The main span of Bridge A ​(2300 ​feet) is​ _____ percent shorter than the main span of Bridge B ​(4700 ​feet).

Response:

B. 255 m

Detailed breakdown:

utilize similar triangles

L / 60 = 85 / 20

L = (85 * 60) / 20

L = 255 m

Answer:  

1.     What are the amplitude and period of the sine function that indicates the positioning of the band members as they start performing?

Answer:  The amplitude is 80 ft and the period is 60 ft.

2.     Edna, seated in the stands, faces Darla and notices that the sine curve starts rising from the left edge of the field. What is the equation for the sine function representing the arrangement of band members at the beginning of their performance?

Answer:  y = 80cos(x*π/30)+80

3.     When the band starts playing, the members move away from the edges, and the sine curve changes to start decreasing at the far left. Darla remains in her position. Now the sine curve is half as tall as it originally was. What is the equation for the updated sine curve depicting the band members' positions?

Answer: y = 40cos(x*π/30)+80

4.     Finally, the entire band shifts closer to the edge of the football field, causing the sine curve to now position itself in the lower half of the field from Edna’s perspective. What is the equation for this sine curve reflecting the band members' positions after these adjustments?

Answer:  y = 40cos(x*π/30)+40

Step-by-step explanation:

Answers:

C - The value of w cannot be negative.

D - The variable l is substituted with the value 20.

E - To isolate the variable w, the subtraction property of equality is applied.

~ .

The result of multiplying 10 by 6 hundreds equals 60 hundreds, which can also be expressed as 6 thousands.

Explanation

This can be simplified as follows:

• 10 times a given quantity of _____ hundreds results in 60 hundreds
• 60 hundreds convert to _____ thousands

We will divide this into two segments:

... Equation-1

... Equation-2

This straightforward multiplication relates to the place value system. We need to perform calculations to find the values of N and M.

Initially, let's focus on Equation-1.

We will move the variable M to one side of the equation in order to isolate it and solve for its value.

Both parts will be divided by 1,000, essentially being multiplied by .

Thus, we conclude with

Next, we process Equation-2 to derive M's value.

Rearranging this equation to place M on the left side appears as follows:

Again, both sides undergo division by 1,000, which translates to multiplication by .

This results in

- - - - - - -

Alternative approach for the second step:

60 hundreds equals to __ thousands

Additional resources

1. A more detailed version of this topic
2. 2 thousands 7 tens divided by 10 equals what?
3. 100 is equivalent to 1/10 of which number?

Keywords: 10 times as many as, blank, hundreds, 60 hundreds, or, thousands, isolate, operations, multiply, divide, fraction, both sides, equal, the opposite, both sides are multiplied by, divided by, rearrange