geno3141

An object 8 inches by 4 inches won't dilate down to 2.25 inches by 1 inch.

Because, to reduce 4 inches down to 1 inch, divide by 4; however, if you divide 8 inches by 4, you get 2 inches, not 2.25 inches.

Thus, you can't use just one scale factor in both directions.

To reduce 8 inches down to 2.25 inches, you need a scale factor of 2.25 / 8  or  0.28125.

To reduce 4 inches down to 1 inch, you need a scale factor of 1 / 4  =  0.25.

To calculate percent decrease:  divide the amount of decrease by the original amount:

     For the 8 inches down to 2.25 inches, the amount of decrease is 8 inches - 2.25 inches = 5.75 inches.

           Now, divide this amount by the original amount:  5.75 inches / 8 inches  =  0.71875  or  71.875%

The percent in the other direction can be calculated in the same way.

To change units, multiply by 1; but multiply in a creative manner:  1  =  1/1  =  60 seconds / 1 minute

So, the rate  4.5 meters / 9 seconds  =  (4.5 meters / 9 seconds) x (60 seconds / 1 minute)

                                                           =  4.5 x 60 meters / 9 minute

(the 'seconds' in the numerator cancels the 'seconds' in the denominator)

Simplify this and you will have your answer.

IF the new logo has the same relative dimensions as the original logo, it is a dilation.

For instance, if the original logo was 6 cm by 9 cm and the new logo is 2 cm by 3 cm (1/3rd as large in both directions), the new logo is a dilation of the old logo.

It would also be a dilation if it were increased instead of decreased.

Amount  =  Rate x Time

For instance, if you know that water leaks at the rate of 2.3 liters per hour, to find out the time that it take for 1 liter to leak:       Amount  =  Rate x Time     --->     1 liter  =  2.3 liters/hour x Time

Divide both sides by 2.3 liters/hour             --->      1/2.3 hours  =  Time

                                                                    --->      0.435 hours  =  Time

(To change decimal hours into minutes, multiply by  60:  0.435 hours x 60 minutes/hour  =  26 minutes.)

Physics started out as being a descriptive science:  light things float, heavy things fall, thrown items make an arc, the moon goes around the earth, etc.

Starting with Galileo, numbers were used to make predictions: what portion of an item floats; how fast do items fall; what kind of an arc is made, how high does the arc rise, how far does the arc go; in what way does the moon go around the earth; etc.

Math is needed to answer these questions, as well as other questions: what is the probability that it will rain tomorrow; how fast does a computer process information; how can we make a more fuel-efficient car?

My pleasure!

Do multiplication before you do either additions and subtractions, so simplify 6(-2t + 4) by using the distributive property.

-10 + 6(-2t + 4)

=  -10 +6(-2t) + (6)(4)

=  -10 - 12t + 24

Now, simplify like terms:

=  14 - 12t

What are the dimensions of the logo before he decreases the size?

12.5 ÷ 6  =  12.5 / 6

Now multiply both the numerator and the denominator by 2. You will have a fraction without any decimals.

Whenever you have a straight line, it will have the same slope no matter what points you use.

To find whether or not these points are on one straight line:  (-4,-2)   (2,2.5)   (8,7)

Find the slope using the first two points; then find the slope using the last two points; if these slopes are the same, then the three points are on the same line. If they aren't the same, then they don't lie on the same line.

Formula for slope:  m  =  (y2 - y1) / (x2 - x1)

Can you take it from here?