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3 years ago

Simplify the expression x^5 • x^7.

Mathematics

1 answer:

avanturin [10]3 years ago

6 0

Answer:

x^12

Step-by-step explanation:

We know that a^b* a^c = a^(b+c)

x^5 * x^7 = x^(5+7) = x^12

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What is the justification for step 1

solniwko [45]

Answer:

what are you talking about??????

6 0

3 years ago

Alexandra has some dimes and some quarters. She has no more than 21 coins worth a minimum of $3.75 combined. If Alexandra has 4

olga55 [171]

Answer:

A minimum of 10 dimes and 11 quarters is what Alexandra will have

Step-by-step explanation:

Let

d = number of dimes

q = number of quarters

Since she has 21 coins altogether,

d + q = 21------------------------equation 1

If these coins are worth $3.75 then

0.10 x d + 0.25 x q = 3.75

which is 0.10d +.25q =3.75 --------------------------equation 2

where $.10 is the value of one dime and $.25 is the value of one quarter

make d the subject of formula from equation 1 d = 21 -q----------equation 3

insert it in equation 2

0.10d +0.25q =3.75

0.10(21-q) + 0.25q = 3.75

0.1(21)-0.1q+0.25q=3.75

2.1 +0.15q = 3.75

0.15q = 3.75-2.1 = 1.65

q = 1.65/0.15 =165/15 =11

since we have the value of q insert in equation 3

d = 21 - q

d = 21-11

d = 10

Alexandra has 10 dimes and 11 quarters.

from my calculation i can see that the a minimum of 10 dimes and 11 quarters is what Alexandra will have

4 0

3 years ago

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

The length of the rectangle is 1/4th the width of the rectangle. The perimeter is 35 ft. How long is the length and width?

Monica [59]

---- x ----
| | 0.25x
---- x ----

x + x + 0.25x + 0.25x = 35
2.5x = 35
x = 35/2.5
x = 14
width is 14

length is 1/4 this.
length = 7/2

6 0

3 years ago

Read 2 more answers

Identify the multiples of the given numbers.

inn [45]

1. 6, 12, 18
2. 8,16,24
3. 12, 24, 36
4. 15, 30, 45, 60
4. 30, 60, 90

5 0

3 years ago

Read 2 more answers