = 2/3.

Step-by-step explanation:

36.

(∛ x- 1) / (√x - 1)

Rationalise the expression:-

Multiply top and bottom by (√x + 1):-

(∛x - 1)(√x + 1) / (√x - 1)(√x + 1)

= x^5/6 + ∛x - √x - 1 / (x - 1)

Applying L'hopital's rule ( differentiating top and bottom of the fraction) we have:

Limit as x ----> 1 of [5/6 x^-1/6 + 1/3 x^(-2/3) - 1/2x^-1/2] / 1

= 5/6(1) + 1/3(1) - 1/2(1) = 2/3 (answer).

8 0

3 years ago

A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each ad

vovikov84 [41]

Solution:

A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult.

First we make inequality according to question.

In a family number of children 3

Charge for 1 child = $y per hour

Charge for 3 children = 3y

Charge for 1 Adult = $x per hour

Charge for 2 adults = 2x

If the family does not want to s[end more than $30 an hour at health club.

$\therefore 2x+3y\leq 30$

Where, x and y should be greater than 0.

$\therefore x\geq 0,y\geq 0$

Now we make the graph of this inequality.

First we take equality of equation and then find x and y table.

2x+3y=30

x y

0 10

6 6

15 0

Here we have inequality. So, we have to take a test point (0,0)

$2(0)+3(0)\leq 30\Rightarrow 0\leq 30$

This statement is true. So, Graph will shade towards the test point (0,0)

Please see the attachment for graph.

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3 years ago

Let f(x) = 3x - 6 and g(x) = x - 2. Find and state its domain.

True [87]

We can write (fg)(x) as: (fg)(x)=3x−6x−2. Factoring the numerator gives: .

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faust18 [17]

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