Given the figure below, find the values of x and z.

Mathematics

1 answer:

slava [35]3 years ago

8 0

Answer:

x = 5 z = 94

Step-by-step explanation:

12x + 26 = 86

12x = 60

x = 5

360 - 172 = 188

z = 188 : 2 = 94

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Leah and Ashley go to the movie theater and purchase refreshments for their friends

klasskru [66]

Answer:

The required system of equations is:

5 m+ 7 n = 113.75

6 m + 14 n = 185.50

The price of 1 bag of popcorn = $10.5

The price of 1 drink = $8.75

Step-by-step explanation:

Let us assume the cost of 1 bag of popcorn = $ m

And, the cost of 1 drink = $ n

Now, Leah spends a total of 113.75 on 5 bags of popcorn and 7 drinks.

Cost of 5 bags + 7 drinks = 5 m + 7 n = $ 113.75

⇒ 5 m+ 7 n = 113.75 .. (1)

Also, Ashley spends a total of 185.50 on 6 bags of popcorn and 14 drinks

Cost of 6 bags + 14 drinks = 6 m + 14 n = $185.50

⇒ 6 m + 14 n = 185.50 .. (2)

So, here the system of equations that can be used to find the price of one bag of popcorn (m) and the price of one drink (n) are

5 m+ 7 n = 113.75 .. (1)

6 m + 14 n = 185.50 .. (2)

Now, to solve this, Multiply (1) with -2 and add with 2, we get:

-10m + 6m - 14 n + 14 n = 185.5 - 227.5

or, - 4 m = -42 , or m = 42/4 = 10.5

Putting the value of m = 10.5 in 5 m+ 7 n = 113.75 , we get n = 8.75

Hence, the price of 1 bag of popcorn = m = $10.5

And the price of 1 drink = n = $8.75

6 0

3 years ago

Members from 6 different school organizations decorated floats for the homecoming parade. How many different ways can first, sec

Alex

<h3>Answer: 120 different ways</h3>

=======================================================

Explanation:

There are...

6 ways to select the first place winner
5 ways to pick the second place winner
4 ways to pick the third place winner

We start with 6, and count down by 1 each time we fill up a slot. We stop once the third slot is filled or accounted for. The countdown is to ensure that we don't pick the same person twice. From here, multiply those values: 6*5*4 = 30*4 = 120

Interestingly, this is equal to 5! = 5*4*3*2*1 = 120 because the 3*2 becomes 6 and that *1 at the end doesn't affect things. Though usually results of permutation problems don't always end up like this. The order matters because a result like ABC is different from BAC, where A,B,C,D,E,F are the six school organizations.

As a slightly longer way to do the problem, you can use the nPr formula which is $_nP_r = \frac{n!}{(n-r)!}$ where n = 6 and r = 3 in this case. The exclamation marks indicate factorial. If you go this route, you should find that one of the steps will involve 6*5*4.