MATHEMATICS MIDDLE SCHOOL

Which of the following is the solution to 9|x+4|>54 ?

Answers

Answer 1

Answer:

Answer:

x < -10, x > 2

Step-by-step explanation:

9|x+4| > 54

|x+4| > 6

Split the absolute value into two equation, positive and negative.

1.)POSITIVE

x+4 > 6

x > 2

2.)NEGATIVE

-(x+4) > 6

-x - 4 > 6

-x > 10

x < -10

Answer 2

Answer:

Answer:

$\large\boxed{x<-10\ \vee\ x>2\to x\in(-\infty,\ -10)\ \cup\ (2,\ \infty)}$

Step-by-step explanation:

$9|x+4|>54\qquad\text{divide both sides by 9}\n\n(9|x+4|)/(9)>(54)/(9)\n\n|x+4|>6\iff x+4>6\ \vee\ x+4<-6\n\nx+4>6\qquad\text{subtract 4 from both sides}\n\nx+4-4>6-4\n\nx>2\n\nx+4<-6\qquad\text{subtract 4 from both sides}\n\nx+4-4<-6-4\n\nx<-10$

Related Questions

you want to put $8,000 in a simple interest account it has a 2% annual interest rate how long must you invest that money to earn $400 in interest
a right triangle has one angle that measures 26 degrees. what is the measure of the other acute angle?
What are the intercepts of this function f(x)=-8x+4
A recipe calls for 4 tab of baking soda and 1 Oz of vanilla. which measurement is greater ? explain
I need help on this...Someone help me please

If 3/7 of a pizza is eaten for lunch and 2/5 is eaten for dinner , how much of the pizza is eatten ?

Answers

29/35 of the pizza was eaten

3/7 + 2/5 = 29/35 Is the answer

1. Renting a bicycle costs $30 for the first day and $10 for each additional day.a. Write an equation in simplified form to find the total cost C for a bike rental ithe number of days d it was rented.b. Find the cost of renting a bike for 5 days.Answer:

Answers

Part a: 30+10d That is your equation. 30 for the start and 10 more for each additional day.
Part b: So there are 4 additional days. Let's fill in the equation and solve.
30+10*4
30+40
$70
The answer is $70

b) Your sister says that the angles ∠DCA and ∠BCA are supplementary angles. Is she correct? Explain your reasoning. (1 point)

Answers

Answer:

She is incorrect.

Step-by-step explanation:

ABCD is a quadrilateral. Angle C measures less than 180 degrees. The sum of the measures of two supplementary angles equals 180 degrees. The sum of the measures of angles DCA and BCA equals the measure of angle C, but angle C measures less than 180 degrees, so the angles are not supplementary.

Answer:

incorrect

Step-by-step explanation:

Sin 2x=check all that apply
A. 2sin x cos x
B. 1-2 sin^2 x
C. 2cos x sin x
D. 2sin x +2cos x

Answers

Answer:

A,C

Step-by-step explanation:

sin 2x=sin (x+x)=sinx cos x+cos x sin x=2 sin x cos x

or =2 cos x sin x

[sinx cox=cos x sin x ]

The edge of one cube is 4 m shorter than the edge of a second cube. The volumes of the two cubes differ by 1216 m^3. Find the edge of the smaller cube.

Answers

Volume of cube, V = edge^3
Let edge of cube#1 = (x-4) m, therefore volume of cube#1, v1 = (x-4)^3 m
Let edge of cube#2 = x m, therefore volume of cube#2, v2 = x^3 m
Diff. in volume (in m) = 1216 = v2-v1 = [ x^3 - (x-4)^3 ]
= x^3 - [(x-4)(x-4)(x-4)]
= x^3 - [x^2 - 8x +16(x - 4)]
= x^3 - [ x^3 - 12x^2 + 48x - 64 ]
= 12x^2 - 48x + 64
= 4 (3x^2 - 12x + 16)
Therefore 4 (3^2 - 12x + 16) = 1216
3x^2 - 12x + 16 = 1216/4 = 304
3x^2 - 12x - 288 = 0
3 (x^2 - 4x - 96) = 0
(x^2 - 4x - 96) = 0
(x - 12) (x + 8) =0
(x-12) = 0
Therefore x = 12 m
Edge of cube#2 = x m = 12m
Edge of cube#1 = (x-4) m = 8m

$a- the\ edge\ of\ the\ smaller\ cube\ \ \ \wedge\ \ \ a>0\nV_a-the\ volume\ of\ the\ smaller\ cube\ \ \ \Rightarrow\ \ \ V_a=a^3\n \n(a+4)^3-a^3=1216\ \ \ \wedge\ \ \ (x+y)^3=x^3+3x^2\cdot y+3x\cdot y^2+y^3\n \na^3+3a^2\cdot 4+3a\cdot 4^2+4^3-a^3=1216\n \n12a^2+48a+64-1216=0\ \ \ \Rightarrow\ \ \ 12a^2+48a-1152=0\ /:12\n \na^2-4a-96=0\ \ \ \Rightarrow\ \ \ \Delta=(-4)^2-4\cdot 1\cdot(-96)=16+384=400\n \n √(\Delta) =20\n \na_1= (4-20)/(2\cdot1) =-8<0,\ \ \ a_2= (4+20)/(2\cdot1) =12>0$

$Ans.\ The\ edge\ of\ the\ smaller\ cube=12\ m$

The sum of two numbers is 38. The greater number is 5 more than twice the lesser number. What is the greater of the two numbers?