Helena builds a shed in her backyard. There is a larger square section for large​ tools, like her lawn​ mower, and a smaller squ

We are given the triangle

△ABC, with m∠A=60° and m∠C=45°, and AB=8.

To start, we will calculate all angles and sides.

Finding angle B:

The total of all angles in a triangle equals 180.

m∠A + m∠B + m∠C = 180.

Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

Calculating BC:

Using the law of sines,

We can substitute in the values.

Finding AC:

Now we'll input the values.

Calculating Perimeter:

We substitute values here as well.

Calculating Area:

Using the area formula,

we can then insert values.

...............Answer

762,508 expressed in expanded form with exponents is:

Solution:

We need to write 762,508 using expanded notation with exponents.

Expanded form indicates how to represent numbers to highlight the individual digit values.

Displaying 762508 in Expanded format

Let's determine the positional values of each digit:

The concept of place value signifies the worth assigned to each digit based on its location.

For 7, the place value is 700,000

In 762508, the digit 7 is located in the hundred-thousands position.

For 6, the place value is 60,000

In 762508, the digit 6 occupies the ten-thousands position.

For 2, the place value is 2,000

In 762508, 2 is in the thousands position.

For 5, the place value is 500

In 762508, 5 is placed in the hundreds position.

For 0, the place value is 0 x 10 = 0

In 762508, 0 is found in the tens position.

For 8, the place value is 8

In 762508, 8 is positioned in the units place.

Thus, the expanded form is:

700,000 + 60,000 + 2,000 + 500 + 0 + 8

Expressed with exponents, it can be written as:

2(4x-11) = 10

Method 1:
Divide both sides by 2:




Then add 11 to both sides:





Finally divide both sides by 4





Method 2:

Use the distributive property:







Add 22 to both sides:





Then divide both sides by 8

Answer:

 -1.7x -3

Step-by-step explanation:

−4.2x+3 +2.5x−6

I prefer to align them one above the other.

−4.2x+3

 2.5x−6

------------------

 -1.7x -3

Ten 63850
hundred 63800
thousand 64000
ten thousand 60,000