MATHEMATICS HIGH SCHOOL

Write a solution in Interval Notation - (you don't have to help me on all, 1 or 2 is fine c: )1) | m | -2 > 0

2) | x - 4 | - 3 > 5

3) | 6 + 9x | ≤ 24

4) | 1 - 5a | > 29

Answers

Answer 1
Answer:

QUESTION 1

The given inequality is

|m|-2>0

We group like terms to get,

|m|>2


This implies that,

-m>2 or m>2.

We simplify the inequality to get,

m<-2 or m>2.

We can write this interval notation to get,

(-\infty,-2)\cup (2,+\infty).


QUESTION 2

|x-4|-3\:>\:5.

We group like terms to get,


|x-4|\:>\:5+3.


|x-4|\:>\:8

We split the absolute value sign to get,

-(x-4)\:>\:8 or x-4\:>\:8


This implies that,


x-4\:<\:-8 or x-4\:>\:8


x\:<\:-8+4 or x\:>\:8+4


x\:<\:-4 or x\:>\:12


We can write this interval notation to get,

(-\infty,-4)\cup (12,+\infty).


QUESTION 3

The given inequality is

|6+9x|\leq 24


We split the absolute value sign to obtain,

-(6+9x)\leq 24 or (6+9x)\leq 24


This simplifies to

6+9x\ge -24 and 6+9x\leq 24


9x\ge -24-6 and 9x\leq 24-6


9x\ge -30 and 9x\leq 18


x\ge -(10)/(3) and x\leq 2

-(10)/(3)\leq x\leq2

We write this in interval form  to get,

[-(10)/(3),2]


QUESTION 4

The given inequality is

|1-5a|>29

We split the absolute value sign to get,

-(1-5a)>29 or 1-5a>29

This simplifies to,

1-5a\:<\:-29 or 1-5a\:>\:29


This implies that,

-5a\:<\:-29-1 or -5a\:>\:29-1


-5a\:<\:-30 or -5a\:>\:28


a\:>\:6 or a\:<\:-(28)/(5)

We write this in interval notation to get,

(-\infty,-(28)/(5))\cup (6,+\infty)

Related Questions

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You 495 miles from home and you are driving toward home at an average of 45mph. How long will it take to drive home if you maintain the same speed? (Hint: When you reach home, the x-value is zero.)
Which measurement is not equivalent to the others?6 pints 3 quarts 36 fl. oz. 12 cups
100 points: Sketch a graph of y = 1x| Then sketch a graph of y = -x + 4 on the same coordinate plane. If you can change colors of your graph, make this one red. In the box below, describe the transformation that took place from y=[xl to y = -1x + 4|​
Which expression correctly represents the product 12(8 5) after applying the distributive property?

What is the quotient (125 – 8x3) ÷ (25 + 10x + 4x2)?–2x + 5
2x – 5
–2x – 5
2x + 5

Answers

For this case we have the following expression:

(125-8x^3)/(25+10x+4x^2)

Factoring the numerator we have:

(-(2x+5)(4x^2+10x+25))/(25+10x+4x^2)

Rewriting the denominator we have:

(-(2x+5)(4x^2+10x+25))/(4x^2+10x+25)

Canceling similar terms we have:

-(2x+5)

-2x-5

Answer:

The quotient of the division is given by:

-2x-5
If you would like to solve (125 - 8x^3) / (25 + 10x + 4x^2), you can do this using the following steps:

(125 - 8x^3) / (25 + 10x + 4x^2) = - ((2x - 5) * (4x^2 + 10x + 25)) / (4x^2 + 10x + 25) = - (2x - 5) = - 2x + 5

The correct result would be - 2x + 5.

In the above figure, ae 2, ce 3, and de 4. What is the length of be

Answers

a 
2) right bottom [tangents drawn to a circle from the same point are equal in length] 
3) a 
4) b 
[Triangles AEC and DEB are similar triangles. So corresponding sides are proportional. So, AE/DE = CE/BE.] 
5) c 
6) a 
7) c 
8) b 
9) a 
10) c 
11) d 
12) a 
13) d 
14) a 
15) b 
16) c 
17) c 

Tell if you need logic behind some other answers too. Specify the questions.

AE=2

CE=3

DE=4

BE=?


AExBE = DExCE

2xBE = 4x3

2xBE = 12

BE = 12/2

BE=6


The answer is 6

What is the value of h when the function is converted to vertex form?
g(x) = x^2 – 6x + 14

Answers

Hello,

g(x)=x²-6x+14=x²-2*3x+9+14-9=(x-3)²+5
h=3, k=5

Solve the following proportion: x+3/2 equal to 7/8

Answers

Step-by-step explanation:

x+ 3/2 = 7/8

3/2 is equivalent to the fraction 12/8

Since the two fractions have common denominators, you can do.

x= 7/8 - 12/8

x=(-5/8)

Hope this helps!!!

Answer:

x = -0.625

Step-by-step explanation:

x+3/2 = 7/8

x + 1.50 = 0.875

x = -0.625

Need help with this now! Giving 100 points and brainliest to whoever can give the best answer to this with an explanation.The graph represents the speed at which Pete’s marble travels. The speed of Stephano’s marble is represented by the equation f=2.25s, where f is the distance in feet and s is the time in seconds. Whose marble will reach the 6-foot mark sooner?

Answers

Answer:

Note. There is a mismatch between the graph and the equation

------------------------------

  • As per the graph, 6 ft is reached at 4 seconds
  • The graphed line is f = 1.5s

------------------------------

If we go by the equation, then:

  • f = 2.25s
  • 6 = 2.25s
  • s = 6/.2,25
  • s = 2.67 seconds

Solve for x
simplify the answer. this is extremely hard

Answers


                                                           D = 1/9 π m² x

Multiply each side by  9 :                     9D = π m² x

Divide each side by  (π m²) :    9D / (π m²)  =  x


Truly exhausting !
the solution is in the application
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