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3 years ago

Given that rectangle MNOP - Rectangle STUV what's the length of TUPlease explain. Thank you.

Mathematics

1 answer:

Kipish [7]3 years ago

6 0

If you mean the two rectangles are similar, then you would set up a proportion as shown below:

$\frac{x}{10}= \frac{6}{4}$
4x = 6(10)
4x = 60
x = $\frac{60}{4}$
x = 15

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A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence

belka [17]

There are several ways the door can be locked, these ways illustrate combination.

There are 3375 possible combinations

From the question, we have:

$\mathbf{n = 5}$ --- the number of digits

$\mathbf{r = 3}$ ---- the number of actions

Each of the three actions can either be:

Pressing one button
Pressing a pair of buttons

The number of ways of pressing a button is:

$\mathbf{n_1 = ^5C_1}$

Apply combination formula

$\mathbf{n_1 = \frac{5!}{(5-1)!1!}}$

$\mathbf{n_1 = \frac{5!}{4!1!}}$

$\mathbf{n_1 = \frac{5 \times 4!}{4! \times 1}}$

$\mathbf{n_1 = 5}$

The number of ways of pressing a pair is:

$\mathbf{n_2 = ^5C_2}$

Apply combination formula

$\mathbf{n_2 = \frac{5!}{(5-2)!2!}}$

$\mathbf{n_2 = \frac{5!}{3!2!}}$

$\mathbf{n_2 = \frac{5 \times 4 \times 3!}{3! \times 2 \times 1}}$

$\mathbf{n_2 = 10}$

So, the number of ways of performing one action is:

$\mathbf{n =n_1 + n_2}$

$\mathbf{n =5 + 10}$

$\mathbf{n =15}$

For the three actions, the number of ways is:

$\mathbf{Action = n^3}$

$\mathbf{Action = 15^3}$

$\mathbf{Action = 3375}$

Hence, there are 3375 possible combinations

Read more about permutation and combination at:

brainly.com/question/4546043

4 0

2 years ago

..............................................

sweet-ann [11.9K]

Answer:

h = 40°

Step-by-step explanation:

These 2 angles are congruent due to the Corresponding Angles Theorem.

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3 years ago

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Find the y-intercept of the line 18x–y=5.

DaniilM [7]

$\text{Write in y=mx+c form, where m is the slope and c is the y-intercept}\\\\~~~~18x-y = 5\\\\\implies y = 18x -5\\\\\text{y-intercept}~ = -5$

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2 years ago

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Rewrite as a simplefied fraction

9966 [12]

Answer:
79/25

Work:

Firstly, you have to change the decimal portion of 3.16 (0.16) into a fraction, then you simplify it by a common factor, which is 4. You then convert your whole number, which is 3, into an improper fraction by multiplying it by 25 and making that the numerator, 25 being the denominator of the fraction. Then, you add the two fractions and voila! You have a simplified fraction!

0.16 = 16/100

16/100 = 4/25

3 x 25 = 75

75/25 + 4/25 = 79/25

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3 years ago

Identify two composite numbers that each have 8 as a factor.

Lemur [1.5K]

Two composite numbers that have 8 as a factor are 16 and 24.

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