Ask question

Ask question

All categories

4 years ago

11

1. A small plane traveled from Warsaw to Rome, averaging 164 miles per hour. The trip took 2 hours. What is the distance from Wa

rsaw to Rome?

1 answer:

jonny [76]4 years ago

5 0

The distance is approximately 2*164... 328 miles.

You might be interested in

DiKsa [7]

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to simplify:

$\displaystyle \frac{a+2}{a^2+a-2}+\frac{3}{a^2-1}$

First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:

$\displaystyle =\frac{a+2}{(a+2)(a-1)}+\frac{3}{(a+1)(a-1)}$

Now, create a common denominator. To do this, we can multiply the first term by (<em>a</em> + 1) and the second term by (<em>a</em> + 2). Hence:

$\displaystyle =\frac{(a+2)(a+1)}{(a+2)(a-1)(a+1)}+\frac{3(a+2)}{(a+2)(a-1)(a+1)}$

Add the fractions:

$\displaystyle =\frac{(a+2)(a+1)+3(a+2)}{(a+2)(a-1)(a+1)}$

Factor:

$\displaystyle =\frac{(a+2)((a+1)+3)}{(a+2)(a-1)(a+1)}$

Simplify:

$\displaystyle =\frac{a+4}{(a-1)(a+1)}$

We can expand. Therefore:

$\displaystyle =\frac{a+4}{a^2-1}$

Problem 2)

We want to simplify:

$\displaystyle \frac{1}{(a-b)(b-c)}+\frac{1}{(c-b)(a-c)}$

Again, let's create a common denominator. First, let's factor out a negative from the second term:

$\displaystyle \begin{aligned} \displaystyle &= \frac{1}{(a-b)(b-c)}+\frac{1}{(-(b-c))(a-c)}\\\\&=\displaystyle \frac{1}{(a-b)(b-c)}-\frac{1}{(b-c)(a-c)}\\\end{aligned}$

Now to create a common denominator, we can multiply the first term by (<em>a</em> - <em>c</em>) and the second term by (<em>a</em> - <em>b</em>). Hence:

$\displaystyle =\frac{(a-c)}{(a-b)(b-c)(a-c)}-\frac{(a-b)}{(a-b)(b-c)(a-c)}$

Subtract the fractions:

$\displaystyle =\frac{(a-c)-(a-b)}{(a-b)(b-c)(a-c)}$

Distribute and simplify:

$\displaystyle =\frac{a-c-a+b}{(a-b)(b-c)(a-c)}=\frac{b-c}{(a-b)(b-c)(a-c)}$

Cancel. Hence:

$\displaystyle =\frac{1}{(a-b)(a-c)}$

4 0

3 years ago

NeTakaya

Angle C prime D prime and A prime

4 0

3 years ago

Read 2 more answers

Please help me with this and thank you so much

Alexxx [7]

Answer:

Step-by-step explanation:

A

6 0

3 years ago

Ken normally leaves work at 5:00 pm, but he is leaving 20 minutes late today. He decides to make up time by taking the toll road

kobusy [5.1K]

Answer:

The correct answer is: $y=\frac{1}{3} x + 20$

Step-by-step explanation:

As stated in the question that x represents the number of minutes his <em>normal</em> commute takes. Here the keyword is normal; in the <em>normal</em> commute, Ken takes side streets instead of the toll road.

However, in this scenario, we have to come up with the equation that takes Ken's commute via <em>toll road</em>.

Ken can travel 3 times faster by taking the toll road (Given), which can be represented in the mathematical terms in terms of x as follows:

$x_{toll\_road}=\frac{1}{3}x$

<em>Without considering Ken getting late, </em>the equation would become the following:

$y=\frac{1}{3} x$ --- (A)

<em>As Ken is leaving late</em>, we have to incorporate that time as well by <em>adding</em> it in the aforementioned equation (A).

In this case, it's 20 minutes; therefore, the equation (A) will become:

$y=\frac{1}{3} x+20$

Hence, the correct answer is $y=\frac{1}{3} x + 20$ .

4 0

3 years ago

Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 7 m

MArishka [77]

<span>The answer is 6 m. To arrive at this answer you solve the following equation: {let x = the original length of the garden) (x+7)^2 = 169 x+7 = 13 x = 13-7 x = 6m</span>

4 0

3 years ago