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1 year ago

Given 3x^2+x-4/x-1 what are the domain and range

Mathematics

1 answer:

Katarina [22]1 year ago

6 0

Answer:

doman: x ≠ 1
range: y ≠ 7

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

<h3>Simplified</h3>

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

$\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1$

<h3>Domain</h3>

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

x ≠ 1

In interval notation, this is ...

(-∞, 1) ∪ (1, ∞)

<h3>Range</h3>

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

y ≠ 7

In interval notation, this is ...

(-∞, 7) ∪ (7, ∞)

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Holly says 4.131131113... is a rational number. Which of the following best describes whether Holly is correct and why?? a.Holly

Leni [432]

Answer:

A. Holly is correct. Repeating decimals are always rational numbers.

Step-by-step explanation:

Rational number is the subset of:

Whole number (Positive integer + 0)
Natural number
Negative integers
Fractions
Decimals (Whether positive or not, whether terminating or non terminating)

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7 0

3 years ago

Read 2 more answers

Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds cont

love history [14]

Answer:

$\approx$ 17.5% per annum

Step-by-step explanation:

<u>Given:</u>

Money invested = $20,000 at the age of 20 years.

Money expected to be $500,000 at the age of 40.

Time = 40 - 20 = 20 years

<em>Interest is compounded annually.</em>

Rate of growth = ?

<u>Solution:</u>

First of all, let us have a look at the formula for compound interest.

$A = P \times (1+\frac{R}{100})^T$

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.

Here, We are given:

P = $20,000

A = $500,000

T = 20 years

R = ?

Putting all the values in the formula:

$500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%$

So, the correct answer is $\approx$ <em>17.5% </em>per annum and compounding annually.

6 0

3 years ago

X2+5x−7 when x=2 can you help me i am wayy back of the class and next month grades close

spin [16.1K]

Answer:

Step-by-step explanation:

x2 + 5x - 7

sub x = 2 in

(2 X 2) + (5 X 2) - 7

4 + 10 - 7

= 7

4 0

2 years ago

Plz help i kind of forgot how to do this<br> its just a review should be easy

Jet001 [13]

This is easy just find out what 5^2 equals which will be 5x5=25 (when dealing with a squared number you will always times it by itself. so if you had 10^2 it would be 100.) so now that we know 5^2 is 25 we then can add the 20 which gets 25+20=45! Hope this helps!

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3 years ago

What is the length of the hypotenuse of the right triangle?

Julli [10]

Answer:

Step-by-step explanation:

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3 years ago