What would the Numbers look like

The image below shows two dilated figures with lines IJ and JK drawn. If the smaller figure was dilated by a scale factor of 2,

Arte-miy333 [17]

Answer:

IJ = 2*KL

Step-by-step explanation:

Given that the smaller figure was dilated to create the bigger figure with a scale factor of 2, it therefore means, the dimensions of the smaller figure was increased by times 2 of its dimensions to create the bigger figure.

Thus, the relationship that would exist between line IJ and KL, is that IJ is twice the size of KL.

The relationship is: IJ = 2*KL

8 0

3 years ago

Please help thanks very much.

Tems11 [23]

Question 1:

This question may look complicated, but we have some unnecessary info.

All we need to know that the angle next to y must also be 30 degrees because of alternate interior angles.

Thus, y + 30 = 180

Subtract both sides by 30

y = 150

Question 2:

Angle a must also be 36 because of alternate interior angles.

We also have a triangle.

We know that 36+77+?=139 because of alternate interior angles.

Let's find the ? angle.

? = 26

Now we know that a+b+?=180 because it's a triangle.

36+b+26=180

b=118

That's all we need. The last choice is the only answer that matches these two answers.

(If you want to find the value of c by solving for it, just see that there's a triangle where all the angles but c is known)

Have an awesome day! :)

5 0

3 years ago

The math problem: If she writes 6 checks for exactly $19.98, what expression describes the change in her bank account?

MAXImum [283]

Your key "word" is the parentheses ( ) that encloses the -19.98. In this case, think of the parentheses as saying multiplication. It means that in all equations, btw.
so, I write six checks at 19.98. The negative sign in front of the 19.98 signifies a decrease in the checking account for each check written

4 0

3 years ago

Using the properties of a parallelogram, can you determine which are parallelograms? Answer choices are in the picture.

madreJ [45]

The following figures are parallelograms:

Figure A

Figure B

Figure E

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Explanation:

If the diagonals of the quadrilateral are the same length (aka congruent), then we can prove that we have the opposite sides parallel. That would conclude in the figure being a parallelogram. Therefore, choice A is a parallelogram because of this fact. Choice C is not a parallelogram because of this.

Also, recall that parallelograms have their opposite sides being the same length. Think of a rectangle, but we can slant the sides as figure B shows. Figure B is a parallelogram due to the opposite sides being the same length. More specifically, it's a rhombus (because all four sides are the same). Any rhombus is a parallelogram, but not the other way around.

One last useful property we'll use is the fact that adjacent angles of a parallelogram are supplementary. This means the angles add to 180. In figure D, the adjacent angles add to 74+105 = 179, which isn't 180. So we rule out choice D. Choice E works though because 55+125 = 180.

8 0

3 years ago

A box with a square base and open top must have a volume of 171500 c m 3 . We wish to find the dimensions of the box that minimi

steposvetlana [31]

Answer:

The dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm

Step-by-step explanation:

The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.

Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are

A = 2lh + lw + 2wh

Now for a box of square base, l = w = x.

So, A = 2xh + x² + 2xh

A = x² + 4xh

Since V = x²h and V = 171500 cm³,

h = V/x² = 171500/x²

substituting h into A, we have

A = x² + 4xh

A = x² + 4x(171500 cm³/x²)

A = x² + 4 × 171500 cm³/x

A = x² + 686000 cm³/x

To find the value of x that minimizes A, we differentiate A with respect to x

So, dA/dx = d[x² + 686000 cm³/x]/dx

dA/dx = 2x - 686000 cm³/x²

equating this to zero, we have

2x - 686000 cm³/x² = 0

2x = 686000 cm³/x²

2x³ = 686000

x³ = 686000 cm³/2

x = ∛(343000 cm³)

x = 70 cm

To determine if this in a minimum dimension for A, we differentiate dA/dx and insert x = 70 cm

So, d²A/dx² = d[2x - 686000 cm³/x²]/dx

d²A/dx² = 2 + 3 × 686000 cm³/x³

d²A/dx² = 2 + 2058000 cm³/x³

with x = 70 cm, we have

d²A/dx² = 2 + 2058000 cm³/(70 cm)³

d²A/dx² = 2 + 2058000 cm³/343000 cm³

d²A/dx² = 2 + 6

d²A/dx² = 8 > 0

So, x = 70 is a minimum value for the dimension

Since h = 171500 cm³/x²

h = 171500 cm³/(70 cm)²

h = 171500 cm³/4900 cm²

h = 35 cm

So, the dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm

4 0

3 years ago