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KengaRu [80]
2 years ago
5

Solve the following absolute value inequality

Mathematics
1 answer:
NikAS [45]2 years ago
8 0

Answer:

x < -1

x > -13

Step-by-step explanation:

\dfrac{4|x+7|}{3}

\implies 4|x+7|

\implies |x+7|

\textsf{Therefore} \ \ x+7  

x+7

\implies x

-(x+7)

\implies -x-7

\implies -x

\implies x > -13

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How do you illustrate<br>quadratic equation<br>in one variable?​
soldi70 [24.7K]

Step-by-step explanation:

Quadratic Equation

Quadratic equation is in the form

ax2+bx+c=0

Where

a, b, & c = real-number constants

a & b = numerical coefficient or simply coefficients

a = coefficient of x2

b = coefficient of x

c = constant term or simply constant

a cannot be equal to zero while either b or c can be zero

Examples of Quadratic Equation

Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.

1. 3x2+2x−8=0

2. x2−9=0

3. 2x2+5x=0

4. sin2θ−2sinθ−1=0

5. x−5x−−√+6=0

6. 10x1/3+x1/6−2=0

7. 2lnx−−−√−5lnx−−−√4−7=0

For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x1/3 + x1/6 - 2 = 0. Let x1/6 = z, thus, x1/3 = z2. The equation can now be written in the form 10z2 + z - 2 = 0, which shows clearly to be quadratic equation.

Roots of a Quadratic Equation

The equation ax2 + bx + c = 0 can be factored into the form

(x−x1)(x−x2)=0

Where x1 and x2 are the roots of ax2 + bx + c = 0.

Quadratic Formula

For the quadratic equation ax2 + bx + c = 0,

x=−b±b2−4ac−−−−−−−√2a

See the derivation of quadratic formula here.

The quantity b2 - 4ac inside the radical is called discriminat.

• If b2 - 4ac = 0, the roots are real and equal.

• If b2 - 4ac > 0, the roots are real and unequal.

• If b2 - 4ac < 0, the roots are imaginary.

Sum and Product of Roots

If the roots of the quadratic equation ax2 + bx + c

= 0 are x1 and x2, then

Sum of roots

x1+x2=−ba

Product of roots

x1x2=ca

You may see the derivation of formulas for sum and product of roots here.

4 0
3 years ago
What is the value of x? 140 34 56
olga55 [171]
I don’t know what you’re tying to say
3 0
2 years ago
An amount of $180 is shared among three people in the ratio x: y: z.
sammy [17]

Answer:

$110 and $30

Step-by-step explanation:

To solve this, we need to know the total share which is,

4 + 11 + 3 = 18

Then, you need to know the fraction of the share over the total, such that

x = \frac{4}{18}

y =  \frac{11}{18}

z =  \frac{3}{18}

So if to find how much that'll be of the $180 for the largest and smallest share,

Largest:

\frac{11}{18}  \times 180 = 110

Smallest:

\frac{3}{18}  \times 180 = 30

6 0
3 years ago
Which triangles (if any) can be shown to be congruent using a rotation? A) 1 and 2 B) 2 and 3 C) 1 and 3 D) none
Talja [164]
The answer is 1 and 3. 
6 0
3 years ago
How can I simplify b x b x b x b
ycow [4]

Answer:

b⁴

Step-by-step explanation:

b x b x b x b

b² x b²

b⁴

4 0
2 years ago
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