Sheila turned on two buzzers at the

Orlov [11]

Not sure if the 2 at the end is part of it all because with it the GCF can only be 1

but,

the GCF of 24a, 3b and 36ab is 3.

4 0

3 years ago

Read 2 more answers

What is the measure of ∠AED?

grigory [225]

AED is adjacent to 44 and these two angles are supplementary, meaning they sum to 180 so...

AED=180-44=136°

4 0

3 years ago

A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

3 years ago

Is 63 a multiple of 4

Pepsi [2]

No cause 4 is a even number. when u multiple any number with 4 its going to be even.

5 0

3 years ago

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You are designing a rectangular playground on your scale the verticals of the rectangle are (6,3), (6,5) and (8,3). What are the

Nadusha1986 [10]

Answer:

The coordinates of the fourth vertex are (8,5)

Step-by-step explanation:

We need to take note that a rectangle is a shape that has 4 sides, with two of them of equal length.

It will also help if we can visualize the points on the graph.

We are given the location of three of the four vertices. These are (6,3), (6,5) ,and (8,3). Let the 4th Vertice be (x,y)

The length of the triangle can be obtained by subtracting the y-coordinates of the vertices.

(6,3) - (6,5)

This will be +3 and +5

5-3 =2

Therefore, the length of the triangle is 2 units on the left side.

Recall that the length of the left side has to be equal to the length of the right side.

Therefore

y-3 =2

y = 5

We will repeat the same process to get the x-coordinate from the breadth

Breadth = 8-6 =2

x-6 =2

x=8

Hence the x = 8

Therefore, the coordinates of the fourth vertex are (8,5)

7 0

2 years ago