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2 years ago

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A rectangle has sides that are 1 cm and 2 cm long. If it is increased by a scale factor of 9, what will be the new area of the r

ectangle?

1 answer:

Reil [10]2 years ago

8 0

Answer:

$162cm^2$

Step-by-step explanation:

The original sides are 1 and 2 centimeters, Increasing both by a factor of 9 results in 9 and 18 centimeters. We multiple to find the area is 162 square centimeters,

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You are at a family reunion and the cooler contains ten bottles of soda; four Sprite, three Dr. Pepper, and three Cherry Coke. T

natita [175]

Answer:

Probability of getting Dr. Pepper the fourth time = $\frac{1}7$

Probability of getting a cherry coke the fifth time = $\frac{1}{3}$

Combined probability = $\frac{1}{21}$

Step-by-step explanation:

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

It is given that first time a Cherry coke is chosen and it is not replaced.

So, number of cherry coke left = 2

Dr. Pepper is chosen twice and is not replaced, so

Number of Dr. Pepper left = 3 - 2 = 1

Total number of soda left = 10 - 3 = 7

So, probability of getting Dr. Pepper the fourth time = $\frac{1}7$

Now, total number of soda left = 7 - 1 = 6

Probability of getting a cherry coke the fifth time = $\frac{2}{6} = \frac{1}{3}$

The combined probability = probability of getting Dr. Pepper the fourth time multiplied with Probability of getting a cherry coke the fifth time

$\Rightarrow \dfrac{1}7 \times \dfrac{1}{3} = \dfrac{1}{21}$

6 0

3 years ago

What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minu

Sunny_sXe [5.5K]

Answer:

<h2> $\frac{(x + 5)(x + 2)}{ {x}^{3} - 9x }$ </h2>

First option is the correct option.

Step-by-step explanation:

$\frac{2x + 5}{ {x}^{2} - 3x } - \frac{3x + 5}{ {x}^{3} - 9x } - \frac{x + 1}{ {x}^{2} - 9 }$

Factor out X from the expression

$\frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x( {x}^{2} - 9)} - \frac{x + 1}{ {x}^{2} - 9}$

Using ${a}^{2} - {b}^{2} = (a - b)(a + b)$ , factor the expression

$\frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x(x - 3)(x + 3) } - \frac{x + 1}{(x - 3)(x + 3)}$

Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )

$\frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)}$

Multiply the parentheses

$\frac{2 {x}^{2} + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)}$

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

$\frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)}$

Distribute -x through the parentheses

$\frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x }{x(x - 3)(x + 3)}$

Using ${a}^{2} - {b}^{2} = (a + b)(a - b)$ , simplify the product

$\frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x}{x( {x}^{2} - 9)}$

Collect like terms

$\frac{ {x}^{2} + 7x + 15 - 5}{x( {x}^{2} - 9)}$

Subtract the numbers

$\frac{ {x}^{2} + 7x + 10}{ x({x}^{2} - 9)}$

Distribute x through the parentheses

$\frac{ {x}^{2} + 7x + 10}{ {x}^{3} - 9x}$

Write 7x as a sum

$\frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x }$

Factor out X from the expression

$\frac{x(x + 5) + 2x + 10}{ {x}^{3} - 9x}$

Factor out 2 from the expression

$\frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x }$

Factor out x + 5 from the expression

$\frac{(x + 5)(x + 2)}{ {x}^{3} - 9x }$

Hope this helps...

Best regards!!

6 0

2 years ago

Read 2 more answers

Under her cell phone plan, Lily pays a flat cost of $55.50 per month and $4 per gigabyte. She

nlexa [21]

Answer:

Hi,can you please answer mine too it's question 9-12 I really need the answer because I have to pass it tomorrow morning:(

Step-by-step explanation:

about your question I'll put it in the comment section:)

4 0

2 years ago

If you know the answer to this, pls let me know! Thanks!!!! :))))

8090 [49]

Answer:

x= 30

Step-by-step explanation:

3x + 50 = 140

3x = 140 -50

3x = 90

x = 90/3

x = 30

3 0

2 years ago

Read 2 more answers

Find the area of the isosceles trapezoid. leave your answer in simplest radical form 4cm 7cm 3cm

nata0808 [166]

The area of a trapezoid is (a+b)/2 * h
a is the length of the small base which is the one on the top and is 4cm
b is the length of the big base which is the one at the bottom and is 4 + 3 + 3 = 10cm
h is the height which is 7cm
So the area is (4+10)/2 * 7
A= 14/2 * 7
A= 7 * 7
A= 49 cm^2

8 0

3 years ago