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3 years ago

What is the solution of x^2+x-6≤0?

1 answer:

8 0

1) Factor the polynomial

x^2 + x - 6 = (x + 3) (x - 2)

So, can solve (x + 3)(x - 2) ≤ 0

The condition for the product of two factors be zero or negative is that the both are zero or have different signs (one positive and the other negative)

a) when x + 3 ≤ 0 and x - 2 ≥ 0

x + 3 ≤ 0 => x ≤ - 3

x - 2 ≥ 0 => x ≥ 2

Given that it is imposible that x be less or equal tha - 3 and greaer or equal than 2, this solution is empy.

b) when x + 3 ≥ 0 and x - 2 ≤ 0

x + 3 ≥ 0 => x ≥ - 3

x - 2 ≤ 0 => x ≤ 2

Solution: - 3 ≤ x ≤ 2 or [-3,2]

You might be interested in

What are the importance of knowing the theorems on midline, trapezoid and kite

lutik1710 [3]

Answer:

It is important because it allows you to calculate the surface area of a trapezoidal prism

Step-by-step explanation:

7 0

2 years ago

Graph the following three equations on your own device and answer the questions below.

Alina [70]

Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.

<h3>What are the characteristics of each of the three functions?</h3>

a) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(10) = 5 · 10 + 7

f(10) = 57

Case 2

f(10) = 10² + 6

f(10) = 106

Case 3

f(10) = 2¹⁰ + 3

f(10) = 1027

b) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(100) = 5 · 100 + 7

f(100) = 507

Case 2

f(100) = 100² + 6

f(100) = 10006

Case 3

f(100) = 2¹⁰⁰ + 3

f(100) = 1.267 × 10³⁰ + 3

c) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(1000) = 5 · 1000 + 7

f(1000) = 5007

Case 2

f(1000) = 1000² + 6

f(1000) = 1000006

Case 3

f(1000) = 2¹⁰⁰⁰ + 3

f(1000) = (1.268 × 10³⁰)¹⁰ + 3

f(1000) = 10.744 × 10³⁰⁰ + 3

f(1000) = 1.074 × 10³⁰¹ + 3

e) The third function increases the fastest.

f) In this part we need to compare the third function with respect to the first and second functions:

5 · x + 7 = 2ˣ + 3

2ˣ - 5 · x = 4

The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other first function at x = 4.81.

x² + 6 = 2ˣ + 3

2ˣ - x² = 3

The solution of the equation is x = 4.588. The function will exceed the other second function at x = 4.588.

g) Yes, exponential functions with bases greater than 1 will surpass polynomic function at any point x such that x > 0.

h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:

Case 1

Domain - All real numbers.

Range - All real numbers

Case 2

Domain - All real numbers.

Range - [6, +∞)

Case 3

Domain - All real numbers.

Range - (3, +∞)

To learn more on functions: brainly.com/question/12431044

#SPJ1

5 0

1 year ago

What is 607/100 as a percent?

777dan777 [17]

607 / 100 = 6.07

6.07 = decimal form

6.07 * 100 = 607%

6 0

2 years ago

Read 2 more answers

What’s the equation of the midline? Determine an equation for this graph ASAP

choli [55]

Answer:

y = -cos(2x)

Step-by-step explanation:

Mean/mid line: y = 0

It's a negative cos, with period pi.

So, y = -cos(2x)

7 0

2 years ago

If 16 is added to one-third of a number, the result is three times the number. What is the number?

AnnZ [28]

First set up the equation based on the description.

$\frac{1}{3}$ x + 16 = 3x

Use subtraction to get the "x"s on one side of the equation. You can next subtract $\frac{1}{3}$ x from both sides.

16 = $\frac{8}{3}$ x

Now you can multiply both sides of the equation by $\frac{3}{8}$ to solve for x

x = 6

4 0

3 years ago