Caeli is designing a flag that will be in the shape of a rectangle. She has 10 square feet of fabric to use, and she wants the h

Answer:

The diagram displaying triangle ABC and the relevant statement along with the answer options is attached.

According to this, the answer is: The length of DC is 28.

Explanation:

From the diagram and the data that segment AB equals segment AC, you comprehend that angles B and C of the isosceles triangle ABC are congruent.

Triangles BED and CFD possess two sets of congruent angles (angle B is congruent to angle D, and angles BED and DFC are congruent), indicating that triangles BED and CFD are similar.

This similarity leads to the proportional relationship:

• DE / DF = DB / DC

Given that the ratio of DE to DF is 5:7, we have:

• 5/7 = DB / DC

Also, it is stated that segment BC is 48.

From the figure:

• BC = DB + DC = 48.

This results in two equations:

• 5/7 = DB / DC

• DB + DC = 48.

Now, we define DC = x, which implies DB = 48 - x, leading to the equation:

• 5 / 7 = (48 - x) / x

Solve this:

• 5x = 7 (48 - x)... [multiplication property: multiply by x and 7]

• 5x = 336 - 7x... [distributive property]

• 12x = 336... [addition property: add 7x to both sides]

• x = 336 / 12... [division property: divide by 12]

• x = 28... [simplification]

Therefore, the length of segment x = DC = 28.

Answer:

CrO₃.

Step-by-step explanation:

First, we will find the chromium percentage in the oxide by using the following process:

Oxygen (O) = 48%

Chromium (Cr) =?

The oxide consists solely of chromium and oxygen, and its chromium percentage is calculated as:

Cr = 100 – percentage of oxygen

Cr = 100 – 48

Cr = 52%

Next, we will determine the empirical formula for the oxide:

Chromium (Cr) = 52%

Oxygen (O) = 48%

Now, we divide by their molar mass:

Cr = 52/52 = 1

O = 48/16 = 3

Now, divide by the lowest value:

Cr = 1/1 = 1

O = 3/1 = 3

Thus, the empirical formula for the oxide is CrO₃.

You may either multiply the numbers or the place value, and both methods will yield the same answer.

(2 thousands, 7 tens) multiplied by 10 results in

... (20 thousands, 70 tens)

or

... (2 ten-thousands, 7 hundreds)