Logan wants to move to a new city. He gathered graphs of temperatures for two different cities. Which statements about the data

the length of a rectangle is 2 inches longer than twice its width. If the area of the rectangle is 24 square inches, what are th

gregori [183]

Answer:

The length is 8 inches and the width is 3 inches

Step-by-step explanation:

Let w represent the width.

The length can be represented by 2w + 2

Use the area formula, A = lw, and plug in the area and the expressions for the length and width:

A = lw

24 = (2w + 2)(w)

Simplify and solve for w:

24 = 2w² + 2w

2w² + 2w - 24

Divide everything by 2:

w² + w - 12

Factor:

(w + 4)(w - 3)

Set equal to 0 and solve for each factor:

w + 4 = 0

w = -4

w - 3 = 0

w = 3

Since the width cannot be negative, the width has to be 3.

Next, find the length by plugging in 3 as w:

2w + 2

2(3) + 2

= 8

So, the length is 8 inches and the width is 3 inches

7 0

3 years ago

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither

Mars2501 [29]

Answer:

b 2/7

Step-by-step explanation:

Because there is a 6/21 chance and 2/7=6/21

8 0

3 years ago

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

Answer all parts of number 1 thank you.

Scorpion4ik [409]

Hi!

1.)

a:A u B=

$(1.0. - 5. \frac{1}{2} .e)$