Conjecture #2- The product of two rational numbers is always?

1. If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter o

tester [92]

Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

so

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

so

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) What would happen to the perimeter and area of a figure if the dimensions were changed NON-proportionally? For example, if the length of a rectangle was tripled, but the width did not change? Or if the length was tripled and the width was decreased by a factor of 1/4?

we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

The new figure and the original figure are not similar figures

therefore

Corresponding sides are not proportional and corresponding angles are not congruent

so

A) If the length of a rectangle was tripled, but the width did not change?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2W ----> P=6L+2W

The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

B) If the length was tripled and the width was decreased by a factor of 1/4?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2(W/4) ----> P=6L+W/2

The perimeter of the new figure and the perimeter of the original figure are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W/4) ----> A=(3/4)LW

The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

5 0

3 years ago

Simplify: 5√3+4√12-2√75

svlad2 [7]

Answer:

8 + $5\sqrt{3}$ $-10\sqrt{7}$

Step-by-step explanation:

i just wrote $5\sqrt{3}$ as a decimal

times 2 with $4\sqrt{1}$ and

times 5 with $-2\sqrt{7}$

i might be wrong but hope this helps

3 0

3 years ago

Monica's school band held a car wash to raise money for

Ksivusya [100]

Answer:

1 is 50 and 2 is 75

Step-by-step explanation:

i did the work

3 0

3 years ago

A bag contains 6 red balls and blue balls. 4 balls are selected at random. find the probability of selecting 4 red balls.

masya89 [10]

Another way is to note that there are (104)(104) (“10 choose 4”) ways to select 4 balls from a collection of 10. If 4 of those 10 balls are “special” in some way (in this case, “special” = “red”), then the number of ways to choose 4 special balls is (44)(44). (The factor of (60)(60) is included to convey that, after choosing 4 special balls, we choose none of the 6 non-special balls.) This line of reasoning gives the second expression.

8 0

3 years ago

tickets for the school play cost $ 8 each for adults and $ 3 for students.what was the cost of 2 adult tickets and 1 student tic

olga nikolaevna [1]

the answer is $19,because you add the cost of 2 adult tickets 18$ and the cost of 1 student ticket 3$ and get 19$

5 0

3 years ago