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Bess [88]
3 years ago
15

What is the solution of 4 |x - 9| + 6 > 42?

Mathematics
1 answer:
Galina-37 [17]3 years ago
8 0

Answer:

0 <x> 18

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 (4 • (x - 9) +  6) -  42  > 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  4x - 72  =   4 • (x - 18)  

Equation at the end of step  3  :

 4 • (x - 18)  > 0  

Step  4  :

4.1    Divide both sides by  4  

Solve Basic Inequality :

4.2      Add  18  to both sides

            x > 18

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Alika [10]

Answer:

The first one is proportional and the second one is not. Because for the first one you can see that if you divide the number of pens by the cost you'll get the same answer for every single one. But for the second one if you divide the number of minutes by words typed you get a different answer for each one. You can also see if it's proportional or not if you draw it on the graph and it's a straight line. If it is the relationship is proportional if it isn't it's not proportional. Hope that makes sense :)

7 0
3 years ago
Read 2 more answers
From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

Step-by-step explanation:

Volume =  height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x  (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so,  4 (3x² - 60x +225)=0

3x² - 60x+225=0   (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

7 0
3 years ago
The base diameter and the height of a cone are both
WITCHER [35]

Answer:

11/ 42. *. X^ 2. * X = I/3 X A * h; if E = 1/3 A

Then the answer is EX

Step-by-step explanation:

Volume of cone= 1/3 * base area * height

= 1/3 * pi* (X/2)^2 * X

= 1/3. * 22/ 7 * X^3/4

= 22/ 21 * X^3 / 4

= 11/21 *. X^2/ 2. *. X

= 11/ 42. * X^3

= 11/ 42. *. X^ 2. * X

3 0
3 years ago
Step by step explanation need it
nasty-shy [4]

Answer:

8/17

Step-by-step explanation:

The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.

The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY

The hypotenuse = XZ

Sin(X) = ZY/XZ

Sin(X) = 1634 = 8 / 17

4 0
3 years ago
Justin made 184 for 8 hours of work. At the same rate, how many hours would he have to work to make 115?
Kisachek [45]

Answer:

8/184

0.0434782609x115

5

Step-by-step explanation:

5

7 0
3 years ago
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