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3 years ago

Solve the inequality: 2(4x - y) > 5x + (2)

Mathematics

1 answer:

tankabanditka [31]3 years ago

8 0

Answer: y < 3/2x - 1

Step-by-step explanation:

2(4x - y) > 5x + 2 First apply distributive property to the other side.

8x - 2y >5x +2 subtract 8x from both sides.

-8x 8x

-2y >-3x + 2 Divide both sides by -2 and that flips the signs direction.

y < 3/2x - 1

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Please answer both I’ll mark you brilliant !

Ymorist [56]

Bruh, I swear I'm getting dumber everyday day!!!

4 0

3 years ago

What is the HCF of 21m³n - 14m²n³ + 35m²n² ?

Dominik [7]

Answer:

7m^2n (i think)

Step-by-step explanation:

4 0

3 years ago

A candy box is made from a piece of cardboard that measures 23 by 13 inches. Squares of equal size will be cut out of each corne

wolverine [178]

Answer:

2.67 inches.

Step-by-step explanation:

Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).

The formula for a rectangular box = L × B × W

= (23 -2y)(13-2y) (y)

= (299 - 46y - 26y + 4y²)y

= 299y - 72y² + 4y³

Now for the maximum volume:

dV/dy = 0

This implies that:

299y - 72y² + 4y³ = 299 - 144y + 12y² = 0

By using the quadratic formula; we have :

$= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}$

where;

a = 12; b = -144 and c = 299

$= \dfrac{-(-144) \pm \sqrt{(-144)^2 -4(12)(299)}}{2(12)}$

$= \dfrac{144 \pm \sqrt{20736 -14352}}{24}$

$= \dfrac{144 \pm \sqrt{6384}}{24}$

$= \dfrac{144 \pm79.90}{24}$

$= \dfrac{144 + 79.90}{24} \ \ OR \ \ \dfrac{144 - 79.90}{24}$

$= 9.33 \ \ OR \ \ 2.67$

Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33

Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.

3 0

3 years ago

Does (-2x+y=6)+ (y-2x=4) have no solution?

DedPeter [7]

Assuming you are asking

does -2x+y=6 and y-2x=4 have a solution

look at them
rewrite first equation by switching x and y
y-2x=6 and
y-2x=4
false since they are same values

there is no solution
these 2 lines are paralell

NO SOLUTION

4 0

4 years ago

An open box will be made from a rectangular piece of cardboard that is 8 in. by 10 in. The box will be cut on the dashed red lin

Anna35 [415]

Answer:

C) 52 in^3

Step-by-step explanation:

The first is to determine the formula of the volume of the box, which would be the following:

V = height * length * width

Knowing that we have a rectangular piece we will determine the maximum volume, we will double a distance x (which will be the height) in the width and length of the piece, therefore as it is on both sides, the length and width are defined from the Following way:

length = 10 - 2 * x

width = 8 - 2 * x

height = x

Now we calculate the volume:

V = x * (10-2 * x) * (8-2 * x)

To determine the maximum volume we will give values to x in order to see how it behaves:

Let x = 2.5

V = (5) * (3) * (2.5) = 37.5

Let x = 2

V = (6) * (4) * (2) = 48

Let x = 1.5

V = (7) * (5) * (1.5) = 52.5

Let x = 1

V = (8) * (6) * (1) = 48

Let x = 0.5

V = (9) * (7) * (0.5) = 31.5

It can be seen that the greatest volume is obtained when the height is equal to 1.5 and its volume is 52.5 in ^ 3

8 0

4 years ago