Thank you if you do help!:,)

ANSWER ASAP: New machine has productivity (measured in the number of produced details) 12% greater than the last model. After re

GREYUIT [131]

The total number of produced details increased by 6.4%

suppose the starting number was x.
suppose x=100
100 +12%= 112
112-5%=106.4
106.4-100=6.4
6.4%

4 0

3 years ago

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BC has a midpoint at M(6, 6). Point C is at (2, 10). Find the coordinates of point B.

agasfer [191]

Answer:

The coordinates of B are (10,2)

Step-by-step explanation:

Hi there!

We know that BC has a midpoint M, with the coordinates (6,6), and the endpoint C, with coordinates (2, 10)

We want to find the coordinates of point B

The midpoint formula is $(\frac{x_1 + x_2}{2}, \frac{y_1+ y_2}{2})$ , where $(x_1, y_1)$ and $(x_2 , y_2)$ are points. In this case, the point C has the values of $(x_1, y_1)$ , and B has the values of $(x_2 , y_2)$

We know that coordinates of M equal $(\frac{x_1 + x_2}{2}, \frac{y_1+ y_2}{2})$

In other words,

$\frac{x_1 + x_2}{2} = 6\\ \frac{y_1+ y_2}{2}=6$

Let's plug 2 for $x_1$ and 10 for $y_1$

So:

$\frac{2 + x_2}{2} = 6\\ \frac{10+ y_2}{2}=6$

Multiply both sides by 2

${2 + x_2} = 12\\{10+ y_2} =12$

Subtract 2 from both sides in the first equation to find the value of $x_2$ :

$x_2=10$

Now, for the second equation, subtract 10 from both sides to find the value of $y_2$

$y_2=2$

Now substitute these values for $(x_2, y_2)$

$(x_2, y_2)=(10,2)$

So the coordinates of point B are (10, 2)

Hope this helps!

3 0

3 years ago

You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

6 0

3 years ago

The equation y - 9 + 9 = 17 + 9 shows which property of equality?

BARSIC [14]

Answer:

No maim

Step-by-step explanation:

It does not

7 0

3 years ago

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Which could be the function graphed below?

Sophie [7]

There’s nothing here lol

5 0

3 years ago

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