Which postulate /theorem can you use to prove the two triangles shown are congruent?

AURORKA [14]

A proportion looks like this:

$a\div b = c\div d$

It means that the quantity a,b,c and d are in the same proportion: the ratio between a and b is the same ratio between c and d.

They are particularly useful in situation when you have an example given, and you want to extrapolate the relationship for another couple.

For example, you can think of the following problem: "Five apples cost 2 dollars. How much will 8 apples cost?"

You can build the proportion

$5\div 2 = 8\div x$

And then solve it for x:

$\dfrac{5}{2}=\dfrac{8}{x} \iff 5x=16 \iff x = \dfrac{16}{5} = 3.2$

6 0

2 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. SEE F

Wewaii [24]

Answer:

1. $P(x)$ ÷ $Q(x)$ ---> $\frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$ ---> $\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}$

3. $P(x) - Q(x)$ ---> $\frac{-2(12x - 5)}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x)$ --> $\frac{12}{(3x - 1)(-3x + 2)}$

Step-by-step explanation:

Given that:

1. $P(x) = \frac{2}{3x - 1}$

$Q(x) = \frac{6}{-3x + 2}$

Thus,

$P(x)$ ÷ $Q(x)$ = $\frac{2}{3x - 1}$ ÷ $\frac{6}{-3x + 2}$

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

$\frac{2}{3x - 1}*\frac{-3x + 2}{6}$

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

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

2. $P(x) + Q(x)$ = $\frac{2}{3x - 1} + \frac{6}{-3x + 2}$

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

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

$\frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)}$

$\frac{12x - 2}{(3x - 1)(-3x + 2)}$

$= \frac{2(6x - 1}{(3x - 1)(-3x + 2)}$

3. $P(x) - Q(x)$ = $\frac{2}{3x - 1} - \frac{6}{-3x + 2}$

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

$\frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)}$

$\frac{-24x + 10}{(3x - 1)(-3x + 2)}$

$= \frac{-2(12x - 5}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2}$

$P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)}$

$P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)}$

4 0

3 years ago

How much is a $450 snowboard with 7.25% sales tax?

Savatey [412]

Answer:

$482.625 ≈ $482.63

Step-by-step explanation:

$\frac{y}{450}: \frac{7.25}{100}$

y · 100 = 450 · 7.25

100y = 3262.5

100y ÷ 100 = 3262.5 ÷ 100

y = 32.625

$450 + $32.625

$482.625

5 0

2 years ago

Read 2 more answers

Which expression represents 9 less than a number?

My name is Ann [436]

Answer:

x-9

Step-by-step explanation:

"Less than" switches the way of the expression.

If the "less than" was not there it would have been:

9-x

"Less" means subtract so you would subtract x from 9.

Hope this helped!

7 0

3 years ago

Read 2 more answers

The price of a European tour includes stopovers at five cities to be selected from 15 cities. In how many ways can a traveler pl

xeze [42]

Answer:

The traveler can plan such a tour in 3003 ways.

Step-by-step explanation:

The order that the cities are chosen is not important, since it is chosen by the company and not by the traveler. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, we have that:

Combinations of 5 cities from a set of 15. So

$C_{15,5} = \frac{15!}{5!10!} = 3003$

The traveler can plan such a tour in 3003 ways.

4 0

2 years ago

Which postulate /theorem can you use to prove the two triangles shown are congruent? ​

Which postulate /theorem can you use to prove the two triangles shown are congruent?